Showing papers in "Physical Review E in 2001"
TL;DR: It is demonstrated that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
Abstract: Recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition to simple undirected, unipartite graphs, we examine the properties of directed and bipartite graphs. Among other results, we derive exact expressions for the position of the phase transition at which a giant component first forms, the mean component size, the size of the giant component if there is one, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within a graph. We apply our theory to some real-world graphs, including the worldwide web and collaboration graphs of scientists and Fortune 1000 company directors. We demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
3,655 citations
TL;DR: In this article, the authors constructed networks of collaboration between scientists in each of these disciplines and proposed a measure of collaboration strength based on the number of papers coauthored by pairs of scientists, and the number other scientists with whom they coauthored those papers.
Abstract: Using computer databases of scientific papers in physics, biomedical research, and computer science, we have constructed networks of collaboration between scientists in each of these disciplines. In these networks two scientists are considered connected if they have coauthored one or more papers together. Here we study a variety of nonlocal statistics for these networks, such as typical distances between scientists through the network, and measures of centrality such as closeness and betweenness. We further argue that simple networks such as these cannot capture variation in the strength of collaborative ties and propose a measure of collaboration strength based on the number of papers coauthored by pairs of scientists, and the number of other scientists with whom they coauthored those papers.
2,528 citations
TL;DR: Dynamical properties of brain electrical activity from different recording regions and from different physiological and pathological brain states are compared and strongest indications of nonlinear deterministic dynamics were found for seizure activity.
Abstract: We compare dynamical properties of brain electrical activity from different recording regions and from different physiological and pathological brain states Using the nonlinear prediction error and an estimate of an effective correlation dimension in combination with the method of iterative amplitude adjusted surrogate data, we analyze sets of electroencephalographic (EEG) time series: surface EEG recordings from healthy volunteers with eyes closed and eyes open, and intracranial EEG recordings from epilepsy patients during the seizure free interval from within and from outside the seizure generating area as well as intracranial EEG recordings of epileptic seizures As a preanalysis step an inclusion criterion of weak stationarity was applied Surface EEG recordings with eyes open were compatible with the surrogates' null hypothesis of a Gaussian linear stochastic process Strongest indications of nonlinear deterministic dynamics were found for seizure activity Results of the other sets were found to be inbetween these two extremes
2,387 citations
TL;DR: Using computer databases of scientific papers in physics, biomedical research, and computer science, a network of collaboration between scientists in each of these disciplines is constructed, and a number of measures of centrality and connectedness in the same networks are studied.
Abstract: Using computer databases of scientific papers in physics, biomedical research, and computer science, we have constructed networks of collaboration between scientists in each of these disciplines. In these networks two scientists are considered connected if they have coauthored one or more papers together. We study a variety of statistical properties of our networks, including numbers of papers written by authors, numbers of authors per paper, numbers of collaborators that scientists have, existence and size of a giant component of connected scientists, and degree of clustering in the networks. We also highlight some apparent differences in collaboration patterns between the subjects studied. In the following paper, we study a number of measures of centrality and connectedness in the same networks.
2,031 citations
TL;DR: It is shown that the probability of a pair of scientists collaborating increases with the number of other collaborators they have in common, and that the probabilities of a particular scientist acquiring new collaborators increases withThe number of his or her past collaborators.
Abstract: We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of a pair of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and power-law degree distributions in networks.
1,867 citations
TL;DR: A dynamical model for the spreading of epidemics in complex networks that implies that scale-free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess.
Abstract: We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null. On the contrary, on a wide range of scale-free networks we observe the absence of an epidemic threshold and its associated critical behavior. This implies that scale-free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess. These results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks.
1,550 citations
TL;DR: A number of local search strategies that utilize high degree nodes in power-law graphs and that have costs scaling sublinearly with the size of the graph are introduced and demonstrated on the GNUTELLA peer-to-peer network.
Abstract: Many communication and social networks have power-law link distributions, containing a few nodes that have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and networking, a fact that can be exploited when designing efficient search algorithms. We introduce a number of local search strategies that utilize high degree nodes in power-law graphs and that have costs scaling sublinearly with the size of the graph. We also demonstrate the utility of these strategies on the GNUTELLA peer-to-peer network.
1,254 citations
TL;DR: It is shown how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.
