Marcus A. M. de Aguiar

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• Doctor of Philosophy
• Professor (Full) at State University of Campinas (UNICAMP)

Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible functional forms, depending on how exactly the bodies are coupled. Which of these forms is better suited to descri...

The process of speciation, where an ancestral species divides in two or more new species, involves several geographic, environmental and genetic components that interact in a complex way. Understanding all these elements at once is challenging and simple models can help unveiling the role of each factor separately. The Derrida-Higgs model describes...

Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, and cardiac cells) or artificial (like metronomes, power grids, and Josephson junctions). The Kuramoto model provides a simple description of these systems and has been useful in the...

Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson junctions). The Kuramoto model provides a simple description of these systems and has been useful in their mathe...

This paper presents a conjecture on the regularized incomplete beta function in the context of majority decision systems modeled through a voter framework. We examine a network where voters interact, with some voters fixed in their decisions while others are free to change their states based on the influence of their neighbors. We demonstrate that...

Swarmalators are oscillators that swarm through space as they synchronize in time. Introduced a few years ago to model many systems that mix synchrony with self-assembly, they remain poorly understood theoretically. Here, we obtain the first analytic results on swarmalators moving in two spatial dimensions by introducing a simplified model where th...

Mitochondrial function relies on the coordinated expression of mitochondrial and nuclear genes, exhibiting remarkable resilience despite high mitochondrial mutation rates. The nuclear compensation mechanism suggests deleterious mitochondrial alleles drive compensatory nuclear mutations to preserve mito-nuclear compatibility. However, prevalence and...

We investigate the role of assortative mating in speciation using the sympatric model of Derrida and Higgs. The model explores the idea that genetic differences create incompatibilities between individuals, preventing mating if the number of such differences is too large. Speciation, however, only happens in this mating system if the number of gene...

We generalize the Kuramoto model by interpreting the N variables on the unit circle as eigenvalues of a N-dimensional unitary matrix U in three versions: general unitary, symmetric unitary, and special orthogonal. The time evolution is generated by N2 coupled differential equations for the matrix elements of U, and synchronization happens when U ev...

We generalize the Kuramoto model by interpreting the $N$ variables on the unit circle as eigenvalues of a $N$-dimensional unitary matrix $U$, in three versions: general unitary, symmetric unitary and special orthogonal. The time evolution is generated by $N^2$ coupled differential equations for the matrix elements of $U$, and synchronization happen...

A dinâmica não-linear não é um tema costumeiramente tratado em cursos de graduação em física. No entanto, sua importância dentro da mecânica clássica e da teoria geral de sistemas dinâmicos é inquestionável. Neste trabalho mostramos que esse assunto pode ser inserido na grade de um curso introdutório de mecânica clássica sem a necessidade de se des...

Nas populações de lagartos Uta stansburiana ocorre um notável polimorfismo de coloração nas gargantas, com tons de laranja, amarelo e azul. Esses fenótipos são determinados por dois alelos que correspondem, cada um, a uma das possíveis cores e seguem uma relação de dominância. Dois modelos, um não espacial e outro espacial, foram desenvolvidos para...

Non-linear dynamics is not a usually covered topic in undergraduate physics courses. However, its importance within classical mechanics and the general theory of dynamical systems is unquestionable. In this work we show that this subject can be included in the schedule of an introductory classical mechanics course without the need to develop a robu...

Synchronization is observed in many natural systems, with examples ranging from neuronal activation to walking pedestrians. The models proposed by Winfree and Kuramoto stand as the classic frameworks for investigating these phenomena. The Kuramoto model, in particular, has been extended in different ways since its original formulation to account fo...

The Kuramoto model, describing the synchronization dynamics of coupled oscillators, has been generalized in many ways over the past years. One recent extension of the model replaces the oscillators, originally characterized by a single phase, by particles with \(D-1\) internal phases, represented by a point on the surface of the unit D-sphere. Part...

The study of higher order interactions in the dynamics of Kuramoto oscillators has been a topic of intense recent research. Arguments based on dimensional reduction using the Ott-Antonsen ansatz show that such interactions usually facilitate synchronization, giving rise to bi-stability and hysteresis. Here we show that three body interactions shift...

Similarly to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possess...

Mitochondrial function relies on the coordinated expression of mitochondrial and nuclear genes, exhibiting remarkable resilience regardless the susceptibility of mitochondrial DNA (mtDNA) to accumulate harmful mutations. A suggested mechanism for preserving this mito-nuclear compatibility is the nuclear compensation, where deleterious mitochondrial...

Similar to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possessin...

Geographic barriers can come and go depending on natural conditions. These fluctuations cause population cycles of expansion and contraction, introducing intermittent migrations that may not hinder speciation but rather promote diversification. Here, we study a neutral two-island speciation model with intermittent migration driven by sea-level fluc...

The multidimensional Kuramoto model describes the synchronization dynamics of particles moving on the surface of D-dimensional spheres, generalizing the original model where particles were characterized by a single phase. In this setup, particles are more easily represented by D-dimensional unit vectors than by D − 1 spherical angles, allowing for...

