Related papers: Wave-Shaped Round Functions and Primitive Groups
We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical $\mathbf L^2(\mathbb R,dx)$ setting. This is done in a framework of {\em iterated function system} (IFS) measures;…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
Soft matters whose constituents are deformable are ubiquitous in nature especially in biological systems-including cells and their organelles-as well as in foams and emulsions. The capacity for deformation in these soft materials gives rise…
Geometrically decorated two-dimensional (2D) discrete surfaces can be more effective than conventional smooth reflectors in managing wave radiation. Constructive non-specular wave scattering permits the scattering angle to be other than…
Multi-Scale and U-shaped Networks are widely used in various image restoration problems, including deblurring. Keeping in mind the wide range of applications, we present a comparison of these architectures and their effects on image…
In this paper, we propose a novel construction for a symmetric encryption scheme, referred as SEBQ which is based on the structure of quasigroup. We utilize concepts of chaining like mode of operation and present a block cipher with…
Rotating spiral waves with a central core composed of phase-randomized oscillators can arise in reaction-diffusion systems if some of the chemical components involved are diffusion-free. This peculiar phenomenon is demonstrated for a…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl--Heisenberg signaling in…
We show that deep networks are better than shallow networks at approximating functions that can be expressed as a composition of functions described by a directed acyclic graph, because the deep networks can be designed to have the same…
The rotation of a quantum liquid induces vortices to carry angular momentum. When the system is composed of multiple components that are distinguishable from each other, vortex cores in one component may be filled by particles of the other…
Projected-BCS wave functions have been proposed as the paradigm for the understanding of disordered spin states (spin liquids). Here we investigate the properties of these wave functions showing how Luttinger liquids, dimerized states, and…
An invex function generalizes a convex function in the sense that every stationary point is a global minimizer. Recently, invex functions and their subclasses have attracted attention in signal processing and machine learning. However,…
We investigate the theory of affine groups in the context of designing radar waveforms that obey the desired wideband ambiguity function (WAF). The WAF is obtained by correlating the signal with its time-dilated, Doppler-shifted, and…
Reversible Boolean function is a one-to-one function which maps $n$-bit input to $n$-bit output. Reversible logic synthesis has been widely studied due to its relationship with low-energy computation as well as quantum computation. In this…
Activation functions are the linchpins of deep learning, profoundly influencing both the representational capacity and training dynamics of neural networks. They shape not only the nature of representations but also optimize convergence…
Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…
We study the efficiency of quantum algorithms which aim at obtaining phase space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions,…
Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such functions are affine equivalent. The…
Topological states in quantum materials are defined by non-trivial topological invariants, such as the Chern number, which are properties of their bulk wave functions. A remarkable consequence of topological wave functions is the emergence…