arXiv subjects

Marcus A. M. de Aguiar

Publications and source records attributed to Marcus A. M. de Aguiar.

At least 55 records · Page 3Linked to original sources

arXiv2021

Complexity reduction in the 3D Kuramoto model

The dynamics of large systems of coupled oscillators is a subject of increasing importance with prominent applications in several areas such as physics and biology. The Kuramoto model, where a set of oscillators move around a circle representing their phases, is a paradigm in this field, exhibiting a continuous transition between disordered and synchronous motion. Reinterpreting the oscillators as rotating unit vectors, the model was extended to allow vectors to move on the surface of D-dimensional spheres, with $D=2$ corresponding to the original model. It was shown that the transition to synchronous dynamics was discontinuous for odd D, raising a lot of interest. Inspired by results in 2D, Ott et al proposed an ansatz for density function describing the oscillators and derived equations for the ansatz parameters, effectively reducing the dimensionality of the system. Here we take a different approach for the 3D system and construct an ansatz based on spherical harmonics decomposition of the distribution function. Our result differs significantly from that proposed in Ott's work and leads to similar but simpler equations determining the dynamics of the order parameter. We derive the phase diagram of equilibrium solutions for several distributions of natural frequencies and find excellent agreement with simulations. We also compare the dynamics of the order parameter with numerical simulations and with the previously derived equations, finding good agreement in all cases. We believe our approach can be generalized to higher dimensions and help to achieve complexity reduction in other systems of equations.

nlin.AO↗

arXiv2020

Modeling Mito-nuclear Compatibility and its Role in Species Identification

Mitochondrial genetic material is widely used for phylogenetic reconstruction and as a barcode for species identification. Here we study how mito-nuclear interactions affect the accuracy of species identification by mtDNA, as well as the speciation process itself. We simulate the evolution of a population of individuals who carry a recombining nuclear genome and a mitochondrial genome inherited maternally. We compare a null model fitness landscape that lacks any mito-nuclear interaction against a scenario in which interactions influence fitness. Fitness is assigned to individuals according to their mito-nuclear compatibility, which drives the coevolution of the nuclear and mitochondrial genomes. When the population breaks into distinct species we analyze the accuracy of mtDNA barcode for species identification. Remarkably, we find that species identification by mtDNA is equally accurate in the presence or absence of mito-nuclear coupling and that the success of the DNA barcode derives mainly from population geographical isolation during speciation. Nevertheless, selection imposed by mito-nuclear compatibility influences the diversification process and leaves signatures in the genetic content and spatial distribution of the populations, in three ways: phylogenetic trees are more balanced; clades correlate strongly with the spatial distribution and; there is a substantial increase in the intraspecies mtDNA similarity. We compare the evolutionary patterns observed in our model to empirical data from copepods (\textit{T. californicus}). We find good qualitative agreement in the geographic patterns and the topology of the phylogenetic tree, provided the model includes selection based on mito-nuclear interactions. These results highlight the role of mito-nuclear compatibility in the speciation process and its reconstruction from genetic data.

q-bio.PE↗

arXiv2020

Laplacian Matrices for Extremely Balanced and Unbalanced Phylogenetic Trees

Phylogenetic trees are important tools in the study of evolutionary relationships between species. Measures such as the index of Sackin, Colless, and Total Cophenetic have been extensively used to quantify tree balance, one key property of phylogenies. Recently a new proposal has been introduced, based on the spectrum of the Laplacian matrix associated with the tree. In this work, we calculate the Laplacian matrix analytically for two extreme cases, corresponding to fully balanced and fully unbalanced trees. For maximally balanced trees no closed form for the Laplacian matrix was derived, but we present an algorithm to construct it. We show that Laplacian matrices of fully balanced trees display self-similar patterns that result in highly degenerated eigenvalues. Degeneracy is the main signature of this topology, since it is totally absent in fully unbalanced trees. We also establish some analytical and numerical results about the largest eigenvalue of Laplacian matrices for these topologies.

