Applied Theoretical Physics

Electroencephalography, magnetoencephalography, or functional magnetic resonance imaging (fMRI) techniques are currently used to estimate functional connectivity patterns between different brain areas. In this talk I'll show how a complex network description might provide new insights into the understanding of human brain connectivity during different pathological and cognitive neuro-dynamical states.

Most networks are embedded in space and consequently, their topology is not independent from spatial constraints. In particular, these constraints can induce a hierarchical organization with hubs controlling specific regions of space, non-trivial correlations between the weights, the connectivity pattern and the actual spatial distances of vertices, and the emergence of anomalous fluctuations in the betweenness-degree correlation function. In this talk I will illustrate these effects both from an empirical and modeling point of view, with various examples ranging from the large-scale air travel network to smaller scales of inter- and intra- cities transportation networks.

Starting already with Huygens in 1665,synchronization in networks of autonomous agents is a paradigmatic example of emergence. If a network's topology is fixed, the time the system needs to achieve a common state is well known. The same cannot be said of networks with evolving topologies, for instance those where the agents are allowed to move. If the topology changes fast, an approximation that averages out the effect of motion is available. However, this approximation is not always realistic, and a more general framework is required. Here we present a conceptual model of networks where topology change is due to agents motion. We demonstrate that as topology changes slower, the approximation does not hold, and the time required for synchronization achievement increases. Our results suggest that the design of mobile device networks should take into account the trade-off between agent speed and interaction frequency, which have opposite effects on the efficiency of synchronization.

The study of complex network systems behavior and the biological reformulation of well established control and communication theories in engineering, may offer new vistas to biomedical research. The key point is that engineering principles provide a bunch of possibly useful "metaphors" to researchers for a novel interpretation of biological phenomena. In fact, systems control methodologies take advantage of the presence of negative or positive feedbacks, feed-forward regulation and other control loops able to produce an appropriate system-level response. For example, the presence of a stabilizing feedback circuit can neutralize the effect of a drug by compensating the levels of the target molecule. It is therefore of paramount importance to recognize that not only the nodes of a network may be important but also the strength of its links. The relationship between kinetics and systemic responses to perturbations offers an intriguing additional dimension in which network biology strategies can be developed.

New communication technologies allow to record dynamical microscopic data on large social systems. Even if the population samples are still limited, the situation if quickly improving. In Italy single vehicle trajectories are monitored by a GPS system for insurance reason. The data concern 2% of the whole vehicle population and the trajectories are sampled at a spatial scale of 2 Km. But we have information on time, positions, instantaneous velocity, covered distance and signal quality; moreover the starting and ending points of each trajectories are recorded. Recent studies of Florence urban area[A.Bazzani et al "Statistical Laws in Urban Mobility from microscopic GPS data in the area of Florence" submitted for publication 2009] have pointed out that in the average the GPS data represent an urban mobility that can be described by an ergodic principle based on the existence of a "mobility energy" for the daily mobility paths and by a Benford's law for the activity downtime distribution. To enrol the system complexity is then necessary to study transient states out of equilibrium, like, for instance, the rise of congestion phenomena in a road network. The GPS data base is not enough detailed to study congestion phenomena in a urban road network, but it can be suitable to detect congestion evolution on larger scale road networks (like an italian region). In this work we analyze the GPS data recorded on the whole Emilia-Romagna region during November 2007 to look for congestion effects and their evolution. We propose to describe the congestion dynamics by using the instant velocity and the trajectories of the monitored vehicles. We consider also the behavior of some selected drivers that are used to move in the considered area. Our aim is to define analytical instruments able to detect and to follow congestion evolution by means of real-time microscopic data, in order to perform a nowcasting approach to govern criticalities.

We propose a simple model of evolution dynamics and demonstrate it in a framework of economic dynamics. New goods and services are endogenously produced through combinations of existing goods. As soon as new goods enter the market they may compete against already existing goods, in other words new products can have destructive effects on existing goods. As a result of this competition existing goods may be driven out from the market - often causing cascades of secondary defects (Schumpeterian gales of destruction). The model leads to generic dynamics characterized by phases of relative economic stability followed by phases of massive restructuring of markets -- which could be interpreted as Schumpeterian business cycles. Model timeseries of product diversity and productivity reproduce several stylized facts of economics timeseries on long timescales such as GDP or business failures, including non-Gaussian fat tailed distributions, volatility clustering etc. The model is phrased in an open, non-equilibrium setup which can be understood as a self organized critical system. Its diversity dynamics can be understood by the time-varying topology of the active production networks.

The complex structure of many social, information and biological networks is underpinned by communities at different scales. These topological modules are often indicative of underlying features and functionalities, such as tightly-knit groups of metabolites or species in biological networks. The presence of well-defined communities also has an effect on the dynamics taking place on a network. A variety of methods and measures have been proposed to uncover these modules, most notably modularity and spectral partitioning. However, these approaches are based on structural, static properties of the network. Here we introduce a definition for the quality of the partition of a network that is based on the statistical properties of a dynamical process taking place on the graph. This measure, denoted the stability of the partition, has an intrinsic dependence on the time-scale of the process, which can be used to uncover community structures at different resolutions. The stability extends and unifies standard community detection algorithms. In particular, both modularity and spectral partitioning are shown to have a dynamical interpretation in the case of undirected networks and can be seen as limiting cases of the stability. Similarly, several multi-resolution methods correspond to linearisations of our measure at short times. In the case of directed networks, however, stability differs from modularity by its non-local nature as it is based on the persistence of probabilistic flows in modules. We apply our method to find multi-scale partitions for different examples and show that the stability can be computed efficiently through the use of extended versions of current algorithms that can deal with large networks. The analysis of social and technological networks has attracted a lot of attention as social networking applications and mobile sensing devices have given us a wealth of real data. Classic studies looked at analysing static or aggregated networks, i.e., networks that do not change over time or built as the results of aggregation of information over a certain period of time. Given the soaring collections of measurements related to very large, real network traces, researchers are quickly starting to realise that connections are inherently varying over time and exhibit more dimensionality than static analysis can capture. In this talk I will propose new temporal distance metrics to quantify and compare the speed (delay) of information diffusion processes taking into account the evolution of a network from a global view. We show how these metrics are able to capture the temporal characteristics of time-varying graphs, such as delay, duration and time order of contacts (interactions). I conclude with results of comparing path length calculations on static and temporal graphs.

