Abstract: Embodiments relate to simplifying large and complex networks and graphs using global connectivity information based on calculated node centralities. An aspect includes calculating node centralities of a graph until a designated number of central nodes are detected. A percentage of the central nodes are then selected as pivot nodes. The neighboring nodes to each of the pivot nodes are then collapsed until the graph shrinks to a predefined threshold of total nodes. Responsive to the number of total nodes reaching the predefined threshold, the simplified graph is outputted.

Abstract: The invention relates to a computer-implemented method for automatically extracting data from a digital image comprising a graphical representation of quantitative data. The method comprises: Basic graphical objects are detected and structural primitives determined comprising grouping the basic graphical objects based on geometric relations. A semantic label is assigned to each of the structural primitives. A spatial data region of the graphical representation is determined using the semantic labels of the structural primitives. Quantitative data values are extracted which are represented by structural primitives within the data region which are assigned with first semantic labels identifying the respective structural primitives to represent quantitative data. The extracted quantitative data values are provided in units of pixels according to an image coordinate system.

Abstract: Embodiments of the present invention provide methods, computer program products, and systems for solving a linear equation system using a hardware-implemented extended solver, wherein a calculation precision is adapted in each iteration step of a solving process is provided. Embodiments of the present invention can be used to perform on-the-fly interpolations using the data associated with the highest resolution of the three-dimensional finite element voxel model to a lower resolution than the highest resolution as well as to perform solving computations of the solving process in the lower resolution.

Abstract: A computing system includes computational memory and digital combinational circuitry operatively coupled with the computational memory. The computational memory is configured to perform computations at a prescribed precision. The digital combinational circuitry is configured to increase the precision of the computations performed by the computational memory. The computational memory and the digital combinational circuitry may be configured to iteratively perform a computation to a predefined precision. The computational memory may include circuitry configured to perform analog computation using values stored in the computational memory, and the digital combinational circuitry may include a central processing unit, a graphics processing unit and/or application specific circuitry. The computational memory may include an array of resistive memory elements having resistance or conductance values stored therein, the respective resistance or conductance values being programmable.

Abstract: Each node in a subset of graph nodes has an associated label value indicating a characteristic of the corresponding item. Matrix data and graph label data are stored. The matrix data defines a matrix representing the graph. The graph label data defines a graph label vector indicating label values associated with nodes of the graph. For at least one set of nodes, test label data is generated defining a test label vector. A propagation function is defined, comprising a set of basis functions, having respective coefficients. The coefficients are calculated which minimize a difference function dependent on difference between the graph label vector and a result of applying the propagation function to the test label vector for said at least one set. New label values are calculated for nodes in K by applying the propagation function with the calculated coefficients to the graph label vector, thereby propagating labels.

Abstract: 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. A function of a logarithm of a mantissa of the real number may be approximated by utilizing a polynomial based on the mantissa. The approximated function of the logarithm may be combined with the exponent for calculating a value comprising a logarithm of the real number. Likewise, an input comprising a floating point representation of a real number and a representation of a second number may be received and an approximation of the real number to the power of the second number may be generated.

Abstract: An iterative refinement apparatus configured to generate data defining a solution vector x for a linear system represented by Ax=b, where A is a predetermined matrix and b is a predetermined vector. An outer solver processes input data, defining the matrix A and vector b, in accordance with an outer loop of an iterative refinement method to generate said data defining the solution vector x. An inner solver processes data items in accordance with an inner loop of the iterative refinement method. The inner solver is configured to process said data items having variable bit-width and data format. A precision controller determines the bit-widths and data formats of the data items adaptively in dependence on the results of the processing steps of the iterative refinement method; the precision controller configured to control operation of the inner solver for processing said data items with the bit-widths and data formats.

Abstract: A method, a computer program product, and a computer system for monitoring and enforcing an automated fee payment in an infrastructure. A mobile device on a verifier's vehicle monitors a record of a transaction of a payment on a distributed ledger. The payment is paid for using a service of the infrastructure and by a mobile device on an infrastructure user's vehicle. The mobile device on the verifier's vehicle captures information of the transaction of the payment and the infrastructure user's vehicle. The information is broadcasted by the mobile device on the infrastructure user's vehicle. The mobile device on the verifier's vehicle determines whether there is a valid transaction of the payment for the service. The mobile device on the verifier's vehicle sends a violation record to an offense reporting address of an infrastructure provider, in response to determining that there is no valid transaction of the payment.

Abstract: A conjugate gradient solver apparatus is provided for generating data defining a solution vector x for a linear system represented by Ax=b where A is a predetermined matrix and b is a predetermined vector. The apparatus includes solver circuitry and a precision controller. The solver circuitry processes input data, defining said matrix A and vector b, in accordance with an iterative conjugate gradient method to generate said data defining the solution vector x. The solver circuitry is adapted to process data items, corresponding to vectors used in said conjugate gradient method, having a variable fixed-point data format. The precision controller determines the fixed-point data formats of respective said data items adaptively during progress of the conjugate gradient method in the solver circuitry.

Abstract: A conjugate gradient solver apparatus is provided for generating data defining a solution vector x for a linear system represented by Ax=b where A is a predetermined matrix and b is a predetermined vector. The apparatus includes solver circuitry and a precision controller. The solver circuitry processes input data, defining said matrix A and vector b, in accordance with an iterative conjugate gradient method to generate said data defining the solution vector x. The solver circuitry is adapted to process data items, corresponding to vectors used in said conjugate gradient method, having a variable fixed-point data format. The precision controller determines the fixed-point data formats of respective said data items adaptively during progress of the conjugate gradient method in the solver circuitry.

