arXiv subjects

Reuven Cohen

Publications and source records attributed to Reuven Cohen.

At least 37 records · Page 2Linked to original sources

arXiv2020

Distance Distribution in Extreme Modular Networks

Modularity is a key organizing principle in real-world large-scale complex networks. Many real-world networks exhibit modular structures such as transportation infrastructures, communication networks and social media. Having the knowledge of the shortest paths length distribution (DSPL) between random pairs of nodes in such networks is important for understanding many processes, including diffusion or flow. Here, we provide analytical methods which are in good agreement with simulations on large scale networks with an extreme modular structure. By extreme modular, we mean that two modules or communities may be connected by maximum one link. As a result of the modular structure of the network, we obtain a distribution showing many peaks that represent the number of modules a typical shortest path is passing through. We present theory and results for the case where inter-links are weighted, as well as cases in which the inter-links are spread randomly across nodes in the community or limited to a specific set of nodes.

physics.soc-ph↗

arXiv2019

Optimal shattering of complex networks

We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible size. We obtain bounds for different regimes of random regular graphs, Erdős-Rényi random graphs, and scale free networks, some of which are tight. We show that the performance of attacks by degree is bounded away from optimality. Finally we present a polynomial time attack algorithm and prove its optimal performance in certain cases.

physics.soc-ph↗

arXiv2019

Unusual changeover in the transition nature of local-interaction Potts models

A combinatorial approach is used to study the critical behavior of a $q$-state Potts model with a round-the-face interaction. Using this approach it is shown that the model exhibits a first order transition for $q>3$. A second order transition is numerically detected for $q=2$. Based on these findings, it is deduced that for some two-dimensional ferromagnetic Potts models with completely local interaction, there is a changeover in the transition order at a critical integer $q_c\leq 3$. This stands in contrast to the standard two-spin interaction Potts model where the maximal integer value for which the transition is continuous is $q_c=4$. A lower bound on the first order critical temperature is additionally derived.

cond-mat.stat-mech↗

arXiv2019

Cardinality Estimation in a Virtualized Network Device Using Online Machine Learning

Cardinality estimation algorithms receive a stream of elements, with possible repetitions, and return the number of distinct elements in the stream. Such algorithms seek to minimize the required memory and CPU resource consumption at the price of inaccuracy in their output. In computer networks, cardinality estimation algorithms are mainly used for counting the number of distinct flows, and they are divided into two categories: sketching algorithms and sampling algorithms. Sketching algorithms require the processing of all packets, and they are therefore usually implemented by dedicated hardware. Sampling algorithms do not require processing of all packets, but they are known for their inaccuracy. In this work we identify one of the major drawbacks of sampling-based cardinality estimation algorithms: their inability to adapt to changes in flow size distribution. To address this problem, we propose a new sampling-based adaptive cardinality estimation framework, which uses online machine learning. We evaluate our framework using real traffic traces, and show significantly better accuracy compared to the best known sampling-based algorithms, for the same fraction of processed packets.

cs.NI↗

arXiv2018

Optimal resource allocation for network functionality

The traditional approach to network robustness, is based on comparing network parameters before and after an event of nodes removal, such as the change in network diameter, the change in giant component size and the existence of giant component. Recently, a new approach to network robustness was presented, where the network functionality during its entire life span (during the node removal event) is considered. This approach considers nodes removal due to aging - a state where nodes can be degenerated and become nonfunctional, when their survival time duration - their lifetime - is passed. Accordingly, a problem that has to be solved is: in the network design stage, how to divide a budget of lifetime between the network's nodes, such that the network functionality during all the stages of nodes removal due to aging, is maximized. To date, the problem has been solved only partially and numerically. In this paper we solve the problem analytically, and derive a criterion for choosing the right set of nodes on which the total lifetime budget should be divided. We also find analytically the best way of dividing the lifetime budget between the chosen set nodes, such that the network robustness with consideration to its functionality in the entire life span, is maximized.

