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A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…
A modal logic that is strong enough to fully characterize the behavior of a system is called expressive. Recently, with the growing diversity of systems to be reasoned about (probabilistic, cyber-physical, etc.), the focus shifted to…
We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define…
The logico-algebraic study of Lewis's hierarchy of variably strict conditional logics has been essentially unexplored, hindering our understanding of their mathematical foundations, and the connections with other logical systems. This work…
Contrastive Vision-Language Models (VLMs) have demonstrated strong zero-shot capabilities. However, their cross-modal alignment remains biased toward English due to limited multilingual multimodal data. Recent multilingual extensions have…
Multi-modal data is becoming more common in big data background. Finding the semantically similar objects from different modality is one of the heart problems of multi-modal learning. Most of the current methods try to learn the inter-modal…
The work described in this paper builds on the polyhedral semantics of the Spatial Logic for Closure Spaces (SLCS) and the geometric spatial model checker PolyLogicA. Polyhedral models are central in domains that exploit mesh processing,…
We study a summability method called almost convergence for bounded measurable functions defined on a locally compact abelian group. We define almost convergence using topologically invariant means and exhibit two different kinds of…
Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the…
The aim of this paper is to introduce an algebraic structure on the set of all coalgebras with the same state space over the given type which allows us to present definitions of weak and delay bisimulation for coalgebras. Additionally, we…
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…
A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…
We study the topology of some simple infinite dimensional singularities arising from spaces of \emph{algebraic formal loops}. We prove that in some simple cases the natural analogue of nearby cycles cohomology for a function on the loop…
We investigate when the categories of all rational $A$-modules and of finite dimensional rational modules are closed under extensions inside the category of $C^*$-modules, where $C^*$ is the cofinite topological completion of $A$. We give a…
There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
We study infinite dimensional tilting modules over a concealed canonical algebra of domestic or tubular type. In the domestic case, such tilting modules are constructed by using the technique of universal localization, and they can be…
We consider simplicial sets equipped with a notion of smallness, and observe that this slight "topological" extension of the "algebraic" simplicial language allows a concise reformulation of a number of classical notions in topology, e.g.…
Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved…
We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…