Abstract: A method of preparing a circuit simulator, said method comprising initializing a normalized adjusted gate voltage value. Then performing the steps of determining a normalized adjusted gate voltage datum in dependence upon the initial normalized adjusted gate voltage value. Storing the normalized adjusted gate voltage datum at a memory address in a one-dimensional array based on the normalized adjusted gate voltage. Decrementing the normalized adjusted gate voltage value by a predetermined decrement amount. And verifying the decremented gate voltage value. Then repeating until a stop gate voltage value is reached.

Abstract: A technique for simultaneously acquiring vehicle identification information and speed information of an RFID tag-attached vehicle by calculating the vehicle speed by using a Doppler shift value extracted from transmission and reception signals between the RFID tag and the RFID reader is disclosed. A method for measuring a vehicle speed by using an RFID reader installed right up on the road or at the roadside includes: transmitting a continuous wave; receiving a reflected wave with respect to the continuous wave from an RFID tag attached to a vehicle which has received the continuous wave; extracting a Doppler shift value from the continuous wave and the reflected wave; and calculating the speed of the vehicle by using the Doppler shift value.

Abstract: One embodiment is directed to an approach to solving a leader-follower problem in which a leader has a set of leader actions and a follower has a set of follower actions. The approach includes receiving an expression of the leader-follower problem as a normal form Stackelberg game. The approach further includes, for each possible follower action, solving a linear program (LP) problem to determine a respective optimal mixed leader strategy, wherein the LP problem optimizes a leader payoff for a given mixed leader strategy and a given fixed follower action over a feasible region that includes only mixed leader strategies that provoke that respective follower action. The approach further includes generating an output derived from the optimal mixed leader strategies, and outputting the output by changing a physical state associated with an interface.

Abstract: Transmission overhead that takes a long period of time in calculating processes with an iterative solution technique is to be suppressed. After its own calculation result is calculated with the calculating processes, calculating processes are repeatedly executed without waiting for a determination as to whether the calculation result is significant. After the calculating processes are started and when an indication that the significance can be determined is transmitted because of reception of calculation results from other computer apparatuses via transmission units, or, when a request as to whether the significance can be determined is sent and an indication that the significance can be determined is obtained as a result of the request, the significance of its own calculation result is determined. When it is determined that the calculation result is significant, the calculation processes are suspended.

Abstract: An apparatus for identifying techniques for solving functions may include a processor. The processor may be configured to identify a function and identify candidate techniques for solving the function. The processor may also be configured to separate a domain of the function into a plurality of domain intervals and determine respective cost indicators for each candidate technique as applied to each domain interval of the function. Further, the processor may be configured to select a technique for each domain interval based on the cost indicators; and provide for configuring an application processor to solve the function via the selected techniques and the respective domain intervals. Associated methods and computer program products may also be provided.

Abstract: A method for performing a signal integrity analysis on an integrated circuit (IC) that includes a plurality of scatterers by dividing the scatterers into subgroups using a nested Huygens' equivalence principle algorithm and solving a set of equations realized thereby with a reduced coupling matrix. The method includes decomposing the IC design into a plurality of small non-overlapping circuit sub-domains, wherein each of the sub-domains is formed as a small, enclosed region. Each sub-domain is analyzed independently of the other sub-domains using only electric fields to represent the interactions of each sub-domains with the other sub-domains as equivalent currents on equivalent surfaces of the plurality of sub-domains. Neighboring equivalent sub-domains are grouped together to form larger sub-domains using equivalent currents on equivalent surfaces to represent the interactions of the sub-domains.

Abstract: In a computing system, evaluating a mathematical expression in presented hierarchically according to the rules of precedence of operations, initial operations at the bottom of the hierarchy may yield values too large to be calculated conventionally, even if the ultimate value of the expression may represent a calculable value. The mathematical expression is evaluated top down to determine if portions of the mathematical expression are re-expressible to simplify the expression and avoid initial or intermediate calculations that would prevent calculation of the mathematical expression. Portions of the original mathematical expression are re-expressible by substituting known mathematical identities, applying arithmetic rules, or treating a portion of the mathematical expression as a variable on which other operations are performed. Once the mathematical expression has been re-expressed, the mathematical expression is simplified, and, if possible, its value calculated.