Abstract: scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ‘‘apparent’’ scaling of the trend. We study how the characteristics of these crossovers depend on ~i! the slope of the linear trend; ~ii! the amplitude and period of the periodic trend; ~iii! the amplitude and power of the power-law trend, and ~iv! the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws—i.e., long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise. In addition, we show how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.
1,227 citations
TL;DR: This paper presents a full velocity difference model for a car-following theory based on the previous models in the literature, and finds that the model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion.
Abstract: In this paper, we present a full velocity difference model for a car-following theory based on the previous models in the literature. To our knowledge, the model is an improvement over the previous ones theoretically, because it considers more aspects in car-following process than others. This point is verified by numerical simulation. Then we investigate the property of the model using both analytic and numerical methods, and find that the model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion.
1,216 citations
TL;DR: An efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models that overcomes the tunneling barrier between coexisting phases at first-order phase transitions.
Abstract: We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models. The density of states is modified at each step when the energy level is visited to produce a flat histogram. By carefully controlling the modification factor, we allow the density of states to converge to the true value very quickly, even for large systems. From the density of states at the end of the random walk, we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature. Using this method, we not only can avoid repeating simulations at multiple temperatures, but we can also estimate the free energy and entropy, quantities that are not directly accessible by conventional Monte Carlo simulations. This algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability. As with the multicanonical Monte Carlo technique, our method overcomes the tunneling barrier between coexisting phases at first-order phase transitions. In this paper, we apply our algorithm to both first- and second-order phase transitions to demonstrate its efficiency and accuracy. We obtained direct simulational estimates for the density of states for two-dimensional ten-state Potts models on lattices up to 200 x 200 and Ising models on lattices up to 256 x 256. Our simulational results are compared to both exact solutions and existing numerical data obtained using other methods. Applying this approach to a three-dimensional +/-J spin-glass model, we estimate the internal energy and entropy at zero temperature; and, using a two-dimensional random walk in energy and order-parameter space, we obtain the (rough) canonical distribution and energy landscape in order-parameter space. Preliminary data suggest that the glass transition temperature is about 1.2 and that better estimates can be obtained with more extensive application of the method. This simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space.
1,111 citations
TL;DR: Wave propagation in a double negative (DNG) medium, i.e., a medium having negative permittivity and negative permeability, is studied both analytically and numerically and the DNG slab solution is used to critically examine the perfect lens concept suggested recently by Pendry.
Abstract: Wave propagation in a double negative (DNG) medium, i.e., a medium having negative permittivity and negative permeability, is studied both analytically and numerically. The choices of the square root that leads to the index of refraction and the wave impedance in a DNG medium are determined by imposing analyticity in the complex frequency domain, and the corresponding wave properties associated with each choice are presented. These monochromatic concepts are then tested critically via a one-dimensional finite difference time domain (FDTD) simulation of the propagation of a causal, pulsed plane wave in a matched, lossy Drude model DNG medium. The causal responses of different spectral regimes of the medium with positive or negative refractive indices are studied by varying the carrier frequency of narrowband pulse excitations. The smooth transition of the phenomena associated with a DNG medium from its early-time nondispersive behavior to its late-time monochromatic response is explored with wideband pulse excitations. These FDTD results show conclusively that the square root choice leading to a negative index of refraction and positive wave impedance is the correct one, and that this choice is consistent with the overall causality of the response. An analytical, exact frequency domain solution to the scattering of a wave from a DNG slab is also given and is used to characterize several physical effects. This solution is independent of the choice of the square roots for the index of refraction and the wave impedance, and thus avoids any controversy that may arise in connection with the signs of these constituents. The DNG slab solution is used to critically examine the perfect lens concept suggested recently by Pendry. It is shown that the perfect lens effect exists only under the special case of a DNG medium with $\ensuremath{\epsilon}(\ensuremath{\omega})=\ensuremath{\mu}(\ensuremath{\omega})=\ensuremath{-}1$ that is both lossless and nondispersive. Otherwise, the closed form solutions for the field structure reveal that the DNG slab converts an incident spherical wave into a localized beam field whose parameters depend on the values of $\ensuremath{\epsilon}$ and $\ensuremath{\mu}.$ This beam field is characterized with a paraxial approximation of the exact DNG slab solution. These monochromatic concepts are again explored numerically via a causal two-dimensional FDTD simulation of the scattering of a pulsed cylindrical wave by a matched, lossy Drude model DNG slab. These FDTD results demonstrate conclusively that the monochromatic electromagnetic power flow through the DNG slab is channeled into beams rather then being focused and, hence, the Pendry perfect lens effect is not realizable with any realistic metamaterial.