q-bio.PE↗

arXiv2020

Measuring Tree Balance with Normalized Tree Area

The study of species organization and their clustering by genetic or phenotypic similarity is carried out with the tools of phylogenetic trees. An important structural property of phylogenetic trees is the balance, which measures how taxa are distributed among clades. Tree balance can be measured using indices such as the Sackin ($S$) and the Total Cophenetic ($Φ$), which are based on the distance between nodes of the tree and its root. Here, we propose a new metric for tree balance, $\bar{d}$, the Area per Pair (APP) of the tree, which is a re-scaled version of the so called tree area. We compute $\bar{d}$ for the rooted caterpillar and maximally balanced trees and we also obtain exact formulas for its expected value and variance under the Yule model. The variance of APP for Yule trees has the remarkable property of converging to an asymptotic constant value for large trees. We compare the Sackin, Total Cophenetic and APP indices for hundreds of empirical phylogenies and show that APP represents the observed distribution of tree balances better than the two other metrics.

q-bio.PE↗

arXiv2020

Quantifying the effects of quarantine using an IBM SEIR model on scalefree networks

The COVID-19 pandemic led several countries to resort to social distancing, the only known way to slow down the spread of the virus and keep the health system under control. Here we use an individual based model (IBM) to study how the duration, start date and intensity of quarantine affect the height and position of the peak of the infection curve. We show that stochastic effects, inherent to the model dynamics, lead to variable outcomes for the same set of parameters, making it crucial to compute the probability of each result. To simplify the analysis we divide the outcomes in only two categories, that we call {best and worst scenarios. Although long and intense quarantine is the best way to end the epidemic, it is very hard to implement in practice. Here we show that relatively short and intense quarantine periods can also be very effective in flattening the infection curve and even killing the virus, but the likelihood of such outcomes are low. Long quarantines of relatively low intensity, on the other hand, can delay the infection peak and reduce its size considerably with more than 50% probability, being a more effective policy than complete lockdown for short periods.

q-bio.PE↗

arXiv2020

Sympatric speciation based on pure assortative mating

Although geographic isolation has been shown to play a key role in promoting reproductive isolation, it is now believed that speciation can also happen in sympatry and with considerable gene flow. Here we present a model of sympatric speciation based on assortative mating that does not require a genetic threshold for reproduction, i.e., that does not directly associate genetic differences between individuals with reproductive incompatibilities. In the model individuals mate with the most similar partner in their pool of potential mates, irrespective of how dissimilar it might be. We show that assortativity alone can lead to the formation of clusters of genetically similar individuals. The absence of a minimal genetic similarity for mating implies the constant generation of hybrids and brings up the old problem of species definition. Here, we define species based on clustering of genetically similar individuals but allowing genetic flow among different species. We show that the results obtained with the present model are in good agreement with empirical data, in which different species can still reproduce and generate hybrids.

q-bio.PE↗

arXiv2019

Synchronization and spatial patterns in forced swarmalators

Swarlamators are particles capable of synchronize and swarm. Here we study the effects produced by an external periodic stimulus over a system of swarmalators that move in two dimensions. When the particles are fixed and interact with equal strength (Kuramoto oscillators) their phases tend to synchronize and lock to the external stimulus if its intensity is sufficiently large. Here we show that in a system of swarmalators the force also shifts the phases and angular velocities leading to synchronization with the external frequency. However, the correlation between phase and spatial location decreases with the intensity of the force, going to zero in what appears to be a second order phase transition. In the regime of zero correlation the particles form a static symmetric circular distribution, following a simple model of aggregation. Interestingly, for intermediate values of the force intensity, a different pattern emerges, with the particles splitting in two clusters centered at opposite sides of the stimulus' location, breaking the radial symmetry. The two-cluster pattern is stable and active, with the clusters slowly rotating around the source while exchanging particles.