physics.soc-ph↗

arXiv2018

Synchronization of chaotic systems: A microscopic description

The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov exponents, that help predict the systems transitions into globally organized states. However, the local, microscopic, description of this emergent process continues to elude us. Here we show that at the microscopic level, synchronization is captured through a gradual process of topological adjustment in phase space, in which the strange attractors of the two coupled systems continuously converge, taking similar form, until complete topological synchronization ensues. We observe the local nucleation of topological synchronization in specific regions of the systems attractor, providing early signals of synchrony, that appear significantly before the onset of complete synchronization. This local synchronization initiates at the regions of the attractor characterized by lower expansion rates, in which the chaotic trajectories are least sensitive to slight changes in initial conditions. Our findings offer an alternative description of synchronization in chaotic systems, exposing its local embryonic stages that are overlooked by the currently established global analysis. Such local topological synchronization enables the identification of configurations where prediction of the state of one system is possible from measurements on that of the other, even in the absence of global synchronization.

nlin.CD↗

arXiv2018

Spontaneous repulsion in the $A+B\to0$ reaction on coupled networks

We study the transient dynamics of an $A+B \rightarrow 0$ process on a pair of randomly coupled networks, where reactants are initially separated. We find that, for sufficiently small fractions $q$ of cross-couplings, the concentration of $A$ (or $B$) particles decays linearly in a first stage and crosses over to a second linear decrease at a mixing time $t_x$. By numerical and analytical arguments, we show that for symmetric and homogeneous structures $t_x\propto(\nicefrac{\langle k \rangle}{q})\log(\nicefrac{\langle k \rangle}{q})$ where $\langle k \rangle$ is the mean degree of both networks. Being this behavior in marked contrast with a purely diffusive process---where the mixing time would go simply like $\langle k\rangle/q$---we identify the logarithmic slowing down in $t_x$ to be the result of a novel spontaneous mechanism of {\em repulsion} between the reactants $A$ and $B$ due to the interactions taking place at the networks' interface. We show numerically how this spontaneous repulsion effect depends on the topology of the underlying networks.

cond-mat.stat-mech↗

arXiv2018

K-shell decomposition reveals hierarchical cortical organization of the human brain

In recent years numerous attempts to understand the human brain were undertaken from a network point of view. A network framework takes into account the relationships between the different parts of the system and enables to examine how global and complex functions might emerge from network topology. Previous work revealed that the human brain features 'small world' characteristics and that cortical hubs tend to interconnect among themselves. However, in order to fully understand the topological structure of hubs one needs to go beyond the properties of a specific hub and examine the various structural layers of the network. To address this topic further, we applied an analysis known in statistical physics and network theory as k-shell decomposition analysis. The analysis was applied on a human cortical network, derived from MRI\DSI data of six participants. Such analysis enables us to portray a detailed account of cortical connectivity focusing on different neighborhoods of interconnected layers across the cortex. Our findings reveal that the human cortex is highly connected and efficient, and unlike the internet network contains no isolated nodes. The cortical network is comprised of a nucleus alongside shells of increasing connectivity that formed one connected giant component. All these components were further categorized into three hierarchies in accordance with their connectivity profile, with each hierarchy reflecting different functional roles. Such a model may explain an efficient flow of information from the lowest hierarchy to the highest one, with each step enabling increased data integration. At the top, the highest hierarchy (the nucleus) serves as a global interconnected collective and demonstrates high correlation with consciousness related regions, suggesting that the nucleus might serve as a platform for consciousness to emerge.

q-bio.NC↗

arXiv2018

Ferromagnetic Potts models with multisite interaction

We study the $q$ states Potts model with four site interaction on the square lattice. Based on the asymptotic behaviour of lattice animals, it is argued that when $q\leq 4$ the system exhibits a second-order phase transition, and when $q > 4$ the transition is first order. The $q=4$ model is borderline. We find ${1}/{\ln q}$ to be an upper bound on $T_c$, the exact critical temperature. Using a low-temperature expansion, we show that $1/(θ\ln q)$, where $θ>1$ is a $q$-dependent geometrical term, is an improved upper bound on $T_c$. In fact, our findings support $T_c=1/(θ\ln q)$. This expression is used to estimate the finite correlation length in first-order transition systems. These results can be extended to other lattices. Our theoretical predictions are confirmed numerically by an extensive study of the four-site interaction model using the Wang-Landau entropic sampling method for $q=3,4,5$. In particular, the $q=4$ model shows an ambiguous finite-size pseudocritical behaviour.

