Evolving Weighted Networks to Simulate Epidemics and Lockdowns

Simulating epidemics is vital to understanding their effect on human populations, and developing models to provide insights into epidemic behaviour is a primary goal of this thesis. A generative evolutionary algorithm is used to evolve weighted personal contact networks that represent physical contact between individuals, and thus possible paths of infection during an epidemic. The evolutionary algorithm evolves a list of edge-editing operations applied to an initial graph. Two initial graphs are considered, a ring graph and a power-law graph. Different probabilities of infection and a wide range of weights are considered, which improve performance over other work. Modified edge operations are introduced, which also improve performance. When attempting to match a given epidemic profile, similar results are obtained when using either initial graph, but both improve performance over other work. The impact of different lockdown strategies upon the total number of infections in an epidemic are evaluated for two models of infection: one in which the disease confers permanent immunity, and one in which it does not. The strategies are based upon the proportion of the population infected at a time in order to trigger lockdown, combined with the proportion of interactions removed during lockdown. The population, its interactions, and the relative strengths of those interactions are stored in a weighted contact network, from which edges are removed during lockdown. These edges are selected using an evolutionary algorithm (EA) designed to minimize total infections. Using the EA to select edges significantly reduces total infections in comparison to random selection. In fact, the EA results for the least strict conditions were similar or better to the random results for the most strict conditions, showing that a judicious choice of restrictions during lockdown has the greatest effect on reducing infections. Further, when using the most strict rules a smaller proportion of interactions can be removed to obtain similar or better results in comparison to removing a higher proportion of interactions for less strict rules

Pandemic: A Graph Evolution Story

The Graph Evolution Tool (GET)was built to generate personal contact networks representing who can infect whom within a community. The tool is expanded in order to permit an infection scheme which divides the community into different districts, thus permitting within-district and between-district infections. The evolutionary algorithm comprising GET is expanded upon to simulate communities which include 512 individuals in up to eight districts, initially infecting one person in one district and spreading through a community. The overall goal is to generate communities that will maximize the length of an epidemic. The problem associated with adequately exploring the numerous parameters accompanying evolutionary algorithms is addressed using a point packing and insight from previous work. The Susceptible-Infected-Removed (SIR)model of infection was chosen as it provides a sufficient balance of simplicity and complexity for the problem

Networks in cognitive science

Networks of interconnected nodes have long played a key role in Cognitive Science, from artificial neural networks to spreading activation models of semantic memory. Recently, however, a new Network Science has been developed, providing insights into the emergence of global, system-scale properties in contexts as diverse as the Internet, metabolic reactions, and collaborations among scientists. Today, the inclusion of network theory into Cognitive Sciences, and the expansion of complex-systems science, promises to significantly change the way in which the organization and dynamics of cognitive and behavioral processes are understood. In this paper, we review recent contributions of network theory at different levels and domains within the Cognitive Sciences.Postprint (author's final draft

Aerospace Medicine and Biology: A continuing bibliography with indexes, supplement 178

This bibliography lists 230 reports, articles, and other documents introduced into the NASA scientific and technical information system in February 1978

