Related papers: A Primer for the Walsh Transform
For one dimensional maps the trajectory scaling functions is invariant under coordinate transformations and can be used to compute any ergodic average. It is the most stringent test between theory and experiment, but so far it has proven…
We lay down the foundations for a systematic study of differentiable and algebraic supervarieties, with a special attention to supergroups.
Evolutionary optimization algorithms are often derived from loose biological analogies and struggle to leverage information obtained during the sequential course of optimization. An alternative promising approach is to leverage data and…
To excel in signal processing or control systems, a deep understanding of transforms is essential. But what exactly is this mathematical tool, and how does it function? In this article, we will explore the fundamentals of transforms, their…
Adaptive mesh refinement techniques are nowadays an established and powerful tool for the numerical discretization of PDE's. In recent years, wavelet bases have been proposed as an alternative to these techniques. The main motivation for…
We present a study demonstrating how random walk algorithms can be used for evolutionary image transition. We design different mutation operators based on uniform and biased random walks and study how their combination with a baseline…
Estimation of distribution algorithms are evolutionary algorithms that use extracted information from the population instead of traditional genetic operators to generate new solutions. This information is represented as a probabilistic…
Advanced observational facilities allow to trace back the chemical evolution of the Universe, on the one hand, from local objects of different ages and, secondly, by direct observations of redshifted objects. The chemical enrichment serves…
We review some of the features of the evolutions equations for transverse momentum dependent parton distributions recently proposed by us. We briefly describe the new ingredients entering the equations and their relationship with ordinary…
Stochastic processes of evolving shapes are used in applications including evolutionary biology, where morphology changes stochastically as a function of evolutionary processes. Due to the non-linear and often infinite-dimensional nature of…
Proteins, essential to biological systems, perform functions intricately linked to their three-dimensional structures. Understanding the relationship between protein structures and their amino acid sequences remains a core challenge in…
A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing…
We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
The diffraction of ultrashort pulse changes its spatial and temporal structure that is crucial for multi-channel communication and location via such pulses. The features of the evolution of broadband pulses discussed for two general…
This note develops some fundamental properties of resultants and related notions. It represents my own personal exploration of this domain, which I found more instructive than seeking answers in the standard literature. Consequently,…
Enzymes are on the front lines of evolution. All living organisms rely on highly efficient, specific enzymes for growth, sustenance, and reproduction; and many diseases are a consequence of a mutation on an enzyme that affects its catalytic…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We study a class of minimal geometric partial differential equations that serves as a framework to understand the evolution of boundaries between states in different pattern forming systems. The framework combines normal growth, curvature…
This document attempts to clarify potential confusion regarding electrostatics calculations, specifically in the context of biomolecular structure and specifically as regards the units typically used to contour/visualize isopotential…