The analysis of social and technological networks has attracted a lot of attention as social networking applications and mobile sensing devices have given us a wealth of real data. Classic studies looked at analysing static or aggregated networks, i.e., networks that do not change over time or built as the results of aggregation of information over a certain period of time. Given the soaring collections of measurements related to very large, real network traces, researchers are quickly starting to realise that connections are inherently varying over time and exhibit more dimensionality than static analysis can capture.
In this talk I will propose new temporal distance metrics to quantify and compare the speed (delay) of information diffusion processes taking into account the evolution of a network from a global view. We show how these metrics are able to capture the temporal characteristics of time-varying graphs, such as delay, duration and time order of contacts (interactions). I conclude with results of comparing path length calculations on static and temporal graphs.

Social insects, such as ants and termites, build collectively large scale nests and complex systems of trails. These structures present a coherent global organization and sometimes appear to show near optimal properties: protection from predators, homeostasis of internal temperature, efficient internal transportation networks. In spite of the coherent global organization, the final form of the nests is the result of simple self-organized processes, and depends on the interactions that individual insects undertake with conspecifics and with the substrate. With a series of experiments on ants, we identify the mechanisms of individual behaviour that are more relevant for understanding the formation of the final nest. In parallel, we take 3D Xray tomography images of different ant and termite nests. By analysing these images and modeling the internal system of galleries with complex networks we can measure the properties of connectivity and transportation of these structures and make hypotheses about the factors that have shaped their growth and their ecological functions.

The analysis of high-frequency log files of a massive multiplayer online game currently played by thousands of users allows to assess socioeconomical dynamics over the past three years. We are able to relate social and economic behavior of the players to a series of stylized facts known to exist in the real world. In particular, we analyze the evolution of underlying growing social networks such as constituted by friends and enemies, communication networks, and measure their characteristic properties. Our data confirm the recently observed phenomena of shrinking diameters and growing average degrees. Clustering coefficients of friend-networks decay in time, while those of enemies grow. A motif analysis displays further striking differences in topological structure between friend and enemy networks. We compare our findings with literature on real world data. With this setup we try to establish a "laboratory" for economical behaviour.

Anyone who ever took an electronics book will be familiar with the fundamental passive circuit elements: the resistor, the capacitor and the inductor. In 1971, starting from symmetry arguments Prof. L. Chua reasoned that there should be a fourth fundamental element, which was called memristor (short for memory resistor). Unlike those three elements, which are allowed in linear time-invariant system theory, memristors are nonlinear and may be described by any of a variety of time-varying functions of electrical charge. It has been showed that such an element has many interesting and valuable circuit properties. Memristance arises naturally in nanoscale systems in which solid-state electronic and ionic transport are coupled under an external bias voltage. These results serve as the foundation for understanding a wide range of hysteretic current-voltage behaviour observed in many nanoscale electronic devices.
On April 30 2008, after 37 years, a team at HP Labs announced the development of a switching memristor. These devices are being developed for application in nanoelectronic memories, computer logic, and neuromorphic computer architectures.

Reference

The missing memristor found - Dmitri B. Strukov, Gregory S. Snider, Duncan R. Stewart and R. Stanley Williams - Nature 453, 80-83 (1 May 2008)

Statistical physics has proven to be an invaluable tool to describe and understand the properties of systems formed by a large number of elementary units. A big challenge is whether the tools and techniques of statistical physics are suitable to explore large scale social phenomena. Most attempts of the literature focus on simple microscopic models, with little or no contact to real social dynamics. A validation of this approach is still lacking and must rely on quantitative evidence about real social systems. Finding regularities on real data is a crucial step in this direction. We will show that voting and citing behaviors are both characterized by scaling and universality. The statistical distribution of the number of votes/cites, suitably normalized, is independent of the particular system considered. This opens the way to a simple modeling of the observed phenomenology.

Detecting communities in graphs is crucial to uncover relationships between nodes of complex networks. We review the topic, from the main concepts and related problems to the description of some of the most popular algorithms. We close with a list of open problems of the field, from the issue of testing algorithms to the question of what structural communities stand for.

The main target of this talk is to give a an unified approach to complex networks' vulnerability after a panoramic view about different approaches to complex network vulnerability.

In this talk I will describe the various activities we have been focussing on in recent years, mainly in the area of mobile networks. We will first discuss our content dissemination approaches in human and vehicular networks which exploit mobility prediction techniques, our work on mobile sensor networks applied to wildlife monitoring with problems related to duty cycling, reprogramming and routing, and the work on analysis of realistic mobility models which include recent work on applications of social networks to temporal contact graphs.