Error correction code (ecc) decoders sharing logic operations, memory controllers including the error correction code decoders, and methods of decoding error correction codes An error correction code (ecc) decoder includes a finite state machine (fsm) controller and a shared logic circuit. The fsm controller generates a first control signal and a second control signal each corresponding to a certain state. Sk Hynix Inc.

Method and electronic device for recognizing a finger A method for recognizing a finger, including: sensing a recognized object which is placed on a fingerprint sensing device to generate a first frame; selecting at least one block from the frame, wherein each of the blocks comprises a plurality of block groups; computing a sequence of characteristic values of each of the block groups according to a plurality of haarlike features; and respectively substituting the sequences of characteristic values of the block groups into a polynomial to determine whether the recognized object is a finger.. . Egis Technology Inc.

Lane deviation suppressing system A lanedeviationsuppressingsystem (1) sets a target point in front of a lane when a vehicle travels, and calculates, as a target trajectory, an trajectory causing the vehicle to travel to the set target trajectory, using a polynomial of fifthorder with respect to time. Then, the system judges that a recalculation of the target trajectory is necessary if the vehicle traveling along the target trajectory returns to the target point after separating from the target point in an orthogonal direction to an extending direction of the lane. Denso Corporation


Method and system for providing a proofofwork A method for providing a proofofwork includes computing, by a verification computing device (vcd), a first linear feedback shift register sequence (lfsrs) using a first polynomial having a first degree and computing, by the vcd, a second lfsrs based on a second polynomial. A challenge, generated by the vcd and using elements of the second lfsrs, is transmitted to the pcd. Nec Europe Ltd.

Polynomial fully homomorphic encryption system based on coefficient mapping transform A polynomial complete homomorphic encryption method based on the coefficient mapping transformation. A plaintext is expressed as a polynomial consisting of a set of random values, two sets of random coefficient factors and a random constant of a specified mapping function, and in the polynomial: the expression and a set of random coefficient factors of the specified mapping function are taken as a key; another set of random coefficient factors, a set of random arguments and random constants of the mapping function are taken as the ciphertexts for homomorphic operations, so that the part of function key performs three different mappings and then undergoes numerical fitting to obtain the family of operational support functions consisting of three subfunctions respectively, which are used to perform the homomorphic operation of the ciphertext based on the family of operational support functions and return to the locality for decryption by the key..

Method of feature exaction from timeseries of spectra to control endpoint of process Methods and systems for using a timeseries of spectra to identify endpoint of an etch process. One method includes accessing a virtual carpet that is formed from a timeseries of spectra for the etch process collected during a training operation. Lam Research Corporation

Freeform surface offaxial threemirror imageside telecentric optical system A freeform surface offaxial threemirror imageside telecentric optical system comprises a primary mirror, a secondary mirror, a tertiary mirror and an image sensor. The secondary mirror is the aperture stop. Hon Hai Precision Industry Co., Ltd.

Oblique camera lens A oblique camera lens includes: a primary mirror configured to reflect a light ray to form a first reflected light; a secondary mirror located on a first path of light reflected from the primary mirror and configured to reflect the first reflected light to form a second reflected light; a tertiary mirror located on a second path of light reflected from the secondary mirror and configured to reflect the second reflected light to form a third reflected light; and an image sensor located on a third path of light reflected from the tertiary mirror and configured to receive the third reflected light; wherein each of the first reflecting surface and the third reflecting surface is a sixth order xy polynomial freeform surface; and a field of view of oblique camera lens in an yaxis direction is greater or equal to 35° and less than or equal to 65°.. . Hon Hai Precision Industry Co., Ltd.

Light locus generation for automatic white balance A light locus of an imaging system is generated in a chromaticity space of two dimensions. The light locus represents a collection of candidate illuminants. Mediatek Inc.

Parallel pipeline logic circuit for generating crc values utilizing lookup table Crc generation circuitry includes a lookuptable storing nbit crc values for m onehot data frames. N and gates for each bit of a mbit data frame receive that bit of the mbit data frame and a different bit of a nbit crc value from the lookuptable corresponding to a position of the bit in the mbit data frame. Stmicroelectronics International N.v.

Transmission method, transmission apparatus, reception method and reception apparatus A lowdensity parity check convolution code (ldpccc) is made, and a signal sequence is sent after being subjected to an errorcorrecting encodement using the lowdensity parity check convolution code. In this case, a lowdensity parity check code of a timevariant period (3g) is created by linear operations of first to 3gth (letter g designates a positive integer) parity check polynomials and input data.. Panasonic Corporation 
Information processing device and information processing method An information processing device includes, a memory, and a processor coupled to the memory and the processor configured to, acquire a neural network, divide the neural network into divided neural networks, identify, based on inputoutput characteristics of the divided neural networks, parameters of each of polynomial neural networks corresponding to each of the divided neural networks, and output another neural network generated by linking the identified polynomial neural networks.. . Fujitsu Limited 
System and parameter estimation of hybrid sinusoidal fmpolynomial phase signal Systems and methods for an elevator. The elevator includes an elevator car to move along a first direction. Mitsubishi Electric Corporation 
Calibration and use of mechanical relay at zero cross This disclosure describes systems, methods, and apparatus for determining a relay delay for a relay of a relay device used to switch ac power to and from a load. The relay delay can be predetermined as a model or polynomial including variables for temperature and age, such that the switching instructions can be sent to the rely a relay delay before a zero crossing of the ac signal that the relay is switching, and where the relay delay accounts for temperature and age of the relay in real time or near real time.. Terralux, Inc. 
Mask blank substrate, multilayer reflective film coated substrate, and mask blank A virtual surface shape, which is an optically effective flat reference surface shape defined by a zernike polynomial, is determined, wherein the zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is secondorder; and the mask blank substrate, in which difference data (pv value) between the maximum value and the minimum value of difference shape between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of two main surfaces is 25 nm or less, is selected.. . 
Offaxis aspheric threemirror optical system An offaxis aspheric threemirror optical system comprises a primary mirror, a secondary mirror, and a tertiary mirror. Relative to a first threedimensional rectangular coordinates system in space, a second threedimensional rectangular coordinates system is defined by a primary mirror location, a third threedimensional rectangular coordinates system is defined by a secondary mirror location, and a fourth threedimensional rectangular coordinates system is defined by a tertiary mirror location. Hon Hai Precision Industry Co., Ltd. 
Error correction circuits and memory controllers including the same An error correction circuit includes a syndrome calculator suitable for generating syndromes from an “n”bit codeword for a single unit of time, an error location polynomial calculator suitable for generating error location polynomial coefficients based on the syndromes provided for the single unit of time, an error location calculator suitable for calculating error locations based on the error location polynomial coefficients for the single unit of time, and an error corrector suitable for correcting errors of the codeword based on the error locations for the single unit of time. The error correction circuit operates in a pipelining manner.. Sk Hynix Inc. 
Cyclic redundancy check calculation for multiple blocks of a message The disclosure relates to technology performing a cyclic redundancy check (crc). Data is divided into a plurality of blocks, each of the plurality of blocks having a fixed size equal to a degree of a generator polynomial. Futurewei Technologies, Inc. 
Rs error correction decoding method A decoding method includes that when encoding at a sending terminal, for a morder primitive polynomial p(x), a primitive field element in galois field gf(2m) is represented by α; a lookup table f(αj) for different power exponents of α is established, where the value of j is selected from all the integers ranging from 0 to 2m−1, with a total number of 2m; a generator polynomial g(x) is expanded to obtain a polynomial with respect to x, with coefficients being an addition or subtraction of the power exponents of α; a remainder polynomial r(x), obtained by dividing code word polynomial q(x) by the generator polynomial g(x), is a polynomial with respect to x, with coefficients being an addition or subtraction of the power exponents of α; and the coefficients of the generator polynomial g(x) and the remainder polynomial r(x) are both calculated using data found in the lookup table f(αj).. . Fujian Landi Commercial Equipment Co., Ltd. 

Imaging spectrometer with freeform surfaces Expanded performance opportunities for imaging spectrometers are described using φpolynomial freeform surfaces in reflective and diffractive optics. The imaging spectrometers are generally of a type that include an entrance aperture for admitting radiation over a range of wavelengths, a detector array, a primary reflective optic with optical power, a secondary reflective diffractive optic, and a tertiary reflective optic with optical power for collectively imaging the entrance aperture onto the detector array through a range of dispersed positions. University Of Rochester 
Device and administering a digital escrow server An administration machine (32) for a digital escrow server (10) stores integer values each corresponding to a machine (32;34;36) of a group of administration machines (30). An initialisation function calls a polynomial function, unique to the administration machine, of a degree less than or equal to the number of administration machines, with each integer value, in order to obtain first secret values. Inria Institut National De Recherche En Informatique Et En Automatique 
Method of arrangement of an algorithm in cyclic redundancy check A method of arrangement of an algorithm to calculate cyclic redundancy check (crc) independent of the length of a polynomial generator and data stream which can be realized in digital implementation with a calculation latency of once clock cycle. The method allows a sequence of information and the corresponding polynomial generator be arranged into a transformation table.. Akribis Systems Pte Ltd 
Phase retrieval using coordinate descent techniques Coordinate descent is applied to recover a signalofinterest from only magnitude information. In doing so, a single unknown value is solved at each iteration, while all other variables are held constant. City University Of Hong Kong 
Method and decoder to adjust an error locator polynomial based on an error parity A method of operation of a decoder includes receiving first data at the decoder. The method further includes generating second data at the decoder based on the first data. Sandisk Technologies Llc 
Automated vehicle crosstraffic detection system A cross traffic detection system suitable for use on an automated vehicle includes an objectdetector, an alertdevice, and a controller. The object detector is used to determine locations of moving objects relative to a host vehicle. Delphi Technologies, Inc. 
Systems and methods for measuring cardiac strain A method for rapid computation of threedimensional displacement and lagrange strain in a high resolution filed of phase data obtained with displacement encoding with stimulated echoes (dense) in magnetic resonance images of the myocardium. The method includes semiautomated segmentation of a region of a heart, phase unwrapping the images in three dimensions, and a custom radial point interpolation method (rpim). Washington University 
Homomorphic evaluation including key switching, modulus switching, and dynamic noise management Homomorphic evaluations of functions are performed. The functions include operation(s). University Of Bristol 
Matrix application apparatus, matrix application method and program To reduce the processing amount of a field multiplication. A matrix application apparatus computes a vector b by multiplying a vector a and a matrix a, provided that a denotes a kth order vector having elements a0, . Nippon Telegraph And Telephone Corporation 
Error locator polynomial decoder and method A decoder configured to decode a representation of the codeword includes an error locator polynomial generator circuit. The error locator polynomial circuit is configured to generate an error locator polynomial based on a decode operation that includes iteratively adjusting values of a first polynomial, a second polynomial, a third polynomial, and a fourth polynomial. Western Digital Technologies, Inc. 

Methods for secure learning of parameters of a convolution neural network, and for secure input data classification A method for secure learning of parameters of a convolution neural network, cnn, for data classification includes the implementation, by data processing of a first server, including receiving from a second server a base of already classified learning data, the learning data being homomorphically encrypted; learning in the encrypted domain, from the learning database, the parameters of a reference cnn including a nonlinear layer (polynomial) operating an at least twodegree polynomial function approximating an activation function; a batch normalization layer before each nonlinear layer (polynomial); and transmitting the learnt parameters to the second server, for decryption and use for classification.. . Safran Identity & Security 
Motion capture system that combines sensors with different measurement ranges Motion capture system with a motion capture element that uses two or more sensors to measure a single physical quantity, for example to obtain both wide measurement range and high measurement precision. For example, a system may combine a lowrange, high precision accelerometer having a range of −24 g to +24 g with a highrange accelerometer having a range of −400 g to +400 g. Blast Motion Inc. 
Improvements on multivariate digital signature schemes based on hfev and new applications of multivariate digital signature schemes for whitebox encryption We present new designs to choose the parameter sets for more efficient hfevbased signature schemes. The key method is to reduce the degree of the central hfevpolynomial while, at the same time, increasing the number of vinegar variables and minus equations. 
Data generating apparatus, data generating method, and data recording system A data generating apparatus is provided that includes a memory storing a program and a processor configured to execute the program to implement processes of sequentially acquiring n sets of data (where n is an integer greater than or equal to 2) included in a predetermined section of time series data and calculating, based on the acquired data, parameter information satisfying a polynomial of degree (k−1) including k random numbers (where k is an integer greater than or equal to 1 and less than n); generating a signature value by adding a signature to secret information based on a secret sharing protocol, the secret information being calculable by acquiring k sets of the acquired data and the parameter information calculated based on the acquired data; and outputting output data including the signature value and a set of the acquired data and the parameter information calculated based on the acquired data.. . Ricoh Company, Ltd. 
Piecewise polynomial evaluation instruction A method includes retrieving, at a processor, a first instruction for performing a first piecewise horner's method operation for a polynomial and executing the first instruction. Executing the first instruction causes the processor to perform operations including accessing one or more lookup tables based on an interval of a first function input to determine a first coefficient of the polynomial for the first input range. Qualcomm Incorporated 
Method and providing ordered sets of arbitrary percentile estimates for varying timespans A method includes interpreting a number of distributed data sets including resource utilization values corresponding to a plurality of distributed hardware resources, creating an approximation of a number of distributions corresponding to the distributed data set, aggregating the created approximations, and the aggregating includes weighting values determined from each of the distributed data sets, such that the aggregated approximations are representative of the distributed data sets. The method further includes creating a number of polynomial terms in response to the created approximations, thereby providing a utilization profile, and solving for a utilization percentile value within the aggregated approximations, where the solving is performed without reference to the distributed data set.. Sevone, Inc. 
Compensating for temperaturedependent hysteresis in a temperature compensated crystal oscillator Hysteresis causes the temperature dependent frequency characteristic of the crystal of a crystal oscillator to be different when the temperature is rising from a previous colder state and when the temperature is falling from a hotter state. A rising temperaturetofrequency mapping polynomial and a falling temperaturetofrequency mapping polynomial are generated and their evaluations are weighted based on a current temperature and past temperature(s). Silicon Laboratories Inc. 
3d building extraction apparatus, method and system Disclosed is a method for 3d building extraction, comprising: extracting building footprints from one or more stereo images for a building; determining, from rational polynomial coefficient of the stereo images, first height estimation of the extracted building footprints; obtaining, from multitemporal sar images for the building, scatters with stable attributes; determining second height estimation for the determined scatters; and combining the first height estimation and the second height estimation to generate a fused height for each of the extracted building footprints.. . The Chinese University Of Hong Kong 
Determination of cd and/or md variations from scanning measurements of a sheet of material Cd variations and/or md variations in scan measurements are determined from spectral components of power spectra of scan measurements taken using two or more scanning speeds. Dominant spectral components having the same spatial frequencies identify cd variations and dominant spectral components having the same temporal frequencies identify md variations. Abb Schweiz Ag 
Generating cryptographic checksums A method (400) of generating a cryptographic checksum for a message m(x) is provided. The method is performed by a communication device, such as a sender or a receiver, and comprises calculating (405) the cryptographic checksum as a first function g of a division of a second function of m(x), f(m(x)), modulo a generator polynomial p(x) of degree n, g(f(m(x)) mod p(x)). Telefonaktiebolaget Lm Ericsson (publ) 

