Abstract: Methods, systems, and apparatus for solving cost optimization problems. In one aspect, a method includes receiving data representing a cost optimization problem in a network, wherein i) the network is represented as a graph of nodes and edges, and ii) each edge comprises an associated cost; mapping the data representing the cost optimization problem in a network to a quadratic unconstrained binary optimization (QUBO) formulation of the cost optimization problem, the QUBO formulation comprising multiple variables with values determined by states of respective qubits, wherein each qubit corresponds to a respective edge of the graph of nodes and edges; obtaining data representing a solution to the cost optimization problem from a quantum computing resource; and initiating an action based on the obtained data representing a solution to the cost optimization problem.

Abstract: A system, computer-readable media, and methods are disclosed for building a decoding table. The system may include one or more registers configured to store a data value based on an order in which one or more lengths were obtained. The system may also include a programmable priority encoder configured to scan the one or more registers for the data value. Further, the system may include a memory configured to store, based on locations of the data value in the one or more registers, at least one of encoding values or letters.

Abstract: An approach is provided for correlation of a signal over time and frequency. The signal is correlated with a bit sequence over time instances and certain frequency offsets, wherein sub-segments of the signal are correlated with sub-segments of the bit sequence to generate a correlation factor associated with each signal sub-segment. The correlation factors are coherently combined to generate a final correlation factor, wherein a respective phase shift (for each frequency offset) is applied to each correlation factor to generate a set of frequency adjusted correlation factors, and the frequency adjusted correlation factors of a respective set are combined to generate the final correlation factor over the signal sub-segments, resulting in the matrix of final correlation factors over time and frequency. A signal parameter estimation is performed, based on the matrix of final correlation factors, to determine a highest correlation value for the signal over the frequency offsets.

Abstract: A system and method for displaying data provided by a sensor in Polar coordinates on a raster scan device operating in Cartesian coordinates. Cartesian coordinates for display points on said raster scan device are converted to corresponding Polar coordinates, and sensor data values for said Polar coordinates are fetched for display on said raster scan device. The coordinates are converted by differentiating the equations mapping Polar coordinates to Cartesian coordinates, and solving the differential relationships using a suitable integration method. Preferable the integration method is a Midpoint method. In order to avoid divisions and speed up the conversion process, synthetic division in Newton-Ralphson iteration is used instead.

Abstract: A system, method, and computer program product are provided for decomposing a sampling task into a plurality of jobs. In operation, a sampling task is identified. Additionally, the sampling task is decomposed into a plurality of jobs. Further, each of the plurality of jobs are processed in parallel. Still yet, each of the plurality of jobs are allowed to terminate independently of the other plurality of jobs.

Abstract: An arithmetic processing system processes a sensing signal and a first approximate offset signal to obtain a second approximate offset signal. The system includes a first arithmetic processor and a second arithmetic processor. The first arithmetic processor receives and processes the sensing signal and the first approximate offset signal to output a first arithmetic signal. The second arithmetic processor processes the first arithmetic signal to output a second arithmetic signal, and the second arithmetic signal is added with a predetermined offset signal to obtain the second approximate offset signal, and the second approximate offset signal is closer to a real offset signal of the sensing signal than the first approximate offset signal. A method of arithmetic processing is also disclosed.

Abstract: A system, method and chip for transforming data through a Rung-Kutta integration of a single point on a plane defined by X, Y, and Z values along X, Y and Z axes from a travel time data volume. The system includes at least one memory bank and at least one alternate memory bank and at least one single cycle Runge-Kutta travel time generator in communication with the memory banks. The single cycle Runge-Kutta travel time generator reads data from the at least one memory bank, and transforms the data by performing a Runge-Kutta integration on points of a plane defined by X, Y, and Z values along X, Y and Z axes in a travel time data volume and slowness data to generate another plane of values with the integration carried forward by a half step; and writes the data back to the at least one alternate memory bank.