nlin.PS↗

arXiv2019

Diverse interactions and ecosystem engineering stabilize community assembly

The complexity of an ecological community can be distilled into a network, where diverse interactions connect species in a web of dependencies. Species interact not only with each other but indirectly through environmental effects, however the role of these ecosystem engineers has not yet been considered in models of ecological networks. Here we explore the dynamics of ecosystem assembly, where the colonization and extinction of species within a community depends on the constraints imposed by trophic, service, and engineering dependencies. We show that our assembly model reproduces many key features of ecological systems, such as the role of generalists during assembly, realistic maximum trophic levels, and increased nestedness with higher frequencies of mutualisms. We find that ecosystem engineering has large and nonlinear effects on extinction rates, facilitating robustness by creating niche space, but at the same time increasing the magnitude of extinction cascades. We emphasize the importance of redundancies in engineered effects and show that such redundancy lowers the barriers to colonization, promoting community diversity. Together, our results suggest that ecological engineers may enhance community diversity while increasing persistence by facilitating colonization and limiting competitive exclusion.

q-bio.PE↗

arXiv2019

Modular structure in C. elegans neural network and its response to external localized stimuli

Synchronization plays a key role in information processing in neuronal networks. Response of specific groups of neurons are triggered by external stimuli, such as visual, tactile or olfactory inputs. Neurons, however, can be divided into several categories, such as by physical location, functional role or topological clustering properties. Here we study the response of the electric junction C. elegans network to external stimuli using the partially forced Kuramoto model and applying the force to specific groups of neurons. Stimuli were applied to topological modules, obtained by the ModuLand procedure, to a ganglion, specified by its anatomical localization, and to the functional group composed of all sensory neurons. We found that topological modules do not contain purely anatomical groups or functional classes, corroborating previous results, and that stimulating different classes of neurons lead to very different responses, measured in terms of synchronization and phase velocity correlations. In all cases, however, the modular structure hindered full synchronization, protecting the system from seizures. More importantly, the responses to stimuli applied to topological and functional modules showed pronounced patterns of correlation or anti-correlation with other modules that were not observed when the stimulus was applied to ganglia.

nlin.AO↗

arXiv2018

Global synchronization of partially forced Kuramoto oscillators on Networks

We study the synchronization of Kuramoto oscillators on networks where only a fraction of them is subjected to a periodic external force. When all oscillators receive the external drive the system always synchronize with the periodic force if its intensity is sufficiently large. Our goal is to understand the conditions for global synchronization as a function of the fraction of nodes being forced and how these conditions depend on network topology, strength of internal couplings and intensity of external forcing. Numerical simulations show that the force required to synchronize the network with the external drive increases as the inverse of the fraction of forced nodes. However, for a given coupling strength, synchronization does not occur below a critical fraction, no matter how large is the force. Network topology and properties of the forced nodes also affect the critical force for synchronization. We develop analytical calculations for the critical force for synchronization as a function of the fraction of forced oscillators and for the critical fraction as a function of coupling strength. We also describe the transition from synchronization with the external drive to spontaneous synchronization.

nlin.AO↗

arXiv2018

Opinion Dynamics on Networks under Correlated Disordered External Perturbations

We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal and ordered bimodal distribution states, characterized by an increase in the vote-share variability of the equilibrium distributions. The random heterogeneities in the external perturbations are shown to affect the critical behavior of the network relative to networks without disorder. The size of the shift in the critical behavior essentially depends on the total fluctuation of the external influence disorder. Furthermore, the external perturbation disorder also has the surprising effect of amplifying the expected support of an already biased opinion. We show analytically that the vote-share variability is directly related to the external influence fluctuations. We extend our analysis by considering a fat-tailed multivariate lognormal disorder, and present numerical simulations that confirm our analytical results. Simulations for other network topologies demonstrate the generalizability of our findings. Understanding the dynamic response of complex systems to disordered external perturbations could account for a wide variety of networked systems, from social networks and financial markets to amorphous magnetic spins and population genetics.

