Related papers: Lattice structures for bisimilar Probabilistic Aut…
We consider some distinguished classes of elements of a multiplicative lattice endowed with coarse lower topologies, and call them lower spaces. The primary objective of this paper is to study the topological properties of these lower…
The phase diagram of binary mixtures of particles interacting via a pair potential of parallel dipoles is computed at zero temperature as a function of composition and the ratio of their magnetic susceptibilities. Using lattice sums, a rich…
In this article we investigate the lattices of Dyck paths of type $A$ and $B$ under dominance order, and explicitly describe their Heyting algebra structure. This means that each Dyck path of either type has a relative pseudocomplement with…
We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.
This paper summarizes the fundamental expressiveness, closure, and decidability properties of various finite-state automata classes with multiple input tapes. It also includes an original algorithm for the intersection of one-way…
We describe an algorithm for determining whether two convex polytopes P and Q, embedded in a lattice, are isomorphic with respect to a lattice automorphism. We extend this to a method for determining if P and Q are equivalent, i.e. whether…
Generalizing a construction of P. Vanhaecke, we introduce a large class of degenerate (i.e., associated to a degenerate Poisson bracket) completely integrable systems on (a dense subset of) the space $\R^{2d+n+1}$, called the generalized…
We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. We show the subword complexity and the growth function create machine invariant classes. So the…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
We prove that the classical integrability condition for almost complex structures on finite-dimensional smooth manifolds also works in infinite dimensions in the case of almost complex structures that are real analytic on real analytic…
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
Machine learning potentials (MLPs) are becoming powerful tools for performing accurate atomistic simulations and crystal structure optimizations. An approach to developing MLPs employs a systematic set of polynomial invariants including…
Integrable systems have provided various insights into physical phenomena and mathematics. The way of constructing many-body integrable systems is limited to few ansatzes for the Lax pair, except for highly inventive findings of conserved…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
We elaborate on the notion of a filtration of an operad defined in terms of a lattice-valued operad serving as an indexing object. That covers ordinary integer-indexed filtrations of associative algebras and operads as a special case, yet…
Let $G$ be a second-countable amenable group with a uniform $k$-approximate lattice $\Lambda$. For a projective discrete series representation $(\pi, \mathcal{H}_{\pi})$ of $G$ of formal degree $d_{\pi} > 0$, we show that $D^-(\Lambda) \geq…
We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata…
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…
Weakly orthomodular and dually weakly orthomodular lattices were introduced by the authors in a recent paper. Similarly as for orthomodular lattices we try to introduce an implication in these lattices which can be easily axiomatized and…
Lattices induced by coverings arise naturally in matroid theory and combinatorial optimization, providing a structured framework for analyzing relationships between independent sets and closures. In this paper, we explore the structural…