Abstract: Systems and methods are provided for improving MRI data acquisition efficiency while providing more detailed information with high resolution and isotropic resolution without gaps. Improved data acquisition efficiency may be achieved by implementing a machine learning algorithm with a hardware processor and a memory to estimate imperfections in fast imaging sequences, such as a multi-shot echo planar imaging (MS-EPI) sequence. These imperfections, such as patient motion, physiological noise, and phase variations, may be difficult to model or otherwise estimate using standard physics-based reconstructions.

Abstract: Systems and methods are provided for improving MRI data acquisition efficiency while providing more detailed information with high resolution and isotropic resolution without gaps. Improved data acquisition efficiency may be achieved by implementing a machine learning algorithm with a hardware processor and a memory to estimate imperfections in fast imaging sequences, such as a multi-shot echo planar imaging (MS-EPI) sequence. These imperfections, such as patient motion, physiological noise, and phase variations, may be difficult to model or otherwise estimate using standard physics-based reconstructions.

Abstract: A system for simulating operation of a VLSI interconnect structure having capacitive and inductive coupling between nodes thereof, including a processor, and a memory, the processor configured to perform obtaining a matrix X and a matrix Y containing different combinations of passive circuit element values for the interconnect structure, the element values for each matrix including inductance L and inverse capacitance P, obtaining an adjacency matrix A associated with the interconnect structure, storing the matrices X, Y, and A in the memory, and performing numerical integration to solve first and second equations.

Abstract: A method of simulating operation of a VLSI interconnect structure having capacitive and inductive coupling between nodes thereof. A matrix X and a matrix Y containing different combinations of passive circuit element values for the interconnect structure are obtained where the element values for each matrix include inductance L and inverse capacitance P. An adjacency matrix A associated with the interconnect structure is obtained. Numerical integration is used to solve first and second equations, each including as a factor the product of the inverse matrix X?1 and at least one other matrix, with first equation including X?1Y, X?1A, and X?1P, and the second equation including X?1A and X?1P.

Abstract: A method of simulating operation of a VLSI interconnect structure having capacitive and inductive coupling between nodes thereof. A matrix X and a matrix Y containing different combinations of passive circuit element values for the interconnect structure are obtained where the element values for each matrix include inductance L and inverse capacitance P. An adjacency matrix A associated with the interconnect structure is obtained. Numerical integration is used to solve first and second equations, each including as a factor the product of the inverse matrix X1 and at least one other matrix, with first equation including X1Y, X1A, and X1P, and the second equation including X1A and X1P.