physics.soc-ph↗

arXiv2017

Inhibition as a determinant of activity and criticality in dynamical networks

A certain degree of inhibition is a common trait of dynamical networks in nature, ranging from neuronal and biochemical networks, to social and technological networks. We study here the role of inhibition in a representative dynamical network model, characterizing the dynamics of random threshold networks with both excitatory and inhibitory links. Varying the fraction of excitatory links has a strong effect on the network's population activity and its sensitivity to perturbation. The average degree $K$, known to have a strong effect on the dynamics when small, loses its influence on the dynamics as its value increases. Instead, the strength of inhibition is a determinant of dynamics and sensitivity here, allowing for criticality only in a specific corridor of inhibition. This criticality corridor requires that excitation dominates, while the balance region corresponds to maximum sensitivity to perturbation. We develop mean-field approximations of the population activity and sensitivity and find that the network dynamics is independent of degree distribution for high $K$. In a minimal model of an adaptive threshold network we demonstrate how the dynamics remains robust against changes in the topology. This adaptive model can be extended in order to generate networks with a controllable activity distribution and specific topologies.

nlin.AO↗

arXiv2017

Registering the evolutionary history in individual-based models of speciation

Understanding the emergence of biodiversity patterns in nature is a central problem in biology. Theoretical models of speciation have addressed this question in the macroecological scale, but little has been investigated in the macroevolutionary context. Knowledge of the evolutionary history allows the study of patterns underlying the processes considered in these models, revealing their signatures and the role of speciation and extinction in shaping macroevolutionary patterns. In this paper we introduce two algorithms to record the evolutionary history of populations in individual-based models of speciation, from which genealogies and phylogenies can be constructed. The first algorithm relies on saving ancestral-descendant relationships, generating a matrix that contains the times to the most recent common ancestor between all pairs of individuals at every generation (the Most Recent Common Ancestor Time matrix, MRCAT). The second algorithm directly records all speciation and extinction events throughout the evolutionary process, generating a matrix with the true phylogeny of species (the Sequential Speciation and Extinction Events, SSEE). We illustrate the use of these algorithms in a spatially explicit individual-based model of speciation. We compare the trees generated via MRCAT and SSEE algorithms with trees inferred by methods that use only genetic distance among extant species, commonly used in empirical studies and applied here to simulated genetic data. Comparisons between tress are performed with metrics describing the overall topology, branch length distribution and imbalance of trees. We observe that both MRCAT and distance-based trees differ from the true phylogeny, with the first being closer to the true tree than the second.

q-bio.PE↗

arXiv2017

Revealing biases in the sampling of ecological interaction networks

The structure of ecological interactions is commonly understood through analyses of interaction networks. However, these analyses may be sensitive to sampling biases in both the interactors (the nodes of the network) and interactions (the links between nodes). These issues may affect the accuracy of empirically constructed ecological networks. We explore the properties of sampled ecological networks by simulating large-scale ecological networks with predetermined topologies, and sampling them with different mathematical procedures. Several types of modular networks were generated, intended to represent a wide variety of communities that vary in size and types of ecological interactions. We sampled these networks with different sampling designs that may be encountered in field experiments. The observed networks generated by each sampling process were analyzed with respect to number and size of components. We show that the sampling effort needed to estimate underlying network properties depends both on the sampling design and on network topology. Networks with random or scale-free modules require more complete sampling compared to networks whose modules are nested or bipartite. Overall, the structure of nested modules was the easiest to detect, regardless of sampling design. Sampling according to species degree was consistently found to be the most accurate strategy to estimate network structure. Conversely, sampling according to module results in an accurate view of certain modules, but fails to provide a global picture of the underlying network. We recommend that these findings are incorporated into the design of projects aiming to characterize large networks of species interactions in the field, to reduce sampling biases. The software scripts developed to construct and sample networks are provided for further explorations of network structure and comparisons to real interaction data.

