Nonautonomous Graphs and Topological Entropy of Nonautonomous Lorenz Systems

In this work, we associate a p-periodic nonautonomous graph to each p-periodic nonautonomous Lorenz system with finite critical orbits. We develop Perron-Frobenius theory for nonautonomous graphs and use it to calculate their entropy. Finally, we prove that the topological entropy of a p-periodic nonautonomous Lorenz system is equal to the entropy of its associated nonautonomous graph.

Defect dynamics in viscous fingering

We study the dynamics of Staffman-Taylor fingering in terms of topological defects of the flow field. The defects are created and/or annihilated at the interface. The route towards the single-finger steady state is characterized by a detailed mechanism for defect annihilation. For small viscosity contrast this mechanism is impeded, and creation of new defects leads the system away from a single-finger solution. Strong evidence for a drastic reduction of the basin of attraction of the Saffman-Taylor finger is presented.

Models that include supercoiling of topological domains reproduce several known features of interphase chromosomes.

Understanding the structure of interphase chromosomes is essential to elucidate regulatory mechanisms of gene expression. During recent years, high-throughput DNA sequencing expanded the power of chromosome conformation capture (3C) methods that provide information about reciprocal spatial proximity of chromosomal loci. Since 2012, it is known that entire chromatin in interphase chromosomes is organized into regions with strongly increased frequency of internal contacts. These regions, with the average size of ∼1 Mb, were named topological domains. More recent studies demonstrated presence of unconstrained supercoiling in interphase chromosomes. Using Brownian dynamics simulations, we show here that by including supercoiling into models of topological domains one can reproduce and thus provide possible explanations of several experimentally observed characteristics of interphase chromosomes, such as their complex contact maps.

Synchronization reveals topological scales in complex networks

We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well-defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.

Information sharing and social network dynamics : a coevolutionary approach

The capacity to interact socially and share information underlies the success of many animal species, humans included. Researchers of many fields have emphasized the evo¬lutionary significance of how patterns of connections between individuals, or the social networks, and learning abilities affect the information obtained by animal societies. To date, studies have focused on the dynamics either of social networks, or of the spread of information. The present work aims to study them together. We make use of mathematical and computational models to study the dynamics of networks, where social learning and information sharing affect the structure of the population the individuals belong to. The number and strength of the relationships between individuals, in turn, impact the accessibility and the diffusion of the shared information. Moreover, we inves¬tigate how different strategies in the evaluation and choice of interacting partners impact the processes of knowledge acquisition and social structure rearrangement. First, we look at how different evaluations of social interactions affect the availability of the information and the network topology. We compare a first case, where individuals evaluate social exchanges by the amount of information that can be shared by the partner, with a second case, where they evaluate interactions by considering their partners' social status. We show that, even if both strategies take into account the knowledge endowments of the partners, they have very different effects on the system. In particular, we find that the first case generally enables individuals to accumulate higher amounts of information, thanks to the more efficient patterns of social connections they are able to build. Then, we study the effects that homophily, or the tendency to interact with similar partners, has on knowledge accumulation and social structure. We compare the case where individuals who know the same information are more likely to learn socially from each other, to the opposite case, where individuals who know different information are instead more likely to learn socially from each other. We find that it is not trivial to claim which strategy is better than the other. Depending on the possibility of forgetting information, the way new social partners can be chosen, and the population size, we delineate the conditions for which each strategy allows accumulating more information, or in a faster way For these conditions, we also discuss the topological characteristics of the resulting social structure, relating them to the information dynamics outcome. In conclusion, this work paves the road for modeling the joint dynamics of the spread of information among individuals and their social interactions. It also provides a formal framework to study jointly the effects of different strategies in the choice of partners on social structure, and how they favor the accumulation of knowledge in the population. - La capacité d'interagir socialement et de partager des informations est à la base de la réussite de nombreuses espèces animales, y compris les humains. Les chercheurs de nombreux domaines ont souligné l'importance évolutive de la façon dont les modes de connexions entre individus, ou réseaux sociaux et les capacités d'apprentissage affectent les informations obtenues par les sociétés animales. À ce jour, les études se sont concentrées sur la dynamique soit des réseaux sociaux, soit de la diffusion de l'information. Le présent travail a pour but de les étudier ensemble. Nous utilisons des modèles mathématiques et informatiques pour étudier la dynamique des réseaux, où l'apprentissage social et le partage d'information affectent la structure de la population à laquelle les individus appartiennent. Le nombre et la solidité des relations entre les individus ont à leurs tours un impact sur l'accessibilité et la diffusion de l'informa¬tion partagée. Par ailleurs, nous étudions comment les différentes stratégies d'évaluation et de choix des partenaires d'interaction ont une incidence sur les processus d'acquisition des connaissances ainsi que le réarrangement de la structure sociale. Tout d'abord, nous examinons comment des évaluations différentes des interactions sociales influent sur la disponibilité de l'information ainsi que sur la topologie du réseau. Nous comparons un premier cas, où les individus évaluent les échanges sociaux par la quantité d'information qui peut être partagée par le partenaire, avec un second cas, où ils évaluent les interactions en tenant compte du statut social de leurs partenaires. Nous montrons que, même si les deux stratégies prennent en compte le montant de connaissances des partenaires, elles ont des effets très différents sur le système. En particulier, nous constatons que le premier cas permet généralement aux individus d'accumuler de plus grandes quantités d'information, grâce à des modèles de connexions sociales plus efficaces qu'ils sont capables de construire. Ensuite, nous étudions les effets que l'homophilie, ou la tendance à interagir avec des partenaires similaires, a sur l'accumulation des connaissances et la structure sociale. Nous comparons le cas où des personnes qui connaissent les mêmes informations sont plus sus¬ceptibles d'apprendre socialement l'une de l'autre, au cas où les individus qui connaissent des informations différentes sont au contraire plus susceptibles d'apprendre socialement l'un de l'autre. Nous constatons qu'il n'est pas trivial de déterminer quelle stratégie est meilleure que l'autre. En fonction de la possibilité d'oublier l'information, la façon dont les nouveaux partenaires sociaux peuvent être choisis, et la taille de la population, nous déterminons les conditions pour lesquelles chaque stratégie permet d'accumuler plus d'in¬formations, ou d'une manière plus rapide. Pour ces conditions, nous discutons également les caractéristiques topologiques de la structure sociale qui en résulte, les reliant au résultat de la dynamique de l'information. En conclusion, ce travail ouvre la route pour la modélisation de la dynamique conjointe de la diffusion de l'information entre les individus et leurs interactions sociales. Il fournit également un cadre formel pour étudier conjointement les effets de différentes stratégies de choix des partenaires sur la structure sociale et comment elles favorisent l'accumulation de connaissances dans la population.

