arXiv subjects

H. E. Stanley

Publications and source records attributed to H. E. Stanley.

At least 37 records · Page 2Linked to original sources

arXiv2012

Critical Points of Correlated Percolation in a Gravitational Link-adding Network Model

Motivated by the importance of geometric information in real systems, a new model for long-range correlated percolation in link-adding networks is proposed with the connecting probability decaying with a power-law of the distance on the two-dimensional(2D) plane. By overlapping it with Achlioptas process, it serves as a gravity model which can be tuned to facilitate or inhibit the network percolation in a generic view, cover a broad range of thresholds. Moreover, it yields a set of new scaling relations. In the present work, we develop an approach to determine critical points for them by simulating the temporal evolutions of type-I, type-II and type-III links(chosen from both inter-cluster links, an intra-cluster link compared with an inter-cluster one, and both intra-cluster ones, respectively) and corresponding average lengths. Numerical results have revealed objective competition between fractions, average lengths of three types of links, verified the balance happened at critical points. The variation of decay exponents $a$ or transmission radius $R$ always shifts the temporal pace of the evolution, while the steady average lengths and the fractions of links always keep unchanged just as the values in Achlioptas process. Strategy with maximum gravity can keep steady average length, while that with minimum one can surpass it. Without the confinement of transmission range, $\bar{l} \to \infty$ in thermodynamic limit, while $\bar{l}$ does not when with it. However, both mechanisms support critical points. In two-dimensional free space, the relevance of correlated percolation in link-adding process is verified by validation of new scaling relations with various exponent $a$, which violates the scaling law of Weinrib's.

cond-mat.dis-nn↗

arXiv2012

Epidemics on Interconnected Networks

Populations are seldom completely isolated from their environment. Individuals in a particular geographic or social region may be considered a distinct network due to strong local ties, but will also interact with individuals in other networks. We study the susceptible-infected-recovered (SIR) process on interconnected network systems, and find two distinct regimes. In strongly-coupled network systems, epidemics occur simultaneously across the entire system at a critical infection strength $β_c$, below which the disease does not spread. In contrast, in weakly-coupled network systems, a mixed phase exists below $β_c$ of the coupled network system, where an epidemic occurs in one network but does not spread to the coupled network. We derive an expression for the network and disease parameters that allow this mixed phase and verify it numerically. Public health implications of communities comprising these two classes of network systems are also mentioned.

physics.soc-ph↗

arXiv2012

Identifying States of a Financial Market

The understanding of complex systems has become a central issue because complex systems exist in a wide range of scientific disciplines. Time series are typical experimental results we have about complex systems. In the analysis of such time series, stationary situations have been extensively studied and correlations have been found to be a very powerful tool. Yet most natural processes are non-stationary. In particular, in times of crisis, accident or trouble, stationarity is lost. As examples we may think of financial markets, biological systems, reactors or the weather. In non-stationary situations analysis becomes very difficult and noise is a severe problem. Following a natural urge to search for order in the system, we endeavor to define states through which systems pass and in which they remain for short times. Success in this respect would allow to get a better understanding of the system and might even lead to methods for controlling the system in more efficient ways. We here concentrate on financial markets because of the easy access we have to good data and because of the strong non-stationary effects recently seen. We analyze the S&P 500 stocks in the 19-year period 1992-2010. Here, we propose such an above mentioned definition of state for a financial market and use it to identify points of drastic change in the correlation structure. These points are mapped to occurrences of financial crises. We find that a wide variety of characteristic correlation structure patterns exist in the observation time window, and that these characteristic correlation structure patterns can be classified into several typical "market states". Using this classification we recognize transitions between different market states. A similarity measure we develop thus affords means of understanding changes in states and of recognizing developments not previously seen.