Abstract: A system and method for decimating a digital signal is disclosed. The system includes an input to receive digital data, a control input to receive a desired decimation rate, and an integrator stage responsive to the input. The system also includes a variable rate down sampling module responsive to the integrator stage and a differentiator stage responsive to the variable rate down sampling module. The down sampling module has a decimation rate that is dynamically adjustable based on the desired decimation rate.

Abstract: A method of prediction is suggested for the characteristics of future values of processes that can be expressed as integrals over future times with different weight functions (kernels), or as anticausal convolution integrals. In particular, all band-limited processes processes are predictable in this sense, as well as high-frequency processes, with zero energy at low frequencies. In addition, process of mixed type can still be predicted using low-pass filter and high-pass filter for this process, to provide separation on low-band and high frequency processes. It is allowed that an outcome of low-pass filter be not a purely band-limited process, but have exponential decay of energy on high frequencies. The algorithm suggested consists of two blocks: separation of a process on band-limited and high-frequency components, and approximation of the transfer function of the anticausal integral that has to be predicted by transfer functions for causal convolution integrals.

Abstract: Systems and techniques are described in which rank-1 lattices are used in computerized image processing, in particular in the context of image synthesis. These include systems and techniques for selection of rank-1 lattices, rasterization on rank-1 lattices, anti-aliasing by rank-1 lattices, and adaptive refinement and filtering by rank-1 lattices.

Abstract: A method of timing recovery comprises receiving an input signal, sampling the input signal to produce a plurality of signal samples, detecting the samples to produce an output signal, and controlling timing of the sampling in response to a maximum-likelihood estimation of timing error between an actual sampling time instant and a desired sampling time instant. Apparatus that performs the method is also provided.

Abstract: A computer program product for a computer graphics system comprises computer executable instructions recorded on a computer-readable medium: instructions executable to enable the computer to generate a selected number of sample points over an integration domain, such that there is at least one sample point in each of a plurality of strata distributed over the domain, the strata being defined by a rank-1 lattice; instructions executable to enable the computer to, for respective ones of the sample points, generate a value for the function at the respective sample point; and instructions executable to enable the computer to use the generated function values in generating an estimate for the value of the integral in relation to at least one object and at least one light source in a scene, the estimate corresponding to a pixel value for the image, to enable the computer to generate a display-controlling electrical output.

Abstract: An arithmetic processing system processes a sensing signal and a first approximate offset signal to obtain a second approximate offset signal. The system includes a first arithmetic processor and a second arithmetic processor. The first arithmetic processor receives and processes the sensing signal and the first approximate offset signal to output a first arithmetic signal. The second arithmetic processor processes the first arithmetic signal to output a second arithmetic signal, and the second arithmetic signal is added with a predetermined offset signal to obtain the second approximate offset signal, and the second approximate offset signal is closer to a real offset signal of the sensing signal than the first approximate offset signal. A method of arithmetic processing is also disclosed.

Abstract: A computer readable medium is configured to determine the integral of the product of a plurality of functions. The computer readable medium includes logic configured to project each function of the plurality of functions into the wavelet domain, logic configured to encode basis coefficients of each function in a wavelet tree, each function being encoded in at least one wavelet tree such that the plurality of functions are represented in the wavelet domain by a plurality of wavelet trees, and logic configured to traverse direct paths through the plurality of wavelet trees to determine the integral of the product of the functions represented by the wavelet trees, along which direct paths an integral coefficient may be nonzero.

Abstract: A tailored response cascaded integrator comb digital filter is disclosed which has a cascaded integrator structure, a cascaded comb structure, a first rate change component, a second rate change component and can additionally include a resonator. The improved structure achieves greater bandwidth without requiring higher sampling rates. In an additional embodiment, a pre-decimated cascaded integrator filter section for a cascaded integrator comb digital filter is disclosed as having a data rate change component and a first integrator structure receiving data at the rate established by the data rate change component and modifying the received data. The pre-decimated filter section can also include a second integration structure. The pre-decimate structure outputs data equivalent to data that would be output by a post-decimated cascaded integrator structure having an equal number of cascaded integrator stages.