cond-mat.stat-mech↗

arXiv2018

Predicting the patterns of spatio-temporal signal propagation in complex networks

A major achievement in the study of complex networks is the observation that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet this universality does not naturally translate to the dynamics of these systems , hindering our progress towards a general theoretical framework of network dynamics. The source of this theoretical gap is the fact that the behavior of a complex system cannot be uniquely predicted from its topology, but rather depends also on the dynamic mechanisms of interaction between the nodes, hence systems with similar structure may exhibit profoundly different dynamic behavior. To bridge this gap, we derive here the patterns of network information transmission, indeed, the essence of a network's behavior, by offering a systematic translation of topology into the actual spatio-temporal propagation of perturbative signals. We predict, for an extremely broad range of nonlinear dynamic models, that the propagation rules condense around three highly distinctive dynamic universality classes, characterized by the interplay between network paths, degree distribution and the interaction dynamics. Our formalism helps us leverage the major advances in the mapping of real world networks, into predictions on the actual dynamic propagation, from the spread of viruses in social networks to the discussion of genetic information in cellular systems.

physics.soc-ph↗

arXiv2017

Abrupt transitions in collaborative social networks

Despite the wide use of networks as a versatile tool for exploring complex social systems, little is known about how to detect and forecast abrupt changes in social systems. In this report, we develop an early warning approach based on network properties to detect such changes. By analysing three collaborative social networks---one co-stardom, one patent and one scientific collaborative network, we discover that abrupt transitions inherent in these networks can serve as a good early warning signal, indicating, respectively, the dissolution of the Soviet Union, the emergence of the "soft matter" research field, and the merging of two scientific communities. We then develop a clique growth model that explains the universal properties of these real networks and find that they belong to a new universality class, described by the Gumbel distribution.

physics.soc-ph↗

arXiv2017

Design of endurable networks in the presence of aging

Networks are designed to satisfy given objectives under specific requirements. While the static connectivity of networks is normally analyzed and corresponding design principles for static robustness are proposed, the challenge still remains of how to design endurable networks that maintain the required level of connectivity during its whole lifespan, against component aging. We introduce network endurance as a new concept to evaluate networks overall performance during its whole lifespan, considering both network connectivity and network duration. We develop a framework for designing an endurable network by allocating the expected lifetimes of its components, given a limited budget. Based on percolation theory and simulation, we find that the maximal network endurance can be achieved with a quantitative balance between network duration and connectivity. For different endurance requirements, we find that the optimal design can be separated into two categories: strong dependence of lifetime on node's degree leads to larger network lifetime, while weak dependence generates stronger network connectivity. Our findings could help network design, by providing a quantitative prediction of network endurance based on network topology.

physics.soc-ph↗

arXiv2017

Optimal cost for strengthening or destroying a given network

Strengthening or destroying a network is a very important issue in designing resilient networks or in planning attacks against networks including planning strategies to immunize a network against diseases, viruses etc.. Here we develop a method for strengthening or destroying a random network with a minimum cost. We assume a correlation between the cost required to strengthen or destroy a node and the degree of the node. Accordingly, we define a cost function c(k), which is the cost of strengthening or destroying a node with degree k. Using the degrees $k$ in a network and the cost function c(k), we develop a method for defining a list of priorities of degrees, and for choosing the right group of degrees to be strengthened or destroyed that minimizes the total price of strengthening or destroying the entire network. We find that the list of priorities of degrees is universal and independent of the network's degree distribution, for all kinds of random networks. The list of priorities is the same for both strengthening a network and for destroying a network with minimum cost. However, in spite of this similarity there is a difference between their p_c - the critical fraction of nodes that has to be functional, to guarantee the existence of a giant component in the network.