TL;DR: A systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, finds that a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions is found.
Abstract: We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow vx(z) scales with height of the pile H, according to vx(z) proportional to H(alpha), with alpha=1.52+/-0.05. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations.
TL;DR: The organizational development of growing random networks is investigated, and the combined age and degree distribution of nodes shows that old nodes typically have a large degree.
Abstract: The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively, and linking each to an earlier node of degree k with an attachment probability ${A}_{k}.$ When ${A}_{k}$ grows more slowly than linearly with k, the number of nodes with k links, ${N}_{k}(t),$ decays faster than a power law in k, while for ${A}_{k}$ growing faster than linearly in k, a single node emerges which connects to nearly all other nodes. When ${A}_{k}$ is asymptotically linear, ${N}_{k}(t)\ensuremath{\sim}{\mathrm{tk}}^{\ensuremath{-}\ensuremath{
u}},$ with $\ensuremath{
u}$ dependent on details of the attachment probability, but in the range $2l\ensuremath{
u}l\ensuremath{\infty}.$ The combined age and degree distribution of nodes shows that old nodes typically have a large degree. There is also a significant correlation in the degrees of neighboring nodes, so that nodes of similar degree are more likely to be connected. The size distributions of the in and out components of the network with respect to a given node---namely, its ``descendants'' and ``ancestors''---are also determined. The in component exhibits a robust ${s}^{\ensuremath{-}2}$ power-law tail, where s is the component size. The out component has a typical size of order $\mathrm{ln}t,$ and it provides basic insights into the genealogy of the network.
TL;DR: Approximate expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual's degree of connectivity within the population are derived.
Abstract: We discuss properties of infection processes on scale-free networks, relating them to the node-connectivity distribution that characterizes the network. Considering the epidemiologically important case of a disease that confers permanent immunity upon recovery, we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual's degree of connectivity within the population. As in an earlier study [R. Pastor-Satorras and A. Vesipignani, Phys. Rev. Lett. 86, 3200 (2001); Phys. Rev. E. 63, 006117 (2001)] for an infection that did not confer immunity upon recovery, the epidemic process--in contrast with many traditional epidemiological models--does not exhibit threshold behavior, and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale-free network. Finally, we discuss effects that arise from finite population sizes, showing that networks of finite size do exhibit threshold effects: infections cannot spread for arbitrarily low transmission probabilities.
TL;DR: Using computer simulations, it is found that models that incorporate all of these features reproduce many of the features of real social networks, including high levels of clustering or network transitivity and strong community structure in which individuals have more links to others within their community than to individuals from other communities.
Abstract: We propose some simple models of the growth of social networks, based on three general principles: (1). meetings take place between pairs of individuals at a rate that is high if a pair has one or more mutual friends and low otherwise; (2). acquaintances between pairs of individuals who rarely meet decay over time; (3). there is an upper limit on the number of friendships an individual can maintain. Using computer simulations, we find that models that incorporate all of these features reproduce many of the features of real social networks, including high levels of clustering or network transitivity and strong community structure in which individuals have more links to others within their community than to individuals from other communities.
TL;DR: An evolutionary version of the Prisoner's Dilemma game, played by agents placed in a small-world network, is studied, observing that different topologies, ranging from regular lattices to random graphs, produce a variety of emergent behaviors.
Abstract: We study an evolutionary version of the Prisoner's Dilemma game, played by agents placed in a small-world network. Agents are able to change their strategy, imitating that of the most successful neighbor. We observe that different topologies, ranging from regular lattices to random graphs, produce a variety of emergent behaviors. This is a contribution towards the study of social phenomena and transitions governed by the topology of the community.
TL;DR: To the knowledge, it is the first multifractal process with continuous dilation invariance properties and stationary increments and it is briefly explained how, in the same way, one can build stationary multifractional processes or positive random measures.
