Related papers: How to explore replicator equations?
The theory of algebraic extensions of Banach algebras is well established, and there are many constructions which yield interesting extensions. In particular, Cole's method for extending uniform algebras by adding square roots of functions…
In general Evolutionary Computation (EC) includes a number of optimization methods inspired by biological mechanisms of evolution. The methods catalogued in this area use the Darwinian principles of life evolution to produce algorithms that…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
Numerous problems of analysis (real and complex) and geometry (analytic, algebraic, Diophantine e.a.) can be reduced to calculation of the ``number of solutions'' of systems of equations, defined by algebraic equalities and differential…
In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
Relation extraction (RE) is a fundamental task in natural language processing, aiming to identify relations between target entities in text. While many RE methods are designed for a single sentence or document, cross-document RE has emerged…
Evolution is a fundamental process that shapes the biological world we inhabit, and reinforcement learning is a powerful tool used in artificial intelligence to develop intelligent agents that learn from their environment. In recent years,…
Relation extraction (RE) is the task of extracting relations between entities in text. Most RE methods extract relations from free-form running text and leave out other rich data sources, such as tables. We explore RE from the perspective…
A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…
We consider the proof system Res($\oplus$) introduced by Itsykson and Sokolov (Ann. Pure Appl. Log.'20), which is an extension of the resolution proof system and operates with disjunctions of linear equations over $\mathbb{F}_2$. We study…
Two combined numerical methods for solving semilinear differential-algebraic equations (DAEs) are obtained and their convergence is proved. The comparative analysis of these methods is carried out and conclusions about the effectiveness of…
Neural ordinary differential equations (ODEs) have attracted much attention as continuous-time counterparts of deep residual neural networks (NNs), and numerous extensions for recurrent NNs have been proposed. Since the 1980s, ODEs have…
In this article, we develop an algorithm suitable for constrained optimization in $\mathbb{R}^n$. The results are developed through standard tools of n-dimensional real analysis and basic concepts of optimization. Indeed, the well known…
The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation…
We propose a reconstruction of the initial system of ordinary differential equations from a single observed variable. The suggested approach is applied to a certain class of systems which includes, in particular, the Rossler system and…
Because of the pervasive use of deep neural networks (DNNs), especially in high-stakes domains, the interpretability of DNNs has received increased attention. The general idea of rationale extraction (RE) is to provide an…
In statistical learning theory, interpolation spaces of the form $[\mathrm{L}^2,H]_{\theta,r}$, where $H$ is a reproducing kernel Hilbert space, are in widespread use. So far, however, they are only well understood for fine index $r=2$. We…