Encoding method, decoding method An encoding method generates an encoded sequence by performing encoding of a given coding rate according to a predetermined parity check matrix. The predetermined parity check matrix is a first parity check matrix or a second parity check matrix. Sun Patent Trust 
Temperature compensation for structured light depth imaging system Disclosed are an apparatus and a method of compensating temperature shifts of a structured light pattern for a depth imaging system. In some embodiments, a depth imaging device includes a light source, an imaging sensor and a processor. Microsoft Technology Licensing, Llc 
Lowlatency decoder for reed solomon codes A decoder includes a syndrome calculator, a key equation solver (kes) and an error corrector. The syndrome calculator is configured to receive an nsymbol code word encoded using a reed solomon (rs) code to include (n−k) redundancy symbols, and to calculate for the code word 2t syndromes si, t=(n−k)/2 is a maximal number of correctable erroneous symbols. Marvell World Trade Ltd. 
Encrypting and decrypting information An example information encryption method that includes acquiring tobeencrypted information and converting the tobeencrypted information into a polynomial of a predetermined format; extracting biometric information, and acquiring biometric data; and substituting the biometric data into the polynomial for calculation to acquire a value of the polynomial and using a twodimensional dataset including the biometric data and the value of the polynomial corresponding to the biometric data as first encrypted information. The techniques of the present disclosure improve the security of information encryption, and reduce the risk of illegal decryption of encrypted information.. Alibaba Group Holding Limited 
Precision crop productionfunction models Systems, apparatuses, and methods as described herein relate to analyzing plant nutrientyield relationships and identifying optimum plant fertilization strategies to improve individual plant yields and overall plant yields. Nutrient data and yield data for plants in all yield ranges, rather than nutrient data and yield data for only the bestperforming plants, is categorized based on the yield data and then analyzed to determine the yield as a function of nutrient condition for each nutrient element for the plants in each yield category. The Regents Of The University Of Californa 
Crc calculation circuit, semiconductor device, and radar system Provided is a crc calculation circuit capable of dealing with various types of generator polynomials with a simple configuration. A crc calculation circuit (100) includes a generator polynomial register (110) configured to store polynomial data, and a plurality of crc calculation units (120) connected in series and provided so as to correspond to the number of bits of input data. Renesas Electronics Corporation 
Adaptive polynomial rendering Embodiments can provide adaptive image filtering. Under this approach, image quality can be enhanced by adjusting an approximation function to better adapt image signals in different parts of an image. Disney Enterprises, Inc. 
Publickey encryption system A key generation device (100) configured to generate a public key (126) for use in a public key encryption device and a corresponding private key (114) for use in a private key decryption device, the key generation device comprising a private key generator (110) configured for obtaining in electronic form a private random value (112, s), and generating the private key (114), the private key comprising the private random value (112), and a public key generator (120) configured for obtaining in electronic form a public set of bivariate polynomials (122, fi(,)), computing a public univariate polynomial (124) by summing over univariate polynomials obtained by substituting the private random value (112, s) into the polynomials of the public set (122, fi (s,)), and generating the public key (126), the public key comprising the public univariate polynomial (124) and the public set (122).. . Koninklijke Philips N.v. 
Protecting polynomial hash functions from external monitoring attacks Systems and methods for protecting from external monitoring attacks cryptographic data processing operations involving computation of a universal polynomial hash function, such as ghash function. An example method may comprise: receiving an input data block, an iteration result value, and a mask value; performing a nonlinear operation to produce a masked result value, wherein a first operand of the nonlinear operation is represented by a combination of the iteration result value and the input data block, and the second operand of the nonlinear operation is represented by a secret hash value, and wherein one of the first operand or the second operand is masked using a mask value; determining, based on the mask value, a mask correction value; and producing a new iteration result value by applying the mask correction value to the masked result value.. Cryptography Research, Inc. 
Variable t bch encoding A system for implementing variable t bch encoders includes: a polynomial multiplier for multiplying a message polynomial by a difference polynomial to achieve a first value, wherein the message polynomial comprises data bits as coefficients and the difference polynomial comprises minimal polynomials that are present in a t error correcting code and are absent from a t−Δt error correcting bch code; a shifter/zeropadder coupled with the bch encoder, the shifter/zeropadder for multiplying the first value by xn−{tilde over (k)} to achieve a second value; a bch encoder coupled with the polynomial multiplier, the bch encoder for dividing the second value by a generator polynomial of the t error correcting bch code and calculating a remainder based on the dividing to achieve a third value; and a polynomial divider for dividing the third value by the difference polynomial to achieve a fourth value comprising parity of the t−Δt error correcting bch code.. . Microsemi Solutions (u.s.), Inc. 

Apparatuses and methods for interleaved bch codes An example methods for interleaved bch codes can include encoding a plurality of portions of data using a first generator polynomial to obtain a plurality of respective bch codewords. The method can include encoding an additional bch codeword based at least in part on a second plurality of portions of data and the plurality of bch codewords using a second generator polynomial. Micron Technology, Inc. 
Reedsolomon decoders and decoding methods Embodiments of the present disclosure provide a high speed low latency rate configurable soft decision and hard decision based pipelined reedsolomon (rs) decoder architecture suitable for optical communication and storage. The proposed rs decoder is a configurable rs decoder that is configured to monitor the channel and adjust code parameters based on channel capacity. Indian Institute Of Science 
Random path generation upon functional decomposition A method of defining a path model from a set of realistic paths is provided, where each path in the set of realistic paths is expanded on piecewise polynomial basis, and a respective centroid function and sequence of eigenfunctions calculated for each expanded representation. A set of principle paths representing the major variation of this set of paths is obtained describing the variations of the set of realistic paths with respect to the centroid. Ecole Nationale De L'aviation Civile 
Secondary synchronization codebook for eutran Providing for secondary synchronization encoding utilizing a primary synchronization channel (psch)related scrambling code is described herein. Scrambled secondary synchronization codes (sscs) can be assigned to multiple base stations of a radio access network (ran). Qualcomm Incorporated 
Scatter simulation with a radiative transfer equation using direct integral spherical harmonics computed tomography A method and apparatus is provided to calculate scatter using a method to determine primary xray flux, firstscatter flux, and multiplescatter flux using an integral formulation of a radiative transfer equation and using sphericalharmonic expansion. The integral for the primary xray flux does not include a sphericalharmonic expansion. Toshiba Medical Systems Corporation 
Modelbased control tuning power production emissions A modelbased control system is configured to select a desired parameter of a machinery configured to produce power and to output emissions and to select an emissions model configured to use the desired parameter as input and to output an emissions parameter. The modelbased control system is additionally configured to tune the emissions model via a tuning system to derive a polynomial setpoint, and to control one or more actuators coupled to the machinery based on the polynomial setpoint.. General Electric Company 
Pattern recognition device, pattern recognition method, and computer program product According to an embodiment, a pattern recognition device recognizes a pattern of an input signal by converting the input signal to a feature vector and matching the feature vector with a recognition dictionary. The recognition dictionary includes a dictionary subspace basis vector for expressing a dictionary subspace which is a subspace of a space of the feature vector, and a plurality of probability parameters for converting similarity calculated from the feature vector and the dictionary subspace into likelihood. Toshiba Digital Solutions Corporation 
Multivariate signature resisting key recovery attack A multivariate signature method for resisting key recovery attack, which establishes a new signature verification condition by adding additional value of signature. The verification condition implies verification of internal information x and y, thereby effectively resisting key recovery attack generated by the existence of equivalence key. Shaanxi University Of Science & Technology 
Methods and performing reedsolomon encoding by lagrangian polynomial fitting An integrated circuit for implementing a reedsolomon encoder circuit is provided. The encoder circuit may include partial syndrome calculation circuitry and matrix multiplication circuitry. Altera Corporation 
Simultaneous multieffect oscillator compensation using piecewise interdependent polynomials A packaged vctcxo may include a crystal oscillator configured to output a signal of a particular frequency and a temperature sensor configured to measure an internal temperature of the crystal oscillator. In addition, the packaged vctcxo may include a microcontroller configured to generate an internal control voltage signal based at least in part on the temperature and an external control voltage received by the packaged vctcxo. Greenray Industries, Inc. 
Simultaneous estimation of respiratory parameters by regional fitting of respiratory parameters A medical ventilator (10) performs a method including: receiving measurements of pressure of air inspired by or expired from a ventilated patient (12) operatively connected with the medical ventilator; receiving measurements of air flow into or out of the ventilated patient operatively connected with the medical ventilator; dividing a breath time interval into a plurality of fitting regions (60); and simultaneously estimating respiratory system's resistance and compliance or elastance, and respiratory muscle pressure in each fitting region by fitting to a time series of pressure and air flow samples in that fitting region. In one approach, the fitting includes parameterizing the respiratory muscle pressure by a continuous differentiable function, such as a polynomial function, over the fitting region. Koninklijke Philips N.v. 
Cryptographic primitive for user authentication A method of biometric authentication includes receiving a biometric input from a user for authentication of the user to access a system. The method includes receiving a set of elements of a field and a random number from an authentication server via a network. Fujitsu Limited 
Polynomialbased homomorphic encryption A method includes generating a secret key for encryption and decoding data. The method includes identifying a set of data in plaintext format. Fujitsu Limited 
Table data recovering in case of image distortion The subject matter of this specification can be implemented in, among other things, a method that includes identifying edges of a section of a document in a source image that includes at least one row of text. The method includes identifying characters in the document. Abbyy Development Llc 
Lowarea fixedpoint polynomials Methods of implementing fixedpoint polynomials in hardware logic include distributing a defined error bound for the whole polynomial between operators in a dataflow graph for the polynomial by solving an optimization problem that outputs an accuracy parameter and a precision parameter for each node. Each operator is then itself optimized to satisfy the part of the error bound allocated to that operator and as defined by the accuracy and precision parameters.. Imagination Technologies Limited 
Secondary reflectors for solar collectors and methods of making the same An aspect of the present disclosure is a device that includes a reflecting surface having a length aligned along a first axis (z), where a crosssection of the reflecting surface in a plane perpendicular to the first axis (z) forms a curve comprising a concave section positioned between a first endpoint and a second endpoint, at least a portion of the concave section is accurately approximated by a polynomial equation, an aperture is formed by a straight line connecting the first endpoint to the second endpoint, and the concave section is configured to focus a plurality of beams of light passing through the aperture onto a focal point.. . Alliance For Sustainable Energy, Llc 
Authentication via group signatures Methods and systems are provided for authenticating a message μ, at a user computer of a group signature scheme, to a verifier computer. The method includes, at the user computer, storing a user id m for the user computer and a user signing key which comprises a signature on the user id m under a secret key of a selectivelysecure signature scheme. International Business Machines Corporation 
Systems and methods for planning paths to guide robots A computerimplemented method is provided for guiding a robot in a robotic system, by creating a refined path, based on an initial path in a threedimensional space. The method includes receiving data related to creating the initial path, including a start point and an endpoint, and generating the initial path by interpolating the start point and the endpoint. Hypertherm, Inc. 
Mask blank substrate, mask blank, and methods for manufacturing them, manufacturing transfer mask, and manufacturing semiconductor device A virtual surface shape, which is an optically effective flat reference surface shape defined by a zernike polynomial, is determined, wherein the zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is secondorder; and the mask blank substrate, in which difference data (pv value) between the maximum value and the minimum value of difference shape between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of two main surfaces is 25 nm or less, is selected.. . 
Lextar Electronics Corporation . . 
Cryptography on an elliptical curve A cryptographic calculation includes obtaining a point p(x,y) from a parameter t on an elliptical curve y2=f(x); and from polynomials x1(t), x2(t), x3(t) and u(t) satisfying: f(x1(t))·f(x2(t))·f(x3(t))=u(t)2 in fq, with q=3 mod 4. Firstly a value of the parameter t is obtained. Morpho 
Multi chargedparticle beam writing apparatus and adjustment the same In one embodiment, a multi chargedparticle beam writing apparatus includes a plurality of blankers switching between on and off state of a corresponding beam among multiple beams, a main deflector deflecting beams having been subjected to blanking deflection to a writing position of the beams in accordance with movement of a stage, a detector scanning a mark on the stage with each of the beams having been deflected by the main deflector and detecting a beam position from a change in intensity of reflected charged particles and a position of the stage, and a beam shape calculator switching an on beam, scanning the mark with the on beam, and calculating a shape of the multiple beams from a beam position. A shape of a deflection field of the main deflector is corrected by using a polynomial representing an amount of beam position shift that is dependent on a beam deflection position of the main deflector and then the mark is scanned with the on beam. Nuflare Technology, Inc. 
Privacypreserving genomic prediction The techniques and/or systems described herein are directed to improvements in genomic prediction using homomorphic encryption. For example, a genomic model can be generated by a prediction service provider to predict a risk of a disease or a presence of genetic traits. Microsoft Technology Licensing, Llc 
Propeller blade beta twist A propeller blade comprises a blade root coupled to a rotor hub and a blade tip. The propeller blade is composed of airfoil crosssections, each crosssection a distance away from the rotor hub. Gopro, Inc. 
Fisheye rendering with lens distortion correction for 360degree video In various implementations, provided are systems and methods for correcting the distortion present in a fisheye image, and rendering the image for display as 360degree video. In various implementations, a computing device can receive 2dimensional video data captured by an omnidirectional camera. Qualcomm Incorporated 
Methods and systems for setting a system of super conducting qubits having a hamiltonian representative of a polynomial on a bounded integer domain Described herein are methods, systems, and media for setting a system of superconducting qubits having a hamiltonian representative of a polynomial on a bounded integer domain via boundedcoefficient encoding. The method comprises: obtaining the polynomial on the bounded integer domain and integer encoding parameters; computing boundedcoefficient encoding using the integer encoding parameters; recasting each integer variable as a linear function of binary variables using the boundedcoefficient encoding, and providing additional constraints on the attained binary variables to avoid degeneracy in the encoding; substituting each integer variable with an equivalent binary representation, and computing the coefficients of the equivalent binary representation of the polynomial on the bounded integer domain; performing a degree reduction on the obtained equivalent binary representation of the polynomial to provide an equivalent polynomial of degree at most two in binary variables; using which, setting local field biases and coupling strengths on the system of superconducting qubits.. 1qb Information Technologies Inc. 
System and voltagecontrolled oscillator calibration A system and method for calibrating a voltagecontrolled oscillator (vco) having both finetuning control and coarsetuning control. The vco frequency can vary monotonically with changes in each of one or more operational conditions. Maxlinear Asia Singapore Pte Ltd 
Apparatus and validating transactional data The invention creates a single use authentication code from (1) predefined unencrypted data from at least one tax form, (2) primary keys, and (3) a secondary key generated from metadata correlated to the input of the unencrypted data, the above elements being used by a data encryption circuit having a polynomial integer encryption (pie) engine, to generate the authentication code. The authentication code is translated into at least one symbol, using, for example, barcode technology, and applied to a tax document or form or otherwise encoded into electronic documents.. 
Estimating risk to a computer network from a high risk failure that occurred on a first or second computer system First and second tchebychev polynomial curves are generated and pass through first and second data points representing previous failures of a first and second computer system of a computer network, respectively. The coordinates of each first and second data point denote a time of occurrence of the failure of the first and second computer system and a severity of the failure of the first and second computer system, respectively. International Business Machines Corporation 
Lightweight key update mechanism with blacklisting based on secret sharing algorithm in wireless sensor networks Various embodiments include a network manager for managing network keys in a network having a plurality of nodes, the device including: a memory; and a processor configured to: determine n nodes to blacklist, wherein n is an integer; select a polynomial function from a plurality of polynomial functions of degree k and wherein the polynomial functions define plurality of secret network keys; generate kn random abscissa values, wherein none of the random abscissa values are not found in a list of node abscissa values; calculate kn polynomial function values for the kn random abscissa values; calculate n polynomial function values for n node abscissa values associated with the n blacklisted nodes; transmit a message to nodes in the network including an indication of the selected polynomial function, the kn random abscissa values, the n node abscissa values associated with the n blacklisted nodes, the kn calculated polynomial function values, and the n calculated polynomial function values.. . Freescale Semiconductor, Inc. 
Public key cryptosystem based on partitioning of galois field elements A postquantum, public key cryptosystem is described which is polynomial based and where the private key polynomial has coefficients from a subset of galois field elements and plain text message polynomials have coefficients from a second subset of galois field elements. The public key polynomial is constructed using the inverse of the private key polynomial and a randomly chosen polynomial having coefficients chosen from a third subset of galois field elements. Pq Solutions Limited 
Systems and methods using digital predistortion to linearize radio transmitter operation A method of linearizing a relationship between a signal to an amplifier and an output signal from the amplifier includes applying an inverse of a transfer function of the amplifier to the signal prior to presenting the signal as the amplifier input. The inverse transfer function is represented by a polynomial defined by a set of coefficients. Meteorcomm Llc 
. . 
. . 
Verification process of authentication or biometric identification The proving entity and the verification entity engage in a sumcheck protocol applied to the polynomial p to verify the result of calculation of the distance between the data.. . 
Nonmalleable obfuscator for sparse functions Described is a system for obfuscating a computer program. Sensitive data of an unprotected computer program is received as input. 
Circuitry and methods for implementing galoisfield reduction Galoisfield reduction circuitry for reducing a galoisfield expansion value, using an irreducible polynomial, includes a plurality of memories, each for storing a respective value derived from the irreducible polynomial and a respective combination of expansion bit values, wherein expansion bits of the expansion value address the plurality of memories to output one or more of the respective values. The galoisfield reduction circuitry also includes exclusiveor circuitry for combining output of the plurality of memories with infield bits of said expansion value. 
Singlepass and multipassbased polynomial approximations for reshaping functions A processor for approximating a reshaping function using a multisegment polynomial receives an input reshaping function. Given a number of target segments (n) and an initial maximum fitting error, in a first pass, it applies a first smoothing filter to the input reshaping function to generate a first smoothed reshaping function. Dolby Laboratories Licensing Corporation 
Logarithm and power (exponentiation) computations using modern computer architectures Embodiments of the present invention may provide the capability to evaluate logarithm and power (exponentiation) functions using either hardware specific instructions, or a hardware specific implementation with reduced memory requirements. An input comprising a floating point representation of a real number may be received and a mantissa and an exponent may be extracted. International Business Machines Corporation 
Evaluating polynomials in hardware logic An accurate implementation of a polynomial using floatingpoint or other rounded arithmetic can be generated using a plurality of hardware logic components which each implement an input polynomial such that the zeros in the input polynomial can be determined correctly. The number of different hardware logic components that are used can be reduced by analysing the set of input polynomials and from it generating a set of polynomial components, where each polynomial in the set of input polynomials which is not also in the set of polynomial components, can be generated from a single one of the polynomial components.. Imagination Technologies Limited 
Offaxis threemirror optical system with freeform surfaces The tertiary mirror is located on a secondary mirror reflected light path. The detector located on a tertiary mirror reflected light path. 
Offaxis threemirror optical system with freeform surfaces An offaxis threemirror optical system with freeform surfaces comprised an aperture, a primary mirror, a secondary mirror, a tertiary mirror, and a detector. The aperture is located on an incident light path. Hon Hai Precision Industry Co., Ltd. 
Lighting device A lighting device, in particular a led lighting device, comprises at least one light source and a reflector extending along and around a longitudinal axis and having an internal reflective surface arranged so as to intercept at least part of the light emitted by the light source and reflect said part towards a light exit opening; the internal reflective surface is a faceted polynomial surface.. . Artemide S.p.a. 
Ophthalmic apparatus with corrective meridians having extended tolerance band by modifying refractive powers in uniform meridian distribution The embodiments disclosed herein include improved toric lenses and other ophthalmic apparatuses (including, for example, contact lens, intraocular lenses (iols), and the like) and associated method for their design and use. The apparatus includes one or more optical zones, including an optical zone defined by a polynomialbased surface coincident at a plurality of meridians having distinct cylinder powers, wherein light incident to a given region of each of the plurality of meridians, and respective regions nearby, is directed to a given point of focus such that the regions nearby to the given region direct light to the given point of focus when the given meridian is rotationally offset from the given region, thereby establishing an extended band of operation, and wherein each of the plurality of meridians is uniformly arranged on the optical zone for a same given added power (in diopters) up to 1.0 d (diopters).. Abbott Medical Optics Inc. 
Ophthalmic apparatus with corrective meridians having extended tolerance band with freeform refractive surfaces The embodiments disclosed herein include improved toric lenses and other ophthalmic apparatuses (including, for example, contact lens, intraocular lenses (iols), and the like) that includes a freeformpolynomial surface area that establishes a band of operational meridian for the apparatus to an intended correction meridian. The freeformpolynomial surface area is defined by a mathematical expression comprising a combination of one or more polynomial expressions (e.g., chebyshevbased polynomial expression, zernikebased polynomial expression, etc.) each having a distinct complex orders.. Abbott Medical Optics Inc. 
Faulttolerant aggregation of encrypted data in a star network One embodiment provides a system that facilitates encrypteddomain aggregation of data in a star network. During operation, the system receives a set of ciphertexts, representing respective encrypted polynomial shares, of an input value from each participant in a plurality of participants. Palo Alto Research Center Incorporated 
Publickey encryption system A key generation device (100) configured to generate a public key (126) for use in a public key encryption device and a corresponding private key (114) for use in a private key decryption device, the key generation device comprising a private key generator (110) configured for obtaining in electronic form a private random value (112, s), and generating the private key (114), the private key comprising the private random value (112), and a public key generator (120) configured for obtaining in electronic form a public set of bivariate polynomials (122, fi(,)), computing a public univariate polynomial (124) by summing over univariate polynomials obtained by substituting the private random value (112, s) into the polynomials of the public set (122, fi(s,)), and generating the public key (126), the public key comprising the public univariate polynomial (124) and the public set (122).. . Koninklijke Philips N.v. 
Instructions and logic to provide general purpose gf(256) simd cryptographic arithmetic functionality Instructions and logic provide general purpose gf(28) simd cryptographic arithmetic functionality. Embodiments include a processor to decode an instruction for a simd affine transformation specifying a source data operand, a transformation matrix operand, and a translation vector. Intel Corporation 
Method of determining lineal parameters of a transmission line A method for determining at least one lineal parameter of a transmission line comprises the following steps: determining at least one measurement of the complex propagation factor γ as a function of frequency on the basis of at least one measurement carried out on the transmission line, determining at least one measurement of the lineal attenuation α of the transmission line equal to the real part of the measurement of the complex propagation factor γ and/or at least one measurement of the phase factor β of the transmission line equal to the imaginary part of the measurement of the complex propagation factor γ, filtering the measurement of the lineal attenuation α and/or the measurement of the phase factor β on the basis of a polynomial frequency regression model dependent on the physical characteristics of the transmission line.. . Commissariat A L'energie Atomique Et Aux Energies Alternatives 
Data generation apparatus, data recording system, and program product A data generation apparatus includes a processor that executes a process including obtaining target data sequentially from timeseries data, the target data including n (n being an integer greater than or equal to 2) data items in a predetermined section of the timeseries data, calculating parameter information satisfying a (k−1) order polynomial based on the target data, the (k−1) order polynomial including k random values, k being an integer greater than or equal to 1 and less than n, associating the target data to the parameter information, outputting the target data and the parameter information associated to the target data, attaching a signature to secret information based on a secret distributed protocol. The secret information is calculable by using k pairs of data including the target data and the parameter information associated to the target data, and outputting the secret information attached with the signature.. Ricoh Company, Ltd. 

