Homesick L\'evy walk: A mobility model having Ichi-go Ichi-e and scale-free properties of human encounters

In recent years, mobility models have been reconsidered based on findings by analyzing some big datasets collected by GPS sensors, cellphone call records, and Geotagging. To understand the fundamental statistical properties of the frequency of serendipitous human encounters, we conducted experiments to collect long-term data on human contact using short-range wireless communication devices which many people frequently carry in daily life. By analyzing the data we showed that the majority of human encounters occur once-in-an-experimental-period: they are Ichi-go Ichi-e. We also found that the remaining more frequent encounters obey a power-law distribution: they are scale-free. To theoretically find the origin of these properties, we introduced as a minimal human mobility model, Homesick L\'evy walk, where the walker stochastically selects moving long distances as well as L\'evy walk or returning back home. Using numerical simulations and a simple mean-field theory, we offer a theoretical explanation for the properties to validate the mobility model. The proposed model is helpful for evaluating long-term performance of routing protocols in delay tolerant networks and mobile opportunistic networks better since some utility-based protocols select nodes with frequent encounters for message transfer.Comment: 8 pages, 10 figure

Timely Data Delivery in a Realistic Bus Network

Abstract—WiFi-enabled buses and stops may form the backbone of a metropolitan delay tolerant network, that exploits nearby communications, temporary storage at stops, and predictable bus mobility to deliver non-real time information. This paper studies the problem of how to route data from its source to its destination in order to maximize the delivery probability by a given deadline. We assume to know the bus schedule, but we take into account that randomness, due to road traffic conditions or passengers boarding and alighting, affects bus mobility. We propose a simple stochastic model for bus arrivals at stops, supported by a study of real-life traces collected in a large urban network. A succinct graph representation of this model allows us to devise an optimal (under our model) single-copy routing algorithm and then extend it to cases where several copies of the same data are permitted. Through an extensive simulation study, we compare the optimal routing algorithm with three other approaches: minimizing the expected traversal time over our graph, minimizing the number of hops a packet can travel, and a recently-proposed heuristic based on bus frequencies. Our optimal algorithm outperforms all of them, but most of the times it essentially reduces to minimizing the expected traversal time. For values of deadlines close to the expected delivery time, the multi-copy extension requires only 10 copies to reach almost the performance of the costly flooding approach. I

On the dynamics of random neuronal networks

We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with the classical integrate-and-fire model. The ergodicity properties of the Markov process associated to finite networks are investigated. We derive the limit in distribution of the sample path of the state of a neuron of the network when its size gets large. The invariant distributions of this limiting stochastic process are analyzed as well as their stability properties. We show that the system undergoes transitions as a function of the averaged connectivity parameter, and can support trivial states (where the network activity dies out, which is also the unique stationary state of finite networks in some cases) and self-sustained activity when connectivity level is sufficiently large, both being possibly stable.Comment: 37 pages, 3 figure

A New Protocol for Cooperative Spectrum Sharing in Mobile Cognitive Radio Networks

To optimize the usage of limited spectrum resources, cognitive radio (CR) can be used as a viable solution. The main contribution of this article is to propose a new protocol to increase throughput of mobile cooperative CR networks (CRNs). The key challenge in a CRN is how the nodes cooperate to access the channel in order to maximize the CRN's throughput. To minimize unnecessary blocking of CR transmission, we propose a so-called new frequency-range MAC protocol (NFRMAC). The proposed method is in fact a novel channel assignment mechanism that exploits the dependence between signal's attenuation model, signal's frequency, communication range, and interference level. Compared .to the conventional methods, the proposed algorithm considers a more realistic model for the mobility pattern of CR nodes and also adaptively selects the maximal transmission range of each node over which reliable transmission is possible. Simulation results indicate that using NFRMAC leads to an increase of the total CRN's throughput by 6% and reduces the blocking rate by 10% compared to those of conventional methods

Scaling in a general class of critical random Boolean networks

We derive analytically the scaling behavior in the thermodynamic limit of the number of nonfrozen and relevant nodes in the most general class of critical Kauffman networks for any number of inputs per node, and for any choice of the probability distribution for the Boolean functions. By defining and analyzing a stochastic process that determines the frozen core we can prove that the mean number of nonfrozen nodes in any critical network with more than one input per node scales with the network size $N$ as $N^{2/3}$, with only $N^{1/3}$ nonfrozen nodes having two nonfrozen inputs and the number of nonfrozen nodes with more than two inputs being finite in the thermodynamic limit. Using these results we can conclude that the mean number of relevant nodes increases for large $N$ as $N^{1/3}$, with only a finite number of relevant nodes having two relevant inputs, and a vanishing fraction of nodes having more than three of them. It follows that all relevant components apart from a finite number are simple loops, and that the mean number and length of attractors increases faster than any power law with network size.Comment: 11 page

Boolean delay equations on networks: An application to economic damage propagation

We introduce economic models based on Boolean Delay Equations: this formalism makes easier to take into account the complexity of the interactions between firms and is particularly appropriate for studying the propagation of an initial damage due to a catastrophe. Here we concentrate on simple cases, which allow to understand the effects of multiple concurrent production paths as well as the presence of stochasticity in the path time lengths or in the network structure. In absence of flexibility, the shortening of production of a single firm in an isolated network with multiple connections usually ends up by attaining a finite fraction of the firms or the whole economy, whereas the interactions with the outside allow a partial recovering of the activity, giving rise to periodic solutions with waves of damage which propagate across the structure. The damage propagation speed is strongly dependent upon the topology. The existence of multiple concurrent production paths does not necessarily imply a slowing down of the propagation, which can be as fast as the shortest path.Comment: Latex, 52 pages with 22 eps figure

A Graphical Adversarial Risk Analysis Model for Oil and Gas Drilling Cybersecurity

Oil and gas drilling is based, increasingly, on operational technology, whose cybersecurity is complicated by several challenges. We propose a graphical model for cybersecurity risk assessment based on Adversarial Risk Analysis to face those challenges. We also provide an example of the model in the context of an offshore drilling rig. The proposed model provides a more formal and comprehensive analysis of risks, still using the standard business language based on decisions, risks, and value.Comment: In Proceedings GraMSec 2014, arXiv:1404.163