q-fin.ST↗

arXiv2011

Robustness of a Tree-like Network of Interdependent Networks

In reality, many real-world networks interact with and depend on other networks. We develop an analytical framework for studying interacting networks and present an exact percolation law for a network of $n$ interdependent networks (NON). We present a general framework to study the dynamics of the cascading failures process at each step caused by an initial failure occurring in the NON system. We study and compare both $n$ coupled Erdős-Rényi (ER) graphs and $n$ coupled random regular (RR) graphs. We found recently [Gao et. al. arXive:1010.5829] that for an NON composed of $n$ ER networks each of average degree $k$, the giant component, $P_{\infty}$, is given by $P_{\infty}=p[1-\exp(-kP_{\infty})]^n$ where $1-p$ is the initial fraction of removed nodes. Our general result coincides for $n=1$ with the known Erdős-Rényi second-order phase transition at a threshold, $p=p_c$, for a single network. For $n=2$ the general result for $P_{\infty}$ corresponds to the $n=2$ result [Buldyrev et. al., Nature, 464, (2010)]. Similar to the ER NON, for $n=1$ the percolation transition at $p_c$, is of second order while for any $n>1$ it is of first order. The first order percolation transition in both ER and RR (for $n>1$) is accompanied by cascading failures between the networks due to their interdependencies. However, we find that the robustness of $n$ coupled RR networks of degree $k$ is dramatically higher compared to the $n$ coupled ER networks of average degree $k$. While for ER NON there exists a critical minimum average degree $k=k_{\min}$, that increases with $n$, below which the system collapses, there is no such analogous $k_{\min}$ for RR NON system.

physics.data-an↗

arXiv2010

Catastrophic Cascade of Failures in Interdependent Networks

Modern network-like systems are usually coupled in such a way that failures in one network can affect the entire system. In infrastructures, biology, sociology, and economy, systems are interconnected and events taking place in one system can propagate to any other coupled system. Recent studies on such coupled systems show that the coupling increases their vulnerability to random failure. Properties for interdependent networks differ significantly from those of single-network systems. In this article, these results are reviewed and the main properties discussed.

physics.data-an↗

arXiv2010

Quarantine generated phase transition in epidemic spreading

We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered (SIR) model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w, and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold w_c separating a phase (w = w_c) where the disease does not spread out. We find that in our model the topology of the network strongly affects the size of the propagation, and that w_c increases with the mean degree and heterogeneity of the network. We also find that w_c is reduced if we perform a preferential rewiring, in which the rewiring probability is proportional to the degree of infected nodes.

physics.soc-ph↗

arXiv2009

Phase Transitions and Dynamics in Bulk and Interfacial Water

New experiments for water at the surface of proteins at very low temperature display intriguing dynamic behaviors. The extreme conditions of these experiments make it difficult to explore the wide range of thermodynamic state points needed to offer a suitable interpretation. Detailed simulations suffer the same problem, where equilibration times at low temperature become unreasonably long. We show how Monte Carlo simulations and mean field calculations of a tractable model of water help interpret the experimental results. Here we summarize the results for bulk water and investigate the thermodynamic and dynamic properties of supercooled water at an interface.

cond-mat.soft↗

arXiv2009

Designing 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 $P_{ij} \sim r_{ij}^{-α}$, where $r_{ij}$ 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 $α\approx 3.0$ was recently found [Bianconi {\it et al.}, arXiv:0810.4412 (2008)].