Data processing system, data processing apparatus, and data processing method A data processing apparatus includes a memory storing a program and a processor configured to execute the program to implement a process of reading signed data including a predetermined number (n) of secret sharing data sets generated for each section of time series data and a signature value calculated for the each section of time series data based on a secret sharing protocol. The n secret sharing data sets include n units of data acquired from each section of time series data and parameter information for a polynomial of a predetermined degree calculated based on the acquired n units of data. Ricoh Company, Ltd. 
Decoding device, information transmission system, decoding method, and nontransitory computer readable medium A decoding device receives transmission data obtained by scrambling according to a polynomial xa+xb+1 where a and b are each an integer, a>b, and a≠2b. The decoding device includes a receiving unit, an error detecting unit, and a correcting unit. Fuji Xerox Co., Ltd. 
Ecc circuit, storage device and memory system Thereby calculating syndromes s and z. An error position polynomial coefficient calculation circuit calculates the coefficient of an error position polynomial to obtain s×z by multiplying s and z by one multiplier. 
Controller for rotary electric machine drive apparatus There is provided a controller for a rotary electric machine drive apparatus capable of reducing dataprocessing load and amount of memories required for a data processing which calculates a voltage command value of the converter which reduces power loss. A controller calculates the required minimum voltage which is required in the case of performing a maximum torque/current control is calculated; calculates a converter loss coefficient which is a coefficient of a polynomial representing a power loss characteristic of the converter; calculates an inverter loss coefficient which is a coefficient of a polynomial representing a power loss characteristic of the inverter; calculates a sum total of loss coefficients for each order of polynomials; calculates the low loss voltage which the sum total power loss becomes a minimum, based on the sum total loss coefficients for each order; sets to the voltage command value of the converter.. Mitsubishi Electric Corporation 
Triangulation device, triangulation method, and recording medium recording program therefor A triangulation device for computing a threedimensional position of a measurement target point using a stereo method, the triangulation device includes: optimum image coordinate estimation unit configured to, based on coordinates of corresponding points corresponding to the measurement target point in two images each of which including an image of the measurement target point, and intrinsic parameters and extrinsic parameters of optical instruments generating the two images, calculate correction vectors by which coordinates of the corrected corresponding points satisfy an epipolar equation composed of the intrinsic parameters and the extrinsic parameters, using a characteristic polynomial including a correction amount of coordinates of the corresponding points or a reciprocal of the correction amount as a variable, and compute coordinates of the corrected corresponding points based on calculated correction vectors; and threedimensional coordinate calculation unit configured to calculate threedimensional coordinates of the measurement target point based on coordinates of the corrected corresponding points, the intrinsic parameters and the extrinsic parameters.. . Nec Corporation 
Respiratory gating system for patient using natural breathing method during radiation therapy, and emitting radiation thereby The present invention relates to a respiratory gating system for a patient using a natural breathing method during radiation therapy, and a method for emitting radiation thereby. A respiratory gating system allowing radiation to be emitted by orienting to the position, which varies according to a patient's breathing, of a subject on which treatment is to be carried out, comprises: a breathing respirator for allowing the patient's respiration amount to be measured; external markers to be respectively adhered to triangulation points outside the human body of the surrounding region of the subject, of the patient, on which treatment is to be carried out; an image diagnosis device for imaging the region of the subject of the patient on which treatment is to be carried out, by photographing the same; and a computer program programmed so as to calculate, as position coordinates, the change in position of the subject on which treatment is to be carried out, according to the respiration amount measured by the computed tomography equipment and the each external marker, through a triangulation method and dual polynomial equations, and to transmit the position coordinates, which changes in real time, to radiation therapy equipment, wherein radiation is emitted by the respiratory gating system, and there is an effect of further increasing the accuracy and stability of the entire radiation therapy result by tracking, in real time, the movement of an organ, which is the subject on which treatment is to be carried out according to breathing, through a respiratory gating system which uses natural breathing rather than a breathing method through the training of the patient.. Catholic University Industry Academic Cooperation Foundation 
Digital signature method and apparatus A method for signing and subsequently verifying a digital message, including the following steps: generating an irreducible monic polynomial f(x) of degree n in a ring fq[x]; generating an irreducible monic polynomial f(y) of degree n in a ring fq[y]; producing first and second finite fields as fq[x]/(f(x)) and fq[y]/(f(y)), respectively; producing a secret isomorphism from the first finite field to the second finite field; producing and publishing a public key that depends on f(y); producing a private key that depends on the secret isomorphism; producing a message digest by applying a hash function to the digital message and the public key; producing a digital signature using the message digest and the private key; and performing a verification procedure utilizing the digital signature and the public key.. . Security Innovation Inc. 
Method and device for calculating a crc code in parallel The disclosure relates to a method performed in a cyclic redundancy check, crc, device for calculating, based on a generator polynomial g(x), a crc code for a message block. The method comprises receiving n segments of the message block in forward order or in reverse order, wherein at least one segment is received in reverse order; calculating for each of the n segments a respective segment crc code based on the generator polynomial g(x), wherein each segment crc is calculated according to the received order of the segment; aligning each of the n segment crc codes; and calculating the crc code for the message block by adding together each of the aligned n segment crc codes. Telefonaktiebolaget Lm Ericsson (publ) 
Sparse map for autonomous vehicle navigation A nontransitory computerreadable medium is provided. The computerreadable medium includes a sparse map for autonomous vehicle navigation along a road segment. Mobileye Vision Technologies Ltd. 
Mask blank substrate, mask blank, transfer mask, and manufacturing semiconductor device Provided are a mask blank substrate which has effectively and extremely high principal surface flatness while a reduction in the manufacturing throughput of the mask blank substrate is suppressed, a mask blank, and a transfer mask. Also provided are manufacturing methods therefor. Hoya Corporation 
System and providing a corrected lane following path through a curve for trailering vehicles A method for providing vehicle steering control through a curve in an autonomously driven or semiautonomously driven vehicle that is towing a trailer. The method determines that the trailer will cross out of the travel lane based on the curvature of the curve and the turn radius of the trailer. Gm Global Technology Operations Llc 
Telefonaktiebolaget Lm Ericsson (publ) . . 
Fixedpoint conjugate gradient digital predistortion (dpd) adaptation A predistortion method and apparatus are provided which use a dpd actuator (225) to apply a memory polynomial formed with first dpd coefficients to a first input signal x[n], thereby generating a first predistorted input signal y[n] which is provided to the nonlinear electronic device (253) to produce the output signal, where the memory polynomial may be adaptively modified with a digital predistortion adapter (224) which computes second dpd coefficients u[n] with an iterative fixedpoint conjugate gradient method which uses n received digital samples of the first predistorted input signal y[n] and a feedback signal z[n] captured from the output signal to process a set of conjugate gradient parameters (u, b, v, r, ω, α, β) at each predetermined interval, thereby updating the first dpd coefficients with the second dpd coefficients u[n] generate a second predistorted input signal which is provided to the nonlinear electronic device.. . Freescale Semiconductor, Inc. 
Singleinput singleoutput twobox polar behavioral model for envelope tracking power amplifiers The singleinput singleoutput twobox polar behavioral model for envelope tracking power amplifiers estimates magnitude and phase of the output signal in separate paths. More specifically, the model is a twobox polar behavioral model using a complex magnitude and phase splitter that feeds a parallel combination of a generalized memory polynomial function and a memoryless polynomial function applied to the input signal's magnitude and phase, respectively. King Fahd University Of Petroleum And Minerals 
Method and system for solving the lagrangian dual of a binary polynomially constrained polynomial programming problem using a quantum annealer A method for solving the lagrangian dual of a binary polynomially constrained polynomial programming problem comprises obtaining a binary polynomially constrained polynomial programming problem; until a convergence is detected, iteratively, providing a set of lagrange multipliers, providing an unconstrained binary quadratic programming problem representative of the lagrangian relaxation of the binary polynomially constrained polynomial programming problem at these lagrange multipliers, providing the unconstrained binary quadratic programming problem to a quantum annealer, obtaining from the quantum annealer at least one corresponding solution, using the at least one corresponding solution to generate a new set of lagrange multipliers; and providing all corresponding bestknown primaldual pairs and bestknown feasible solutions after convergence.. . 1qb Information Technologies Inc. 
Gas turbine engine airfoil An airfoil for a turbine engine includes pressure and suction sides extending in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip. The airfoil has a relationship between an axial leading edge location and a span position that is at least a third order polynomial with a generally ushaped curve having an initial negative slope followed by a positive slope. United Technologies Corporation 
Methods and systems for prediction of sensor response time Methods and systems are provided for predicting response time of a particulate matter (pm) sensor and resetting the pm sensor upon completion of response time prediction, independent of actual or predicted soot load on pm sensor. Soot accumulation data collected during steady state vehicle operation may be fitted with a timebased polynomial function and sensor output and regeneration schedule may be estimated from the curve fit even if the overall signal is noisy.. Ford Global Technologies, Llc 
Systems and methods for estimating modulation transfer function in an optical system A method of determining a modulation transfer function (mtf) for an image includes receiving an image captured through the optical system, performing edge detection on columns or rows in the image to calculate a plurality of edge points, calculating a plurality polynomials to fit to the calculated edge points, each of the plurality of polynomials varying in degree, selecting a polynomial from the plurality of polynomials to represent the detected edge, and estimating the mtf based on the selected polynomial.. . Google Inc. 
Method and association rules with graph patterns Graph pattern association rules (gpars) are proposed for social media marketing. Extending association rules for itemsets, gpars help discover regularities between entities in social graphs, and identify potential customers by exploring social influence. Futurewei Technologies, Inc. 
Decoding device, information transmission system, decoding method, and nontransitory computer readable medium A decoding device receives transmission data obtained by scrambling according to a polynomial xa+xb+1 where a and b are each an integer, a>b, and a≠2b. The decoding device includes a receiving unit, an error detecting unit, and a correcting unit. Fuji Xerox Co., Ltd. 
Efficient synthesis of probabilistic quantum circuits with fallback A probabilistic quantum circuit with fallback (pqfs) is composed as a series of circuit stages that are selected to implement a target unitary. A final stage is conditioned on unsuccessful results of all the preceding stages as indicated by measurement of one or more ancillary qubits. Microsoft Technology Licensing, Llc 
Motion capture system that combines sensors with different measurement ranges Motion capture system with a motion capture element that uses two or more sensors to measure a single physical quantity, for example to obtain both wide measurement range and high measurement precision. For example, a system may combine a lowrange, high precision accelerometer having a range of −24 g to +24 g with a highrange accelerometer having a range of −400 g to +400 g. Blast Motion Inc. 
Computing processor Improved computing processor. In an embodiment, one or more roots of a perturbed polynomial equation, comprising a plurality of terms, are computed, assuming a nonzero coefficient for a highestorder one of the plurality of terms. 
Cryptography on a simplified elliptical curve A cryptographic calculation includes obtaining a point p(x,y) from a parameter t on an elliptical curve y2=f(x) and from polynomials satisfying: −f(x1(t))·f(x2(t))=u(t)2 in the finite body fq, irrespective of the parameter t, q=3 mod 4. A value of the parameter t is obtained and the point p is determined by: (i) calculating x1=x1(t), x2=x2(t) and u=u(t); (ii) testing whether the term f(x−1) is a squared term in the finite body fq and, if so, calculating the square root of the term f(x1), the point p having x1 as abscissa and y1, the square root of the term f(x1), as ordinate; (iii) otherwise, calculating the square root of the term f(x2), the point p having x2, as abscissa and y2, the square root of the term f(x2), as ordinate. Morpho 
Method and digital undervoltage detection and control A method and apparats for undervoltage detection and correction is disclosed. An ic includes sensors implemented in various functional circuit blocks. Apple Inc. 
Circuit verification A method enables arithmetic circuit verification with improved runtime complexity by coupling reverse engineering and a sat solver together. The method provides a netlist f of a first arithmetic circuit and a netlist g of a second arithmetic circuit; and improves the runtime complexity by conducting equivalence checking between the netlist f and the netlist g such that structural difference between the netlist f and the netlist g is minimized by reverse engineering before generating a conjunctive normal form (cnf) encoding that is solved by a satisfiability (sat) solver such that the arithmetic circuit verification is completed in polynomial time rather than in exponential time.. Easylogic Technology Limited 
Method to obtain data concerning the upper profile of an element of a railway track or switch A method to obtain data concerning the upper profile of an element of a railway track or switch by means of an electronic measuring module mounted on a cart and provided with at least one laser profilometer to acquire a sequence of images while the cart moves forward along the railway track so that each image comprises a point cloud indicative of the upper profile in correspondence with a respective plane transverse to the forward moving direction of the cart. The method provides that, for each point cloud, a respective piecewise polynomial function, preferably a spline function, that approximates the point cloud, is generated, so as to transform original data consisting of said point cloud into compressed data consisting of parameters of the piecewise polynomial function.. General Impianti S.r.l. 
Cryptography on an elliptical curve A cryptographic calculation includes obtaining a point p(x,y) from a parameter t on an elliptical curve y2=f(x); and from polynomials x1(t), x2(t), x3(t) and u(t) satisfying: f(x1(t))·f(x2(t))·f(x3(t))=u(t)2 in fq, with q=3 mod 4. Firstly a value of the parameter t is obtained. Morpho 
Method for characterization of a layered structure In an embodiment, a method comprises fitting a spectroscopic data of a layer in a layered structure to a dielectric function having a real part and an imaginary part; confirming that the dielectric function is physically possible; based on the dielectric function not being physically possible, repeating the fitting the spectroscopic data, or, based on the dielectric function being physically possible, defining an n degree polynomial to the dielectric function; determining a second derivative and a third derivative of the n degree polynomial; equating the second derivative to a first governing equation and the third derivative to a second governing equation and determining a constant of the first governing equation and the second governing equation; and based on the key governing equations, determining one or more of a band gap, a thickness, and a concentration of the layer.. . Globalfoundries, Inc. 
Method and efficiently implementing the advanced encryption standard Implementations of advanced encryption standard (aes) encryption and decryption processes are disclosed. In one embodiment of sbox processing, a block of 16 byte values is converted, each byte value being converted from a polynomial representation in gf(256) to a polynomial representation in gf((22)4). Intel Corporation 

