An analog scheme for fixed-point computation-Part II: Applications

Abstract

Abstract-In a companion paper [6] we presented theoretical analysis of an analog network for fixed-point computation. This paper applies these results to several applications from numerical analysis and combinatorial optimization, in particular: 1) solving systems of linear equations; 2) nonlinear programming; 3) dynamic programing; and 4) network flow computations. Schematic circuits are proposed for representative cases and implementation issues are discussed. Exponential convergence is established for a fixed-point computation that determines the stationary probability vector for a Markov chain. A fixedpoint formulation of the single source shortest path problem (SPP) that will always converge to the exact shortest path is described. A proposed implementation, on a 2-complementary metal-oxide-semiconductor (CMOS) process, for a fully connected eight-node network is described in detail. The accuracy and settling time issues associated with the proposed design approach are presented.

DIFT Games: Dynamic Information Flow Tracking Games for Advanced Persistent Threats

“…is a non-expansive map and hence from Theorem 2.2 in [46] iterates v n k (s), for all s ∈ S and k ∈ {D, A}, converge to an asymptotically stable critical point. Thus condition (3) is satisfied.…”

Static feedback circuit methodology for solving fixed-point equations

“…Some work has been done in providing theory and application of analog VLSI circuits for solving fixed point equations (e.g., Borkar and Soumyanath [1], [2]). In contrast, this paper provides a new methodology using static feedback circuits that can solve difficult optimization problems without the use of extrinsic capacitors, relying simply on the convergence of these circuits to their DC operating point.…”

Optimal path finding with space‐ and time‐variant metric weights via multi‐layer CNN

“…If an arithmetic cell is arranged to compute Equation (1) at each node, the processing of Equation (1) is conÿned to the local operation of min and summation. In fact, the min circuits are more complicated than max circuits for the practical implementation [15]. Fortunately, some arrangement of Equation (1) allows the min operation to be represented with the simpler circuit of max operation.…”