q-bio.PE↗

arXiv2017

Speciation in the Derrida-Higgs model with finite genomes and spatial populations

The speciation model proposed by Derrida and Higgs demonstrated that a sexually reproducing population can split into different species in the absence of natural selection or any type of geographic isolation, provided that mating is assortative and the number of genes involved in the process is infinite. Here we revisit this model and simulate it for finite genomes, focusing on the question of how many genes it actually takes to trigger neutral sympatric speciation. We find that, for typical parameters used in the original model, it takes of the order of $10^5$ genes. We compare the results with a similar spatially explicit model where about 100 genes suffice for speciation. We show that when the number of genes is small the species that emerge are strongly segregated in space. For larger number of genes, on the other hand, the spatial structure of the population is less important and the species distribution overlap considerably.

q-bio.PE↗

arXiv2016

Voting Contagion

Social influence plays an important role in human behavior and decisions. The sources of influence can be generally divided into external, which are independent of social context, or as originating from peers, such as family and friends. An important question is how to disentangle the social contagion by peers from external influences. While a variety of experimental and observational studies provided insight into this problem, identifying the extent of social contagion based on large-scale observational data with an unknown network structure remains largely unexplored. By bridging the gap between the large-scale complex systems perspective of collective human dynamics and the detailed approach of the social sciences, we present a parsimonious model of social influence, and apply it to a central topic in political science -- elections and voting behavior. We provide an analytical expression of the county vote-share distribution in a two party system, which is in excellent agreement with 92 years of observed U.S. presidential election data. Analyzing the social influence topography over this period reveals an abrupt transition in the patterns of social contagion -- from low to high levels of social contagion. The results from our analysis reveal robust differences among regions of the United States in terms of their social influence index. In particular, we identify two regions of 'hot' and 'cold spots of social influence, each comprising states that are geographically close. These results suggest that social contagion effects are becoming more instrumental in shaping large scale collective political behavior, which is at the core of democratic societies.

physics.soc-ph↗

arXiv2016

Multiconfigurational quantum propagation with trajectory-guided generalized coherent states

A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability. The approach is illustrated with simple models for interacting bosons trapped in double- and triple-well potentials, most adequately described in terms of SU(2) and SU(3) bosonic coherent states, respectively.

quant-ph↗

arXiv2015

Binary dynamics on star networks under external perturbations

We study a binary dynamical process that is a representation of the voter model with opinion makers. The process models an election with two candidates but can also describe the frequencies of a biallelic gene in a population or atoms with two spin orientations in a magnetic material. The system is represented by a network whose nodes have internal states labeled 0 or 1, and nodes that are connected can influence each other. The network is perturbed by a set of external nodes whose states are fixed in 0 or 1 and that can influence all nodes of the network. The fixed nodes play the role of opinion makers in the voter model, mutation rates in population genetics or temperature in a magnetic material. The quantity of interest is the probability $ρ(m,t)$ that $m$ nodes are in state 1 at time $t$. Here we study this process on star networks and compare the results with those obtained for networks that are fully connected. In both cases a transition from disordered to ordered equilibrium states is observed as the number of external fixed nodes becomes small, but it differs significantly between the two network topologies. For fully connected networks the probability distribution becomes uniform at the critical point, which is independent of the network size. For star networks, on the other hand, the equilibrium distribution $ρ(m)$ splits in two peaks, reflecting the two possible states of the central node. We obtain approximate analytical solutions that hold near the transition and that clarify the role of the central node in the process. We show that the different character of the transition also manifest itself in the magnetization of system, obtained in the limit of large $N$. Finally, extending the analysis to two star networks we compare our results with simulations in scalefree networks, detecting the presence of hubs.

nlin.AO↗