physics.soc-ph↗

arXiv2016

MTS Sketch for Accurate Estimation of Set-Expression Cardinalities from Small Samples

Sketch-based streaming algorithms allow efficient processing of big data. These algorithms use small fixed-size storage to store a summary ("sketch") of the input data, and use probabilistic algorithms to estimate the desired quantity. However, in many real-world applications it is impractical to collect and process the entire data stream, the common practice is thus to sample and process only a small part of it. While sampling is crucial for handling massive data sets, it may reduce accuracy. In this paper we present a new framework that can accurately estimate the cardinality of any set expression between any number of streams using only a small sample of each stream. The proposed framework consists of a new sketch, called Maximal-Term with Subsample (MTS), and a family of algorithms that use this sketch. An example of a possible query that can be efficiently answered using the proposed sketch is, How many distinct tuples appear in tables $T_1$ and $T_2$, but not in $T_3$? The algorithms presented in this paper answer such queries accurately, processing only a small sample of the tuples in each table and using a constant amount of memory. Such estimations are useful for the optimization of queries over very large database systems. We show that all our algorithms are unbiased, and we analyze their asymptotic variance.

cs.DB↗

arXiv2016

On Simultaneous Percolation with Two Disk Types

In this paper we consider the simultaneous percolation of two Gilbert disk models. The two models are connected through excluding disks, which prevent elements of the second model to be in the vicinity of the first model. Under these assumptions we characterize the region of densities in which the two models both have a unique infinite connected component. The motivation for this work is the co-existence of two cognitive radio networks.

cs.NI↗

arXiv2016

A Minimal Variance Estimator for the Cardinality of Big Data Set Intersection

In recent years there has been a growing interest in developing "streaming algorithms" for efficient processing and querying of continuous data streams. These algorithms seek to provide accurate results while minimizing the required storage and the processing time, at the price of a small inaccuracy in their output. A fundamental query of interest is the intersection size of two big data streams. This problem arises in many different application areas, such as network monitoring, database systems, data integration and information retrieval. In this paper we develop a new algorithm for this problem, based on the Maximum Likelihood (ML) method. We show that this algorithm outperforms all known schemes and that it asymptotically achieves the optimal variance.

cs.DS↗

arXiv2015

Spatio-temporal propagation of cascading overload failures

Different from the direct contact in epidemics spread, overload failures propagate through hidden functional dependencies. Many studies focused on the critical conditions and catastrophic consequences of cascading failures. However, to understand the network vulnerability and mitigate the cascading overload failures, the knowledge of how the failures propagate in time and space is essential but still missing. Here we study the spatio-temporal propagation behavior of cascading overload failures analytically and numerically. The cascading overload failures are found to spread radially from the center of the initial failure with an approximately constant velocity. The propagation velocity decreases with increasing tolerance, and can be well predicted by our theoretical framework with one single correction for all the tolerance values. This propagation velocity is found similar in various model networks and real network structures. Our findings may help to predict and mitigate the dynamics of cascading overload failures in realistic systems.

physics.soc-ph↗

arXiv2015

Cardinality Estimation Meets Good-Turing

Cardinality estimation algorithms receive a stream of elements whose order might be arbitrary, with possible repetitions, and return the number of distinct elements. Such algorithms usually seek to minimize the required storage and processing at the price of inaccuracy in their output. Real-world applications of these algorithms are required to process large volumes of monitored data, making it impractical to collect and analyze the entire input stream. In such cases, it is common practice to sample and process only a small part of the stream elements. This paper presents and analyzes a generic algorithm for combining every cardinality estimation algorithm with a sampling process. We show that the proposed sampling algorithm does not affect the estimator's asymptotic unbiasedness, and we analyze the sampling effect on the estimator's variance.

cs.DS↗