Related papers: Analytic theories around the simplest screw
A simple and accurate relationship is demonstrated that links the average shortest path, nodes, and edges in a complex network. This relationship takes advantage of the concept of link density and shows a large improvement in fitting…
We introduce a class of rings using which we define the concept of skew regularity for quaternion-valued functions over quaternions. It is shown that the notion of skew regularity coincides with the concept of slice regularity over…
We give a generalized definition of stretch that simplifies the efficient construction of low-stretch embeddings suitable for graph algorithms. The generalization, based on discounting highly stretched edges by taking their $p$-th power for…
Analytic function, also called window function, is to query the aggregation of data over a sliding window. For example, a simple query over the online stock platform is to return the average price of a stock of the last three days. These…
In this article we show that extendability from one side of a simple analytic curve is a rare phenomenon in the topological sense in various spaces of functions. Our result can be proven using Fourier methods combined with other facts or by…
We study simplicity of Lie skew braces from both global and infinitesimal perspectives. After reviewing the correspondence between connected Lie skew braces, simply transitive affine actions, and post-Lie algebras, we investigate ideals and…
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
Network connectivity is usually addressed for convex domains where a direct line of sight exists between any two transmitting/receiving nodes. Here, we develop a general theory for the network connectivity properties across a small opening,…
In this paper we survey many results on the Dirichlet space of analytic functions. Our focus is more on the classical Dirichlet space on the disc and not the potential generalizations to other domains or several variables. Additionally, we…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
We present a generalization of Schlick's bias and gain functions -- simple parametric curve-shaped functions for inputs in [0, 1]. Our single function includes both bias and gain as special cases, and is able to describe other smooth and…
We present a class of solvable models that resemble string theories in many respects but have a strikingly different non-perturbative sector. In particular, there are no exponentially small contributions to perturbation theory in the string…
The syntactic structure of sentences exhibits a striking regularity: dependencies tend to not cross when drawn above the sentence. We investigate two competing explanations. The traditional hypothesis is that this trend arises from an…
Many complicated network problems can be easily understood on small networks. Difficulties arise when small networks are combined into larger ones. Fortunately, the mathematical theory of sheaves was constructed to address just this kind of…
Analytical expressions are provided for the configurations of an inextensible, flexible, twistable inertial string rotating rigidly about a fixed axis. Solutions with trivial radial dependence are helices of arbitrary radius and pitch.…
Data science offers a powerful tool to understand objects in multiple sciences. In this paper we utilize concept of data science, most notably topological data analysis, to extend our understanding of knot theory. This approach provides a…
We present a single operation for constructing skew diagrams whose corresponding skew Schur functions are equal. This combinatorial operation naturally generalises and unifies all results of this type to date. Moreover, our operation…
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…
An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar…