The size distribution of cities: a kinetic explanation

We present a kinetic approach to the formation of urban agglomerations which is based on simple rules of immigration and emigration. In most cases, the Boltzmann-type kinetic description allows to obtain, within an asymptotic procedure, a Fokker--Planck equation with variable coefficients of diffusion and drift, which describes the evolution in time of some probability density of the city size. It is shown that, in dependence of the microscopic rules of migration, the equilibrium density can follow both a power law for large values of the size variable, which contains as particular case a Zipf's law behavior, and a lognormal law for middle and low values of the size variable. In particular, connections between the value of Pareto index of the power law at equilibrium and the disposal of the population to emigration are outlined. The theoretical findings are tested with recent data of the populations of Italy and Switzerland

On the Separation of Topology-Free Rank Inequalities for the Max Stable Set Problem

In the context of finding the largest stable set of a graph, rank inequalities prescribe that a stable set can contain, from any induced subgraph of the original graph, at most as many vertices as the stability number of the former. Although these inequalities subsume many of the valid inequalities known for the problem, their exact separation has only been investigated in few special cases obtained by restricting the induced subgraph to a specific topology. In this work, we propose a different approach in which, rather than imposing topological restrictions on the induced subgraph, we assume the right-hand side of the inequality to be fixed to a given (but arbitrary) constant. We then study the arising separation problem, which corresponds to the problem of finding a maximum weight subgraph with a bounded stability number. After proving its hardness and giving some insights on its polyhedral structure, we propose an exact branch-and-cut method for its solution. Computational results show that the separation of topology-free rank inequalities with a fixed right-hand side yields a substantial improvement over the bound provided by the fractional clique polytope (which is obtained with rank inequalities where the induced subgraph is restricted to a clique), often better than that obtained with Lovasz's Theta function via semidefmite programming

Sekcijas "Latvijas uzņēmumu konkurētspēja ārējos tirgos (EKOSOC VPP 5.2.1)" Ekonomikas un vadības fakultātē (19. februāris, 2016): Referātu tēzes

A fundamental and computationally challenging optimization task in wireless networks is to maximize the number of simultaneous transmissions, subject to signal-to-noise-and-interference ratio (SINR) requirements at the receivers. The conventional approach guaranteeing global optimality is to solve an integer programming model with explicit SINR constraints. These constraints are however numerically very difficult. We develop a new integer programming algorithm based on a much more effective representation of the SINR constraints. Computational experiments demonstrate that the new approach performs significantly better in proving optimality.©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Antonio Capone, Lei Chen, Stefano Gualandi and Di Yuan, A New Computational Approach for Maximum Link Activation in Wireless Networks under the SINR Model, 2011, IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, (10), 5, 1368-1372. http://dx.doi.org/10.1109/TWC.2011.030311.10077

Analytical Validation of Two Assays for Equine Ceruloplasmin Ferroxidase Activity Assessment

: Ceruloplasmin (Cp) assessment in biological samples exploits the oxidase activity of this enzyme against several substrates, such as p-phenylenediamine (p-P), o-dianisidine (o-D) and, most recently, ammonium iron(II) sulfate (AIS). Once developed in humans, these assays are often used in veterinary medicine without appropriately optimizing in the animal species of interest. In this study, two assays using AIS and o-D as substrates have been compared and validated for Cp oxidase activity assessment in horse's plasma. The optimization of the assays was performed mainly by varying the buffer pH as well as the buffer and the substrate molar concentration. Under the best analytical conditions obtained, the horse blood serum samples were treated with sodium azide, a potent Cp inhibitor. In the o-D assay, 500 µM sodium azide treatment completely inhibits the enzymatic activity of Cp, whereas, using the AIS assay, a residual analytical signal was still present even at the highest (2000 µM) sodium azide concentration. Even though the analytical values obtained from these methods are well correlated, the enzymatic activity values significantly differ when expressed in Units L-1. A disagreement between these assays has also been detected with the Bland-Altman plot, showing a progressive discrepancy between methods with increasing analytical values

TEspeX: consensus-specific quantification of transposable element expression preventing biases from exonized fragments

Summary: Transposable elements (TEs) play key roles in crucial biological pathways. Therefore, several tools enabling the quantification of their expression were recently developed. However, many of the existing tools lack the capability to distinguish between the transcription of autonomously expressed TEs and TE fragments embedded in canonical coding/non-coding non-TE transcripts. Consequently, an apparent change in the expression of a given TE may simply reflect the variation in the expression of the transcripts containing TE-derived sequences. To overcome this issue, we have developed TEspeX, a pipeline for the quantification of TE expression at the consensus level. TEspeX uses Illumina RNA-seq short reads to quantify TE expression avoiding counting reads deriving from inactive TE fragments embedded in canonical transcripts. Availability and implementation: The tool is implemented in python3, distributed under the GNU General Public License (GPL) and available on Github at https://github.com/fansalon/TEspeX (Zenodo URL: https://doi.org/10.5281/zenodo.6800331). Supplementary information: Supplementary data are available at Bioinformatics online

The Equivalence of Fourier-based and Wasserstein Metrics on Imaging Problems

We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the original one, the new Fourier-based metrics are well-defined also for probability distributions with different centers of mass, and for discrete probability measures supported over a regular grid. Among other properties, it is shown that, in the discrete setting, these new Fourier-based metrics are equivalent either to the Euclidean-Wasserstein distance $W_2$, or to the Kantorovich-Wasserstein distance $W_1$, with explicit constants of equivalence. Numerical results then show that in benchmark problems of image processing, Fourier metrics provide a better runtime with respect to Wasserstein ones.Comment: 18 pages, 2 figures, 1 tabl