Related papers: Scrambled Polynomial Lattice Rules for Infinite-Di…
The paper presents a short overview of the theoretical, numerical and experimental works on the critical behavior of a dilute polymer solution of long-flexible polymer chains confined in semi-infinite space restricted by a surface or in a…
Mathematical modeling is a standard approach to solve many real-world problems and {\em diversity} of solutions is an important issue, emerging in applying solutions obtained from mathematical models to real-world problems. Many studies…
Random sequential adsorption of binary mixtures of extended objects on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding random walks on the…
Noisy probabilistic relational rules are a promising world model representation for several reasons. They are compact and generalize over world instantiations. They are usually interpretable and they can be learned effectively from the…
The adaptive constraints relaxing rule for swarm algorithms to handle with the problems with equality constraints is presented. The feasible space of such problems may be similiar to ridge function class, which is hard for applying swarm…
A problem of incorporating the expert rules into machine learning models for extending the concept-based learning is formulated in the paper. It is proposed how to combine logical rules and neural networks predicting the concept…
Solving inverse problems in physics is central to understanding complex systems and advancing technologies in various fields. Iterative optimization algorithms, commonly used to solve these problems, often encounter local minima, chaos, or…
We propose the use of machine learning techniques to find optimal quadrature rules for the construction of stiffness and mass matrices in isogeometric analysis (IGA). We initially consider 1D spline spaces of arbitrary degree spanned over…
An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
Lattices of compatibly embedded finite fields are useful in computer algebra systems for managing many extensions of a finite field $\mathbb{F}_p$ at once. They can also be used to represent the algebraic closure $\bar{\mathbb{F}}_p$, and…
This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously used. Firstly, we design a continuation algorithm that…
String theory in 4 dimensions has the unique feature that a topological term, the oriented self-intersection number, can be added to the usual action. It has been suggested that the corresponding theory of random surfaces wold be free from…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
The ubiquity of neural networks (NNs) in real-world applications, from healthcare to natural language processing, underscores their immense utility in capturing complex relationships within high-dimensional data. However, NNs come with…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…
We propose a new method to construct maximin distance designs with arbitrary number of dimensions and points. The proposed designs hold interleaved-layer structures and are by far the best maximin distance designs in four or more…
We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic,convex-repulsive…
A randomised trapezoidal quadrature rule is proposed for continuous functions which enjoys less regularity than commonly required. Indeed, we consider functions in some fractional Sobolev space. Various error bounds for this randomised rule…