Abstract: A method of reducing a first data word corresponding to a polynomial C(x) and having a length of a maximum of 2n?1 to a second data word of a length of a maximum m which in a binary finite field GF(2m) whose elements are of a maximum length m corresponds to a polynomial C?0(x) equivalent to C(x), wherein m is smaller than or equal to n, includes partitioning of the first data word into a binary first sub-data word C0 and a binary second sub-data word C1, repeated right-shift of C1 to form summand terms until a respective summand term is associated with each non-disappearing term of a reduction trinomial or pentanomial which is not the term xm, adding the summand terms formed to the first sub-data word to form a sum data word and applying the partitioning step to the summand data word formed until the ascertained sum data word is of a length of a maximum m and forms the desired second data word.

Abstract: Electrical impedance tomography method comprising: an electrical measurement step during which pre-determined electrical conditions are imposed on the surface of a medium to be imaged, while generating a mechanical disturbance at predefined points of the medium by locally modifying the impedance of the medium and an electrical parameter is measured at several points on the surface of the medium; and a calculation step during which the electrical impedance is determined at several points in the internal volume of the medium, taking into account the measurements carried out during the disturbance, as a function of a law for modification of the electrical impedance by this disturbance.

Abstract: Many signal processing devices require the solution to a system of equations with a Toeplitz, or block Toeplitz, coefficient matrix. This solution can be obtained with increased efficiency by separating the initial system of equations into a number of systems of equations with reduced dimensions. The solution to the initial system of equations is then calculated from the solutions to the systems of equations with reduced dimensions.

Abstract: The present invention relates to a solution for solving an ill-posed inverse problem in image analysis, e.g. in an electron tomography application in order to recover a structure of a sample. The solution is provided for instance as a method comprising steps of determining reliable prior knowledge about the solution, determining initial guess for the solution and determining the corresponding forward operator, deciding upon model of stochasticity, deciding on suitable regularization method, deciding on updating scheme, and producing a sequence using the set configuration.

Abstract: A parallel physics solver may solve an equation to determine the characteristics of motion after a collision. In some embodiments, the physics solver solves the equation AX=B, where A is a sparse constrained matrix and B is the right hand vector. The sparse constrained matrix may be formed of 6×K blocks, where K is a tuning parameter that divides into the width of a single instruction multiple data processor used to implement the physics solver, without residue.

Abstract: A method for generating an accelerated and/or decelerated chaotic sequence. The method involves selecting a plurality of polynomial equations constructed from an acc-dec variable v. The method also involves selecting a value for the acc-dec variable v for advancing or stepping back a chaotic sequence generation by at least one cycle at a given time. The method further involves using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations using the acc-dec variable v. The solutions iteratively computed and expressed as RNS residue values. The method involves determining a series of digits in a weighted number system based on the RNS residue values.

Abstract: The present invention relates to Group-based trust management scheme (GTMS) of wireless sensor networks. GTMS evaluates the trust of a group of sensor nodes in contrast to traditional trust management schemes that always focused on trust values of individual nodes. This approach gives us the benefit of requiring less memory to store trust records at each sensor node in the network. It uses the clustering attributes of wireless sensor networks that drastically reduce the cost associated with trust evaluation of distant nodes. Uniquely it provides not only a mechanism to detect malicious or faulty nodes, but also provides some degree of a prevention mechanism.

Abstract: When a real symmetric matrix is tridiagonalized using a shared memory scalar parallel computer, the matrix is divided into threads to be updated. In the updating, the data of the lower triangular portion is for the calculation utilizing the symmetry in the matrix. The lower triangular matrix portion is divided into columns, and the resultant pieces are assigned to respective CPUs so that an equal number of elements are assigned to each of the CPUs. Also, the computation is performed simultaneously in the column and row directions once for each loading of the data in order to reduce the number of times data is loaded into memory. The lower triangular matrix portion of the diagonal block matrix portion is divided into one small square matrix and two small triangular matrices recursively so that they are updated.

Abstract: A graphing calculator includes: a touchscreen display unit having a formula display area and a graph display area; a formula input section configured to receive a calculation formula; a formula display control section configured to control the touchscreen display unit to display the calculation formula in the formula display area; a formula drag determining section configured to determine whether the calculation formula is dragged to the graph display area; a function calculating section configured to perform a calculation corresponding to a type of a function included in the calculation formula; a range setting section configured to set coordinate ranges to be used for generating a graph image; and a graph display control section configured to generate a graph image corresponding to the calculation formula and the calculation result according to the coordinate ranges.