Poster presented at Conference on Complex Systems 2023

Swarmalators are phase oscillators that cluster in space, like fireflies flashing in a swarm to attract mates. Interactions between particles, which tend to synchronize their phases and align their motion, decrease with the distance and phase difference between them, coupling the spatial and phase dynamics. In this work, we explore the effects of i...

The Kuramoto model, describing the synchronization dynamics of coupled oscillators, has been generalized in many ways over the past years. One recent extension of the model replaces the oscillators, originally characterized by a single phase, by particles with D-1 internal phases, represented by a point on the surface of the unit D-sphere. Particle...

Swarmalators are phase oscillators that cluster in space, like fireflies flashing on a swarm to attract mates. Interactions between particles, which tend to synchronize their phases and align their motion, decrease with the distance and phase difference between them, coupling the spatial and phase dynamics. In this work, we explore the effects of d...

Indirect effects shape many aspects of our day to day life. While in social networks indirect effects drive our opinion and behaviour, in economical networks they affect the interdependence among global markets, and in contact networks they drive how contagious diseases spread. In this study we show that indirect effects can also shape one of the m...

Geographic barriers prevent migration between populations, thereby facilitating speciation through allopatry. However, these barriers can exhibit dynamic behavior in nature, promoting cycles of expansion and contraction of populations. Such oscillations cause temporal variations in migration that do not necessarily prevent speciation; on the contra...

The Kuramoto model describes how coupled oscillators synchronize their phases as the intensity of the coupling increases past a threshold. The model was recently extended by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit vector; fo...

Mitochondrial and nuclear genomes must be co-adapted to ensure proper cellular respiration and energy production. Mito-nuclear incompatibility reduces individual fitness and induces hybrid infertility, which can drive reproductive barriers and speciation. Here, we develop a birth–death model for evolution in spatially extended populations under sel...

The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a frustrated version that resulted in dynamic behavior of the order parameter, even when the average natural frequency of the oscillators is zero....

Evolution is usually pictured as a tree where ancient species branch into new ones and eventually disappear. In this simplified view, the balance between speciation and extinction fully determines the diversity of life. Hybridization, however, introduces another level of complexity, allowing neighboring branches of the tree to interact, mixing thei...

Geographic isolation is a central mechanism of speciation, but perfect isolation of populations is rare. Although speciation can be hindered if gene flow is large, intermediate levels of migration can enhance speciation by introducing genetic novelty in the semi‐isolated populations or founding small communities of migrants. Here we consider a two‐...

The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a {\it frustrated} version that resulted in dynamic behavior of the order parameter, even when the average natural frequency of the oscillators is...

Geographic isolation is a central mechanism of speciation, but perfect isolation of populations is rare. Although speciation can be hindered if gene flow is large, intermediate levels of migration can enhance speciation by introducing genetic novelty in the semi-isolated populations or founding small communities of migrants. Here we consider a two...

Micro-evolutionary processes acting in populations and communities ultimately produce macro-evolutionary patterns. However, current models of species life histories -- including processes of speciation, persistence, hybridization, and eventual extinction -- rarely connect these two time scales. This leaves us with a limited theoretical understandin...

Kuramoto’s original model describes the dynamics and synchronization behavior of a set of interacting oscillators represented by their phases. The system can also be pictured as a set of particles moving on a circle in two dimensions, which allows a direct generalization to particles moving on the surface of higher dimensional spheres. One of the k...

Kuramoto's original model describes the dynamics and synchronization behavior of a set of interacting oscillators represented by their phases. The system can also be pictured as a set of particles moving on a circle in two dimensions, which allows a direct generalization to particles moving on the surface of higher dimensional spheres. One of the k...

Mutation and drift play opposite roles in genetics. While mutation creates diversity, drift can cause gene variants to disappear, especially when they are rare. In the absence of natural selection and migration, the balance between the drift and mutation in a well-mixed population defines its diversity. The Moran model captures the effects of these...

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 syn...

Although traditional models of epidemic spreading focus on the number of infected, susceptible and recovered individuals, a lot of attention has been devoted to integrate epidemic models with population genetics. Here we develop an individual-based model for epidemic spreading on networks in which viruses are explicitly represented by finite chains...

Evolution is usually pictured as a tree where ancient species branch into new ones and eventually disappear. In this simplified view, the balance between speciation and extinction fully determines the diversity of life. Hybridization, how-ever, introduces another level of complexity, allowing neighboring branches of the tree to interact, mixing the...

Although traditional models of epidemic spreading focus on the number of infected, susceptible and recovered individuals, a lot of attention has been devoted to integrate epidemic models with population genetics. Here we develop an individual-based model for epidemic spreading on networks in which viruses are explicitly represented by finite chains...

Mutation and drift play opposite roles in genetics. While mutation creates diversity, drift can cause gene variants to disappear, especially when they are rare. In the absence of natural selection and migration, the balance between the drift and mutation in a well-mixed population defines its diversity. The Moran model captures the effects of these...

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 syn...

The International Conference on Complex Systems (ICCS) offers a unique interdisciplinary venue for researchers from the physical and biological sciences, social sciences, psychology and cognitive science, engineering, medicine, human systems, and global systems. This proceedings volume gathers selected papers from the conference. The New England C...