Synchronization in Complex Networks Under Uncertainty

La sincronització en xarxes és la música dels sistemes complexes. Els ritmes col·lectius que emergeixen de molts oscil·ladors acoblats expliquen el batec constant del cor, els patrons recurrents d'activitat neuronal i la sincronia descentralitzada a les xarxes elèctriques. Els models matemàtics són sòlids i han avançat significativament, especialment en el problema del camp mitjà, on tots els oscil·ladors estan connectats mútuament. Tanmateix, les xarxes reals tenen interaccions complexes que dificulten el tractament analític. Falta un marc general i les soluciones existents en caixes negres numèriques i espectrals dificulten la interpretació. A més, la informació obtinguda en mesures empíriques sol ser incompleta. Motivats per aquestes limitacions, en aquesta tesi proposem un estudi teòric dels oscil·ladors acoblats en xarxes sota incertesa. Apliquem propagació d'errors per predir com una estructura complexa amplifica el soroll des dels pesos microscòpics fins al punt crític de sincronització, estudiem l'efecte d'equilibrar les interaccions de parelles i d'ordre superior en l'optimització de la sincronia i derivem esquemes d'ajust de pesos per mapejar el comportament de sincronització en xarxes diferents. A més, un desplegament geomètric rigorós de l'estat sincronitzat ens permet abordar escenaris descentralitzats i descobrir regles locals òptimes que indueixen transicions globals abruptes. Finalment, suggerim dreceres espectrals per predir punts crítics amb àlgebra lineal i representacions aproximades de xarxa. En general, proporcionem eines analítiques per tractar les xarxes d'oscil·ladors en condicions sorolloses i demostrem que darrere els supòsits predominants d'informació completa s'amaguen explicacions mecanicistes clares. Troballes rellevants inclouen xarxes particulars que maximitzen el ventall de comportaments i el desplegament exitós del binomi estructura-dinàmica des d'una perspectiva local. Aquesta tesi avança la recerca d'una teoria general de la sincronització en xarxes a partir de principis mecanicistes i geomètrics, una peça clau que manca en l'anàlisi, disseny i control de xarxes neuronals biològiques i artificials i sistemes d'enginyeria complexos.La sincronización en redes es la música de los sistemas complejos. Los ritmos colectivos que emergen de muchos osciladores acoplados explican el latido constante del corazón, los patrones recurrentes de actividad neuronal y la sincronía descentralizada de las redes eléctricas. Los modelos matemáticos son sólidos y han avanzado significativamente, especialmente en el problema del campo medio, donde todos los osciladores están conectados entre sí. Sin embargo, las redes reales tienen interacciones complejas que dificultan el tratamiento analítico. Falta un marco general y las soluciones en cajas negras numéricas y espectrales dificultan la interpretación. Además, las mediciones empíricas suelen ser incompletas. Motivados por estas limitaciones, en esta tesis proponemos un estudio teórico de osciladores acoplados en redes bajo incertidumbre. Aplicamos propagación de errores para predecir cómo una estructura compleja amplifica el ruido desde las conexiones microscópicas hasta puntos críticos macroscópicos, estudiamos el efecto de equilibrar interacciones por pares y de orden superior en la optimización de la sincronía y derivamos esquemas de ajuste de pesos para mapear el comportamiento en estructuras distintas. Una expansión geométrica del estado sincronizado nos permite abordar escenarios descentralizados y descubrir reglas locales que inducen transiciones abruptas globales. Por último, sugerimos atajos espectrales para predecir puntos críticos usando álgebra lineal y representaciones aproximadas de red. En general, proporcionamos herramientas analíticas para manejar redes de osciladores en condiciones ruidosas y demostramos que detrás de las suposiciones predominantes de información completa se ocultaban claras explicaciones mecanicistas. Hallazgos relevantes incluyen redes particulares que maximizan el rango de comportamientos y la explicación del binomio estructura-dinámica desde una perspectiva local. Esta tesis avanza en la búsqueda de una teoría general de sincronización en redes desde principios mecánicos y geométricos, una pieza clave que falta en el análisis, diseño y control de redes neuronales biológicas y artificiales y sistemas de ingeniería complejos.Synchronization in networks is the music of complex systems. Collective rhythms emerging from many interacting oscillators appear across all scales of nature, from the steady heartbeat and the recurrent patterns in neuronal activity to the decentralized synchrony in power-grids. The mathematics behind these processes are solid and have significantly advanced lately, especially in the mean-field problem, where oscillators are all mutually connected. However, real networks have complex interactions that difficult the analytical treatment. A general framework is missing and most existing results rely on numerical and spectral black-boxes that hinder interpretation. Also, the information obtained from measurements is usually incomplete. Motivated by these limitations, in this thesis we propose a theoretical study of network-coupled oscillators under uncertainty. We apply error propagation to predict how a complex structure amplifies noise from the link weights to the synchronization onset, study the effect of balancing pair-wise and higher-order interactions in synchrony optimization, and derive weight-tuning schemes to map the synchronization behavior of different structures. Also, we develop a rigorous geometric unfolding of the synchronized state to tackle decentralized scenarios and to discover optimal local rules that induce global abrupt transitions. Last, we suggest spectral shortcuts to predict critical points using linear algebra and network representations with limited information. Overall, we provide analytical tools to deal with oscillator networks under noisy conditions and prove that mechanistic explanations were hidden behind the prevalent assumptions of complete information. Relevant finding include particular networks that maximize the range of behaviors and the successful unfolding of the structure-dynamics interplay from a local perspective. This thesis advances the quest of a general theory of network synchronization built from mechanistic and geometric principles, a key missing piece in the analysis, design and control of biological and artificial neural networks and complex engineering systems

