Maximum Estrada Index of Bicyclic Graphs

Let $G$ be a simple graph of order $n$, let $\lambda_1(G),\lambda_2(G),...,\lambda_n(G)$ be the eigenvalues of the adjacency matrix of $G$. The Esrada index of $G$ is defined as $EE(G)=\sum_{i=1}^{n}e^{\lambda_i(G)}$. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order

Fractional-order susceptible-infected model: definition and applications to the study of COVID-19 main protease

We propose a model for the transmission of perturbations across the amino acids of a protein represented as an interaction network. The dynamics consists of a Susceptible-Infected (SI) model based on the Caputo fractional-order derivative. We find an upper bound to the analytical solution of this model which represents the worse-case scenario on the propagation of perturbations across a protein residue network. This upper bound is expressed in terms of Mittag-Leffler functions of the adjacency matrix of the network of inter-amino acids interactions. We then apply this model to the analysis of the propagation of perturbations produced by inhibitors of the main protease of SARS CoV-2. We find that the perturbations produced by strong inhibitors of the protease are propagated far away from the binding site, confirming the long-range nature of intra-protein communication. On the contrary, the weakest inhibitors only transmit their perturbations across a close environment around the binding site. These findings may help to the design of drug candidates against this new coronavirus.Comment: 21 pages, 2 figure

Communicability in temporal networks

A first-principles approach to quantify the communicability between pairs of nodes in temporal networks is proposed. It corresponds to the imaginary-time propagator of a quantum random walk in the temporal network, which accounts for unique structural and temporal characteristics of both streaming and nonstreaming temporal networks. The influence of the system's temperature on the perdurability of information and how the communicability identifies patterns of communication hidden in the temporal and topological structure of the networks are also studied for synthetic and real-world systems

Structural patterns in complex networks through spectral analysis

The study of some structural properties of networks is introduced from a graph spectral perspective. First, subgraph centrality of nodes is defined and used to classify essential proteins in a proteomic map. This index is then used to produce a method that allows the identification of superhomogeneous networks. At the same time this method classify non-homogeneous network into three universal classes of structure. We give examples of these classes from networks in different real-world scenarios. Finally, a communicability function is studied and showed as an alternative for defining communities in complex networks. Using this approach a community is unambiguously defined and an algorithm for its identification is proposed and exemplified in a real-world network

Crime and punishment: An introductory analysis in a noncooperative framework

The purpose of this paper is twofold. First, it seeks to provide the unsophisticated reader with an introduction to modelling issues of crime and punishment; and, second, it seeks to introduce a noncooperative analytical framework as the basic modelling technique to analyze issues of crime and punishment. To those purposes, I introduce a simple model from which important policy recommendations follow from the noncooperative interaction between criminals and the rest of society

Insider trading: regulation, securities markets, and welfare under risk aversion

I analyze in this paper the impact of insider trading regulation (ITR) on a securities market and on social welfare. I argue below that the imposition of ITR forces a reallocation of wealth and risk that decreases social welfare. Three reasons explain this resulto First, ITR increases the volatility of securities prices, thus making the market more risky; second, it worsens the risk sharing among investors; and, third, it diverts resources from the productive sector of the economy. Further, although I formally establish conditions under which ITR makes society better off, largue that those conditions cannot be used to justify the imposition of this regulation

Communicability Angles Reveal Critical Edges for Network Consensus Dynamics

We consider the question of determining how the topological structure influences a consensus dynamical process taking place on a network. By considering a large dataset of real-world networks we first determine that the removal of edges according to their communicability angle -an angle between position vectors of the nodes in an Euclidean communicability space- increases the average time of consensus by a factor of 5.68 in real-world networks. The edge betweenness centrality also identifies -in a smaller proportion- those critical edges for the consensus dynamics, i.e., its removal increases the time of consensus by a factor of 3.70. We justify theoretically these findings on the basis of the role played by the algebraic connectivity and the isoperimetric number of networks on the dynamical process studied, and their connections with the properties mentioned before. Finally, we study the role played by global topological parameters of networks on the consensus dynamics. We determine that the network density and the average distance-sum -an analogous of the node degree for shortest-path distances, account for more than 80% of the variance of the average time of consensus in the real-world networks studied.Comment: 15 pages, 2 figure

The power to tax: a lecture of Hayek

This article describes the argumentative structure of Hayek on the relationship between power to tax and redistribution. It is observed throughout its work giving special attention to two works: The Constitution of Liberty (1959) and Law, Legislation and Liberty, vol3; The Political Order of Free People, 1979) Hayek describes one of the arguments most complete information bout SFP progressive tax systems (progressive tax). According to the author the history of the tax progressive system, works against such a tax model and deploys a variety of arguments in his favorite spot by critics: liberal democracy.Power to Tax, Redistribution, Government, Progressive Tax, Democracy, Hayek