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Ara\'ujo, Kinyon and Konieczny (2011) pose several problems concerning the construction of arbitrary commuting graphs of semigroups. We observe that every star-free graph is the commuting graph of some semigroup. Consequently, we suggest…
Creating a complex work of art like music necessitates profound creativity. With recent advancements in deep learning and powerful models such as transformers, there has been huge progress in automatic music generation. In an accompaniment…
We present a new set of generators for unitary maps over \otimes^n(C^2) which differs from the traditional rotation-based generating set in that it uses a single-parameter family of 1-qubit unitaries J(a), together with a single 2-qubit…
We propose a natural, bivariate, generalization of the nonsingular similarity relations considered by T. Fine. We also provide an enumeration formulae and a generating tree for those relations. The latter allow us to give a new bijection…
Deep generative neural networks have proven effective at both conditional and unconditional modeling of complex data distributions. Conditional generation enables interactive control, but creating new controls often requires expensive…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
In 2021, Gupta and Suzumura proposed a novel algorithm for enumerating all bounded-length simple cycles in directed graphs. In this work, we present concrete examples demonstrating that the proposed algorithm fails to enumerate certain…
In this work, we study the generalized sorting problem, where we are given a set of $n$ elements to be sorted, but only a subset of all possible pairwise element comparisons is allowed. We look at the problem from the perspective of the…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
An algorithm for the generation of shuttling sequences is necessary for the operation of a linear segmented ion-trap quantum computer. The present work provides an implementation of an algorithm that produces sequences proved to be optimal…
In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we…
Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
Here, we present a family of time series with a simple growth constraint. This family can be the basis of a model to apply to emerging computation in business and micro-economy where global functions can be expressed from local rules. We…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
Humans can only interact with part of the surrounding environment due to biological restrictions. Therefore, we learn to reason the spatial relationships across a series of observations to piece together the surrounding environment.…
Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A group $G$ is left-orderable if and only if $G \times…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
We devise constant-factor approximation algorithms for finding as many disjoint cycles as possible from a certain family of cycles in a given planar or bounded-genus graph. Here disjoint can mean vertex-disjoint or edge-disjoint, and the…
A constructive method is provided that outputs a directed graph which is named a broken crown graph, containing $5n-9$ vertices and $k$ Hamiltonian cycles for any choice of integers $n \geq k \geq 4$. The construction is not designed to be…