Related papers: Higher-Order Autocorrelations on Finite Abelian Gr…
The modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and ask for the optimal value of one of them while…
I discuss a family of statistical-mechanics models in which (some classes of) elements of a finite group $G$ occupy the (directed) edges of a lattice; the product around any plaquette is constrained to be the group identity $e$. Such a…
The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to…
There are distributed graph algorithms for finding maximal matchings and maximal independent sets in $O(\Delta + \log^* n)$ communication rounds; here $n$ is the number of nodes and $\Delta$ is the maximum degree. The lower bound by Linial…
The existing algorithm to compute and verify the automata associated with an automatic group deals only with the subclass of shortlex automatic groups. This paper describes the extension of the algorithm to deal with automatic groups…
Autocorrelation is a defining characteristic of time-series data, where each observation is statistically dependent on its predecessors. In the context of deep time-series forecasting, autocorrelation arises in both the input history and…
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…
Gathering training data is a key step of any supervised learning task, and it is both critical and expensive. Critical, because the quantity and quality of the training data has a high impact on the performance of the learned function.…
Divergences are fundamental to the information criteria that underpin most signal processing algorithms. The alpha-beta family of divergences, designed for non-negative data, offers a versatile framework that parameterizes and continuously…
Learning-augmented algorithms have been attracting increasing interest, but have only recently been considered in the setting of explorable uncertainty where precise values of uncertain input elements can be obtained by a query and the goal…
Let $\varphi:V\times V\to W$ be a bilinear map of finite vector spaces $V$ and $W$ over a finite field $\mathbb{F}_q$. We present asymptotic bounds on the number of isomorphism classes of bilinear maps under the natural action of…
Correlation clustering is a widely used technique in unsupervised machine learning. Motivated by applications where individual privacy is a concern, we initiate the study of differentially private correlation clustering. We propose an…
Let $ x $ be an element of a finite group $ G $ and denote the order of $ x $ by $ \mathrm{ord}(x) $. We consider a finite group $ G $ such that $ \gcd(\mathrm{ord}(x),\mathrm{ord}(y))\leqslant 2 $ for any two vanishing elements $ x $ and $…
Quantum control is necessary for a variety of modern quantum technologies as it allows to optimally manipulate quantum systems. An important problem in quantum control is to establish whether the control objective functional has trapping…
Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the…
This work describes the implementation and application of a correlation determination method based on Self Organizing Maps and Bayesian Inference (SOMBI). SOMBI aims to automatically identify relations between different observed parameters…
Out-of-time-order correlators (OTOCs) are central probes of quantum scrambling, and their generalizations have recently become key primitives for both benchmarking quantum advantage and learning the structure of Hamiltonians. Yet their…
The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of…
Higher-order information theory has become a rapidly growing toolkit in computational neuroscience, motivated by the idea that multivariate dependencies can reveal aspects of neural computation and communication that are invisible to…
The power graph of a group $G$, denoted as $P(G)$, constitutes a simple undirected graph characterized by its vertex set $G$. Specifically, vertices $a,b$ exhibit adjacency exclusively if $a$ belongs to the cyclic subgroup generated by $b$…