Statistical Mechanics of maximal independent sets

The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and covering constraints. It is known that finding minimum and maximum-density maximal independent sets are hard optimization problems. In this paper, we use cavity method of statistical physics and Monte Carlo simulations to study the corresponding constraint satisfaction problem on random graphs. We obtain the entropy of maximal independent sets within the replica symmetric and one-step replica symmetry breaking frameworks, shedding light on the metric structure of the landscape of solutions and suggesting a class of possible algorithms. This is of particular relevance for the application to the study of strategic interactions in social and economic networks, where maximal independent sets correspond to pure Nash equilibria of a graphical game of public goods allocation

Travelling wave ion mobility-derived collision cross section for mycotoxins: Investigating interlaboratory and interplatform reproducibility

Parent and modified mycotoxin analysis remains a challenge because of their chemical diversity, the presence of isomeric forms, and the lack of analytical standards. The creation and application of a collision cross section (CCS) database for mycotoxins may bring new opportunities to overcome these analytical challenges. However, it is still an open question whether common CCS databases can be used independently from the instrument type and ion mobility mass spectrometry (IM-MS) technologies, which utilize different methodologies for determining the gas-phase mobility. Here, we demonstrated the reproducibility of CCS measurements for mycotoxins in an interlaboratory study (average RSD 0.14% ± 0.079) and across different traveling wave IM-MS (TWIMS) systems commercially available (ΔCCS% < 2). The separation in the drift time dimension of critical pairs of isomers for modified mycotoxins was also achieved. In addition, the comparison of measured and predicted CCS values, including regulated and emerging mycotoxins, was addressed

Consensus and ordering in language dynamics

We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB) state. Proposed in the context of language competition and emergence, the AB state was associated with bilingualism and synonymy respectively. We show that the two models are equivalent in the mean field approximation, though the differences at the microscopic level have non-trivial consequences. To point them out, we investigate an extension of these dynamics in which confidence/trust is considered, focusing on the case of an underlying fully connected graph, and we show that the consensus-polarization phase transition taking place in the Naming Game is not observed in the AB model. We then consider the interface motion in regular lattices. Qualitatively, both models show the same behavior: a diffusive interface motion in a one-dimensional lattice, and a curvature driven dynamics with diffusing stripe-like metastable states in a two-dimensional one. However, in comparison to the Naming Game, the AB-model dynamics is shown to slow down the diffusion of such configurations.Comment: 7 pages, 6 figure

New experimental techniques for fracture testing of highly deformable materials

A new experimental method for measuring strain fields in highly deformable materials has been developed. This technique is based on an in-house developed Digital Image Correlation (DIC) system capable of accurately capturing localized or non-uniform strain distributions. Thanks to the implemented algorithm based on a Semi-Global Matching (SGM) approach, it is possible to constraint the regularity of the displacement field in order to significantly improve the reliability of the evaluated strains, especially in highly deformable materials. Being originally introduced for Digital Surface Modelling from stereo pairs, SGM is conceived for performing a one-dimensional search of displacements between images, but here a novel implementation for 2D displacement solution space is introduced. SGM approach is compared with the previously in-house developed implementation based on a local Least Squares Matching (LSM) approach. A comparison with the open source code Ncorr and with some FEM results is also presented. The investigation using the present DIC method focuses on 2D full-field strain maps of plain and notched specimens under tensile loading made of two different highly deformable materials: hot mix asphalt and thermoplastic composites for 3D-printing applications. In the latter specimens, an elliptical hole is introduced to assess the potentiality of the method in experimentally capturing high strain gradients in mixed-mode fracture situations

Graph Reconstruction via Distance Oracles

We study the problem of reconstructing a hidden graph given access to a distance oracle. We design randomized algorithms for the following problems: reconstruction of a degree bounded graph with query complexity $\tilde{O}(n^{3/2})$; reconstruction of a degree bounded outerplanar graph with query complexity $\tilde{O}(n)$; and near-optimal approximate reconstruction of a general graph

A minimal model for congestion phenomena on complex networks

We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase and a congested phase, critical points and different scaling behaviors in the system size. It consists of random walkers on a queueing network with one-range repulsion, where particles can be destroyed only if they can move. We focus on the dependence on the topology as well as on the level of traffic control. We are able to obtain transition curves and phase diagrams at analytical level for the ensemble of uncorrelated networks and numerically for single instances. We find that traffic control improves global performance, enlarging the free-flow region in parameter space only in heterogeneous networks. Traffic control introduces non-linear effects and, beyond a critical strength, may trigger the appearance of a congested phase in a discontinuous manner. The model also reproduces the cross-over in the scaling of traffic fluctuations empirically observed in the Internet, and moreover, a conserved version can reproduce qualitatively some stylized facts of traffic in transportation networks

The Naming Game in Social Networks: Community Formation and Consensus Engineering

We study the dynamics of the Naming Game [Baronchelli et al., (2006) J. Stat. Mech.: Theory Exp. P06014] in empirical social networks. This stylized agent-based model captures essential features of agreement dynamics in a network of autonomous agents, corresponding to the development of shared classification schemes in a network of artificial agents or opinion spreading and social dynamics in social networks. Our study focuses on the impact that communities in the underlying social graphs have on the outcome of the agreement process. We find that networks with strong community structure hinder the system from reaching global agreement; the evolution of the Naming Game in these networks maintains clusters of coexisting opinions indefinitely. Further, we investigate agent-based network strategies to facilitate convergence to global consensus.Comment: The original publication is available at http://www.springerlink.com/content/70370l311m1u0ng3

Router-level community structure of the Internet Autonomous Systems

The Internet is composed of routing devices connected between them and organized into independent administrative entities: the Autonomous Systems. The existence of different types of Autonomous Systems (like large connectivity providers, Internet Service Providers or universities) together with geographical and economical constraints, turns the Internet into a complex modular and hierarchical network. This organization is reflected in many properties of the Internet topology, like its high degree of clustering and its robustness. In this work, we study the modular structure of the Internet router-level graph in order to assess to what extent the Autonomous Systems satisfy some of the known notions of community structure. We show that the modular structure of the Internet is much richer than what can be captured by the current community detection methods, which are severely affected by resolution limits and by the heterogeneity of the Autonomous Systems. Here we overcome this issue by using a multiresolution detection algorithm combined with a small sample of nodes. We also discuss recent work on community structure in the light of our results

Heterogenous mean-field analysis of a generalized voter-like model on networks

We propose a generalized framework for the study of voter models in complex networks at the the heterogeneous mean-field (HMF) level that (i) yields a unified picture for existing copy/invasion processes and (ii) allows for the introduction of further heterogeneity through degree-selectivity rules. In the context of the HMF approximation, our model is capable of providing straightforward estimates for central quantities such as the exit probability and the consensus/fixation time, based on the statistical properties of the complex network alone. The HMF approach has the advantage of being readily applicable also in those cases in which exact solutions are difficult to work out. Finally, the unified formalism allows one to understand previously proposed voter-like processes as simple limits of the generalized model