相关论文: Refined Cyclic Sieving on Words for the Major Inde…

A word over an ordered alphabet is said to be clustering if identical letters appear adjacently in its Burrows-Wheeler transform. Such words are strictly related to (discrete) interval exchange transformations. We use an extended version of…

We characterize relative notions of syndetic and thick sets using, what we call, "derived" sets along ultrafilters. Manipulations of derived sets is a characteristic feature of algebra in the Stone-\v{C}ech compactification and its…

In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with…

Time series classification is an application of particular interest with the increase of data to monitor. Classical techniques for time series classification rely on point-to-point distances. Recently, Bag-of-Words approaches have been used…

In this paper we address the problem of discovering a small set of frequent serial episodes from sequential data so as to adequately characterize or summarize the data. We discuss an algorithm based on the Minimum Description Length (MDL)…

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson…

With Zipf's law being originally and most famously observed for word frequency, it is surprisingly limited in its applicability to human language, holding over no more than three to four orders of magnitude before hitting a clear break in…

In a valued constraint satisfaction problem (VCSP), the goal is to find an assignment of labels to variables that minimizes a given sum of functions. Each function in the sum depends on a subset of variables, takes values which are rational…

The seminal work of Bencz\'ur and Karger demonstrated cut sparsifiers of near-linear size. Subsequent extensions have yielded sparsifiers for hypergraph cuts and more recently linear codes over Abelian groups. A decade ago, Kogan and…

While self-reflection can enhance language model reliability, its underlying mechanisms remain opaque, with existing analyses often yielding correlation-based insights that fail to generalize. To address this, we introduce…

We define the Witt coindex of a link with non-trivial Alexander polynomial, as a concordance invariant from the Seifert form. We show that it provides an upper bound for the (locally flat) slice Euler characteristic of the link, extending…

We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The…

Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…

A problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in…

Human-annotated textual explanations are becoming increasingly important in Explainable Natural Language Processing. Rationale extraction aims to provide faithful (i.e., reflective of the behavior of the model) and plausible (i.e.,…

We consider a probability measure on cycle-rooted spanning forests (CRSFs) introduced by Kenyon. CRSFs are spanning subgraphs, each connected component of which has a unique cycle; they generalize spanning trees. A generalization of…

The celebrated Stallings' decomposition theorem states that the splitting of a finite index subgroup $H$ of a finitely generated group $G$ as an amalgamated free product or an HNN-extension over a finite group implies the same for $G$. We…

We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…

The spiked model is an important special case of the Wishart ensemble, and a natural generalization of the white Wishart ensemble. Mathematically, it can be defined on three kinds of variables: the real, the complex and the quaternion. For…

In 2000, Babson and Steingr\'{i}msson generalized the notion of permutation patterns to the so-called vincular patterns, and they showed that many Mahonian statistics can be expressed as sums of vincular pattern occurrence statistics. STAT…