Abstract: Implementing a 1D stencil code via SIMD instructions on a computer with vector registers having N processing elements (PEs), among them a set of coefficient vector registers, a set of at most N data vector registers, and a set of result vector registers. The M stencil coefficients are loaded in a particular pattern into M+N?1 coefficient vector registers. Successive sets of N consecutive data values are received, and each data value of a set is loaded into all PEs of a data vector register of the set of data vector registers. The result vector registers accumulate sums of products of consecutive coefficient vector registers with corresponding data vector registers. The contents of any result vector register containing a sum of all coefficient vector register-data vector register products is output, and the result vector register is reused for accumulating.

Abstract: Implementing a 1D stencil code via SIMD instructions on a computer with vector registers having N processing elements (PEs), among them a set of coefficient vector registers, a set of at most N data vector registers, and a set of result vector registers. The M stencil coefficients are loaded in a particular pattern into M+N?1 coefficient vector registers. Successive sets of N consecutive data values are received, and each data value of a set is loaded into all PEs of a data vector register of the set of data vector registers. The result vector registers accumulate sums of products of consecutive coefficient vector registers with corresponding data vector registers. The contents of any result vector register containing a sum of all coefficient vector register-data vector register products is output, and the result vector register is reused for accumulating.

Abstract: Systems and methods for combined matrix-vector and matrix-transpose vector multiply for block sparse matrices. Exemplary embodiments include a method of updating a simulation of physical objects in an interactive computer, including generating a set of representations of objects in the interactive computer environment, partitioning the set of representations into a plurality of subsets such that objects in any given set interact only with other objects in that set, generating a vector b describing an expected position of each object at the end of a time interval h, applying a biconjugate gradient algorithm to solve A*?v=b for the vector ?v of position and velocity changes to be applied to each object wherein the q=Ap and qt=AT(pt) calculations are combined so that A only has to be read once, integrating the updated motion vectors to determine a next state of the simulated objects, and converting the simulated objects to a visual.

Abstract: Systems and methods for combined matrix-vector and matrix-transpose vector multiply for block sparse matrices. Exemplary embodiments include a method of updating a simulation of physical objects in an interactive computer, including generating a set of representations of objects in the interactive computer environment, partitioning the set of representations into a plurality of subsets such that objects in any given set interact only with other objects in that set, generating a vector b describing an expected position of each object at the end of a time interval h, applying a biconjugate gradient algorithm to solve A*?v=b for the vector ?v of position and velocity changes to be applied to each object wherein the q=Ap and qt=AT(pt) calculations are combined so that A only has to be read once, integrating the updated motion vectors to determine a next state of the simulated objects, and converting the simulated objects to a visual.

Abstract: Systems and methods for combined matrix-vector and matrix-transpose vector multiply for block sparse matrices. Exemplary embodiments include a method of updating a simulation of physical objects in an interactive computer, including generating a set of representations of objects in the interactive computer environment, partitioning the set of representations into a plurality of subsets such that objects in any given set interact only with other objects in that set, generating a vector b describing an expected position of each object at the end of a time interval h, applying a biconjugate gradient algorithm to solve A*?v=b for the vector ?v of position and velocity changes to be applied to each object wherein the q=Ap and qt=AT(pt) calculations are combined so that A only has to be read once, integrating the updated motion vectors to determine a next state of the simulated objects, and converting the simulated objects to a visual.

Abstract: Systems and methods for combined matrix-vector and matrix-transpose vector multiply for block sparse matrices. Exemplary embodiments include a method of updating a simulation of physical objects in an interactive computer, including generating a set of representations of objects in the interactive computer environment, partitioning the set of representations into a plurality of subsets such that objects in any given set interact only with other objects in that set, generating a vector b describing an expected position of each object at the end of a time interval h, applying a biconjugate gradient algorithm to solve A*?v=b for the vector ?v of position and velocity changes to be applied to each object wherein the q=Ap and qt=AT(pt) calculations are combined so that A only has to be read once, integrating the updated motion vectors to determine a next state of the simulated objects, and converting the simulated objects to a visual.

Abstract: A system for placing a visible "watermark" on a digital image is disclosed, wherein an image of the watermark is combined with the digital image. The pixels of the watermark image are examined, and for each pixel whose value is not a specified "transparent" value, the corresponding pixel of the original image is modified by changing its brightness but its chromaticities. This results in a visible mark which allows the contents of the image to be viewed clearly, but which discourages unauthorized use of the image.