Error locator polynomial decoder and method A decoder includes an error locator polynomial generator circuit configured to determine, during a first cycle of a clock signal, a first value of a parameter. The first value of the parameter is associated with a first iteration of a decode operation and is based on a value of an error locator polynomial associated with a prior iteration of the decode operation. Western Digital Technologies, Inc. 
Piecewise interlayer prediction for signals with enhanced dynamic range Pixel data of a video sequence with enhanced dynamic range (edr) are predicted based on pixel data of a corresponding video sequence with standard dynamic range (sdr) and a piecewise interlayer predictor. The output parameters of the piecewise predictor are computed based atleast on two sets of precomputed values and a prediction cost criterion. Dolby Laboratories Licensing Corporation 
Twodimensional piecewise approximation to compress image warping fields Techniques to prewarp an image based on an image warping map comprising a number of cells where each cell corresponds to a polynomial approximation for a number of corresponding pixels to be warped are described. An image warping map can be generated by partitioning a per pixel warping map into cells and approximating the pixel movements of each cell with a polynomial function.. 
System and controlling multiple electric drives An electric vehicle includes a plurality of electric drive units coupled to one or more axles of the electric vehicle. The drive units have an associated power loss map that is approximated by a plurality of secondorder polynomials. Ford Global Technologies, Llc 
Scattering and reflection identification system and method A method of forming an image of a region of interest using a pulseecho imaging device is described. The method includes the steps of transmitting a pulse, discriminating an echo of the pulse by comparison to a plurality of hermite polynomials, and determining a color for display based on the comparison. University Of Rochester 
Methods, devices, and computer programs for compensating nonlinearities of a communication channel A method, carried out by a gateway transmitter (400), aims at compensating the nonlinearities of a communication channel (500) comprising a repeater (510). A plurality of digital signals is modulated (s10) on a plurality of carriers, wherein symbols of the constellation diagram used for modulation of each carrier are distorted in accordance with a predistortion function. Ses S.a. 
Optimal index selection in polynomial time A method for performing analysis may use a minimal set of indices for an input query including identifying the input query including primitive searches that are accelerated using indices, computing a minimal set of indices for the input query using an optimal, polynomialtime algorithm, and performing relational data analysis using the minimal set of indices for input queries.. . Oracle International Corporation 
System and method to control the operation of transmission using engine fuel consumption data A system and method of controlling the operation of a transmission using fuel consumption data. The system and method includes controlling the operation of a vehicle transmission which is operatively connected to an engine having operating characteristics and operatively connected to a transmission control module having access to a memory. Allison Transmission, Inc. 
Device for determining a shared key A first device (300) configured to determine a shared key with a second device (350). In cryptography, a keyagreement protocol is a protocol whereby two or more parties that may not yet share a common key can agree on such a key. Koninklijke Philips N.v. 
Transmission circuit for ultrasonic diagnosis and transmitting ultrasonic wave A transmission circuit for ultrasonic diagnosis includes a delay processing circuit that delays a transmission signal pattern and an operational circuit that calculates a delay time. A transmission timing for supplying the transmission signal pattern to a plurality of piezo electric elements corresponding to a plurality of channels is approximated by a multidimensional polynomial with locations of the plurality of piezo electric elements being variables so that the transmission timing becomes linear or arclike. Sii Semiconductor Corporation 
Flexible polynomialbased interleaver Techniques are disclosed relating to circuitry configured to interleave data, e.g., for use to process error correcting codes for wireless data transmission. In some embodiments an apparatus includes one or more circuit elements configured to receive input data samples, a plurality of polynomial coefficients, a start index, and information indicating a window size for nonsequential traversal of interleaver indices. 
Efficient two party oblivious transfer using a leveled fully homomorphic encryption A querying node generates public keys, secret keys, and switch key matrices. A public key associated with a first level and the switch key matrices are sent to a receiving node. 
Gas turbine engine A method of manufacturing a gas turbine engine including designing a row of vanes provided upstream of an asymmetric gas flow volume. The method includes two dimensionally optimising camberline and stagger angle of each vane, including using orthogonal polynomials to modify the camberline and stagger angle of each vane.. 
Deformable membrane assemblies A deformable membrane assembly comprising a fixed support, a fluidfilled envelope, one wall of which is formed by an elastic membrane that is held under tension around its edge by a flexible membrane supporting member, the supporting member being coupled to the fixed support at a plurality of discrete control points around the supporting member by engaging members for controlling the position of the membrane edge; and an adjuster for adjusting the pressure of the fluid within the envelope to adjust the shape of the membrane; wherein at least three control points are provided that are situated around the membrane edge at spaced locations selected to increase the energy of the lowest order outofplane bending mode of the supporting member while allowing the membrane to deform according to one or more selected zernike polynomials. An article of eyewear comprising such a deformable membrane assembly is also disclosed.. 
Identification an entity The present invention relates to a biometric identification method of an entity comprising computation of a matching value between biometric data of an entity u and reference biometric data u′, by application of a function f to said biometric data by performing a noninteractive, publicly verifiable computation method comprising: representation of said function in the form of an arithmetic circuit converted into a polynomial representation, and generation of keys, determination of matching value by evaluating the arithmetic circuit having the biometric data of the entity and the reference biometric data as inputs, generation of proof of correction of the computation execution of the matching values, verification of said received proof, representation of said function comprising encoding of an integer k>1 of binary integers of a vector of a biometric datum on at least one input wire of the circuit, and the function f comprising at least m scalar products, if the divider m is equal to 2 or 3, evaluation of the circuit iteratively comprises computation of each of the m scalar products by means of n/km multiplication operators, storage and summation of m results of computations of said scalar products and if the divider m is greater than or equal to 4, evaluation of the circuit iteratively comprises computation of each of the m scalar products by alternatively using a first or a second subcircuit to compute the sum of the scalar product of the values of the input wires of this subcircuit and of a value stored in a storage memory of the other subcircuit.. . Safran Identity & Security 
Generating cryptographic checksums A method (500) of generating a cryptographic checksum for a message m(x) is provided. The method comprises pseudorandomly selecting (502) a generator polynomial p(x) from the set of polynomials of degree n over a galois field and calculating (504) the cryptographic checksum as a first function g of a division of a second function of m(x), ƒ(m(x)), modulo p(x), g(ƒ(m(x))mod p(x)). Telefonaktiebolaget Lm Ericsson (publ) 
Fully homomorphic encryption from monoid algebras A blueprint that produces a family of fhe schemes given any homomorphic monoidal encryption scheme. The ciphertext space is a subspace of the monoid algebra over f2 generated by the initial encryption monoid. Certsign S.a. 
Homomorphic encryption with optimized encoding The techniques and/or systems described herein are directed to improvements in homomorphic encryption to improve processing speed and storage requirements. For example, the techniques and/or systems can be used on a client device to encode data to be sent to a remote server, to be operated on while maintaining confidentiality of data. Microsoft Technology Licensing, Llc 
Coding method, decoding method, coder, and decoder An encoding method of generating an encoded sequence by performing encoding of a given encoding rate based on a predetermined parity check matrix. The predetermined matrix is either a first parity check matrix or a second parity check matrix. Sun Patent Trust 
Polynomial mixture for frequency domain multiuser channel estimation and tracking in a wireless communication network Methods and systems for obtaining improved channel estimates for frequencymultiplexed data transmissions such as ofdm, ofdma, or scfdma transmissions overcome the limitations of the static assumption by using a polynomial or other fitting function to fit and model the frequency dependence of the channel coefficients, so that estimates can be applied to larger subcarrier groups. Some embodiments provide channel estimates for a singular signal source, while other embodiments provide joint channel estimates for a plurality of signal sources. Collision Communications, Inc. 