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 nucl...

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....

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 associ...

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...

The shape of a phylogenetic tree is defined by the sequence of speciation events, represented by its branching points, and extinctions, represented by branch interruptions. In a neutral scenario of parapatry and isolation by distance, species tend to branch off the original population one after the other, leading to highly unbalanced trees. In this...

The complexity of an ecological community can be distilled into a network, where diverse interactions connect species in a web of dependencies. Species interact directly with each other and indirectly through environmental effects, however to our knowledge the role of these ecosystem engineers has not been considered in ecological network models. H...

Mitochondrial genetic material (mtDNA) is widely used for phylogenetic reconstruction and as a barcode for species identification. The utility of mtDNA in these contexts derives from its particular molecular properties, including its high evolutionary rate, uniparental inheritance, and small size. But mtDNA may also play a fundamental role in speci...

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....

Biodiversity loss is a hallmark of our times, but predicting its consequences is challenging. Ecological interactions form complex networks with multiple direct and indirect paths through which the impacts of an extinction may propagate. Here we show that accounting for these multiple paths connecting species is necessary to predict how extinctions...

Swarmalators are particles that exhibit coordinated motion and, at the same time, synchronize their intrinsic behavior, represented by internal phases. Here, we study the effects produced by an external periodic stimulus over a system of swarmalators that move in two dimensions. The system represents, for example, a swarm of fireflies in the presen...

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 n...

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 n...

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 int...

The structure of ecological interactions is commonly understood through analyses of interaction networks. However, these analyses may be sensitive to sampling biases with respect to both the interactors (the nodes of the network) and interactions (the links between nodes), because the detectability of species and their interactions is highly hetero...

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 ex...

The spatial distribution of populations can influence the evolutionary outcome of species inter- actions. The variation in direction and strength of selection across local communities creates geographic selection mosaics that, when combined with gene flow and genomic processes such as genome duplication or hybridization, can fuel ongoing coevolutio...

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...

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 eq...

Phylogenetic trees are representations of evolutionary relationships among species and contain signatures of the processes responsible for the speciation events they display. Inferring processes from tree properties, however, is challenging. To address this problem we analysed a spatially-explicit model of speciation where genome size and mating ra...

Phylogenetic trees are representations of evolutionary relationships among species and contain signatures of the processes responsible for the speciation events they display. Inferring processes from tree properties, however, is challenging. To address this problem we analysed a spatially-explicit model of speciation where genome size and mating ra...

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 done to connect microevolutionary processes with macroevolutionary patterns. Knowledge of the evolutionary history allows the study of pattern...

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), because the detectability of species and their interactions is highly heterogeneous. Thes...

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 eq...

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...

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...

Social influence plays an important role in human behavior and decisions. Sources of influence can be divided as 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 experimen...

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....

Phylogenetic trees are systematic tools to describe relatedness among species. The inference of biological trees aims to find the best phylogenetic tree that reconstructs the evolution of a group of species. Computer models that simulate the speciation process can track population dynamics and record information about genealogic relationships. In t...

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 e...

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 e...

According to apparent competition theory, the co-occurrence of two species that share the same predators appears to affect each other's population growth and abundance. However, due to habitat loss and over-hunting, top predators are being made rare worldwide. Considering that apparent competitors share similar resources, we would expect the absenc...

Interspecific interactions are affected by community context and, as a consequence, show spatial variation in magnitude and sign. The selective forces imposed by interactions at the mutualism-antagonism interface are a consequence of the traits involved and their matching between species. If mutualistic and antagonistic communities are linked by ge...

Social influence plays an important role in human behavior and decisions. Sources of influence can be divided as 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 experimen...

Hot spot analysis of social influence: 1920 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....

Hot spot analysis of social influence: 1940 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....

Hot spot analysis of social influence: 1948 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....

Hot spot analysis of social influence: 1952 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....

Hot spot analysis of social influence: 1972 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....

Hotspots of social contagion: 92 years of presidential elections. S1 Movie shows colored maps that reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic. This analysis was perform...

Hot spot analysis of social influence: 1960 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....

Hot spot analysis of social influence: 1984 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....

Hot spot analysis of social influence: 1988 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....

Results of random permutation tests of spatial autocorrelation using Moran’s I statistic. This analysis was performed with a contiguity spatial weight matrix (row normalized) that indicates whether states share a boundary or not. The variable of concern is the social influence index calculated using Eq 7 in the main text. The observed Moran’s I sta...

Testing for a break in the level of social influence using the Mann-Whiney U-test. The Mann—Whitney U-test is a nonparametric test that assesses whether one of two random variables is stochastically larger than the other. Given a time-series of social influence from 1920 to 2012, we define for each election year, y, two samples of social influence:...

Hot spot analysis of social influence: 1924 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....

Hot spot analysis of social influence: 1932 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....

Hot spot analysis of social influence: 1936 US presidential election. The colored areas reflect the significance (p-value) of local concentration of social influence for each state. The p-values for each state are derived from a random permutation test of local clustering using the Getis-Ord Local Gi* statistic (see Fig 5 in main text for details)....