Abstract: Systems and methods for improving the efficiency of propagating electronic messages are provided. In some embodiments, a feed of activities on a network such as an online social network (OSN) is analyzed to determine influenced activity probabilities and intrinsic activity probabilities for participants in the network. A Helmhotz Green's Function matrix is determined in order to calculate an overall influence weight for each participant in the network. A Woodbury-Sherman-Morrison formula may be used to accelerate computation of the Helmholtz Green's Function matrix, thus allowing efficient updates to the overall influence weights based on newly monitored activities. The participants with the highest overall influence weights may be selected to propagate a new message, thus providing the greatest likely distribution of the message with the fewest originating transmissions.

Abstract: Systems and methods for improving the efficiency of propagating electronic messages are provided. In some embodiments, a feed of activities on a network such as an online social network (OSN) is analyzed to determine influenced activity probabilities and intrinsic activity probabilities for participants in the network. A Helmhotz Green's Function matrix is determined in order to calculate an overall influence weight for each participant in the network. A Woodbury-Sherman-Morrison formula may be used to accelerate computation of the Helmholtz Green's Function matrix, thus allowing efficient updates to the overall influence weights based on newly monitored activities. The participants with the highest overall influence weights may be selected to propagate a new message, thus providing the greatest likely distribution of the message with the fewest originating transmissions.

Abstract: Redundancy extraction in electromagnetic simulation of an electronic device/system includes discretizing first and second spaced conductive layers of a computer model of an electronic device/system into first and second meshes M1 and M2. For each edge between cells of each mesh, a current flow across the edge in response to application of an exemplary bias to the geometry is determined. A square impedance matrix Z* is determined which, for each instance of equal magnitude and opposite direction current flows (EMODCF) in edges E1 and E2 of M1 and M2, has one less row and one less column than the total number of edges in M1 and M2. A voltage column vector V* is also determined which, for each instance of EMODCF, has one less row than the total number of edges in M1 and M2. A current column vector [I*]=[V*]/[Z*] is then determined.

Abstract: Methods and devices configured to provide a key-free, one-way coding of sensitive data such that efficient parallel scaling methods may be used to perform computations related to the sensitive initial data without risking unwanted disclosure of the sensitive initial data are provided. In some embodiments, a set of intermediate representations of the initial data set is calculated using a one-way computation. The set of intermediate representations is then sent to a server computing system for calculating results in a scalable manner. The initial data is secured from unwanted access at the server computing system at least because the one-way computation does not allow the initial data to be derived from the intermediate representations.

Abstract: Redundancy extraction in electromagnetic simulation of an electronic device/system includes discretizing first and second spaced conductive layers of a computer model of an electronic device/system into first and second meshes M1 and M2. For each edge between cells of each mesh, a current flow across the edge in response to application of an exemplary bias to the geometry is determined. A square impedance matrix Z* is determined which, for each instance of equal magnitude and opposite direction current flows (EMODCF) in edges E1 and E2 of M1 and M2, has one less row and one less column than the total number of edges in M1 and M2. A voltage column vector V* is also determined which, for each instance of EMODCF, has one less row than the total number of edges in M1 and M2. A current column vector [I*]=[V*]/[Z*] is then determined.

Abstract: In a method of electronic design automation, discretized meshes of layers of current conducting materials of a computerized device model are determined. Each discretized mesh corresponds to the current conducting material of one model layer. For each discretized mesh, a corresponding impedance matrix having cells is determined. Each cell includes an impedance value Zij which is based on a voltage (Vi) induced in a cell i of the discretized mesh due to a current (Ij) flowing in a cell j of the discretized mesh. A subset of the cells, including impedance values, of the impedance matrices is dispatched to node computers via an electronic communications network. In response to dispatching the cells of the impedance matrices, charge densities estimated by the node computers to exist on a subset of the cells of the discretized meshes are returned.

Abstract: A novel approach to determining PageRank for web pages views the problem as being comparable to solving for an electromagnetic field problem. This view of ranking web pages enables appropriate entries for a matrix G of the web (or a subset), so that fast-solver techniques can be employed to iterate G, solving for ranks, or a dominant eigenstructure, achieving an O(N log N) performance in time and memory requirements. The specific solver technique that is used can be, for example, a fast multi-pole method (FMM), or a multilevel low-rank compression method. Once the problem is correctly formulated, it is not necessary to create the matrix G. Local information can be queried on demand by the solver. This approach can also be used to determine different scores of web pages, such as TrustRank, which is indicative of their trustworthiness.

Abstract: In a method of electronic design automation, discretized meshes of layers of current conducting materials of a computerized device model are determined. Each discretized mesh corresponds to the current conducting material of one model layer. For each discretized mesh, a corresponding impedance matrix having cells is determined. Each cell includes an impedance value Zij which is based on a voltage (Vi) induced in a cell i of the discretized mesh due to a current (Ij) flowing in a cell j of the discretized mesh. A subset of the cells, including impedance values, of the impedance matrices is dispatched to node computers via an electronic communications network. In response to dispatching the cells of the impedance matrices, charge densities estimated by the node computers to exist on a subset of the cells of the discretized meshes are returned.

Abstract: An approach that efficiently solves for a desired parameter of a system or device that can include both electrically large fast multipole method (FMM) elements, and electrically small QR elements. The system or device is setup as an oct-tree structure that can include regions of both the FMM type and the QR type. An iterative solver is then used to determine a first matrix vector product for any electrically large elements, and a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large elements and the electrically small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter.

