Related papers: Set systems: order types, continuous nondeterminis…
We study three types of order convergence and related concepts of order continuous maps in partially ordered sets, partially ordered abelian groups and partially ordered vector spaces, respectively. An order topology is introduced such that…
We consider the spectrum of the evolution operator for bound chaotic systems by evaluating its trace. This trace is known to approach unity as $t \rightarrow \infty$ for bound systems. It is written as the Fourier transform of the…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
Classes of set functions along with a choice of ground set are a bedrock to determine and develop corresponding variants of greedy algorithms to obtain efficient solutions for combinatorial optimization problems. The class of approximate…
Recurrence determinism, one of the fundamental characteristics of recurrence quantification analysis, measures predictability of a trajectory of a dynamical system. It is tightly connected with the conditional probability that, given a…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
Eight categorical soundness and completeness theorems are established within the framework of algebraic theories. Exactly six of the eight deduction systems exhibit complete semantics within the cartesian monoidal category of sets. The…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
The back-and-forth relations $M\leq_\alpha N$ are central to computable structure theory and countable model theory. It is well-known that the relation $\{(M,N) : M \leq_\alpha N\}$ is (lightface) $\Pi^0_{2\alpha}$. We show that this is…
Shannon's information theory deliberately excludes message semantics. This paper develops a rigorous framework for semantic communication that integrates formal proof systems with Shannon-theoretic tools. We introduce an axiomatic…
Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of constructor terms in the left-hand side; the computational intuition is that rules cannot build new data…
The spatial logistic model is a system of point entities (particles) in $\mathbb{R}^d$ which reproduce themselves at distant points (dispersal) and die, also due to competition. The states of such systems are probability measures on the…
Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis.…
The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…
Set functions are functions (or signals) indexed by the powerset (set of all subsets) of a finite set N. They are fundamental and ubiquitous in many application domains and have been used, for example, to formally describe or quantify loss…
We give an example of two ordered structures M, N in the same language L with the same universe, the same order and admitting the same one-variable definable subsets such that M is a model of the common theory of o-minimal L-structures and…
Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated games. Here we show that cooperation remains…
This paper proposes a tractable family of remainder-form mixed-monotone decomposition functions that are useful for over-approximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a…
Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted…
This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi…