arXiv subjects

Sergio R. Souza

Publications and source records attributed to Sergio R. Souza.

16 recordsLinked to original sources

arXiv2025

Tilings of a bounded region of the plane by maximal one-dimensional tiles

We study the tiling of a two-dimensional region of the plane by $K$-cell one-dimensional tiles, or $K$-mers. Unlike previous studies, which typically allowed for one single value of $K$ or sometimes a small assortment of fixed values, here a tiling may concomitantly employ $K$-mers comprising any number $K$ of cells, provided a maximality constraint is satisfied. In essence, this constraint requires each of the $K$-mers in use to be as lengthy as possible, given its surroundings in the resulting tiling. Maximality aims to limit the variety of possible tilings while allowing for interesting behavior in terms of the statistical physical observables of interest. In fact, by introducing an energy function based on cell contacts and parameterizing it appropriately, we have been able to observe relatively unexpected behavior, including the suggestion of phase transitions as the system's temperature evolves.

cond-mat.stat-mech↗

arXiv2025

Energy shifts in predissociating levels of diatomic molecules: The case of N$_2$ (C$''^5Π_u$) and N$_2$(1$^7Σ^+_u$) interacting states

This work presents a perturbative calculation methodology for evaluating the energy shifts and broadening of vibrational energy levels, caused by interactions between bound and unbound dissociative electronic states. The method is validated against previously semiclassical analyzed cases, demonstrating remarkable consistency. We successfully applied this approach to the N$_2$ molecule, which exhibits a strong spin-orbit interaction between the bound C$''^5Π_u$ and the repulsive 1$^7Σ^+_u$ electronic states, around 36 cm$^{-1}$. This interaction constitutes an major pathway for N($^{2}$D) production, important in both excitation and quenching in plasma afterglows. As a result, the maximum absolute shift of 0.15 cm$^{-1}$ was found for the C$''^5Π_u$ ($v$ = 7) and maximum broadening of 0.45 cm$^{-1}$ was calculated for $v$ = 8, demonstrating significant perturbation of the C$''^5Π_u$ by the 1$^7Σ^+_u$ state. The results obtained were compared with direct calculations of the predissociation rates of the C$''^5Π_u$ bound state, showing very good agreement.

physics.atom-ph↗

arXiv2023

Configuration space partitioning in tilings of a bounded region of the plane

Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much of this interest has revolved around fundamental geometrical problems such as minimizing the variety of tile types to be used, and also around important applications in areas such as crystallography as well as others. All these applications are of course confined to finite spatial regions, but in many cases they refer back directly to progress in tiling the whole, unbounded plane. Tilings of bounded regions of the plane have also been actively studied, but in general the additional complications imposed by the boundary conditions tend to constrain progress to mostly indirect results, such as recurrence relations. Here we study the tiling of rectangular regions of the plane by rectangular tiles. The tile types we use are squares, dominoes, and straight tetraminoes. For this set of tile types, not even recurrence relations seem to be available. Our approach is to seek to characterize this complex system through some fundamental physical quantities. We do this on two parallel tracks, one analytical for what seems to be the most complex special case still amenable to such approach, the other based on the Wang-Landau method for state-density estimation. Given a simple energy function based solely on tile contacts, we have found either approach to lead to illuminating depictions of entropy, temperature, and above all partitions of the configuration space. The notion of a configuration, in this context, refers to how many tiles of each type are used. We have found that certain partitions help bind together different aspects of the system in question and conjecture that future applications will benefit from the possibilities they afford.

cond-mat.stat-mech↗

arXiv2020

Interspecies evolutionary dynamics mediated by public goods in bacterial quorum sensing

Bacterial quorum sensing is the communication that takes place between bacteria as they secrete certain molecules into the intercellular medium that later get absorbed by the secreting cells themselves and by others. Depending on cell density, this uptake has the potential to alter gene expression and thereby affect global properties of the community. We consider the case of multiple bacterial species coexisting, referring to each one of them as a genotype and adopting the usual denomination of the molecules they collectively secrete as public goods. A crucial problem in this setting is characterizing the coevolution of genotypes as some of them secrete public goods (and pay the associated metabolic costs) while others do not but may nevertheless benefit from the available public goods. We introduce a network model to describe genotype interaction and evolution when genotype fitness depends on the production and uptake of public goods. The model comprises a random graph to summarize the possible evolutionary pathways the genotypes may take as they interact genetically with one another, and a system of coupled differential equations to characterize the behavior of genotype abundance in time. We study some simple variations of the model analytically and more complex variations computationally. Our results point to a simple trade-off affecting the long-term survival of those genotypes that do produce public goods. This trade-off involves, on the producer side, the impact of producing and that of absorbing the public good. On the non-producer side, it involves the impact of absorbing the public good as well, now compounded by the molecular compatibility between the producer and the non-producer. Depending on how these factors turn out, producers may or may not survive.

q-bio.PE↗

arXiv2018

Co-evolution of the mitotic and meiotic modes of eukaryotic cellular division

The genetic material of a eukaryotic cell comprises both nuclear DNA (ncDNA) and mitochondrial DNA (mtDNA). These differ markedly in several aspects but nevertheless must encode proteins that are compatible with one another. Here we introduce a network model of the hypothetical co-evolution of the two most common modes of cellular division for reproduction: by mitosis (supporting asexual reproduction) and by meiosis (supporting sexual reproduction). Our model is based on a random hypergraph, with two nodes for each possible genotype, each encompassing both ncDNA and mtDNA. One of the nodes is necessarily generated by mitosis occurring at a parent genotype, the other by meiosis occurring at two parent genotypes. A genotype's fitness depends on the compatibility of its ncDNA and mtDNA. The model has two probability parameters, $p$ and $r$, the former accounting for the diversification of ncDNA during meiosis, the latter for the diversification of mtDNA accompanying both meiosis and mitosis. Another parameter, $λ$, is used to regulate the relative rate at which mitosis- and meiosis-generated genotypes are produced. We have found that, even though $p$ and $r$ do affect the existence of evolutionary pathways in the network, the crucial parameter regulating the coexistence of the two modes of cellular division is $λ$. Depending on genotype size, $λ$ can be valued so that either mode of cellular division prevails. Our study is closely related to a recent hypothesis that views the appearance of cellular division by meiosis, as opposed to division by mitosis, as an evolutionary strategy for boosting ncDNA diversification to keep up with that of mtDNA. Our results indicate that this may well have been the case, thus lending support to the first hypothesis in the field to take into account the role of such ubiquitous and essential organelles as mitochondria.

q-bio.PE↗

arXiv2015

Quasispecies dynamics on a network of interacting genotypes and idiotypes: Applications to autoimmunity and immunodeficiency

In spite of their many facets, the phenomena of autoimmunity and immunodeficiency seem to be related to each other through the subtle links connecting retroviral mutation and action to immune response and adaptation. In a previous work, we introduced a network model of how a set of interrelated genotypes (called a quasispecies, in the stationary state) and a set of interrelated idiotypes (an idiotypic network) interact. That model, which does not cover the case of a retroviral quasispecies, was instrumental for the study of quasispecies survival when confronting the immune system and led to the conclusion that, unlike what happens when a quasispecies is left to evolve by itself, letting genotypes mutate too infrequently leads to the destruction of the quasispecies. Here we extend that genotype-idiotype interaction model by the addition of a further parameter ($ν$) to account for the action of retroviruses (i.e., the destruction of idiotypes by genotypes). We give simulation results within a suitable parameter niche, highlighting the issues of quasispecies survival and of the onset of autoimmunity through the appearance of the so-called pathogenic idiotypes. Our main findings refer to how $ν$ and $λ$, a parameter describing the rate at which idiotypes get stimulated, relate to each other. While for $ν>λ$ the quasispecies survives at the expense of weakening the immune system significantly or even destroying it, for $ν<λ$ the fittest genotypes of the quasispecies become mimicked inside the immune system as pathogenic idiotypes. The latter is in agreement with the current understanding of the HIV quasispecies.

q-bio.PE↗

arXiv2013

Quasispecies dynamics on a network of interacting genotypes and idiotypes: Formulation of the model

A quasispecies is the stationary state of a set of interrelated genotypes that evolve according to the usual principles of selection and mutation. Quasispecies studies have invariably concentrated on the possibility of errors during genotype replication and their role in promoting either the survival or the demise of the quasispecies. In a previous work [V. C. Barbosa, R. Donangelo, and S. R. Souza, J. Theor. Biol. 312, 114 (2012)], we introduced a network model of quasispecies dynamics, based on a single probability parameter ($p$) and capable of addressing several plausibility issues of previous models. Here we extend that model by pairing its network with another one aimed at modeling the dynamics of the immune system when confronted with the quasispecies. The new network is based on the idiotypic-network model of immunity and, together with the previous one, constitutes a network model of interacting genotypes and idiotypes. The resulting model requires further parameters and as a consequence leads to a vast phase space. We have focused on a particular niche in which it is possible to observe the trade-offs involved in the quasispecies' survival or destruction. Within this niche, we give simulation results that highlight some key preconditions for quasispecies survival. These include a minimum initial abundance of genotypes relative to that of the idiotypes and a minimum value of $p$. The latter, in particular, is to be contrasted with the stand-alone quasispecies network of our previous work, in which arbitrarily low values of $p$ constitute a guarantee of quasispecies survival.

q-bio.PE↗

arXiv2011

Quasispecies dynamics with network constraints

A quasispecies is a set of interrelated genotypes that have reached a situation of equilibrium while evolving according to the usual Darwinian principles of selection and mutation. Quasispecies studies invariably assume that it is possible for any genotype to mutate into any other, but recent finds indicate that this assumption is not necessarily true. Here we revisit the traditional quasispecies theory by adopting a network structure to constrain the occurrence of mutations. Such structure is governed by a random-graph model, whose single parameter (a probability p) controls both the graph's density and the dynamics of mutation. We contribute two further modifications to the theory, one to account for the fact that different loci in a genotype may be differently susceptible to the occurrence of mutations, the other to allow for a more plausible description of the transition from adaptation to degeneracy of the quasispecies as p is increased. We give analytical and simulation results for the usual case of binary genotypes, assuming the fitness landscape in which a genotype's fitness decays exponentially with its Hamming distance to the wild type. These results support the theory's assertions regarding the adaptation of the quasispecies to the fitness landscape and also its possible demise as a function of p.

q-bio.PE↗

arXiv2010

Early appraisal of the fixation probability in directed networks

In evolutionary dynamics, the probability that a mutation spreads through the whole population, having arisen in a single individual, is known as the fixation probability. In general, it is not possible to find the fixation probability analytically given the mutant's fitness and the topological constraints that govern the spread of the mutation, so one resorts to simulations instead. Depending on the topology in use, a great number of evolutionary steps may be needed in each of the simulation events, particularly in those that end with the population containing mutants only. We introduce two techniques to accelerate the determination of the fixation probability. The first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably. This technique is computationally advantageous for some of the so-called layered networks. The second technique, which is not restricted to layered networks, consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value, and counting that event as having led to a total spread of the mutation. For large populations, and regardless of the network's topology, we demonstrate, both analytically and by means of simulations, that using a threshold of about 100 mutants leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full-fledged simulations. We have observed speedups of two orders of magnitude for layered networks with 10000 nodes.

q-bio.PE↗

arXiv2008

Network growth for enhanced natural selection

Natural selection and random drift are competing phenomena for explaining the evolution of populations. Combining a highly fit mutant with a population structure that improves the odds that the mutant spreads through the whole population tips the balance in favor of natural selection. The probability that the spread occurs, known as the fixation probability, depends heavily on how the population is structured. Certain topologies, albeit highly artificially contrived, have been shown to exist that favor fixation. We introduce a randomized mechanism for network growth that is loosely inspired in some of these topologies' key properties and demonstrate, through simulations, that it is capable of giving rise to structured populations for which the fixation probability significantly surpasses that of an unstructured population. This discovery provides important support to the notion that natural selection can be enhanced over random drift in naturally occurring population structures.

q-bio.PE↗

arXiv2007

Emergence of scale-free behavior in networks from limited-horizon linking and cost trade-offs

We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are not too far apart on the sphere may be considered for being joined by an edge. Given two such nodes, the joining occurs only if the gain of doing it surpasses the cost. Our model is based on a multiplicative parameter lambda that regulates, in a function of node degrees, the maximum geodesic distance that is allowed between nodes for them to be considered for joining. For n nodes distributed uniformly on the sphere, and for lambda*sqrt(n) within limits that depend on cost-related parameters, we have found that our growth mechanism gives rise to power-law distributions of node degree that are invariant for constant lambda*sqrt(n). We also study connectivity- and distance-related properties of the networks.

cond-mat.stat-mech↗

arXiv2005

Emergence of scale-free networks from local connectivity and communication trade-offs

We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the addition of edges. A new edge is added between two nodes depending on the trade-off between a gain and a cost function of local connectivity and communication properties. We report on simulation results that indicate the appearance of power-law distributions of node degrees for selected parameter combinations.

cond-mat.stat-mech↗

arXiv2003

Directed cycles and related structures in random graphs: II--Dynamic properties

We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity at all times and another that allows the appearance of nontrivial directed cycles, we provide analytic and simulation results related to the distributions of degrees. Within the latter strategy, in particular, we investigate the appearance and behavior of the strong components that were our subject in the first part of this study.

cond-mat.stat-mech↗

arXiv2003

Directed cycles and related structures in random graphs: I- Static properties

We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component, called cycle components and knots, which are important in random networks that represent certain computational systems.

cond-mat↗

arXiv2000

Physics of Fashion Fluctuations

We consider a market where many agents trade many different types of products with each other. We model development of collective modes in this market, and quantify these by fluctuations that scale with time with a Hurst exponent of about 0.7. We demonstrate that individual products in the model occationally become globally accepted means of exchange, and simultaneously become very actively traded. Thus collective features similar to money spontaneously emerge, without any a priori reason.

cond-mat↗

arXiv2000

Modelling an Imperfect Market

We propose a simple market model where agents trade different types of products with each other by using money, relying only on local information. Value fluctuations of single products, combined with the condition of maximum profit in transactions, readily lead to persistent fluctuations in the wealth of individual agents.

cond-mat↗