Flexible estimation of temporal point processes and graphs

Handling complex data types with spatial structures, temporal dependencies, or discrete values, is generally a challenge in statistics and machine learning. In the recent years, there has been an increasing need of methodological and theoretical work to analyse non-standard data types, for instance, data collected on protein structures, genes interactions, social networks or physical sensors. In this thesis, I will propose a methodology and provide theoretical guarantees for analysing two general types of discrete data emerging from interactive phenomena, namely temporal point processes and graphs. On the one hand, temporal point processes are stochastic processes used to model event data, i.e., data that comes as discrete points in time or space where some phenomenon occurs. Some of the most successful applications of these discrete processes include online messages, financial transactions, earthquake strikes, and neuronal spikes. The popularity of these processes notably comes from their ability to model unobserved interactions and dependencies between temporally and spatially distant events. However, statistical methods for point processes generally rely on estimating a latent, unobserved, stochastic intensity process. In this context, designing flexible models and consistent estimation methods is often a challenging task. On the other hand, graphs are structures made of nodes (or agents) and edges (or links), where an edge represents an interaction or relationship between two nodes. Graphs are ubiquitous to model real-world social, transport, and mobility networks, where edges can correspond to virtual exchanges, physical connections between places, or migrations across geographical areas. Besides, graphs are used to represent correlations and lead-lag relationships between time series, and local dependence between random objects. Graphs are typical examples of non-Euclidean data, where adequate distance measures, similarity functions, and generative models need to be formalised. In the deep learning community, graphs have become particularly popular within the field of geometric deep learning. Structure and dependence can both be modelled by temporal point processes and graphs, although predominantly, the former act on the temporal domain while the latter conceptualise spatial interactions. Nonetheless, some statistical models combine graphs and point processes in order to account for both spatial and temporal dependencies. For instance, temporal point processes have been used to model the birth times of edges and nodes in temporal graphs. Moreover, some multivariate point processes models have a latent graph parameter governing the pairwise causal relationships between the components of the process. In this thesis, I will notably study such a model, called the Hawkes model, as well as graphs evolving in time. This thesis aims at designing inference methods that provide flexibility in the contexts of temporal point processes and graphs. This manuscript is presented in an integrated format, with four main chapters and two appendices. Chapters 2 and 3 are dedicated to the study of Bayesian nonparametric inference methods in the generalised Hawkes point process model. While Chapter 2 provides theoretical guarantees for existing methods, Chapter 3 also proposes, analyses, and evaluates a novel variational Bayes methodology. The other main chapters introduce and study model-free inference approaches for two estimation problems on graphs, namely spectral methods for the signed graph clustering problem in Chapter 4, and a deep learning algorithm for the network change point detection task on temporal graphs in Chapter 5. Additionally, Chapter 1 provides an introduction and background preliminaries on point processes and graphs. Chapter 6 concludes this thesis with a summary and critical thinking on the works in this manuscript, and proposals for future research. Finally, the appendices contain two supplementary papers. The first one, in Appendix A, initiated after the COVID-19 outbreak in March 2020, is an application of a discrete-time Hawkes model to COVID-related deaths counts during the first wave of the pandemic. The second work, in Appendix B, was conducted during an internship at Amazon Research in 2021, and proposes an explainability method for anomaly detection models acting on multivariate time series

How individuals change language

Languages emerge and change over time at the population level though interactions between individual speakers. It is, however, hard to directly observe how a single speaker's linguistic innovation precipitates a population-wide change in the language, and many theoretical proposals exist. We introduce a very general mathematical model that encompasses a wide variety of individual-level linguistic behaviours and provides statistical predictions for the population-level changes that result from them. This model allows us to compare the likelihood of empirically-attested changes in definite and indefinite articles in multiple languages under different assumptions on the way in which individuals learn and use language. We find that accounts of language change that appeal primarily to errors in childhood language acquisition are very weakly supported by the historical data, whereas those that allow speakers to change incrementally across the lifespan are more plausible, particularly when combined with social network effects

Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.Comment: 8 page

The Optimal Control of Infectious Diseases via Prevention and Treatment

This paper characterizes the optimal control of a recurrent infectious disease through the use of treatment and preventive non-pharmaceutical interventions such as social distancing and curfews. We find that under centralized decision making, treatment induces positive destabilizing feedback effects, while prevention induces negative stabilizing feedback effects. While optimal treatment pushes prevalence towards the extremes, optimal prevention pushes it towards interior solutions. As a result, the dynamic system may admit multiple steady states and the optimal policy may be history dependent. We find that steady state prevalence levels in decentralized equilibrium must be equal to or higher than the socially optimal levels. The differences between the equilibrium outcome and the social optimum derive from the existence of a pure externality effect and a separate smallness effect due to individuals being small. Last, we derive two separate corrective subsidy schemes that decentralize the socially optimal outcome, namely subsidies to prevention and treatment and a tax on the infected