Abstract: A PPU-enhanced computer system is provided including a Physics Processing Unit (PPU), a Graphics Processing Unit (GPU), a Central Processing Unit (CPU) and a main memory, wherein the system creates an animation from application data stored in the main memory by data communication between the GPU, PPU, CPU and main memory. The system may include a memory controller and a chip set connecting the bus structure to the CPU and GPU through an I/O interface and connecting the PPU though a bus structure. The PPU may be a separate processing core logically grouped with the CPU and GPU processing cores. In this preferred embodiment, the CPU, GPU and PPU receive data from a common L2 cache and/or a main system memory.

Abstract: An apparatus for calculating a representation of a result operand of the non-linear logical operation between a first operand and a second operand includes a first logic gate and a second logic gate. Each operand is represented by two auxiliary operands, which, when linearly combined together result in the respective operand. The first and second logic gates are designed such that an average energy consumption of the first or second logic gate is substantially equal to a plurality of combinations of auxiliary operands at the beginning of a first operation cycle and auxiliary operands at the beginning of a second operating cycle, the average energy being derivable from a plurality of different orders of occurrences of the first to fourth auxiliary operands.

Abstract: One embodiment of the present invention provides a system that uses a computer to evaluate a function within a domain using an interval computing technique. During operation, the system receives the function and the domain over which the function is to be evaluated. Next, the system creates a set of sampling subdomains within the domain by generating a set of boxes of different sizes which are located at different positions across the domain. The system then performs evaluations on the set of sampling subdomains to generate evaluation results. Next, the system sorts the evaluation results based on box size. The system then selects a box size from the different box sizes by identifying a largest box size which achieves tight bounds on the evaluation results. The system next discretizes the domain into subdomains of the selected box size.

Abstract: Methods, apparatus, and articles of manufacture for performing calculations using reduced-width data are disclosed. In particular, an example method determines reduced-width data values associated with generating and evaluating functions. Some of the reduced-width data values are stored within instructions in an instruction memory during a compile phase and retrieved from instruction memory during a runtime phase.

Abstract: The solution program causes a computer to execute step 1 for performing, in parallel, the LU decomposition on the column block comprising a plurality of columns and for storing the result in the working area; step 2 for canceling the row permutation on the left of each column to the result in step 1 and for copying back the result in the array in compress mode; step 3 for saving the portion which may be damaged by updating the band matrix corresponding to the result in step 1; step 4 for updating the band matrix in parallel by using the result in step 1; and step 5 for returning the saved portion in step 3 to the result in step 4.

Abstract: The present invention provides a singular value decomposition apparatus that can perform processing in parallel at high speed and high accuracy.

Abstract: The invention relates to a method and device for transferring signal data from a sender to one or more receivers. The invention includes receiving a quantity as a function of time, arranging the quantity into a first polynomial to obtain values for polynomial coefficients of a first continuous signal, and transferring the values of the polynomial coefficients of the first continuous signal via a first data transfer link to one or more receivers.

Abstract: A method of configuring a communication channel prior to the transmission of an input signal along the communication channel, the communication channel comprising a plurality of sub-channels, the method comprising determining the strength of the input signal and in accordance with the determined signal strength, selecting a set of the plurality of sub-channels and transmitting said in put signal along the set of sub-channels in parallel, wherein each of the sub-channels has a predetermined noise characteristic such that the set of selected sub-channels exhibits a combined noise characteristic in which the standard deviation of the noise is proportional to the signal strength.

Abstract: A system for solving linear equations comprises a first circuit including a first multiplication module for multiplying a first row of a matrix by a first instance of a vector variable to generate a first product, and a first linear solver module for calculating an updated first element of the vector variable using the first product. A second circuit includes a second multiplication module for multiplying a second row of the matrix by a second instance of the vector variable to generate a second product, and a second linear solver module for calculating an updated second element of the vector variable using the second product. An interface module updates the second instance of the vector variable with the first updated element, and updates the first instance of the vector variable with the second updated element.

Abstract: This invention proposed a new algorithm. By multiply the proposed weight coefficients of this invention, CSP and CSS can be computed without computing for the mean(s) of the data. After the proposed weight coefficients of this invention undergo factorization, it can promote a new recursive and real time updatable computation method. To test the accuracy of the new invention, the StRD data were separately tested using SAS ver 9.0, SPSS ver 15.0 and EXCEL 2007 for comparison. The results showed that the accuracy of the results of the proposed invention exceeds the level of accuracy of SAS ver 9.0, SPSS ver 15.0 and EXCEL 2007. Aside from an accurate computation, this new invented algorithm can also produce efficient computations.