Using Pareto optimality to explore the topology and dynamics of the human connectome.

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

Nature of the Epidemic Threshold for the Susceptible-Infected-Susceptible Dynamics in Networks

We develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.

Structure and dynamics of the membrane attaching nitric oxide transporter nitrophorin 7

Nitrophorins represent a unique class of heme proteins that are able to perform the delicate transportation and release of the free-radical gaseous messenger nitric oxide (NO) in a pH-triggered manner. Besides its ability to bind to phospholipid membranes, the N-terminus contains an additional Leu-Pro-Gly stretch, which is a unique sequence trait, and the heme cavity is significantly altered with respect to other nitrophorins. These distinctive features encouraged us to solve the X-ray crystallographic structures of NP7 at low and high pH and bound with different heme ligands (nitric oxide, histamine, imidazole). The overall fold of the lipocalin motif is well preserved in the different X-ray structures and resembles the fold of other nitrophorins. However, a chain-like arrangement in the crystal lattice due to a number of head-to-tail electrostatic stabilizing interactions is found in NP7. Furthermore, the X-ray structures also reveal ligand-dependent changes in the orientation of the heme, as well as in specific interactions between the A-B and G-H loops, which are considered to be relevant for the biological function of nitrophorins. Fast and ultrafast laser triggered ligand rebinding experiments demonstrate the pH-dependent ligand migration within the cavities and the exit route. Finally, the topological distribution of pockets located around the heme as well as from inner cavities present at the rear of the protein provides a distinctive feature in NP7, so that while a loop gated exit mechanism to the solvent has been proposed for most nitrophorins, a more complex mechanism that involves several interconnected gas hosting cavities is proposed for NP7.

The European Union and Assembling Biofuel Development – topological investigations concerning the associations between law, policy and space

Biofuels for transport are a renewable source of energy that were once heralded as a solution to multiple problems associated with poor urban air quality, the overproduction of agricultural commodities, the energy security of the European Union (EU) and climate change. It was only after the Union had implemented an incentivizing framework of legal and political instruments for the production, trade and consumption of biofuels that the problems of weakening food security, environmental degradation and increasing greenhouse gases through land-use changes began to unfold. In other words, the difference between political aims for why biofuels are promoted and their consequences has grown – which is also recognized by the EU policy-makers. Therefore, the global networks of producing, trading and consuming biofuels may face a complete restructure if the European Commission accomplishes its pursuit to sideline crop-based biofuels after 2020. My aim with this dissertation is not only to trace the manifold evolutions of the instruments used by the Union to govern biofuels but also to reveal how this evolution has influenced the dynamics of biofuel development. Therefore, I study the ways the EU’s legal and political instruments of steering biofuels are coconstitutive with the globalized spaces of biofuel development. My analytical strategy can be outlined through three concepts. I use the term ‘assemblage’ to approach the operations of the loose entity of actors and non-human elements that are the constituents of multi-scalar and -sectorial biofuel development. ‘Topology’ refers to the spatiality of this European biofuel assemblage and its parts whose evolving relations are treated as the active constituents of space, instead of simply being located in space. I apply the concept of ‘nomosphere’ to characterize the framework of policies, laws and other instruments that the EU applies and construes while attempting to govern biofuels. Even though both the materials and methods vary in the independent articles, these three concepts characterize my analytical strategy that allows me to study law, policy and space associated with each other. The results of my examinations underscore the importance of the instruments of governance of the EU constituting and stabilizing the spaces of producing and, on the other hand, how topological ruptures in biofuel development have enforced the need to reform policies. This analysis maps the vast scope of actors that are influenced by the mechanism of EU biofuel governance and, what is more, shows how they are actively engaging in the Union’s institutional policy formulation. By examining the consequences of fast biofuel development that are spatially dislocated from the established spaces of producing, trading and consuming biofuels such as indirect land use changes, I unfold the processes not tackled by the instruments of the EU. Indeed, it is these spatially dislocated processes that have pushed the Commission construing a new type of governing biofuels: transferring the instruments of climate change mitigation to land-use policies. Although efficient in mitigating these dislocated consequences, these instruments have also created peculiar ontological scaffolding for governing biofuels. According to this mode of governance, the spatiality of biofuel development appears to be already determined and the agency that could dampen the negative consequences originating from land-use practices is treated as irrelevant.

