A vast class of exponential functions are shown to be deterministic. This includes whose exponents polynomial-like or "piece-wise" close polynomials after differentiation. Many these proved disjoint from the M\"obius function.

Abstract In this paper, we present an algebraic approach to the precise and global verification explanation of Rectifier Neural Networks , a subclass Piece-wise Linear (PLNNs), i.e., networks that semantically represent piece-wise affine functions. Key our is symbolic execution these allows construction equivalent Typed Affine Decision Structures (TADS). Due their deterministic sequential natur...

Tropical Newton-Puiseux polynomials, defined as piece-wise linear functions with rational coefficients of the variables, play a role tropical algebraic functions. We provide explicit formulas for polynomials being zeroes univariate polynomial parametric coefficients.

We explore an intersection-based remap method between meshes consisting of isoparametric elements. present algorithms for the case serendipity elements (QUAD8 elements) and piece-wise constant (cell-centered) discrete fields. demonstrate convergence properties this with a few numerical experiments.

Abstract This paper presents a multiplierless image-cipher, with extendable 2048-bit key-space, based on 4-dimensional (4D) quantized piece-wise linear cat map (PWLCM). The PWLCM exhibits limit-cycles of 4-bit encoded integers periods greater than 10 7 . synthesis the in finite state space allows to eliminate undesirable precision effect due hardware realization. proposed image-cipher combines ...