Abstract: A system for performing multi-dimensional quantum search, quantum computation, quantum memory, quantum storage, and quantum retrieval includes a structure and method for: enabling components and systems for quantum search, and more particularly to improved local and remote quantum computing and search components and systems; quantum memory component and systems; quantum storage components and systems; quantum retrieval components and systems; quantum logic gates; classical (non-quantum) search components and systems; integrated quantum-classical search components and systems; and integrated quantum-classical cryptosystems.

Abstract: The application of finite differences methods to solve boundary value problems typically involves a discretization of such a problem across an orthogonal array of discrete grid points. This leads to an array of difference equations which is solved numerically within the constraints of the boundary conditions to yield solutions at the grid point locations. However, the accuracy of the solutions is limited with conventional finite differences methods when the boundary conditions are not represented exactly within the orthogonal array of discrete grid points, as when the boundary conditions are curved or slanted surfaces. The invention described herein provides finite differences methods for solving boundary value problems more accurately than with conventional finite differences methods, particularly when curved or slanted boundary surfaces correspond to terminations of a known analytical function.

Abstract: A system and methods for converting data for an object of interest, which is characterized by a function ƒ, between a digital form and an analog form. In one embodiment, the method includes the steps of locally selecting a plurality of data sample points in the order of N, N being an integer, wherein the data sample points are in a first form of data type, performing a transformation in a shift invariant space to the locally selected data sample points to obtain a new data set that is in a second form of data type different from the first form of data type, and reconstructing the object of interest ƒ from the new data set. In one embodiment, the first form of data type is one of the the digital form and the analog form, and the second form of data type is one of the digital form and the analog form that is different from the first form of data type. In other words, the first form of data type can be in digital form, and the corresponding second form of data type is in analog form, and vice versa.

Abstract: A method (and structure) for performing a matrix subroutine, includes storing data for a matrix subroutine call in a computer memory in an increment block size that is based on a cache size.

Abstract: The cyclic combinatorial method and system includes an optimizing programming method embodied in a computing machine in order to provide the capability to solve cyclic optimization problems. The method can be used to solve optimization problems having cyclic 0-1 matrices, such as network problems and cyclic workforce scheduling. The method identifies cyclically distinct solutions by enumerating cyclically distinct combinations of basic dual variables. The method can determine how many cyclically distinct combinations of m (m?n) objects can be selected, given n cyclic objects. The method integrates partition and cyclic permutation operations in order to generate cyclically distinct selections (solutions). After cyclically enumerating all dual solutions, rules are described for recognizing the set of dominant solutions. A class of problems, which includes cyclic labor scheduling, can be efficiently solved using the cyclic combinatorial method and system.

Abstract: In order to design on-chip interconnect structures in a flexible way, a CAD approach is advocated in three dimensions, describing high frequency effects such as current redistribution due to the skin-effect or eddy currents and the occurrence of slow-wave modes. The electromagnetic environment is described by a scalar electric potential and a magnetic vector potential. These potentials are not uniquely defined, and in order to obtain a consistent discretization scheme, a gauge-transformation field is introduced. The displacement current is taken into account to describe current redistribution and a small-signal analysis solution scheme is proposed based upon existing techniques for static fields in semiconductors. In addition methods and apparatus for refining the mesh used for numerical analysis is described.

Abstract: This disclosure relates to performing a query for a search term of a database containing a plurality of structured documents. Those structured documents that do not include the search term are ferreted or filtered out during an initial search. Matched structured documents which are those structured documents that do contain the search term are evaluated by ranking the individual elements based on how well each individual element matches the search term, and indicating to the user the ranking of the individual elements wherein the individual elements can be accessed by the user.

Abstract: The present disclosure presents novel shape comparison methods. Methods for determining shape similarity between a query molecule and a target molecule and methods for screening one or more molecules in a database based on shape similarity to a query molecule are described.

Abstract: Bias plays an important role in factor analysis and is often implicitly made use of, for example, to constrain solutions to factors that conform to physical reality. However, when components are collinear, a large range of solutions may exist that satisfy the basic constraints and fit the data equally well. In such cases, the introduction of mathematical bias through the application of constraints may select solutions that are less than optimal. The biased alternating least squares algorithm of the present invention can offset mathematical bias introduced by constraints in the standard alternating least squares analysis to achieve factor solutions that are most consistent with physical reality. In addition, these methods can be used to explicitly exploit bias to provide alternative views and provide additional insights into spectral data sets.