Error correction A circuit arrangement for determining a correction signal on the basis of at least one bit error of a binary word is specified, including a plurality of subcircuits (st), wherein a respective subcircuit is provided for a bit position to be corrected of the binary word, wherein each of the subcircuits provides at least two locator polynomial values, and comprising a selection unit, which determines a correction signal depending on the locator polynomial values and depending on an error signal (err, e). A method for driving such a circuit arrangement is furthermore proposed.. Infineon Technologies Ag 
Systems and methods for service demand based performance prediction with varying workloads Systems and methods for service demand based performance prediction with varying workloads are provided. Chebyshev nodes serve as optimum number of load testing points to minimize polynomial interpolation error rates. Tata Consultancy Services Limited 
Lithographic apparatus and exposure method A method including determining a position of a first pattern in each of a plurality of target portions on a substrate, based on a fitted mathematical model, wherein the first pattern includes at least one alignment mark, wherein the mathematical model is fitted to a plurality of alignment mark displacements (dx, dy) for the alignment marks in the target portions, and wherein the alignment mark displacements are a difference between a respective nominal position of the alignment mark and measured position of the alignment mark; and transferring a second pattern onto each of the target portions, using the determined position of the first pattern in each of the plurality of target portions, wherein the mathematical model includes polynomials z1 and z2: z1=r2 cos(2θ) and z2=r2 sin(2θ) in polar coordinates (r, θ) or z1=x2−y2 and z2=xy in cartesian coordinates (x, y).. . Asml Netherlands B.v. 
Magentic resonance spectroscopy pulse sequence, acquistion, and processing system and method Systems and methods are provided for processing a set of multiple serially acquired magnetic resonance spectroscopy (mrs) free induction decay (fid) frames from a multiframe mrs acquisition series from a region of interest (roi) in a subject, and for providing a postprocessed mrs spectrum. Processing parameters are dynamically varied while measuring results to determine the optimal postprocessed results. Nocimed, Inc. 
Algebraic generators of sequences for communication signals A device for modulating communication signals comprises a transceiver for receiving and transmitting the signal, a storage medium storing computer implemented programme code components to generate sequences and a processor in communication with the storage medium and transceiver. The processor executes computer implemented programme code components to generate a family of shift sequences or arrays using exponential, logarithmic or index functions and a polynomial or a rational function polynomial in t∈p−1 for a finite field p of prime p. Optimark, Llc 
Crc update mechanism A cyclic redundancy code (crc) update device includes an input coupled to obtain an old crc that corresponds to an old header of a communication packet, a crc storage device to store crc coefficients, a crc calculator coupled to receive a modified old header of the communication packet and calculate a new crc on the modified old header, and a polynomial multiplier coupled to the crc storage device to receive the new crc, obtain a corresponding coefficient from the crc storage device, and generate an update for the crc of the frame.. . 
Process variable transmitter with selflearning loop diagnostics A twowire process variable transmitter for use in an industrial process includes a process variable sensor configured to sense a process variable of a process fluid of the industrial process. Output circuitry provides an output on a twowire process control loop which is related to the sensed process variable. Rosemount Inc. 
Error locator polynomial decoder and method An apparatus includes a convergence detector circuit coupled to an error locator polynomial generator circuit. The convergence detector circuit includes at least two computation circuits configured to generate at least two convergence signals based on a mutual error locator polynomial from the error locator polynomial generator circuit and on at least two different sets of syndromes. Western Digital Technologies, Inc. 
System and voltagecontrolled oscillator calibration A system and method for calibrating a voltagecontrolled oscillator (vco) having both finetuning control and coarsetuning control. The vco frequency can vary monotonically with changes in each of one or more operational conditions. Maxlinear Asia Singapore Pte Ltd. 
3d lighting Techniques are disclosed for displaying a graphical element in a manner that simulates threedimensional (3d) visibility (including parallax and shadowing). More particularly, a number of images, each captured with a known spatial relationship to a target 3d object, may be used to construct a lighting model of the target object. Apple Inc. 
Apparatus and methods for nondeterministic computing In the disclosed nondeterministic computing apparatus and methods, a user problem to be solved is represented as a nondeterministic turing machine m with an input x to it. A method for deterministic simulation of m on x is disclosed, which performs assumptions and refutations. 
Solving npcomplete problems without hyper polynomial cost Within satisfaction problems or any decision or other problem which is reducible to a satisfaction problem, the invention tracks the paths along which implications propagate and identifies conditional contradictions and subsequently moves the contradictions back down the implicational paths toward assumptions or other unreasoned assertions in order to expel the contradictions. The action is completed in less time than is incurred by existing methods and thus provides a performance improvement to the devices, software, or processes which address such problems. 
Method and processing performing arithmetic operation A method of performing an arithmetic operation by a processing apparatus includes determining a polynomial expression approximating an arithmetic operation to be performed on a variable; adaptively determining upper bits for addressing a lookup table (lut) according to a variable section to which the variable belongs; obtaining coefficients of the polynomial expression from the lut by addressing the lut using a value of the upper bits; and performing the arithmetic operation by calculating a result value of the polynomial expression using the coefficients.. . Samsung Electronics Co., Ltd. 
Method and associated decoding circuit for decoding an error correction code A method for decoding an error correction code and an associated decoding circuit are provided, where the method includes the steps of: calculating a set of error syndromes of the error correction code, where the error correction code is a terror correcting code and has capability of correcting t errors, and a number s of the set of error syndromes is smaller than t; sequentially determining a set of coefficients within a plurality of coefficients of an error locator polynomial of the error correction code according to at least one portion of error syndromes within the set of error syndromes for building a roughlyestimated error locator polynomial; performing a chien search to determine a plurality of roots of the roughlyestimated error locator polynomial; and performing at least one check operation to selectively utilize a correction result of the error correction code as a decoding result of the error correction code.. . Silicon Motion Inc. 
Method for determining parameter values of an induction machine by means of polynominal calculations A method for determining parameter values of an induction machine. The method may be executed by a dedicated computer system. Ishou University 
Spiral polynomial division multiplexing A method for communicating using polynomialbased signals. In such a method, a set of basis polynomial functions used to generate waveforms may be identified, wherein each of the basis polynomial functions in the set of basis polynomial functions is orthogonal to each of the other basis polynomial functions in the set of basis polynomial functions in a coordinate space. Astrapi Corporation 
Gps data correction for automated vehicle A system for automated operation of a hostvehicle includes an objectsensor, a globalpositioningsystem (gps) receiver, and a controller. The objectsensor is used to determine a firstpolynomial indicative of a preferredsteeringpath based on an object detected proximate to a hostvehicle. Delphi Technologies, Inc. 
Cryptographic system and computer readable medium A cryptographic system (10) performs a cryptographic process using a basis. B and a basis b*. Mitsubishi Electric Corporation 
Eyelid shape estimation Systems and methods for eyelid shape estimation are disclosed. In one aspect, after receiving an eye image of an eye (e.g., from an image capture device), an eyebox is generated over an iris of the eye in the eye image. Magic Leap, Inc. 
Programmable mip catch and release technology Programmable molecular imprinted polymers (mips) that have modified binding site kinetics for target imprintable entities (ties) that operate to control the adsorption, binding, release and equilibrium distribution of related materials into and out of the mips, which are useful for the controlled adsorption, controlled release and control of concentrations of such materials in media including gases, liquids, fluids, biological systems, solutions and other environments. When a collective plurality of the mips with modified binding site kinetics are combined, the resulting mip systems can be tailored to exhibit pseudo zero and firstorder kinetics, as well as higher kinetic profiles, and when further combined with timedelay functionality, can be tailored to exhibit delayed uptake and release, ramped uptake and release of materials, step functions, polynomial, geometric, exponential and other unique kinetic profiles of material exchange between the novel mips and a fluid media that are not readily achievable by other means.. The Decaf Company, Llc 

Programmable mip catch and release technology Programmable molecular imprinted polymers (mips) that have modified binding site kinetics for target imprintable entities (ties) that operate to control the adsorption, binding, release and equilibrium distribution of related materials into and out of the mips, which are useful for the controlled adsorption, controlled release and control of concentrations of such materials in media including gases, liquids, fluids, biological systems, solutions and other environments. When a collective plurality of the mips with modified binding site kinetics are combined, the resulting mip systems can be tailored to exhibit pseudo zero and firstorder kinetics, as well as higher kinetic profiles, and when further combined with timedelay functionality, can be tailored to exhibit delayed uptake and release, ramped uptake and release of materials, step functions, polynomial, geometric, exponential and other unique kinetic profiles of material exchange between the novel mips and a fluid media that are not readily achievable by other means.. The Decaf Company, Llc 
Programmable mip catch and release technology Programmable molecular imprinted polymers (mips) that have modified binding site kinetics for target imprintable entities (ties) that operate to control the adsorption, binding, release and equilibrium distribution of related materials into and out of the mips, which are useful for the controlled adsorption, controlled release and control of concentrations of such materials in media including gases, liquids, fluids, biological systems, solutions and other environments. When a collective plurality of the mips with modified binding site kinetics are combined, the resulting mip systems can be tailored to exhibit pseudo zero and firstorder kinetics, as well as higher kinetic profiles, and when further combined with timedelay functionality, can be tailored to exhibit delayed uptake and release, ramped uptake and release of materials, step functions, polynomial, geometric, exponential and other unique kinetic profiles of material exchange between the novel mips and a fluid media that are not readily achievable by other means.. The Decaf Company, Llc 
Apparatus to transmit data using different scramble generator polynomials A first processor included in a transmission device stores a first generator polynomial in a portion of a first data scrambled by using the first generator polynomial, and transmits the first data including the first generator polynomial. A second processor included in a reception device receives the first data, descrambles the first data by using the first generator polynomial, and generates a second data by scrambling the descrambled first data by using a second generator polynomial different from the first generator polynomial.. Fujitsu Limited 
Weighted memory polynomial power amplifiers predistortion A system and method for linearizing a power amplifier using digital predistortion technique is provided including processing circuitry, the processing circuitry configured to apply a digital predistortion function based on a weighted static polynomial function, a weighted dynamic polynomial function and a threshold parameter which splits the nonlinear transfer characteristics of the device under test into a region where the static nonlinearity predominates and a region where the dynamic distortions predominate.. . King Fahd University Of Petroleum And Minerals 
Fault level estimation power converters A method for fault level estimation for a power converter quickly after a fault clearing event includes a step of providing a training dataset with an input variable set and a corresponding system fault level output variable. The method further includes a step of deducing a hypothesis function based on the training dataset and estimating the system fault level quickly after the fault clearing event using the hypothesis function. Siemens Aktiengesellschaft 
Desired zmp trajectory generating device for a mobile robot A device for generating a desired zmp trajectory for a mobile robot includes a polynomial function coefficient group determining section (53a) which determines, by regarding the desired zmp trajectory as a trajectory expressed by a polynomial function, a desired coefficient group composed of desired values of coefficients in respective terms of the polynomial function. The polynomial function coefficient group determining section uses a quadratic evaluation function including square values of the coefficients included in the desired coefficient group as variables and a plurality of constraint conditions each configured by a linear equality or linear inequality about the coefficients, to determine the desired coefficient group, by a solution method for a quadratic programming problem, in such a way as to minimize a value of the evaluation function while fulfilling the constraint conditions.. Honda Motor Co., Ltd. 
Threedimensional facial reconstruction method and system The present invention is applicable to the field of image processing technology, provides a threedimensional facial reconstruction method and system comprising: arranging threedimensional imaging units with the same configuration on both of left side and right side of a target human face; implementing binocular calibration to the threedimensional imaging units; establishing a polynomial relation between 3d point cloud coordinates captured by the threedimensional imaging units and corresponding phases according to a result of the binocular calibration and determining the transformation relation among the 3d point cloud coordinates captured by two threedimensional imaging units; capturing image sequences on the left side and right side of the target human face by the threedimensional imaging units to obtain absolute phases of the image sequences; mapping the absolute phases of the image sequences to the 3d point cloud coordinates by using the polynomial relationship; unifying the 3d point cloud coordinates of the threedimensional imaging units to a global coordinate system according to the transformation relationship. The present invention implements a rapid threedimensional reconstruction of a face and improves the processing efficiency of threedimensional facial reconstruction.. Shenzhen University 
Programmable temperature compensated voltage generator A programmable temperature compensated voltage reference is disclosed. In an exemplary embodiment, an apparatus includes a digitaltoanalog converter (dac) that uses a reference voltage and a code to generate a dac output voltage. Ixys Corporation 
Gas turbine engine airfoil An airfoil for a turbine engine includes pressure and suction sides that extend in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip. The airfoil has a relationship between a tangential leading edge location and a span position that corresponds to a curve that is at least a third order polynomial with a generally sshaped curve that has an initial negative slope followed by a positive slope and then a second negative slope. United Technologies Corporation 
Method and generating harmonics using polynomial nonlinear functions A method and apparatus for generating harmonics using polynomial nonlinear functions. Polynomial functions are used to produce harmonics of an input signal up to a predetermined order, and that match a preferred set of characteristics. Tempo Semiconductor, Inc. 
Sparse map for autonomous vehicle navigation A nontransitory computerreadable medium is provided. The computerreadable medium includes a sparse map for autonomous vehicle navigation along a road segment. Mobileye Vision Technologies Ltd. 
Rolling process learning control device An instantaneous value of a learning coefficient is calculated based on a gap between a result value and a result recalculation value, and an update value of the learning coefficient is calculated from the instantaneous value. The calculated update value is recorded in a cell corresponding to present rolling conditions. Toshiba Mitsubishielectric Industrial Systems Corporation 
Key agreement device and method An initiating keyagreement device (100) and a responding keyagreement device (200) are provided, configured to generate a symmetric key shared between them. The devices are configured for generating in electronic form a private random value (112, 212), obtaining in electronic form a public set of bivariate polynomials (122) and computing a univariate polynomial (124, 222) by summing the univariate polynomials obtained by substituting the private random value (112, 212) into the polynomials of the public set (122). Koninklijke Philips N.v. 
Motion capture system that combines sensors with different measurement ranges Motion capture system with a motion capture element that uses two or more sensors to measure a single physical quantity, for example to obtain both wide measurement range and high measurement precision. For example, a system may combine a lowrange, high precision accelerometer having a range of −24 g to +24 g with a highrange accelerometer having a range of −400 g to +400 g. Blast Motion Inc. 
Hybrid tablelookup algorithm for functions A method and system for approximating functions, including a function approximation repository, which includes a hybrid lookup table configured to store coefficients associated with polynomials in factored form (pffs), and a results store configured to store results. The system also includes a function approximation device that includes two processors, memory, an io module and a function approximation module, which includes functionality to receive a request to approximate the function for an argument; verify that the argument falls within a function interval; perform a determination to find a subinterval in which the argument falls; select a pff associated with the subinterval; obtain pff coefficients associated with the pff from the hybrid lookup table; evaluate the pff using the pff coefficients and the argument to obtain a result; store the result in the results store; and return the result as an answer to the requesting entity via the io module.. Oracle International Corporation 
Fraunhofergesellscahft Zur Foerdering Der Angewandten Forschung E.v. . . 
Apparatus, wireless batch calibration A wireless batch calibration apparatus, a wireless batch calibration system and a wireless batch calibration method. The wireless batch calibration apparatus includes a wireless transceiver, a processor circuit and a storage circuit. Industrial Technology Research Institute 
Energy efficient polynomial kernel generation in fullduplex radio communication A polynomial kernel generator is configured to mitigate nonlinearity in a receiver path from a transmitter path comprising a nonlinear component in a communication device or system. The polynomial kernel generator operates to generate polynomial kernels that can be utilized to model the nonlinearity as a function of a piecewise polynomial approximation applied to a nonlinear function of the nonlinearity. Intel Corporation 
Concept for encoding of information Wherein m is an order of the predictive polynomial a(z) and l is greater or equal to zero, wherein the converter is configured to obtain the frequency values by establishing a strictly real spectrum derived from p(z) and a strictly imaginary spectrum from q(z) and by identifying zeros of the strictly real spectrum derived from p(z) and the strictly imaginary spectrum derived from q(z).. . 
Stress and temperature compensated hall sensor, and method An integrated semiconductor device for measuring a magnetic field, comprising: a hall sensor, a first lateral isotropic sensor having a first stress sensitivity and a first temperature sensitivity, a second lateral isotropic sensor having a second stress sensitivity and a second temperature sensitivity, optional amplifying means, digitization means; and calculation means configured for calculating a stress and temperature compensated hall value in the digital domain, based on a predefined formula which can be expressed as an nth order polynomial in only two parameters. These parameters may be obtained directly from the sensor elements, or they may be calculated from a set of two simultaneous equations. Melexis Technologies Sa 

