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The homological conjectures, which date back to Peskine, Szpiro and Hochster in the late sixties, make fundamental predictions about syzygies and intersection problems in commutative algebra. They were settled long ago in the presence of a…
Bisimulation equivalence (or bisimilarity) of first-order grammars is decidable, as follows from the decidability result by Senizergues (1998, 2005) that has been given in an equivalent framework of equational graphs with finite out-degree,…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…
This paper argues for a wider use of the functional theory of randomness, a modification of the algorithmic theory of randomness getting rid of unspecified additive constants. Both theories are useful for understanding relationships between…
We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant…
The notion of regular pair $(A,B)$ for two nonempty closed convex subsets $A$ and~$B$ of a Hilbert space $\H$ was introduced by Borwein and Bauschke in 1993 to ensure convergence (in norm) of the alternating projection method to some point…
The notion of abundance of certain type of configuration in certain large sets was first proved by Furstenberg and Glazner in 1998. After that many author investigate abundance of different types of configurations in different types of…
We prove that in a countable theory T fully stable over a predicate P, any complete set A has the existence property. This means that A can be extended to a model of T without changing the P-part. In particular, T has the Gaifman property:…
In Bayesian multilevel models, the data are structured in interconnected groups, and their posteriors borrow information from one another due to prior dependence between latent parameters. However, little is known about the behaviour of the…
We propose an uncertainty-complementarity balance relation and build quantitative connections among non-locality, complementarity, and uncertainty. Our balance relation, which is formulated in a theory-independent manner, states that for…
This paper exposes a contradiction in the Zermelo-Fraenkel set theory with the axiom of choice (ZFC). While Godel's incompleteness theorems state that a consistent system cannot prove its consistency, they do not eliminate proofs using a…
We establish multiple recurrence and convergence results for pairs of zero entropy measure preserving transformations that do not satisfy any commutativity assumptions. Our results cover the case where the iterates of the two…
The uncertainty relation for continuous variables due to Byalinicki-Birula and Mycielski expresses the complementarity between two $n$-uples of canonically conjugate variables $(x_1,x_2,\cdots x_n)$ and $(p_1,p_2,\cdots p_n)$ in terms of…
This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the…
In this paper we provide a unified combinatorial approach to establish a connection between Stirling permutations, cycle structures of permutations and perfect matchings. The main tool of our investigations is MY-sequences. In particular,…
We give several new characterizations of completely monotone functions and Bernstein functions via two approaches: the first one is driven algebraically via elementary preserving mappings and the second one is developed in terms of the…
This work focuses on recurrence and ergodicity of switching diffusions consisting of continuous and discrete components, in which the discrete component takes values in a countably infinite set and the rates of switching at current time…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
Mixed quantum-classical spin systems have been proposed in spin chain theory and, more recently, in magnon spintronics. However, current models of quantum-classical dynamics beyond mean-field approximations typically suffer from…
Anderson modules form a generalization of Drinfeld modules and are commonly understood as the counterpart of abelian varieties but with function field coefficients. In an attempt to study their ``motivic theory'', two objects of semilinear…