Abstract: A method for manufacturing an ink-jet head includes the step of forming, in a substrate, through holes respectively corresponding to conductors on one face of the substrate and each having its diameter increasing from the one face toward the other face of the substrate. Here, the through holes are formed in such a manner as to satisfy R>d/2+t/tan ?, where: d represents a width of an opening of the through hole on the one face; ? represents an angle of inclination of a sidewall defining the through hole with respect to the one face; R represents a shortest distance from the center of the through hole to a periphery of an electrode that neighbors an electrode corresponding to the through hole; and t represents a thickness of the substrate.

Abstract: A computer executable method of processing a representation of a modal interval spherical projection is provided. A representation of a vector comprised of modal intervals X, Y, and Z is provided wherein each modal interval of the modal intervals are delimited by first and second marks of a digital scale. An analytical expression of an azimuthal spherical projection is partitioned into terms of a pair of independent functions wherein a function of the pair exhibits a monotonicity over piecewise domains of the function. A modal interval analysis is performed upon the function wherein arguments of said piecewise domains are modal intervals.

Abstract: An error function calculation device, which performs processing of calculating an error function FM(T) having T (positive real number) as a variable and M (M is an integer of 0 or more) as an order, includes a coefficient table and a calculation section. The coefficient table stores a value of FM+i(T0)/FM(T0) (i is at least one integer among 1 to n, and n is a natural number) calculated for T0, obtained by an n-th order polynomial approximation of the error function FM(T), or a multiplied value which is obtained by multiplying the value of FM+i(T0)/FM(T0) by a constant. The calculation section reads the value of FM+i(T0)/FM(T0) or the multiplied value from the coefficient table, and performs at least a part of the processing of calculating a value of the error function FM(T) by a fixed-point arithmetic using the value of FM+i(T0)/FM(T0) or the multiplied value.

Abstract: A method is provided for generating a chaotic sequence. The method includes selecting a plurality of polynomial equations. The method also includes using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The method further includes determining a series of digits in a weighted number system (e.g., a binary number system) based on the RNS residue values. According to an aspect of the invention, the method includes using a Chinese Remainder Theorem process to determine a series of digits in the weighted number system based on the RNS residue values. According to another aspect of the invention, the determining step comprises identifying a number in the weighted number system that is defined by the RNS residue values.

Abstract: A system and technique, called Solution Enumeration technique, for finding efficient algorithms for NP-hard combinatorial problems is presented. The solution space of these problems grows exponentially with the problem size. Some examples in this class are: Hamiltonian Circuit, SAT, Graph Isomorphism, and Perfect Matching problems. The core of this technique is a graph theoretical model of an NP-hard problem, viz., counting the perfect matchings in a bipartite graph. This technique is then applied to develop deterministic algorithms using polynomial sequential time or polylogarithmic parallel time (for massively parallel computers) for the search and counting associated with all NP-complete problems. In the past no polynomial time algorithms for these problems were found, and thus are believed to be intractable. This invention thus makes a theoretical as well as practical contribution to the field of computing, and has practical applications in many diverse areas.

Abstract: An instrument for measuring the size and characteristics of a particle contained in a sample of particles. A particle sample is introduced into a sample chamber. The sample particles are subjected to centrifugal forces so that large particles travel in the sample chamber at velocities greater than small particles. Light is shown upon the particles as they travel in the sample chamber. The particles diffract the light. The diffracted light is then received by detectors that convert the diffracted light into corresponding electronic signals. The electronic signals are analyzed to determine the size and characteristics of the particles that caused the diffracted light.

Abstract: A system and method for automatically generating a computation mesh for use with an analytical tool, the computation mesh having a plurality of ?-grid lines and ?-grid lines intersecting at grid points positioned with respect to an inner boundary and an outer boundary. The system and method include one or more mesh equations having one or more source terms that include: a grid clustering component based on a Jacobian scaling parameter, a source decay parameter, and one or more first point distance parameters, and a cell shape modifying source component based on one or more source parameters selected from the group consisting of a smoothing source parameter, an area source parameter, an orthagonality source parameter, and any combinations thereof.

Abstract: A sender-side process directed to processing an electronic message destined for a recipient, comprising producing a solution to a computational problem involving at least a portion of the message. A degree of effort associated with solving the problem may be assessed. The message is further processed according to the degree of effort by determining whether the degree of effort was within a range set by the sender or the recipient and if not, the computational problem is adjusted and solved again. The message is then transmitted to a recipient, who is informed of both the problem and solution. The recipient executes a recipient side process, comprising: assessing the degree of effort associated with generation of the message based on the problem and solution; and further processing the message in accordance with the degree of effort. The degree of effort is indicative of the legitimacy of the message; e.g., is it “SPAM”.