Abstract: A novel approach to determining PageRank for web pages views the problem as being comparable to solving for an electromagnetic field problem. This view of ranking web pages enables appropriate entries for a matrix G of the web (or a subset), so that fast-solver techniques can be employed to iterate G, solving for ranks, or a dominant eigenstructure, achieving an O(N log N) performance in time and memory requirements. The specific solver technique that is used can be, for example, a fast multi-pole method (FMM), or a multilevel low-rank compression method. Once the problem is correctly formulated, it is not necessary to create the matrix G. Local information can be queried on demand by the solver. This approach can also be used to determine different scores of web pages, such as TrustRank, which is indicative of their trustworthiness.

Abstract: A method and system for combining the process variations in circuits and distributed interconnect-based electromagnetic (EM) objects in order to capture a statistical behavior of overall circuit performance parameters. In an exemplary approach, a coupled circuit-EM system is decoupled at the points where the EM objects connect to the circuit portion, and circuit ports are defined at those points. The sources of variation are identified and used to determine Y-parameters for the ports with EM elements and for all EM elements based on the SPICE-like and EM full-wave simulations. A response surface is generated for each variable and is used to extract circuit and EM parameters by generating many random vectors representing combinations of the random variables. These Y-parameters are merged to produce a probability density function (PDF) of one or more performance metrics for the electronic device or system.

Abstract: In one exemplary approach, a Schur complement-based boundary element method (BEM) is employed for predicting the motion of arbitrarily shaped three-dimensional particles under combined external and fluidic force fields. The BEM relies on modeling the surface of the computational domain, significantly reducing the number of unknowns when compared to volume-based methods. In addition, the Schur complement-based scheme enables a static portion of the computation to be computed only once for use in subsequent time steps, which leads to a tremendous reduction in solution time during time-stepping in the microfluidic domain. Parallelized oct-tree based O(N) multilevel iterative solvers are also used to accelerate the setup and solution costs.

Abstract: A method and system to efficiently create electromagnetic coupled basis functions for an electronic circuit that is defined by geometry data and topology data. The geometry data for the circuit are read, and a three-dimensional mesh of polygons for the circuit is created. External port geometry and internal port geometry (internal ports occur where vias are attached to conductive layers) are determined from the geometry data. Circuit electromagnetic basis functions are then created as are loop-tree formations that are coupled to the basis functions. The loops include local loops, via loops, and hole loops. The three-dimensional mesh is efficiently created by extruding a two-dimensional mesh for each layer and via in the circuit.

Abstract: In a method, system and computer readable medium for determining a composite circuit model of a 3D geometry, first and second sides of an analytical model of the 3D geometry are discretize into first and second surface and/or volume meshes. For each mesh, a current that flows in each cell thereof and the a voltage induced in the cell in response to the application of an exemplary bias to the geometry are determined. For each mesh, from the currents flowing in the cells thereof and voltages induced in the cells thereof, a corresponding circuit model is determined. The circuit models of the meshes are then combined to form a composite circuit model for the geometry.

Abstract: An approach that efficiently solves for a desired parameter of a system or device that can include both electrically large FMM elements, and electrically small QR elements. The system or device is setup as an oct-tree structure that can include regions of both the FMM type and the QR type. An iterative solver is then used to determine a first matrix vector product for any electrically large elements, and a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large elements and the electrically small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter.

Abstract: A method and system for combining the process variations in circuits and distributed interconnect-based electromagnetic (EM) objects in order to capture a statistical behavior of overall circuit performance parameters. In an exemplary approach, a coupled circuit-EM system is decoupled at the points where the EM objects connect to the circuit portion, and circuit ports are defined at those points. The sources of variation are identified and used to determine Y-parameters for the ports with EM elements and for all EM elements based on the SPICE-like and EM full-wave simulations. A response surface is generated for each variable and is used to extract circuit and EM parameters by generating many random vectors representing combinations of the random variables. These Y-parameters are merged to produce a PDF of one or more performance metrics for the electronic device or system.

Abstract: A method and system to efficiently create electromagnetic coupled basis functions for an electronic circuit that is defined by geometry data and topology data. The geometry data for the circuit are read, and a three-dimensional mesh of polygons for the circuit is created. External port geometry and internal port geometry (internal ports occur where vias are attached to conductive layers) are determined from the geometry data. Circuit electromagnetic basis functions are then created as are loop-tree formations that are coupled to the basis functions. The loops include local loops, via loops, and hole loops. The three-dimensional mesh is efficiently created by extruding a two-dimensional mesh for each layer and via in the circuit.

Abstract: Analyzing interactions between vias in multilayered electronic packages that include at least two spaced-apart conducting planes, and multiple vias that connect signal traces on different layers. Voltages at active via ports are represented as magnetic ring current sources, which generate electromagnetic modes inside the plane structure. Substantial electromagnetic coupling between vias occurs. A full-wave solution of multiple scattering among cylindrical vias in planar waveguides is derived using Foldy-Lax equations. By using the equivalence principle, the coupling is decomposed into interior and exterior problems. For the interior problem, the dyadic Green's function is expressed in terms of vector cylindrical waves and waveguide modes. The Foldy-Lax equations for multiple scattering among the cylindrical vias are applied, and waveguide modes are decoupled in the Foldy-Lax equations.

Abstract: Analyzing interactions between vias in multilayered electronic packages that include at least two spaced-apart conducting planes, and multiple vias that connect signal traces on different layers. Voltages at active via ports are represented as magnetic ring current sources, which generate electromagnetic modes inside the plane structure. Substantial electromagnetic coupling between vias occurs. A full-wave solution of multiple scattering among cylindrical vias in planar waveguides is derived using Foldy-Lax equations. By using the equivalence principle, the coupling is decomposed into interior and exterior problems. For the interior problem, the dyadic Green's function is expressed in terms of vector cylindrical waves and waveguide modes. The Foldy-Lax equations for multiple scattering among the cylindrical vias are applied, and waveguide modes are decoupled in the Foldy-Lax equations.