Circuitry and decomposable decoder Decoder circuitry for an input channel having a data rate, where a codeword on the input channel includes a plurality of symbols, includes options to provide a first output channel having that data rate, and a plurality of second output channels having slower data rates. The decoder circuitry includes syndrome calculation circuitry, polynomial calculation circuitry, and searchandcorrect circuitry. Altera Corporation 
Fingerprint template based on fuzzy feature point information and fingerprint identification method The present invention discloses a fingerprint template and a fingerprint identification method based on fuzzy feature point information. The fingerprint template contains several pieces of incomplete feature point information, including registration information and comparison information, wherein only coordinate information and attribute information of feature points and a value of a polynomial are recorded. 
Apparatus and generating bidirectional chirp signal by using phase accumulation polynomial The present invention relates to an apparatus and method for generating a bidirectional chirp signal by using a phase accumulation polynomial, and the apparatus for generating a bidirectional chirp signal according to an embodiment may include an extraction unit extracting time interval information from the output of a frequency accumulator, a polynomial handling unit applying the phase accumulation polynomial to the extracted time interval information to generate a polynomial output value, and a bidirectional chirp signal output unit outputting a bidirectional chirp signal on the basis of the generated polynomial output value.. . Korea Aerospace Research Institute 
Characterizing crude oil using laser induced ultraviolet fluorescence spectroscopy Embodiments of the present disclosure describe a method for determining a property of an uncharacterized crude oil sample using a polynomial equation correlating the property to a spectrum index and density of crude oil. The polynomial equation may include constants determined using a data fitting method and a data base of spectral data, density data, and standard properties data of a plurality of crude oils.. Saudi Arabian Oil Company 
. . 
System and hybrid wireless video transmission A system and method provides highquality video streaming in wireless video communications. The system includes a digital codec, an analog codec, and a power controller. Mitsubishi Electric Research Laboratories, Inc. 
Oneshot decoder for twoerrorcorrecting bch codes A decoder includes a syndrome generator for receiving a codeword and generating at least two syndromes based on the codeword, an error location polynomial generator for generating an errorlocation polynomial based on the syndromes, an error location determiner for determining at least one error location based on the errorlocation polynomial, and an error corrector for correcting the codeword based on the one error location. The error location polynomial generator includes a logic for receiving the syndromes and generating a combination of the syndromes as a combination of coefficients of the errorlocation polynomial, and a key equation solver for generating the errorlocation polynomial based on the combination of the coefficients and finding at least one root of the errorlocation polynomial. Sk Hynix Memory Solutions Inc. 
. . 
Serverassisted secure exponentiation In one embodiment, a method for secure computation, includes receiving in a server, over a communication channel from a device external to the server a request to perform a modular exponentiation operation in which an exponent of the operation comprises a secret value, wherein the secret value is not provided to the server, and at least two parameters that encode the secret value in accordance with a polynomial or matrix homomorphic encryption of the secret value computed by the device, and performing in the server, in response to the request, a homomorphic exponentiation using the at least two parameters received from the device without decrypting the secret value in the server, so as to generate an output that is indicative of a result of the modular exponentiation operation.. . Cisco Technology, Inc. 
Asymmetrical chaotic encryption Implementations and techniques for asymmetrical chaotic encryption are generally disclosed. One disclosed method for asymmetrical encryption includes determining a ciphertext control block from data, where the ciphertext control block is based at least in part on one or more chebyshev polynomials. Empire Technology Development Llc 
Cryptographic processing method and cryptographic processing device A computer generates a third encrypted polynomial that corresponds to a result of encrypting a third polynomial by use of a result of multiplying a first encrypted polynomial by a second encrypted polynomial, and outputs cryptographic information that represents the third encrypted polynomial. The first encrypted polynomial is a polynomial obtained by encrypting a first polynomial that corresponds to a first vector, and the second encrypted polynomial is a polynomial obtained by encrypting a second polynomial that corresponds to a second vector. Fujitsu Limited 
Ion beam scanner for an ion implanter A magnetic system for uniformly scanning an ion beam across a semiconductor wafer comprises a magnetic scanner having ac and dc coil windings each of which extend linearly along internal pole faces of a magnetic core. The ac and dc coil windings are mutually orthogonal; a time dependent magnetic component causes ion beam scanning whilst a substantially static (dc) field component allows the ion beam to be bent in an orthogonal plane. Nissin Ion Equipment Co., Ltd. 
Neural networks for encrypted data Embodiments described herein are directed to methods and systems for performing neural network computations on encrypted data. Encrypted data is received from a user. Microsoft Technology Licensing, Llc. 
Circuitry and generating cyclic redundancy check signatures Circuitry and methods for generating parallel crc signature bits are disclosed. The circuitry includes a data input for receiving parallel data input. Texas Instruments Incorporated 
Korschtype compact threemirror anastigmat telescope A threemirror anastigmat telescope comprises at least a concave first mirror, a convex second mirror and a concave third mirror, the three mirrors arranged so that the first mirror and the second mirror form, from an object at infinity, an intermediate image situated between the second mirror and the third mirror, the third mirror forming, from this intermediate image, a final image in the focal plane of the telescope. In the architecture of the telescope, at least the surface of the concave third mirror is a φpolynomial surface.. Thales 
Magnetic measurement system A magnetic measurement system includes a heart magnetic field sensor that measures a first magnetic field and a second magnetic field, a noise magnetic sensor that measures the second magnetic field, and a magnetic measurement apparatus that computes an approximate value of the second magnetic field in the heart magnetic field sensor by using a measurement value in the noise magnetic sensor and a multivariable polynomial. The magnetic measurement apparatus subtracts the approximate value of the second magnetic field from a measurement value in the heart magnetic field sensor.. Seiko Epson Corporation 
System and method hybrid quantumconventional architecture for wireless networks A hybrid quantumconventional computing system and method for analyzing band capture data and determining if a solution is an nphard problem or a polynomial time problem. The nphard problem is processed by a quantum computing system and the polynomial time problem is processed by a conventional computing system. Cable Television Laboratories, Inc. 
Lowpower partialparallel chien search architecture with polynomial degree reduction A device includes a controller, and the controller includes a root detection circuit having multiple sets of multipliers. A method includes configuring the root detection circuit according to a degree of a polynomial. Sandisk Technologies Inc. 
Quanton representation for emulating quantumlike computation on classical processors The quanton virtual machine approximates solutions to nphard problems in factorial spaces in polynomial time. The data representation and methods emulate quantum computing on classical hardware but also implement quantum computing if run on quantum hardware. Kyndi, Inc. 
System, apparatus, and measuring ion concentration with a standard deviation correction Embodiments of the inventive concept include a portable ion concentration apparatus including a controller, a storage section to store one or more data samples, an amplifier circuit, and a chemical field effect transistor (chemfet). The chemfet and the amplifier circuit can indicate a quantity of nitrate levels in a sample media or a reference media. Suprasensor Technologies, Llc 
Method and modeling of gnss pseudorange measurements for interpolation, extrapolation, reduction of measurement errors, and data compression Polynomial regression models are used to reduce errors in measurements of pseudorange between a gnss satellite and a receiving station; for data compression by replacing a large number of measurements with a small number of coefficients of the model polynomial, optionally combined with modeling residuals; for extrapolating usefully accurate estimates of future range between the gnss satellite and the receiving station; and for providing usefully accurate estimates of future coefficient values of the polynomial regression models themselves.. . Subcarrier Systems Corporation 
Circuitry and methods for implementing galoisfield reduction Galoisfield reduction circuitry for reducing a galoisfield expansion value, using an irreducible polynomial, includes a plurality of memories, each for storing a respective value derived from the irreducible polynomial and a respective combination of expansion bit values, wherein expansion bits of the expansion value address the plurality of memories to output one or more of the respective values. The galoisfield reduction circuitry also includes exclusiveor circuitry for combining output of the plurality of memories with infield bits of said expansion value. Altera Corporation 
Subjective wavefront refraction using continuously adjustable wave plates of zernike function A wavefront device produces adjustable amplitudes in optical path differences and adjustable axis orientation angles. Two substantially identical wave plates have a wavefront profile of at least the third order zernike polynomial function which are not circularly symmetric, as denoted by z(i,j) where i≧3 and j≠0. 
Methods and devices for adaptive autonomous polynomial interpolation of time series data A method of performing maintenance. Data is received from a plurality of physical sensors that measure parameters of parts of the platform, wherein a data point is missing from the data. The Boeing Company 
System for sharing a cryptographic key A system (200) for configuring a network device (300) for sharing a key, the shared key being • bits long, the system comprising:—a key material obtainer (210) for—obtaining in electronic form a first private set of bivariate polynomials (252, {hacek over (z)}″(,)), and a second private set of reduction integers (254, f″), with each bivariate polynomial in the first set there is associated a reduction integer of the second set, and a public global reduction integer (256, . . Koninklijke Philips N.v. 
Nbase numbers to physical wire states symbols translation method System, methods and apparatus are described that facilitate a device to encode/decode data in a data communications interface coupled to a plurality of wires. The device determines a value of a sequence of data bits allocated to a frame, converts the value into a sequence of symbols associated with the frame, and transmits the sequence of symbols to a receiver. Qualcomm Incorporated 
Modulo calculation using polynomials Hardware logic arranged to perform modulo calculation with respect to a constant value b is described. The modulo calculation is based on a finite polynomial ring with polynomial coefficients in gf(2). Imagination Technologies Limited 
System and displaying weapon engagement feasibility Disclosed is a system and method for generating, in an aircraft (1) in flight, a display indicative of the feasibility of a weapon carried on the aircraft (1) successfully engaging a determined target (5, t) and/or the feasibility of a weapon carried on the target (5, t) successfully engaging the aircraft (1). The method comprises: using a performance envelope of the weapon and performance envelope(s) for one or more different types of aircraft (1), determining a further performance envelope specifying the performance of the weapon when carried by any of the different aircraft (1) types; determining coefficients for a generic polynomial that fit the generic polynomial to the further performance envelope; uploading, to the aircraft (1), the generated coefficients; and, on the aircraft (1), reconstructing the further performance envelope and generating the feasibility display.. Bae Systems Plc 
Memory controller, semiconductor memory device, and control semiconductor memory device A memory controller is a memory controller including an encoder that productcodes, with a linear code, data to be recorded in a memory section and a decoder that decodes productcoded data read out from the memory section. The encoder and the decoder share a parity generation circuit including a plurality of remainder calculating and retaining sections, each including a remainder calculation circuit by a generator polynomial and a retaining circuit that retains an output of the remainder calculation circuit.. Kabushiki Kaisha Toshiba 
Configurable multilane scrambler for flexible protocol support Various structures and methods are disclosed related to configurable scrambling circuitry. Embodiments can be configured to support one of a plurality of protocols. Altera Corporation 
Policybased key sharing Methods of providing policy based access to master keys, enabling keys to be distributed to groups of users in a secure manner while minimizing disruptions to the user in the event of changes to group membership or changes to user attributes. User attributes are identified. Oracle International Corporation 
Method for acquiring parameters of dynamic signal The application discloses a method for acquiring parameters of a dynamic signal, including: selecting a dynamic sample signal sequence of a power grid to constitute an autocorrelation matrix; determining an effective rank of the autocorrelation matrix and the number of frequency components of the dynamic sample signal sequence; establishing an ar model, and solving a model parameter of the ar model; determining an expression and a complex sequence of the dynamic sample signal sequence by using a prony algorithm, wherein the dynamic sample signal sequence is represented by the complex sequence with a minimum square error; and substituting a root of a characteristic polynomial corresponding to the model parameter into the complex sequence and solving various parameters of the dynamic sample signal sequence. In the application, with the idea of ar parameter model, a current signal is considered to be a linear combination of signals at previous time points.. Chongqing University 
Cryptographic processing device and cryptographic processing method A cryptographic processing device includes a processor that generates a first encrypted polynomial, a receiver that receives cryptographic information representing a fourth encrypted polynomial, and cryptographic information representing a second random number, the fourth encrypted polynomial including a first operation result that is a result of an operation of a fifth vector and a sixth vector, the first operation result being obtained by a second encrypted polynomial and a third encrypted polynomial, wherein the second encrypted polynomial is obtained based on the first encrypted polynomial, the second random number, and a second polynomial that corresponds to a third vector obtained by adding zero to the second vector, and the third encrypted polynomial is obtained based on the fifth vector obtained by adding zero to a fourth vector. The processor generates a second operation result that is a result of an operation of the second vector and the fourth vector.. Fujitsu Limited 
Radio frequency receiver capable of determining a noise estimate in case of received power unbalanced antennas and operating thereof The present application suggests a receiver and a method of operating thereof for determining a noise estimate based on a radio frequency signal from an interference source over different propagation paths through a plurality of antennas. A covariance matrix estimator coupled through separate processing paths to a respective one of the plurality of antennas is arranged to determine an estimate of a covariance matrix based on the received radio frequency signal. Freescale Semiconductor, Inc. 
Encoding method, decoding method An encoding method generates an encoded sequence by performing encoding of a given coding rate according to a predetermined parity check matrix. The predetermined parity check matrix is a first parity check matrix or a second parity check matrix. Sun Patent Trust 
Memory controller, memory system, and decoding method A memory controller includes: an encoder configured to generate a block product code which includes a first code and a second code as component codes, the first code and the second code being linear cyclic codes; a memory interface configured to write the block product code to a nonvolatile memory, and to read a received word from the nonvolatile memory; and a decoder configured to perform a decoding using a code constraint corresponding to a generator polynomial as a common divisor between a generator polynomial of the first code and a generator polynomial of the second code with respect to a symbol of an area which is not subjected to a code constraint of the first code but subjected to a code constraint of the second code.. . Kabushiki Kaisha Toshiba 
Behavioral model and predistorter for modeling and reducing nonlinear effects in power amplifiers The behavioral model and predistorter for modeling and reducing nonlinear effects in power amplifiers addresses the model size estimation problem. The gmp model is replaced by the hybrid memory polynomial/envelope memory polynomial (hmem) model within a twin nonlinear twobox structure to reduce the number of variables involved in the model size estimation problem, without compromising model accuracy and digital predistorter performance. King Fahd University Of Petroleum And Minerals 
Threedimensional positioning method A threedimensional positioning system includes establishing a geometric model for optical and radar sensors, obtaining rational function conversion coefficients, refining the rational function model and positioning threedimensional coordinates. The system calculates rational polynomial coefficients from a geometric model of optical and radar sensors, followed by refining a rational function model by determined ground control points and object image space intersection. National Central University 
Filter for network intrusion and virus detection Methods and apparatus to perform string matching for network packet inspection are disclosed. In some embodiments there is a set of string matching slice circuits, each slice circuit of the set being configured to perform string matching steps in parallel with other slice circuits. Intel Corporation 
Key sharing device and system for configuration thereof A method of configuring a network device for key sharing and a method for a first network device to determine a shared key are provided. The method of configuring uses a private private modulus, and a modulus (p1) a public modulus (n), and a bivariate polynomial (f1) having integer coefficients, the binary representation of the public modulus and the binary representation of the private modulus are the same in at least key length (b) consecutive bits. Koninklijke Philips N.v. 
Method and modeling of gnss pseudorange measurements for interpolation, extrapolation, reduction of measurement errors, and data compression Polynomial regression models are used to reduce errors in measurements of pseudorange between a gnss satellite and a receiving station; for data compression by replacing a large number of measurements with a small number of coefficients of the model polynomial, optionally combined with modeling residuals; for extrapolating usefully accurate estimates of future range between the gnss satellite and the receiving station; and for providing usefully accurate estimates of future coefficient values of the polynomial regression models themselves.. . Sakata Seed Corporation 
Secondary synchronization codebook for eutran Providing for secondary synchronization encoding utilizing a primary synchronization channel (psch)related scrambling code is described herein. Scrambled secondary synchronization codes (sscs) can be assigned to multiple base stations of a radio access network (ran). Qualcomm Incorporated 