Abstract: This invention describes a software method for computers for solving integer programming problems containing systems of linear equations where part of or all of the variables may take only integer values. Said software method consists of 4 main steps. First, all of or part of said system is transformed into a regularized system. In a second step, the regularized system is further transformed into an ordered system. In a third step, the regularized and ordered system is further transformed into a non-interfering system. In a last step, solutions to said system are determined by finding solutions which are common to all equations of said system. This is done by using a successive and recursive approximation algorithm. Finally, prior to executing said 4 steps, said system may have to be conditioned such every variable-coefficient of the system is non-zero.

Abstract: This invention describes a software method for computers for solving integer programming problems containing systems of linear equations where part of or all of the variables may take only integer values. Said software method consists of 2 main steps. First, the arithmetic binary decision diagrams associated to the equations of the system are constructed. A solution to any of said equations is determined by finding an allowed path through the associated arithmetic binary decision diagram. Then, solutions common to all equation of the system are determined by searching for common paths between the arithmetic binary decision diagrams of the equations. Searching for common paths between said arithmetic binary decision diagrams is done by determining correspondences between the nodes of said arithmetic binary decision diagrams.

Abstract: A recursive lambda rule engine (114, 302) includes a first multiplier (204) that sequentially multiplies each of series of inputs by a nonlinearity determining parameter and supplies results to a second multiplier (214) that multiplies the output of the first multiplier (204) by a previous output of the engine (114, 302). A three input adder (220, 228) sequentially sums the output of the second multiplier (214), inputs from the series of inputs, and the previous output of the engine (114, 302). A shift register (244) is used to feedback the output of the engine (114, 302) to the three input adder (220, 228) and second multiplier (214). A MUX (234) is used to route an initial value through the shift register (244) for the first cycle of operation.

Abstract: There is disclosed method, software and apparatus for evaluating a function f in a computing device using a reduction, core approximation and final reconstruction stage. According to one embodiment of the invention, an argument reduction stage uses an approximate reciprocal table in the computing device. According to another embodiment, an approximate reciprocal instruction I is operative on the computing device to use the approximate reciprocal table such that the argument reduction stage provides that—C:=I(X) and R:=X×C?1, the core approximation stage provides that p(R) is computed so that it approximates f(1+R), and the final reconstruction stage provides that T=f(1/C) is fetched and calculated if necessary, and f(X) is reconstructed based on f(X)=f([1/C]×[X×C])=g(f(1/C), f(1+R)).

Abstract: A shape of a mirror face of a shape-deformable mirror that reduces aberration and has a simple configuration is calculated in a simple method. The shape of the mirror face of the shape-deformable mirror 14a is approximately calculated using fourth and fifth terms of the Zernike Polynomials. Furthermore, one of the Zernike coefficients C4 and C5, which configure the fourth and fifth terms of the Zernike Polynomials respectively, is expressed as a value with the other coefficient as a variable by using the following expression: C5/C4=2{1?cos(2?)}/(cos(2?)+3). The expression is substituted in the Zernike Polynomials, thereby the shape of the mirror face of the shape-deformable mirror 14a is approximated as a linear function, and thus can be calculated in a simple calculation.

Abstract: A technique for solving a set of wave equations in a region uses points arranged in a grid spanning the region or coefficients of wave expansion for objects located in the region. The grid points or the coefficients are partitioned into blocks on multiple levels, and block impedance matrices encoding the wave equations is derived for pairs of blocks. The block impedance matrix need not be calculated as it is written as the product of two non-square matrices, denoted U and V. Each of U and V have one linear dimension which is only of the order of the rank of the block impedance matrix levels. The rank is predetermined by coarse sampling. Two examples of the use of the invention are given: solving surface integral equations and Foldy Lax equations for partial waves.

Abstract: For sequentially input data string, the outliner and the change point are detected through calculation of the outlier score and the change point score by combining a time-series model learning device to learn the generation mechanism of the read data series as the time-series statistic model, a score calculator to calculate the outlier score of each data based on the time-series model parameter and the input data, a moving average calculator to calculate the moving average of the outlier score, a time-series model learning device to learn the generation mechanism of the moving average series as the time-series statistic model and the above score calculator that further calculates the outlier score of the moving average based on the moving average of the outlier score and outputs the result as the change point score of the original data.