physics.soc-ph↗

arXiv2008

Automated identification of neurons and their locations

Individual locations of many neuronal cell bodies (>10^4) are needed to enable statistically significant measurements of spatial organization within the brain such as nearest-neighbor and microcolumnarity measurements. In this paper, we introduce an Automated Neuron Recognition Algorithm (ANRA) which obtains the (x,y) location of individual neurons within digitized images of Nissl-stained, 30 micron thick, frozen sections of the cerebral cortex of the Rhesus monkey. Identification of neurons within such Nissl-stained sections is inherently difficult due to the variability in neuron staining, the overlap of neurons, the presence of partial or damaged neurons at tissue surfaces, and the presence of non-neuron objects, such as glial cells, blood vessels, and random artifacts. To overcome these challenges and identify neurons, ANRA applies a combination of image segmentation and machine learning. The steps involve active contour segmentation to find outlines of potential neuron cell bodies followed by artificial neural network training using the segmentation properties (size, optical density, gyration, etc.) to distinguish between neuron and non-neuron segmentations. ANRA positively identifies 86[5]% neurons with 15[8]% error (mean[st.dev.]) on a wide range of Nissl-stained images, whereas semi-automatic methods obtain 80[7]%/17[12]%. A further advantage of ANRA is that it affords an unlimited increase in speed from semi-automatic methods, and is computationally efficient, with the ability to recognize ~100 neurons per minute using a standard personal computer. ANRA is amenable to analysis of huge photo-montages of Nissl-stained tissue, thereby opening the door to fast, efficient and quantitative analysis of vast stores of archival material that exist in laboratories and research collections around the world.

physics.bio-ph↗

arXiv2007

A transactional theory of fluctuations in company size

Detailed empirical studies of publicly traded business firms have established that the standard deviation of annual sales growth rates decreases with increasing firm sales as a power law, and that the sales growth distribution is non-Gaussian with slowly decaying tails. To explain these empirical facts, a theory is developed that incorporates both the fluctuations of a single firm's sales and the statistical differences among many firms. The theory reproduces both the scaling in the standard deviation and the non-Gaussian distribution of growth rates. Earlier models reproduce the same empirical features by splitting firms into somewhat ambiguous subunits; by decomposing total sales into individual transactions, this ambiguity is removed. The theory yields verifiable predictions and accommodates any form of business organization within a firm. Furthermore, because transactions are fundamental to economic activity at all scales, the theory can be extended to all levels of the economy, from individual products to multinational corporations.

physics.soc-ph↗

arXiv2007

Breakdown of the Stokes-Einstein Relation in Supercooled Water

Supercooled water exhibits a breakdown of the Stokes-Einstein relation between the diffusion constant $D$ and the alpha relaxation time $τ_α$. For water simulated with the TIP5P and ST2 potentials, we find that the temperature of the decoupling of diffusion and alpha relaxation correlates with the temperature of the maximum in specific heat that corresponds to crossing the Widom line $T_W(P)$. Specifically, we find that our results for $Dτ_α/T$ collapse onto a single master curve if temperature is replaced by $T-T_W(P)$, where $T_W(P)$ is the temperature where the constant-pressure specific heat achieves a maximum. Also, we find agreement between our ST2 simulations and experimental values of $Dτ_α/T$. We further find that the size of the mobile molecule clusters (dynamical heterogeneities) increases sharply near $T_W(P)$. Moreover, our calculations of mobile particle cluster size $ _w$ for different pressures, where $t^*$ is the time for which the mobile particle cluster size is largest, also collapse onto a single master curve if $T$ is replaced by $T-T_W(P)$. The crossover to a more locally structured low density liquid (LDL) environment as $T\to T_W(P)$ appears to be well correlated with both the breakdown of the Stokes-Einstein relation and the growth of dynamic heterogeneities.

cond-mat.soft↗

arXiv2006

Optimal Path and Minimal Spanning Trees in Random Weighted Networks

We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for the minimum distance. For Erdős-Rényi (ER) and scale free networks (SF), with parameter $λ$ ($λ>3$), we find that the small-world nature is destroyed. We also find numerically that for weak disorder the length of the optimal path scales logaritmically with the size of the networks studied. We also review the transition between the strong and weak disorder regimes in the scaling properties of the length of the optimal path for ER and SF networks and for a general distribution of weights, and suggest that for any distribution of weigths, the distribution of optimal path lengths has a universal form which is controlled by the scaling parameter $Z=\ell_{\infty}/A$ where $A$ plays the role of the disorder strength, and $\ell_{\infty}$ is the length of the optimal path in strong disorder. The relation for $A$ is derived analytically and supported by numerical simulations. We then study the minimum spanning tree (MST) and show that it is composed of percolation clusters, which we regard as "super-nodes", connected by a scale-free tree. We furthermore show that the MST can be partitioned into two distinct components. One component the {\it superhighways}, for which the nodes with high centrality dominate, corresponds to the largest cluster at the percolation threshold which is a subset of the MST. In the other component, {\it roads}, low centrality nodes dominate. We demonstrate the significance identifying the superhighways by showing that one can improve significantly the global transport by improving a very small fraction of the network.