Transmitting method and transmitting apparatus A lowdensity parity check convolution code (ldpccc) is made, and a signal sequence is sent after being subjected to an errorcorrecting encodement using the lowdensity parity check convolution code. In this case, a lowdensity parity check code of a timevariant period (3g) is created by linear operations of first to 3gth (letter g designates a positive integer) parity check polynomials and input data.. Panasonic Corporation 
Simultaneous edge enhancement and nonuniform noise removal using refined adaptive filtering A method for denoising magnetic resonance images includes estimating a normalization field corresponding to a magnetic resonance imaging device and acquiring a nonnormalized image from the magnetic resonance imaging device. A noise level estimation process is performed with the nonnormalized image to yield a noise level. Siemens Aktiengesellschaft 
Method and system for lithography processwindowmaximizing optical proximity correction An efficient opc method of increasing imaging performance of a lithographic process utilized to image a target design having a plurality of features. The method includes determining a function for generating a simulated image, where the function accounts for process variations associated with the lithographic process; and optimizing target gray level for each evaluation point in each opc iteration based on this function. Asml Netherlands B.v 
Geographical condition prediction A method and system for forecasting the conditions of locations is provided. The method includes receiving in real time from a user in a specified location, a specified future timeframe associated with a future condition of the specified location. International Business Machines Corporation 
Gas turbine engine airfoil An airfoil for a turbine engine includes pressure and suction sides that extend in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip. The airfoil has a relationship between a total chord length and a span position and corresponds to a curve that has an increasing total chord length from the 0% span position to a first peak. United Technologies Corporation 
Multivariate public key signature/ verification system and signature/verification method Multivariate public key signature/verification system including a signature module and a verification module. The signature module contains a processor, first affine transformation inversion component, isomorphic inversion component, trapdoor component, isomorphic component, and second affine transformation inversion component. South China University Of Technology 
Method and system for homomorphicly randomizing an input In one embodiment, a method for reducing information leakage in order to counter side channel attacks against a secure execution environment is described, the method including receiving at the secure execution environment a first input comprising a key comprising a sequence of k input elements in a commutative ring, cr, receiving at the secure execution environment a second input comprising a text comprising a sequence of p input elements in the commutative ring, cr, defining an input inp comprising a sequence of j input elements, wherein inp comprises either one or both of the first input or the second input, performing one of a matrix randomization operation or a polynomial randomization operation on the inputs, and producing a randomized output.. . Cisco Technology, Inc. 
Encoding apparatus, transmission apparatus, encoding method and transmission method An encoding method and encoder of a timevarying ldpccc with high error correction performance are provided. In an encoding method of performing low density parity check convolutional coding (ldpccc) of a time varying period of q using a parity check polynomial of a coding rate of (n−1)/n (where n is an integer equal to or greater than 2), the time varying period of q is a prime number greater than 3, the method receiving an information sequence as input and encoding the information sequence using equation 1 as a gth (g=0, 1, . Panasonic Intellectual Property Corporation Of America 
Iterative decoding lfsr sequences with a low falsealarm probability A messagepassing iterative decoding method of an associated lfsr sequence (or msequence) as a simplex code, to a parity matrix h. The method includes determining a set of parity polynomials with a low weight obtained by combining the parity equations of the matrix h. Commissariat A L'energie Atomique Et Aux Energies Alternatives 
Methods and calculating electromagnetic scattering properties of a structure and for reconstruction of approximate structures A method of calculating electromagnetic scattering properties of a structure, the structure including materials of differing properties and the structure being periodic in at least one lateral direction and extending in a vertical direction, comprises: numerically solving a volume integral equation for electromagnetic scattering for a plurality of modes in the at least one lateral direction, by performing, for each respective mode, integration (1350) of a pseudospectral polynomial (chebyshev) expansion in the vertical direction multiplied by a id green's function using the same sample points in the orthogonal direction for all of the plurality of modes. The integration is performed by solving a regularized linear system of equations between first (1116) and second (1120) discrete transformation steps to compute (1118) values of a regularized chebyshev expansion coefficient vector (γ). Asml Netherlands B.v. 
A method and a device for determining the mass flow rate and the presence or absence of a liquid flowing in a pipe A device (1) for determining the mass flow rate of milk turbulently flowing with air in a pipe (2) in pulsed milk slugs comprises sampling a signal from a microphone (8) of the device (1) indicative of sonic signals produced by the milk flow. The sampled signals are read by a microprocessor (15) which applies a fast fourier transform to the sampled signal to produce the frequency domain of the sampled signal. Dairymaster 
System and encoding and controlled authentication A system and method for encoding and controlled authentication of security documents, id cards, tickets and products and the like is described which can provide a secure means to determine them to be authentic. The method involves encoding the surface of the said security documents or id cards or tickets and the like with of a pair of identity components comprising a pair of unique numbers, or a combination of a uniquely encoded image and a unique number, or a combination of a unique barcode and a unique number, or a combination of encoded images. 
Frequencydivision multiplexing (fdm) using soft clipping (sc) A method comprising mapping data onto odd frequency subcarriers of a plurality of nonoverlapping frequency subcarriers, wherein each of the nonoverlapping frequency subcarriers comprises a center frequency that is an odd integer multiple of a lowest center frequency, producing a time signal based on the mapping, applying soft clipping (sc) to signal amplitudes of the time signal according to a polynomial function, and producing a positiveamplitude signal based on the applying.. . Futurewei Technologies, Inc. 
Method for the correction of electron proximity effects A method for projecting an electron beam onto a target includes correction of the scattering effects of the electrons in the target. This correction is made possible by a calculation step of a point spread function having a radial variation according to a piecewise polynomial function.. Aselta Nanographics 
Wafer inspection with focus volumetric method Disclosed are methods and apparatus for detecting defects in a semiconductor sample. An inspection tool is used to collect intensity data sets at a plurality of focus settings from each of a plurality of xy positions of the sample. Klatencor Corporation 
Method and efficiently implementing the advanced encryption standard Implementations of advanced encryption standard (aes) encryption and decryption processes are disclosed. In one embodiment of sbox processing, a block of 16 byte values is converted, each byte value being converted from a polynomial representation in gf(256) to a polynomial representation in gf((22)4). Intel Corporation 
Cryptographic processing device and cryptographic processing method A memory stores therein a first vector. A processor generates a first encrypted polynomial by encrypting a first polynomial that corresponds to a first binary vector obtained by performing a binary transformation on elements of the first vector. Fujitsu Limited 
Clusters of polynomials for data points A method, system and storage device are generally directed to determining for each of a plurality of data points, a neighborhood of data points about each such data point. For each such neighborhood of data points, a projection set of polynomials is generated based on candidate polynomials. 
Digital modulator nonlinearity correction A nonlinear distorter is configured to mitigate nonlinearity from a nonlinear component of a nonlinear system. The nonlinear distorter operates to model the nonlinearity as a function of a piecewise polynomial approximation applied to segments of a nonlinear function of the nonlinearity. 
Cryptographic processing device and cryptographic processing method A memory stores therein first cryptographic information that represents an encrypted polynomial obtained by encrypting a first polynomial that corresponds to a first vector. From a terminal that receives second cryptographic information that represents an encrypted monomial obtained by encrypting a monomial generated by use of a random number, a receiver receives third cryptographic information that represents an encrypted result obtained by encrypting a result of a multiplication of a second polynomial that corresponds to a second vector by the monomial. Fujitsu Limited 
Offaxis threemirror optical system with freeform surfaces An offaxis threemirror optical system with freeform surfaces includes a primary mirror, a secondary mirror, a tertiary mirror, and an image sensor. The primary mirror receives light rays first and the secondary mirror is located on a path of light reflected from the primary mirror. Hon Hai Precision Industry Co., Ltd. 
Privacy preserving setbased biometric authentication A method includes extracting a set of enrollment feature points from an enrollment biometric measurement. The method also includes randomly selecting one or more enrollment code words from an error correction code. Fujitsu Limited 
Homomorphic evaluation including key switching, modulus switching, and dynamic noise management A homomorphic evaluation of a function is performed on input ciphertext(s), which were encrypted using an encryption scheme that includes multiple integer moduli. Each ciphertext contains one or more elements of an mth cyclotomic number field, where m is an integer. University Of Bristol 
Surface patch techniques for computational geometry A method and system for computer aided design (cad) is disclosed for designing geometric objects, wherein interpolation and/or blending between such objects is performed while deformation data is being input. Thus, a designer obtains immediate feedback to input modifications without separately entering a command(s) for performing such deformations. Freedesign, Inc. 
Method, apparatus and program product for prediction Technology for predictions of a value over time which relies upon and implements a topologic space and surface analysis enabling insertion of future dates and generation of more accurate predictive values for resource demand and other values of interest for analysis. Polynomial equations are generated from the surface analysis by regression and factoring to enable forecasting and acknowledgment of various factors such as weather and the like.. 
Ultrasound for representing the propagation of ultrasound waves in a guide of linearly variable thickness Device for the representation, in a frequencywave number reference frame fk, of the propagation of an ultrasound wave in a dihedral guide (1), which comprises ultrasound emitters (2) referenced by “ej” with j an integer varying between 1 and n, n a strictly positive integer and ultrasound receivers (3) referenced by “ri” with i an integer varying between 1 and m, m a strictly positive integer, the receivers being disposed spatially over a first segment of a straight line according to a regular pitch “a”, which comprises means for processing the signal received by the receivers, originating from the emitters, and in which the processing means comprise means for calculating a modified discrete spatial fourier transform, for a spatial integration variable “x”, centered in the middle of said first segment and running through the receivers in the direction of increasing x, and for a wave vector k(x) equal to a product k.p(x), with k a constant coefficient in x and included between 0 and 2*pi/a, and with p(x) a polynomial in x, of coefficient of degree 0 in x equal to 1 and of coefficient “c” of degree 1 in x such that c.a lies between − 1/10 and + 1/10. . Université Pierre Et Marie Curie  Paris 6 
System and estimating material density A method implemented using one or more computer processors for estimating the density of a material in an annular space includes receiving detector data representative of scattered photons resulting from interaction of a material in an annular space with radiation from a radiation source and detected by a plurality of radiation detectors. The method further includes performing a set of monte carlo simulations and generating polynomial models of the detector data based on the set of monte carlo simulations. General Electric Company 
System for sharing a cryptographic key A system (200) for configuring a network device (300) for key sharing is provided, and a first (300) and second network device configured to determine a shared key between them. The system comprises a key material obtainer (210) for obtaining in electronic form a public global reduction polynomial (216, n(t)), a first private set of bivariate polynomials (212, fi(,)), and a second private set of reduction polynomials (214, qi(t)), with each bivariate polynomial in the first set a reduction polynomial of the second set being associated, and a polynomial manipulation unit (220) for computing a univariate private key polynomial (228) from the first and second private sets by mapping an identity number (a) of the network device to an identity polynomial, obtaining a set of univariate polynomials by for each particular polynomial of the first private set, substituting the identity polynomial (a) into said particular polynomial fi(a,) and reducing modulo the reduction polynomial associated with said particular polynomial, and summing the set of univariate polynomials, the system is configured for electronically storing the generated univariate private key polynomial (228, 236) and the public global reduction polynomial (216, n(t)) at the network device. Koninklijke Philips N.v. 
Signal segmentation method and crc attachment reducing undetected error The present invention provides for applying a cyclic redundancy check (crc) to a data signal. The present invention includes attaching a first crc to a first data signal block having a first length, segmenting the first data signal block attached with the first crc into a plurality of second data signal blocks having a length shorter than the first length, respectively generating a second crc for each second data signal block, and attaching the generated second crc to the respective second data signal block. Lg Electronics Inc. 
Touch panel device and correcting coordinates on touch panel A touch panel device includes: a detection unit that detects coordinates of a pressed point on an input surface of a touch panel; and a correction unit that corrects the coordinates detected by the detection unit to obtain corrected coordinates, wherein the correction unit approximates, when a predetermined number of reference points arranged on the input surface are pressed, curves passing through coordinates of the reference points by second order or higher order polynomial equations, specifies, when an arbitrary point on the input surface is pressed, a region including coordinates of the arbitrary point from regions obtained by dividing the input surface by the curves, calculates distances from the coordinates of the arbitrary point to curves that define the specified region among the curves with the second order or higher order polynomial equations, and calculates the corrected coordinates based on a location of the specified region and the distances.. . Fujitsu Component Limited 
Electronic signature system Electronic signature system comprising an electronic key generation device (100) for generating a digital signingkey for digitally signing digital data and a corresponding verificationkey for digitally verifying said digitally signed data, an electronic signature generation device (200) for generating a digital signature for digital data using a digital signingkey obtained from an electronic key generation device, and an electronic signature verification device (300) for verifying a digital signature generated by an electronic signature generation device. The verifier has access to a commitment integer and corresponding polynomial derived from private keying material, enabling verification of signature polynomials derived the same private keying material.. Koninklijke Philips N.v. 
Multidimensional encryption A method of encrypting data is provided. The method includes generating a key and encrypting data using the key. Unsene, Ehf. 
Access control in a network The teachings relates to a method 200 performed in a processor 30, 32 for calculating a 10 bits cyclic redundancy check, crc, value for a message m(x). The method 200 comprises: determining 201 length of the message to be greater than 64 bits; adapting 202 the message 5 m(x) to have a length of n*128 bits, wherein n is a positive integral number, folding 203, n1 times, of 128 bits by using a pclmulqdq instruction comprising performing a carryless multiplication of two 64bits operands; folding 204 of 64 bits by using the pclmulqdq instruction, providing a 64 bit message m′(x); 10 wherein the folding 203 of 128 bits and folding 204 of 64 bits are adapted for use of the pclmulqdq instruction to calculate a 10 bit crc by: adapting degree of p(x) k(x) to 32 by setting k(x)=x22, wherein p(x) is a polynomial of degree 10, and wherein □ denotes the carryless multiplication, and performing the folding of 128 bits 15 and folding of 64 bits by [m(x)∥x22]mod[p(x). x22]; calculating 205 the 10 bits payload crc value for the message m(x) by using a crc10 tablelookup algorithm. 
Method for using a computer graphics system for changing the shape of the surface of models of geometric solids with the aid of deformation and device for implementing same The proposed method for using a computer graphics system for changing the shape of models of geometric solids with the aid of deformation is characterized in that it is used for producing geometric solids which mate with one another as they were relative to one another and have mating surfaces, which require manufacture with precision accuracy (up to 10 micrometres), for example toothed screws (cylindrical, conical) of a screw compressor unit, gear trains, gears of a gear pump and similar mating pairs of geometric solids. The proposed method consists in that deformation of a model (3) of a semifinished product (3) of a first mating solid (1) is performed with the aid of a model (7) of a first tool (7), whose surface is automatically calculated using several mathematical laws, each of which is a polynomial in which at least one of the coefficients represents one of several characteristics defining the geometry of the shape of the surface of the second geometric solid (2). Vert Rotors Uk Limited 
Prediction using method, apparatus and program product Technology for predictions of a value over time which relies upon and implements a topologic space and surface analysis enabling insertion of future times and generation of more accurate predictive values for resource demand and other values of interest for analysis. The topological surface is generated on a cylindrical coordinate system. 
Vector based geophysical modeling of subsurface volumes Method and system are described for modeling one or more geophysical properties of a subsurface volume. The method includes computing vector volumes from geophysical data to enhance subsurface features, where the vectors may be estimated by steps, including the following. 
Method to incorporate skin and core material properties in performance analysis of high pressure die casting aluminum components A method, device and article of manufacture for determining properties in a high pressure die cast component. Upon receipt of geometric information that corresponds to a location of interest within the component, a raytriangle intersection relationship is used to calculate a wall thickness of the location of interest; this relationship is simplified by being used in conjunction with an octreebased relationship. Gm Global Technology Operations Llc 
