Related papers: Semigroups for dynamical processes on metric graph…

This work presents the use of graph learning for the prediction of multi-step experimental outcomes for applications across experimental research, including material science, chemistry, and biology. The viability of geometric learning for…

In this paper, we study linear programming based approaches to the maximum matching problem in the semi-streaming model. The semi-streaming model has gained attention as a model for processing massive graphs as the importance of such graphs…

Differential equations on metric graphs can describe many phenomena in the physical world but also the spread of information on social media. To efficiently compute the solution is a hard task in numerical analysis. Solving a design…

This survey describes the method of approximation of operator semigroups, based on the Chernoff theorem. We outline recent results in this domain as well as clarify relations between constructed approximations, stochastic processes,…

This is a survey of using Minsky machines to study algorithmic problems in semigroups, groups and other algebraic systems.

Dynamical systems on hypergraphs can display a rich set of behaviours not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hypergraph structure, an interesting question is thus how much…

In this paper, we propose a semi-parametric model for autonomous nonlinear dynamical systems and devise an estimation procedure for model fitting. This model incorporates subject-specific effects and can be viewed as a nonlinear…

The Koopman linearization of measure-preserving systems or topological dynamical systems on compact spaces has proven to be extremely useful. In this article we look at dynamics given by continuous semiflows on completely regular spaces…

In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…

Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…

We study transport processes on infinite networks. The solution of these processes can be modeled by an operator semigroup on a suitable Banach space. Classically, such semigroups are strongly continuous and therefore their asymptotic…

Classical geometric and topological operations on polyhedra, maps and polytopes often give rise to structures with the same symmetry group as the original one, but with more flags. In this paper we introduce the notion of voltage operations…

We study a one-parameter family of binomial-convolution operators acting on sequences. These operators form an additive semigroup with an explicit inverse, and they subsume iterated classical binomial transforms as a special case. We…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…

We consider the set of ($n\times n\times n$) cubic stochastic matrices of type (1,2) together with different multiplication rules that not only retain their stochastic properties but also endow this set with an associative semigroup…

To capture the global structure of a dynamical system we reformulate dynamics in terms of appropriately constructed topologies, which we call flow topologies; we call this process topologization. This yields a description of a semi-flow in…

We summarize semiclassical modeling methods, including drift-diffusion, kinetic transport equation and Monte Carlo simulation approaches, utilized in studies of spin dynamics and transport in semiconductor structures. As a review of the…

This paper aims to improve existing results about using averaging method for analysis of dynamic systems on time scales. We obtain a more accurate estimate for proximity between solutions of original and averaged systems regarding…

In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since…

We use algebras of pseudodifferential operators on groupoids to study geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators are in our algebras. This then leads to…