cond-mat.dis-nn↗

arXiv2006

A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment

We present a preferential attachment growth model to obtain the distribution $P(K)$ of number of units $K$ in the classes which may represent business firms or other socio-economic entities. We found that $P(K)$ is described in its central part by a power law with an exponent $ϕ=2+b/(1-b)$ which depends on the probability of entry of new classes, $b$. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution $P(K)$ is exponential. Using analytical form of $P(K)$ and assuming proportional growth for units, we derive $P(g)$, the distribution of business firm growth rates. The model predicts that $P(g)$ has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent $ζ=3$. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates.

physics.soc-ph↗

arXiv2006

A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence

We introduce a model of proportional growth to explain the distribution $P(g)$ of business firm growth rates. The model predicts that $P(g)$ is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent $ζ=3$. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. We test the model at different levels of aggregation in the economy, from products, to firms, to countries, and we find that the its predictions are in good agreement with empirical evidence on both growth distributions and size-variance relationships.

physics.data-an↗

arXiv2006

Glass transition in biomolecules and the liquid-liquid critical point of water

Using molecular dynamics simulations, we investigate the relation between the dynamic transitions of biomolecules (lysozyme and DNA) and the dynamic and thermodynamic properties of hydration water. We find that the dynamic transition of the macromolecules, sometimes called a ``protein glass transition'', occurs at the temperature of dynamic crossover in the diffusivity of hydration water, and also coincides with the maxima of the isobaric specific heat $C_P$ and the temperature derivative of the orientational order parameter. We relate these findings to the hypothesis of a liquid-liquid critical point in water. Our simulations are consistent with the possibility that the protein glass transition results from crossing the Widom line, which is defined as the locus of correlation length maxima emanating from the hypothesized second critical point of water.

cond-mat.soft↗

arXiv2006

Violation of market efficiency in transition economies

We analyze the European transition economies and show that time series for most of major indices exhibit (i) power-law correlations in their values, power-law correlations in their magnitudes, and (iii) asymmetric probability distribution. We propose a stochastic model that can generate time series with all the previous features found in the empirical data.

physics.soc-ph↗

arXiv2006

Thermodynamic and Dynamic Anomalies for Dumbbell Molecules Interacting with a Repulsive Ramp-Like Potential

Using collision driven discrete molecular dynamics (DMD), we investigate the thermodynamics and dynamics of systems of 500 dumbbell molecules interacting by a purely repulsive ramp-like discretized potential, consisting of $n$ steps of equal size. We compare the behavior of the two systems, with $n = 18$ and $n = 144$ steps. Each system exhibits both thermodynamic and dynamic anomalies, a density maximum and the translational and rotational mobilities show anomalous behavior. Starting with very dense systems and decreasing the density, both mobilities first increase, reache a maximum, then decrease, reache a minimum, and finally increase; this behavior is similar to the behavior of SPC/E water. The regions in the pressure-temperature plane of translational and rotational mobility anomalies depend strongly on $n$. The product of the translational diffusion coefficient and the orientational correlation time increases with temperature, in contrast with the behavior of most liquids.

cond-mat.soft↗

arXiv2005

The Growth of Business Firms: Theoretical Framework and Empirical Evidence

We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the model's predictions agree with empirical growth distributions and size-variance relationships.

physics.data-an↗