Manufacture of nonrectilinear features Methods and apparatus are disclosed for symbolic methods using algebraic geometry (e.g., based on a gröbner basis of tangent space polynomials of parametric curves). For example, the design, optimization and verification of silicon photonic wave guides using parametric polynomials and/or gröbner basis functions can be used to perform envelope generation, rectification, manufacturability checking, singularity detection, reticle and etch processing model generation, tapering loss minimization, and bend loss minimization. Mentor Graphics Corporation 
Methods for objectively determining the visual axis of the eye and measuring its refraction Provided herein are methods for objectively determining a visual axis of an eye. An optical axis of a measuring instrument is aligned with an unambiguously determinable axis of the eye which is the pupillary axis crossing the vertex of an anterior surface of a cornea and perpendicular to the vertex. Tracey Technologies, Corp. 
Adaptive reshaping for layered coding of enhanced dynamic range signals An encoder receives an input enhanced dynamic range (edr) image to be coded in a layered representation. Input images may be gammacoded or perceptuallycoded using a bitdepth format not supported by one or more video encoders. Dolby Laboratories Licensing Corporation 
Fast calibration A computer implemented method of calibrating a device comprising the steps of: deriving an analytic expression for a variable to be optimised of the device in terms of at least one parameter of the device, transforming the analytic expression into polynomial form of the at least one parameter of the device, the polynomial form comprising n coefficients, capturing at least n samples of a value of the variable from the device under calibration, each sample being a result of a different independent predetermined value of the at least one parameter, applying the captured variable values and the corresponding at least one parameter values to the polynomial form, obtaining optimal values of the at least one parameter from the applying step to calibrate the device.. . Sequans Communications S.a. 
Encoding method, and decoding method An encoding method generates an encoded sequence by performing encoding of a given coding rate according to a predetermined parity check matrix. The predetermined parity check matrix is a first parity check matrix or a second parity check matrix. Panasonic Intellectual Property Corporation Of America 
Weighted memory polynomial power amplifiers predistortion A system and method for linearizing a power amplifier using digital predistortion technique is provided including processing circuitry, the processing circuitry configured to apply a digital predistortion function based on a weighted static polynomial function, a weighted dynamic polynomial function and a threshold parameter which splits the nonlinear transfer characteristics of the device under test into a region where the static nonlinearity predominates and a region where the dynamic distortions predominate.. . King Fahd University Of Petroleum And Minerals 
Fast, energyefficient exponential computations in simd architectures In one embodiment, a computerimplemented method includes receiving as input a value of a variable x and receiving as input a degree n of a polynomial function being used to evaluate an exponential function ex. A first expression a*(x−ln(2)*kn(xf))+b is evaluated, by one or more computer processors in a single instruction multiple data (simd) architecture, as an integer and is read as a double. International Business Machines Corporation 
Fast, energyefficient exponential computations in simd architectures In one embodiment, a computerimplemented method includes receiving as input a value of a variable x and receiving as input a degree n of a polynomial function being used to evaluate an exponential function ex. A first expression a*(x−ln(2)*kn(xf))+b is evaluated, by one or more computer processors in a single instruction multiple data (simd) architecture, as an integer and is read as a double. International Business Machines Corporation 
Method and publickey encrypted communication A method and an apparatus for publickey encrypted communication includes: encrypting, by a first device, random information according to a first public key to obtain a first ciphertext; encrypting, by the first device, plaintext information according to a second public key to obtain a second ciphertext, where the plaintext information is unencrypted data to be sent by the first device to a second device, the first public key is represented in a form of a polynomial, the first public key is obtained through calculation on a truncated polynomial ring according to system parameters, the second public key is represented in a form of a polynomial, the second public key is randomly selected on a truncated polynomial ring, and the random information is randomly selected on a truncated polynomial ring; and sending, by the first device, the first ciphertext and the second ciphertext to the second device.. . Huawei Technologies Co.,ltd. 
Polynomial texture mapping and reflectance transformation imaging apparatus and techniques An image enhancement device and related techniques in support of polynomial texture mapping (ptm) (also known as reflectance transformation imaging (rti)) photography. The device may include a number of pod legs that extend from a camera focal plane to a base location around an object of interest. 
Open loop correction for optical proximity detectors An optical proximity detector includes a driver, light detector, analog frontend, sensor(s) that sense correction factor(s) (e.g., temperature, supply voltage and/or forward voltage drop), and a digital back end. The driver drives the light source to emit light. Intersil Americas Llc 
Systems and methods for measurement of input current of voltage regulator In accordance with embodiments of the present disclosure, an information handling system may include an information handling resource, a voltage regulator, a nontransitory computerreadable medium, and a controller. The voltage regulator may be coupled to the information handling resource and configured to deliver electrical energy to the information handling resource. Dell Products L.p. 
Method for measuring the plasma concentration of an analyte directly on a whole blood sample Where dp is the corrected analyte amount, dst is the measured analyte amount, dh is the measured haematocrit level, and pa is a nonconstant polynomial of a degree greater than or equal to 1 having as indeterminate values the measured analyte amount, dst, and the measured haematocrit level, dh, and having its polynomial coefficients depending on the analyte.. . 
Mask blank substrate, mask blank, transfer mask, and manufacturing semiconductor device A virtual reference surface that becomes an optically effective flat reference surface defined by a zernike polynomial which is composed of only terms in which the order of a variable related to a radius is the second or lower order, and includes one or more terms in which the order of the variable related to the radius is the second order is set, and a mask blank substrate satisfying the condition that data (pv value) relating to the difference between the maximum value and the minimum value of the difference data between the reference surface and the measured shape of the mask blank substrate is oneeighth or less of an exposure wavelength (a) is selected.. . 
Implementing fixedpoint polynomials in hardware logic A method implements fixedpoint polynomials in hardware logic. In an embodiment the method comprises distributing a defined error bound for the whole polynomial between operators in a dataflow graph for the polynomial and optimizing each operator to satisfy the part of the error bound allocated to that operator. Imagination Technologies Limited 
Phase locked loop with modified loop filter A loop filter in a modified phase locked loop has a proportional path generating first output signal that is proportional to an input signal and an integral path for generating a second output signal that is an integral of the input signal. An additional functional path generates a third output signal that is a predetermined function of the input signal. Microsemi Semiconductor Ulc 
Techniques for distributing secret shares Various embodiments are generally directed to an apparatus, method and other techniques generating one or more polynomial elements for a polynomial function using a node value of a pseudo random number generator tree as a seed value, the polynomial function comprising a secret value and the polynomial elements, and the pseudo random number generator tree at least partially matching at least one other pseudo random number generator tree on another device, generating a plurality of share values based on the one or more polynomial elements and the polynomial function and distributing a share value of the plurality of share values to a device.. . 
Sample rate converter and converting sample rate A sample rate converter and a method of converting a sample rate are disclosed herein. The sample rate converter includes a data delay unit, a clock rate conversion unit, a lagrange polynomial filter unit, a resample position calculation unit, and a resample position compensation unit. Electronics And Telecommunications Research Institute 
Ultrawideband frequency position modulation using nonlinear compressed sensing A frequency position modulation system for encoding signals for transmission. A signal's discrete frequency support is used to represent symbols. The Government Of The United States Of America, As Represented By The Secretary Of The Navy 
Systems and methods for computing mathematical functions Mathematical functions are computed in a single pipeline performing a polynomial approximation (e.g. A quadratic approximation, or the like) using data tables for rcp, sqrt, exp or log using a single pipeline according and opcodes. Vivante Corporation 
Encrypting and decrypting information An example information encryption method that includes acquiring tobeencrypted information and converting the tobeencrypted information into a polynomial of a predetermined format; extracting biometric information, and acquiring biometric data; and substituting the biometric data into the polynomial for calculation to acquire a value of the polynomial and using a twodimensional dataset including the biometric data and the value of the polynomial corresponding to the biometric data as first encrypted information. The techniques of the present disclosure improve the security of information encryption, and reduce the risk of illegal decryption of encrypted information.. Alibaba Group Holding Limited 
Evaluation of polynomials with floatingpoint components A method identifies a floating point implementation of a polynomial that is accurately evaluable. The method comprises determining whether the polynomial has an allowable variety defined by a plurality of subvarieties, and, if so, partitioning the input domain of the polynomial into a plurality of subdomains about the subvarieties. Imagination Technologies Limited 
Multidimension variable predictive modeling for yield analysis acceleration In one example, a method for evaluating a system includes constructing a macromodel of the system comprising a multipleorder polynomial equation that defines a boundary between at least one failure region and a nonfailure region for a performance indicator with respect to at least one variable of the system. The method further includes obtaining importance samples for the at least one variable that are biased to the at least one failure region, and calculating indicator values for the performance indicator by applying the importance samples to the macromodel.. International Business Machines Corporation 
Lee metric error correcting code A memory device may include memory components for storing data. The memory device may also include a controller that determines whether one or more errors exist in a data packet stored in the memory components. Micron Technology, Inc. 
Error detecting device and error detecting method An error detecting device includes a memory that stores therein first remainders corresponding to a plurality of bit positions p×p (p is an integer equal to or greater than zero) at a predetermined bit interval p among all of remainders obtained by dividing monomials, which correspond to the respective bit positions in a bit string represented by a polynomial, by a generator polynomial for generating an error detecting code, and a processor configured to acquire, from the memory, the first remainders corresponding to p×p of p×p+q (q is an integer equal to or greater than zero and smaller than p) representing normal bit positions of bits of 1 among all of the bits of an input bit string, obtain a cumulative addition result by shifting each of the acquired first remainders by q bits to obtain shift results.. . Fujitsu Limited 
Method for acquiring a gold sequence by double iterative decoding A method for acquiring a gold code, obtained as a sum of a first msequence (x) and a second msequence (yi), the first msequence being generated by a first generator polynomial (gx) and the second msequence being generated by a second generator polynomial (gy), the weight of the first generator polynomial being lower than the weight of the second generator polynomial, the acquiring method involving a first step of message passing decoding according to a first bipartite graph the edges of which are determined by the coefficients of the first generator polynomial, a decimation step using a predetermined decimation factor, and a second step of message passing decoding according to a second bipartite graph the edges of which are determined by a third generator polynomial having a minimum weight generating a third msequence having the same length as that of the second msequence.. . Commissariat A L'energie Atomique Et Aux Energies Alternatives 
Distorted image correction apparatus and method With regard to a distortion correction apparatus and method which are applicable to hardware for realtime distortion correction, provided are a distorted image correction apparatus and method for correcting a distortion of an image by using a nonpolynomial estimation function suitable for a hardware operation, and for correcting the distortion of the image by utilizing a morphing form.. . Nextchip Co., Ltd. 
Design and analysis of silicon photonics array wave guides Methods and apparatus are disclosed for symbolic methods using algebraic geometry (e.g., based on a gröbner basis of tangent space polynomials of parametric curves). For example, the design, optimization and verification of silicon photonic wave guides using parametric polynomials and/or gröbner basis functions can be used to perform envelope generation, rectification, manufacturability, singularity detection, reticle and etch processing model generation, tapering loss minimization, and bend loss minimization. Mentor Graphics Corporation 
Encoding method, decoding method An encoding method generates an encoded sequence by performing encoding of a given coding rate according to a predetermined parity check matrix. The predetermined parity check matrix is a first parity check matrix or a second parity check matrix. Panasonic Intellectual Property Corporation Of America 
Digital predistortion and postdistortion based on segmentwise piecewise polynomial approximation A nonlinear distorter is configured to mitigate nonlinearity from a nonlinear component of a nonlinear system. The nonlinear distorter operates to model the nonlinearity as a function of a piecewise polynomial approximation applied to segments of a nonlinear function of the nonlinearity. Infineon Technologies Ag 
Harmonic encoding for fwi A deterministic method for selecting a set of encoding weights for simultaneous encodedsource inversion of seismic data that will cause the iterative inversion to converge faster than randomly chosen weights. The encoded individual source gathers are summed (83), forming a composite gather, and simulated in a single simulation operation. 
Gas turbine engine airfoil An airfoil of a turbine engine includes pressure and suction sides that extend in a radial direction from a 0% span position at an inner flow path location to a 100% span position at an airfoil tip. The airfoil has a relationship between a tangential stacking offset and a span position that is at least a third order polynomial curve that includes at least one positive and negative slope. United Technologies Corporation 
Tamper detector with hardwarebased random number generator A system includes a tamper detector that includes a linear feedback shift register (lfsr) for generating pseudorandom coded detection signals as a function of seed values and a generator polynomial. The generator polynomial is loaded from a controller to the lfsr via software, and the seed values are directly loaded from a hardwarebased random number generator to the lfsr. Freescale Semiconductor, Inc. 
Secure data processing method and use in biometry The invention relates to a processing method, including the calculation of one function between a datum to be compared and a reference datum. The function can be written in the form of a sum of: a term that depends on the datum to be compared, a term that depends on the reference datum, and a polynomial, such that all the monomials of the polynomial include at least one coordinate of each datum. Morpho 
Systems and methods for error correction coding Described are methods, systems, and apparatus, including computer program products for error correction coding and decoding procedures for data storage or transfer. A plurality of data blocks is received. Raidix Corporation 
Audio processing An audio processing system (100) for spatial synthesis comprises an upmix stage (110) receiving a decoded mchannel downmix signal (x) and outputting, based thereon, an nchannel upmix signal (y), wherein 2≦m<n. The upmix stage comprises a downmix modifying processor (120), which receives the mchannel downmix signal and outputting a modified downmix signal (d1, d2) obtained by cross mixing and nonlinear processing of the downmix signal, and further comprises a first mixing matrix (130) receiving the downmix signal and the modified downmix signal, forming an nchannel linear combination of the downmix signal channels and modified downmix signal channels only and outputting this as the nchannel upmix signal. Dolby International Ab 
Accurate curvature estimation algorithm for path planning of autonomous driving vehicle A method for identifying roadway curvature that includes determining a range of interest and collecting shape points from a map database from a current position of the vehicle to an end of the range of interest that define the location of the roadway. The method converts the shape points from world geodetic system 84 (wgs84) coordinates to utm coordinates, and then fits a single set of polynomial equations to define a curve using the converted shape points. Gm Global Technology Operations Llc 
Method of controlling a transmission having an impeller clutch Impeller speed, which is difficult to measure when a torque converter includes an impeller clutch, is estimated based on a known relationship among impeller speed, turbine speed, and turbine torque. Turbine torque may be directly measured by a turbine torque sensor or estimated based on other measurements such as output shaft torque or vehicle acceleration. Ford Global Technologies, Llc 
Polynomial constructing a nondeterministic (np) turing machine A nondeterministic turning machine (ntm) performs computations using a spatial binary enumeration system, a threedimensional relation system, a simulatedhuman logic system, and a bijectiveset memory system. The ntm may be used to perform a variety of computational tasks, such as multiple sequence alignment, factorization, and other nondeterministic polynomial algorithms in polynomial time. 
Bestfit affinity sensorless conversion means or technique for pump differential pressure and flow monitoring The present invention provides apparatus, including a hydronic sensorless pumping system, that features a signal processor or processing module configured to receive signaling containing information about motor readout values of power and speed, and also about pump and system characteristics equations together with empirical power equations that are constructed by a polynomial bestfit function together with pump affinity laws based upon a pump curve published by a pump manufacturer; and determine corresponding signaling containing information about a pump or system pressure and a flow rate at the motor readout values of power and speed, based upon the signaling received.. . Fluid Handling Llc. 
. . 
Spatial arithmetic sequence alignment A computer system aligns two or more sequences with each other to identify similarities and differences between the aligned sequences. The sequences may, for example, represent proteins. 