Structure and magnetic properties of polydisperse ferrofluids: a molecular dynamics study

We study by Langevin molecular dynamics simulations systematically the influence of polydispersity in the particle size, and subsequently in the dipole moment, on the physical properties of ferrofluids. The polydispersity is in a first approximation modeled by a bidisperse system that consists of small and large particles at different ratios of their volume fractions. In the first part of our investigations the total volume fraction of the system is fixed, and the volume fraction phi(L) of the large particles is varied. The initial susceptibility chi and magnetization curve of the systems show a strong dependence on the value of phi(L). With the increase of phi(L), the magnetization M of the system has a much faster increment at weak fields, and thus leads to a larger chi. We performed a cluster analysis that indicates that this is due to the aggregation of the large particles in the systems. The average size of these clusters increases with increasing phi(L). In the second part of our investigations, we fixed the volume fraction of the large particles, and increased the volume fraction phi(S) of the small particles in order to study their influence on the chain formation of the large ones. We found that the average aggregate size formed by large particles decreases when phi(S) is increased, demonstrating a significant effect of the small particles on the structural properties of the system. A topological analysis of the structure reveals that the majority of the small particles remain nonaggregated. Only a small number of them are attracted to the ends of the chains formed by large particles.

SUPPORT OF MAXIMIZING MEASURES FOR TYPICAL C(0) DYNAMICS ON COMPACT MANIFOLDS

Given a compact manifold X, a continuous function g : X -> IR, and a map T : X -> X, we study properties of the T-invariant Borel probability measures that maximize the integral of g. We show that if X is a n-dimensional connected Riemaniann manifold, with n >= 2, then the set of homeomorphisms for which there is a maximizing measure supported on a periodic orbit is meager. We also show that, if X is the circle, then the ""topological size"" of the set of endomorphisms for which there are g maximizing measures with support on a periodic orbit depends on properties of the function g. In particular, if g is C(1), it has interior points.

Vortex dynamics in mesoscopic superconducting square of variable surface

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Closed string thermal torus from thermo field dynamics

In this Letter a topological interpretation for the string thermal vacuum in the thermo field dynamics (TFD) approach is given. As a consequence, the relationship between the imaginary time and TFD formalisms is achieved when both are used to study closed strings at finite temperature. The TFD approach starts by duplicating the system's degrees of freedom, defining an auxiliary (tilde) string. In order to lead the system to finite temperature a Bogoliubov transformation is implemented. We show that the effect of this transformation is to glue together the string and the tilde string to obtain a torus. The thermal vacuum appears as the boundary state for this identification. Also, from the thermal state condition, a Kubo-Martin-Schwinger condition for the torus topology is derived. © 2005 Elsevier B.V. All rights reserved.

The dynamics of a one-dimensional parabolic problem versus the dynamics of its discretization

In this paper we prove that the spatial discretization of a one dimensional system of parabolic equations. with suitably small step size, contains exactly the same asymptotic dynamics as the continuous problem. (C) 2000 Academic Press.

STRUCTURE AND DYNAMICS: THE TRANSITION FROM NONEQUILIBRIUM TO EQUILIBRIUM IN INTEGRATE-AND-FIRE DYNAMICS

The transient and equilibrium properties of dynamics unfolding in complex systems can depend critically on specific topological features of the underlying interconnections. In this work, we investigate such a relationship with respect to the integrate-and-fire dynamics emanating from a source node and an extended network model that allows control of the small-world feature as well as the length of the long-range connections. A systematic approach to investigate the local and global correlations between structural and dynamical features of the networks was adopted that involved extensive simulations (one and a half million cases) so as to obtain two-dimensional correlation maps. Smooth, but diverse surfaces of correlation values were obtained in all cases. Regarding the global cases, it has been verified that the onset avalanche time (but not its intensity) can be accurately predicted from the structural features within specific regions of the map (i.e. networks with specific structural properties). The analysis at local level revealed that the dynamical features before the avalanches can also be accurately predicted from structural features. This is not possible for the dynamical features after the avalanches take place. This is so because the overall topology of the network predominates over the local topology around the source at the stationary state.