Abstract: A variable-gain integrator includes a variable-gain multiplier for multiplying digital input data that are input in time sequence by variable gain, an adder for adding output data from the variable multiplier to previous integration data, a clip circuit for limiting output data from the adder to a predetermined range to obtain integration data, an integration value storage device for storing the integration data obtained from the clip circuit and supplying the integration data that are stored to the adder as the previous integration data, and a fixed multiplier for multiplying the integration data obtained by the clip circuit by fixed gain.

Abstract: When numerically integrating an integrand function A over an unbounded domain, a vector map f converts an m (m≧1)-dimensional vector into an m-dimensional vector wherein a multidimensional density function &rgr; of the limiting distribution resulting from repeatedly applying the map f to a predetermined m-dimensional vector u is analytically solvable. A first storage unit stores an m-dimensional vector x, a second storage unit stores a scalar value w, a first computing unit computes a vector x′=f(x), a second computing unit computes a scalar value w′=A(x)/&rgr;(x), an update unit updates values in the first and second storage units and by storing the vector x′ on the first storage unit and adding the scalar value w′ to a value to be stored in the second storage unit, and an output unit computes a scalar value s=w/(c+1) when the number of update times by the update unit becomes c (c≧1) and outputs the result.

Abstract: Embodiments of a two-dimensional pyramid filter architecture are described.

Abstract: To provide a numerical integration system and method, suitable for a high-order dimensional Monte Carlo calculation and having high convergence speed without incurring a calculation time penalty, a multi-dimensional sequence is first converted into a one-dimensional value. Then the conversion is optimized in accordance with characteristics of a model. A summation calculation is corrected by using an averaged weight, instead of correcting the values of a random sequence. Then a histogram is prepared to correct the overall shape of the distribution of a random number sequence. DA sum is calculated for each group obtained when the histogram is prepared. As a result, the convergence speed is increased without sacrificing the calculation time.

Abstract: When numerically integrating an integrand function A over an unbounded domain, a vector map f converts an m (m≧1)-dimensional vector into an m-dimensional vector wherein a multidimensional density function &rgr; of the limiting distribution resulting from repeatedly applying the map f to a predetermined m-dimensional vector u is analytically solvable. A first storage unit stores an m-dimensional vector x, a second storage unit stores a scalar value w, a first computing unit computes a vector x′=f(x), a second computing unit computes a scalar value w′=A(x)/&rgr;(x), an update unit updates values in the first and second storage units and by storing the vector x′ on the first storage unit and adding the scalar value w′ to a value to be stored in the second storage unit, and an output unit computes a scalar value s=w/(c+1) when the number of update times by the update unit becomes c (c≧1) and outputs the result.

Abstract: A method of determination an input signal changed in time and its integral value has the steps of integrating an input signal to a given value of an integration result for a final point, and performing calculations also for a plurality of intermediate points.

Abstract: A comb filter is provided for achieving substantial attenuation of aliasing or imaging bans of a signal to be filtered. The comb filter can perform decimation or interpolation, depending upon its application. Integration can include an integration term with adjustable voltage accumulation at a particular sample point in time. The accumulation factor can be an integer or fractional number and is introduced at a sample count value L within each of M number of samples formed by the rate change switch within the comb filter. The amount of gain being introduced can possibly vary depending on the number of accumulation cycles programmed within configuration registers of the digital signal processor which carries out the comb filter functions. The programmable accumulator avoids having to implement a multiplication operation and the complexities associated therewith.

Abstract: A computer implemented method for efficiently evaluating a Fourier sine/cosine transform of a bounded analytical function is described. The transform is computed in a plurality of steps which reduces the required transform to a sum of two terms which can be efficiently evaluated using a digital computer. The computer evaluates the first and second terms as definite integrals. The first integral is evaluated via standard techniques, and the second integral is evaluated as a definite integral of a sum of terms which converges. The method is advantageously used to provide a model of semiconductor devices which takes into account quantum mechanical effects while minimizing compute operation time. A look-up table of semiconductor carrier density versus spatially dependent field values can optionally be constructed.