Abstract: Embodiments of the present invention provide methods, computer program products, and systems for solving a linear equation system using a hardware-implemented extended solver, wherein a calculation precision is adapted in each iteration step of a solving process is provided. Embodiments of the present invention can be used to perform on-the-fly interpolations using the data associated with the highest resolution of the three-dimensional finite element voxel model to a lower resolution than the highest resolution as well as to perform solving computations of the solving process in the lower resolution.

Abstract: Embodiments related to calculating node centralities in large and complex networks and graphs. An aspect includes approximating a product of a matrix exponential and a random probe vector of an adjacency matrix, wherein the adjacency matrix represents a graph. A diagonal of the adjacency matrix is computed based on the product of the matrix exponential and the random probe vector. The node centralities are then calculated based on the computed diagonal until a designated number of central nodes has been detected according to embodiments.

Abstract: A method for processing linear systems of equations and finding a nx1 vector x satisfying Ax=b where A is a symmetric, positive-definite nxn matrix corresponding to nxn predefined high-precision elements and b is an n1 vector corresponding to n predefined high-precision elements. A first iterative process generates n low-precision elements corresponding to an nx1 vector x1 satisfying A1x1=b1 where A1, b1 are elements in low precision. The elements are converted to high-precision data elements to obtain a current solution vector x. A second iterative process generates n low-precision data elements corresponding to an nx1 correction vector dependent on the difference between the vector b and the vector product Ax. Then there is produced from the n low-precision data elements of the correction vector respective high-precision data elements of an nx1 update vector u. The data elements of the current solution vector x are updated such that x=x±u.

Abstract: In one embodiment, a computer-implemented 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. In the first expression, Kn(xf) is a polynomial function of the degree n, xf is a fractional part of x/ln(2), A=252/ln(2), and B=1023*252. The result of reading the first expression as a double is returned as the value of the exponential function with respect to the variable x.

Abstract: In one embodiment, a computer-implemented 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. In the first expression, Kn(xf) is a polynomial function of the degree n, xf is a fractional part of x/ln(2), A=252/ln(2), and B=1023*252. The result of reading the first expression as a double is returned as the value of the exponential function with respect to the variable x.

Abstract: Embodiments related to calculating node centralities in large and complex networks and graphs. An aspect includes approximating a product of a matrix exponential and a random probe vector of an adjacency matrix, wherein the adjacency matrix represents a graph. A diagonal of the adjacency matrix is computed based on the product of the matrix exponential and the random probe vector. The node centralities are then calculated based on the computed diagonal until a designated number of central nodes has been detected according to embodiments.

Abstract: A conjugate gradient solver apparatus is provided for generating data defining a solution vector x for a linear system represented by Ax=b where A is a predetermined matrix and b is a predetermined vector. The apparatus includes solver circuitry and a precision controller. The solver circuitry processes input data, defining said matrix A and vector b, in accordance with an iterative conjugate gradient method to generate said data defining the solution vector x. The solver circuitry is adapted to process data items, corresponding to vectors used in said conjugate gradient method, having a variable fixed-point data format. The precision controller determines the fixed-point data formats of respective said data items adaptively during progress of the conjugate gradient method in the solver circuitry.

Abstract: A method for processing linear systems of equations and finding a nx1 vector x satisfying Ax=b where A is a symmetric, positive-definite nxn matrix corresponding to nxn predefined high-precision elements and b is an n1 vector corresponding to n predefined high-precision elements. A first iterative process generates n low-precision elements corresponding to an nx1 vector x1 satisfying A1x1=b1 where A1, b1 are elements in low precision. The elements are converted to high-precision data elements to obtain a current solution vector x. A second iterative process generates n low-precision data elements corresponding to an nx1 correction vector dependent on the difference between the vector b and the vector product Ax. Then there is produced from the n low-precision data elements of the correction vector respective high-precision data elements of an nx1 update vector u. The data elements of the current solution vector x are updated such that x=x±u.

Abstract: A conjugate gradient solver apparatus is provided for generating data defining a solution vector x for a linear system represented by Ax=b where A is a predetermined matrix and b is a predetermined vector. The apparatus includes solver circuitry and a precision controller. The solver circuitry processes input data, defining said matrix A and vector b, in accordance with an iterative conjugate gradient method to generate said data defining the solution vector x. The solver circuitry is adapted to process data items, corresponding to vectors used in said conjugate gradient method, having a variable fixed-point data format. The precision controller determines the fixed-point data formats of respective said data items adaptively during progress of the conjugate gradient method in the solver circuitry.

Abstract: An iterative refinement apparatus configured to generate data defining a solution vector x for a linear system represented by Ax=b, where A is a predetermined matrix and b is a predetermined vector. An outer solver processes input data, defining the matrix A and vector b, in accordance with an outer loop of an iterative refinement method to generate said data defining the solution vector x. An inner solver processes data items in accordance with an inner loop of the iterative refinement method. The inner solver is configured to process said data items having variable bit-width and data format. A precision controller determines the bit-widths and data formats of the data items adaptively in dependence on the results of the processing steps of the iterative refinement method; the precision controller configured to control operation of the inner solver for processing said data items with the bit-widths and data formats.