Abstract: We introduce a class of multifractal processes, referred to as multifractal random walks (MRWs). To our knowledge, it is the first multifractal process with continuous dilation invariance properties and stationary increments. MRWs are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio. The MRWs are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments. We briefly explain how, in the same way, one can build stationary multifractal processes or positive random measures.
TL;DR: Methods to determine the eigenvalues of networks comparable in size to real systems are developed, obtaining several surprising results on the spectra of adjacency matrices corresponding to models of real-world graphs.
Abstract: results on the spectra of adjacency matrices corresponding to models of real-world graphs. We find that when the number of links grows as the number of nodes, the spectral density of uncorrelated random matrices does not converge to the semicircle law. Furthermore, the spectra of real-world graphs have specific features, depending on the details of the corresponding models. In particular, scale-free graphs develop a trianglelike spectral density with a power-law tail, while small-world graphs have a complex spectral density consisting of several sharp peaks. These and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks.
TL;DR: An efficient algorithm is described that can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system.
Abstract: We describe in detail an efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system. We demonstrate our algorithm by using it to investigate a number of issues in percolation theory, including the position of the percolation transition for site percolation on the square lattice, the stretched exponential behavior of spanning probabilities away from the critical point, and the size of the giant component for site percolation on random graphs.
TL;DR: A method for experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data is proposed and an index that quantifies the asymmetry in coupling is introduced.
Abstract: We propose a method for experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. The technique is applicable to both noisy and chaotic systems that can be nonidentical or even structurally different. We introduce an index that quantifies the asymmetry in coupling.
TL;DR: It is shown that the lowest moments of fractional Brownian motion are actually all identical, except the second moment of the velocity, which provides a simple criterion that enable us to distinguish these two non-Markovian processes.
Abstract: We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffusion exhibit the same power-law behavior. Here we show that their lowest moments are actually all identical, except the second moment of the velocity. This provides a simple criterion that enable us to distinguish these two non-Markovian processes.
TL;DR: It is concluded that grown graphs, however randomly they are constructed, are fundamentally different from their static random graph counterparts.
Abstract: We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability $\ensuremath{\delta},$ two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time steps. In the limit of large t, the resulting graph displays surprisingly rich characteristics. In particular, a giant component emerges in an infinite-order phase transition at $\ensuremath{\delta}=1/8.$ At the transition, the average component size jumps discontinuously but remains finite. In contrast, a static random graph with the same degree distribution exhibits a second-order phase transition at $\ensuremath{\delta}=1/4,$ and the average component size diverges there. These dramatic differences between grown and static random graphs stem from a positive correlation between the degrees of connected vertices in the grown graph---older vertices tend to have higher degree, and to link with other high-degree vertices, merely by virtue of their age. We conclude that grown graphs, however randomly they are constructed, are fundamentally different from their static random graph counterparts.
TL;DR: A recently introduced stochastic model for fluid dynamics with continuous velocities and efficient multiparticle collisions is investigated, and it is shown how full Galilean-invariance can be achieved for arbitrary Mach numbers.
Abstract: A recently introduced stochastic model for fluid dynamics with continuous velocities and efficient multiparticle collisions is investigated, and it is shown how full Galilean-invariance can be achieved for arbitrary Mach numbers. Analytic expressions for the viscosity and diffusion constant are also derived and compared with simulation results. Long-time tails in the velocity and stress autocorrelation functions are measured.
TL;DR: The impact of global traffic light control strategies in a recently proposed cellular automaton model for vehicular traffic in city networks, which combines basic ideas of the Biham-Middleton-Levine model for city traffic and the Nagel-Schreckenberg model for highway traffic, is studied.
Abstract: We study the impact of global traffic light control strategies in a recently proposed cellular automaton model for vehicular traffic in city networks. The model combines basic ideas of the Biham-Middleton-Levine model for city traffic and the Nagel-Schreckenberg model for highway traffic. The city network has a simple square lattice geometry. All streets and intersections are treated equally, i.e., there are no dominant streets. Starting from a simple synchronized strategy, we show that the capacity of the network strongly depends on the cycle times of the traffic lights. Moreover, we point out that the optimal time periods are determined by the geometric characteristics of the network, i.e., the distance between the intersections. In the case of synchronized traffic lights, the derivation of the optimal cycle times in the network can be reduced to a simpler problem, the flow optimization of a single street with one traffic light operating as a bottleneck. In order to obtain an enhanced throughput in the model, improved global strategies are tested, e.g., green wave and random switching strategies, which lead to surprising results.
