Related papers: Nondeterministic Behaviours in Double Categorical …
As historically acknowledged in the Reasoning about Actions and Change community, intuitiveness of a logical domain description cannot be fully automated. Moreover, like any other logical theory, action theories may also evolve, and thus…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…
Biological networks have two modes. The first mode is static: a network is a passage on which something flows. The second mode is dynamic: a network is a pattern constructed by gluing functions of entities constituting the network. In this…
We propose to model the persistent-transient duality in human behavior using a parent-child multi-channel neural network, which features a parent persistent channel that manages the global dynamics and children transient channels that are…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
Semitoric systems are a type of four-dimensional integrable system for which one of the integrals generates a global $S^1$-action; these systems were classified by Pelayo and Vu Ngoc in terms of five symplectic invariants. We introduce and…
The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group…
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging…
Extracting the rules of real-world multi-agent behaviors is a current challenge in various scientific and engineering fields. Biological agents independently have limited observation and mechanical constraints; however, most of the…
We develop a learning-based algorithm for the distributed formation control of networked multi-agent systems governed by unknown, nonlinear dynamics. Most existing algorithms either assume certain parametric forms for the unknown dynamic…
In general, many dynamic processes are involved with interacting variables, from physical systems to sociological analysis. The interplay of components in the system can give rise to confounding dynamic behavior. Many approaches model…
While the properties of materials at microscopic scales are well described by fundamental quantum mechanical equations and electronic structure theories, the emergent behavior of mesoscopic or macroscopic composites is no longer governed…
We prove a structure result on proper extensions of two-sided restriction semigroups in terms of partial actions, generalizing respective results for monoids and for inverse semigroups and upgrading the latter. We introduce and study…
This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…
The saddle-node bifurcation on an invariant circle (SNIC) is one of the codimension-one routes to creation or destruction of a periodic orbit in a continuous-time dynamical system. It governs the transition from resting behaviour to…
While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, selection of possibly high-dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we…
We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix…