We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...
In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific classes of interact ...
We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...
Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...
Translation elongation plays an important role in regulating protein concentrations in the cell, and dysregulation of this process has been linked to several human diseases. In this study, we use data from ribo-seq experiments to model ribosome densities, ...
In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...
New particle formation (NPF) substantially contributes to global cloud condensation nuclei (CCN), and their climate impacts. Individual NPF events are also thought to increase local CCN, cloud droplet number (CDN), and cloud albedo. High resolution simulat ...
Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...
Arctic clouds are sensitive to atmospheric particles since these are sometimes in such low concentrations that clouds cannot always form under supersaturated water vapor conditions. This is especially true in the late summer, when aerosol concentrations ar ...
Throughout history, the pace of knowledge and information sharing has evolved into an unthinkable speed and media. At the end of the XVII century, in Europe, the ideas that would shape the "Age of Enlightenment" were slowly being developed in coffeehouses, ...
