André A. Moreira

Mitigation of malicious attacks on networks

Terrorist attacks on transportation networks have traumatized modern societies. With a single blast, it has become possible to paralyze airline traffic, electric power supply, ground transportation or Internet communication. How and at which cost can one restructure the network such that it will become more robust against a malicious attack? We introduce a new measure for robustness and use it to devise a method to mitigate economically and efficiently this risk. We demonstrate its efficiency on the European electricity system and on the Internet as well as on complex networks models. We show that with small changes in the network structure (low cost) the robustness of diverse networks can be improved dramatically whereas their functionality remains unchanged. Our results are useful not only for improving significantly with low cost the robustness of existing infrastructures but also for designing economically robust network systems.

Towards Design Principles for Optimal Transport Networks

We investigate the optimal design of networks for a general transport system. Our network is built from a regular two-dimensional (d = 2) square lattice to be improved by adding long-range connections (shortcuts) with probability Pij ∼ r −α ij , where rij is the Euclidean distance between sites i and j, and α is a variable exponent. We introduce a cost constraint on the total length of the additional links and find optimal transport in the system for α = d + 1. Remarkably, this condition remains optimal, regardless of the strategy used for navigation, being based on local or global knowledge of the network structure, in sharp contrast with the results obtained for unconstrained navigation using global or local information, where the optimal conditions are α = 0 and α = d, respectively. The validity of our theoretical results is supported by data on the US airport network, for which α ≈ 3.0 was recently found [Bianconi et al., arXiv:0810.4412 (2008)].

Thermostatistics of Overdamped Motion of Interacting Particles

We show through a nonlinear Fokker-Planck formalism, and confirm by molecular dynamics simulations, that the overdamped motion of interacting particles at T=0, where T is the temperature of a thermal bath connected to the system, can be directly associated with Tsallis thermostatistics. For sufficiently high values of T, the distribution of particles becomes Gaussian, so that the classical Boltzmann-Gibbs behavior is recovered. For intermediate temperatures of the thermal bath, the system displays a mixed behavior that follows a novel type of thermostatistics, where the entropy is given by a linear combination of Tsallis and Boltzmann-Gibbs entropies.

How to make a fragile network robust and vice versa.

We investigate topologically biased failure in scale-free networks with a degree distribution P(k) proportional, variantk;{-gamma}. The probability p that an edge remains intact is assumed to depend on the degree k of adjacent nodes i and j through p_{ij} proportional, variant(k_{i}k_{j});{-alpha}. By varying the exponent alpha, we interpolate between random (alpha=0) and systematic failure. For alpha>0 (<0) the most (least) connected nodes are depreciated first. This topological bias introduces a characteristic scale in P(k) of the depreciated network, marking a crossover between two distinct power laws. The critical percolation threshold, at which global connectivity is lost, depends both on gamma and on alpha. As a consequence, network robustness or fragility can be controlled through fine-tuning of the topological bias in the failure process.

Mesoscopic modeling for nucleic acid chain dynamics

To gain a deeper insight into cellular processes such as transcription and translation, one needs to uncover the mechanisms controlling the configurational changes of nucleic acids. As a step toward this aim, we present here a mesoscopic-level computational model that provides a new window into nucleic acid dynamics. We model a single-stranded nucleic as a polymer chain whose monomers are the nucleosides. Each monomer comprises a bead representing the sugar molecule and a pin representing the base. The bead-pin complex can rotate about the backbone of the chain. We consider pairwise stacking and hydrogen-bonding interactions. We use a modified Monte Carlo dynamics that splits the dynamics into translational bead motion and rotational pin motion. By performing a number of tests, we first show that our model is physically sound. We then focus on a study of the kinetics of a DNA hairpin--a single-stranded molecule comprising two complementary segments joined by a noncomplementary loop--studied experimentally. We find that results from our simulations agree with experimental observations, demonstrating that our model is a suitable tool for the investigation of the hybridization of single strands.

Tsallis thermostatistics for finite systems: a Hamiltonian approach

The derivation of the Tsallis generalized canonical distribution from the traditional approach of the Gibbs microcanonical ensemble is revisited (Phys. Lett. A 193 (1994) 140). We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann–Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi–Pasta–Ulam chain of anharmonic oscillators.

Competitive cluster growth in complex networks

In this work we propose an idealized model for competitive cluster growth in complex networks. Each cluster can be thought of as a fraction of a community that shares some common opinion. Our results show that the cluster size distribution depends on the particular choice for the topology of the network of contacts among the agents. As an application, we show that the cluster size distributions obtained when the growth process is performed on hierarchical networks, e.g., the Apollonian network, have a scaling form similar to what has been observed for the distribution of a number of votes in an electoral process. We suggest that this similarity may be due to the fact that social networks involved in the electoral process may also possess an underlining hierarchical structure.

Different topologies for a herding model of opinion.

Understanding how opinions spread through a community or how consensus emerges in noisy environments can have a significant impact on our comprehension of social relations among individuals. In this work a model for the dynamics of opinion formation is introduced. The model is based on a nonlinear interaction between opinion vectors of agents plus a stochastic variable to account for the effect of noise in the way the agents communicate. The dynamics presented is able to generate rich dynamical patterns of interacting groups or clusters of agents with the same opinion without a leader or centralized control. Our results show that by increasing the intensity of noise, the system goes from consensus to a disordered state. Depending on the number of competing opinions and the details of the network of interactions, the system displays a first- or a second-order transition. We compare the behavior of different topologies of interactions: one-dimensional chains, and annealed and complex networks.

Fracturing the Optimal Paths

Optimal paths play a fundamental role in numerous physical applications ranging from random polymers to brittle fracture, from the flow through porous media to information propagation. Here for the first time we explore the path that is activated once this optimal path fails and what happens when this new path also fails and so on, until the system is completely disconnected. In fact many applications can also be found for this novel fracture problem. In the limit of strong disorder, our results show that all the cracks are located on a single self-similar connected line of fractal dimension D(b) approximately = 1.22. For weak disorder, the number of cracks spreads all over the entire network before global connectivity is lost. Strikingly, the disconnecting path (backbone) is, however, completely independent on the disorder.

Extended phase-space dynamics for the generalized nonextensive thermostatistics

We apply a variant of the Nosé thermostat to derive the Hamiltonian of a nonextensive system that is compatible with the canonical ensemble of the generalized thermostatistics of Tsallis. This microdynamical approach provides a deterministic connection between the generalized nonextensive entropy and power-law behavior. For the case of a simple one-dimensional harmonic oscillator, we confirm by numerical simulation of the dynamics that the distribution of energy H follows precisely the canonical q statistics for different values of the parameter q. The approach is further tested for classical many-particle systems by means of molecular dynamics simulations. The results indicate that the intrinsic nonlinear features of the nonextensive formalism are capable of generating energy fluctuations that obey anomalous probability laws. For q<1 a broad distribution of energy is observed, while for q>1 the resulting distribution is confined to a compact support.