Related papers: Density of group languages in shift spaces
We estimate the $n$-gram entropies of natural language texts in word-length representation and find that these are sensitive to text language and genre. We attribute this sensitivity to changes in the probability distribution of the lengths…
We endow the set of all invariant measures of a topological dynamical system with a metric $\bar{\rho}$, which induces a topology stronger than the the weak$^*$-topology. Then, we study the closedness of ergodic measures within a…
We explore the relationship between subgroups and the possible shifts of finite type (SFTs) that can be defined on the group. In particular, we investigate two group invariants, weak periodicity and strong periodicity, defined via symbolic…
M. Beiglb\"ock, V. Bergelson, and A. Fish proved that if $G$ is a countable amenable group and $A$ and $B$ are subsets of $G$ with positive Banach density, then the product set $AB$ is piecewise syndetic. This means that there is a finite…
We unify and extend some previous results about cubic ergodic averages and sets of positive density in products of groups. This provides a joint generalization of earlier work of the author in the case of two commuting actions of an…
In this paper, we investigate the nature of the density metric, which is employed in the literature on smart specialization and the product space. We find that although density is supposed to capture relatedness between a country's current…
Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem…
In this work, we explore the following question: If two words in a finitely generated free group have identical images as word maps on every finite group, must they be endomorphic to each other? In this regard, we introduce weak profinite…
Constraint languages that arise from finite algebras have recently been the object of study, especially in connection with the Dichotomy Conjecture of Feder and Vardi. An important class of algebras are those that generate congruence…
We present a clustering-based language model using word embeddings for text readability prediction. Presumably, an Euclidean semantic space hypothesis holds true for word embeddings whose training is done by observing word co-occurrences.…
We establish effective versions of Oppenheim's conjecture for generic inhomogeneous quadratic forms. We prove such results for fixed shift vectors and generic quadratic forms. When the shift is rational we prove a counting result which…
Sets of moving entities can form groups which travel together for significant amounts of time. Tracking such groups is an important analysis task in a variety of areas, such as wildlife ecology, urban transport, or sports analysis.…
Current natural language systems designed for multi-step claim validation typically operate in two phases: retrieve a set of relevant premise statements using heuristics (planning), then generate novel conclusions from those statements…
We introduce the task of out-of-order membership to a formal language L, where the letters of a word w are revealed one by one in an adversarial order. The length |w| is known in advance, but the content of w is streamed as pairs (i, w[i]),…
Consider a class of probability distributions which is dense in the space of all probability distributions on $\mathbb{R}^{d}$ with respect to weak convergence, for every $d\in\mathbb{N}$. Then, we construct various explicit classes of…
We investigate inflection structure of a synthetic language using Latin as an example. We construct a bipartite graph in which one group of vertices correspond to dictionary headwords and the other group to inflected forms encountered in a…
We investigate the expressive power of first-order quantifications in the context of monadic second-order logic over pictures. We show that k+1 set quantifier alternations allow to define a picture language that cannot be defined using k…
Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an…
We establish new characterizations of primitive elements and free factors in free groups, which are based on the distributions they induce on finite groups. For every finite group $G$, a word $w$ in the free group on $k$ generators induces…
We study random words in a weighted regular language that achieve the maximal free energy using thermodynamics formalism. In particular, typical words in the language are algorithmically generated which have applications in computer…