TL;DR: The FFPE is shown to be compatible with the Scher-Montroll approach for dispersive transport, and thus is applicable in a large variety of disordered systems.
Abstract: Recently, Metzler et al. [Phys. Rev. Lett. 82, 3563 (1999)], introduced a fractional Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field, and a Boltzmann thermal heat bath. In this paper we present the solution of the FFPE in terms of an integral transformation. The transformation maps the solution of ordinary Fokker-Planck equation onto the solution of the FFPE, and is based on Levy's generalized central limit theorem. The meaning of the transformation is explained based on the known asymptotic solution of the continuous time random walk (CTRW). We investigate in detail (i) a force-free particle, (ii) a particle in a uniform field, and (iii) a particle in a harmonic field. We also find an exact solution of the CTRW, and compare the CTRW result with the corresponding solution of the FFPE. The relation between the fractional first passage time problem in an external nonlinear field and the corresponding integer first passage time is given. An example of the one-dimensional fractional first passage time in an external linear field is investigated in detail. The FFPE is shown to be compatible with the Scher-Montroll approach for dispersive transport, and thus is applicable in a large variety of disordered systems. The simple FFPE approach can be used as a practical tool for a phenomenological description of certain types of complicated transport phenomena.
TL;DR: This work has found zero-velocity, moving and exploding pulsating localized structures, period doubling of pulsations and the sequence of PD bifurcations, and found chaotic pulsating solitons of the Ginzburg-Landau equation.
Abstract: The complex Ginzburg-Landau equation (CGLE) is a standard model for pulse generation in mode-locked lasers with fast saturable absorbers. We have found complicated pulsating behavior of solitons of the CGLE and regions of their existence in the five-dimensional parameter space. We have found zero-velocity, moving and exploding pulsating localized structures, period doubling (PD) of pulsations and the sequence of PD bifurcations. We have also found chaotic pulsating solitons. We have plotted regions of parameters of the CGLE where pulsating solutions exist. We also demonstrate the coexistence (bi- and multistability) of different types of pulsating solutions in certain regions of the parameter space of the CGLE.
TL;DR: The mesoscopic nonequilibrium thermodynamics theory is used to derive the general kinetic equation of a system in the presence of potential barriers, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries.
Abstract: We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.
TL;DR: Analysis of the thermal expansivity of thin polystyrene films on silicon substrates with thicknesses of 10-200 nm finds well-defined glass transitions, and detailed analysis of the expansivities shows that for thinner films the transition width is broadened, while the strength of the transition is reduced.
Abstract: We have used ellipsometry to study the thermal expansivity of thin polystyrene films on silicon substrates with thicknesses of 10--200 nm. We find well-defined glass transitions, and detailed analysis of the expansivities shows that for thinner films the transition width is broadened, while the strength of the transition, defined by the difference between the expansivities in the liquid and glassy state, is reduced; the expansivity in the glassy state is higher than in the bulk. These phenomena are consistent with the idea that a layer of roughly constant thickness, of order 10 nm, near the surface of the film has liquidlike thermal properties at all experimental temperatures.
TL;DR: The analysis provides an estimate of the effective number of statistically independent degrees of freedom, denoted N(eff), that a large correlated system can have, and shows that positive correlations decrease the estimation capability of the network, relative to the uncorrelated population.
Abstract: Neuronal representations of external events are often distributed across large populations of cells. We study the effect of correlated noise on the accuracy of these neuronal population codes. Our main question is whether the inherent error in the population code can be suppressed by increasing the size of the population N in the presence of correlated noise. We address this issue using a model of a population of neurons that are broadly tuned to an angular variable in two dimensions. The fluctuations in the neuronal activities are modeled as Gaussian noises with pairwise correlations that decay exponentially with the difference between the preferred angles of the correlated cells. We assume that the system is broadly tuned, which means that both the correlation length and the width of the tuning curves of the mean responses span a substantial fraction of the entire system length. The performance of the system is measured by the Fisher information (FI), which bounds its estimation error. By calculating the FI in the limit of a large N, we show that positive correlations decrease the estimation capability of the network, relative to the uncorrelated population. The information capacity saturates to a finite value as the number of cells in the population grows. In contrast, negative correlations substantially increase the information capacity of the neuronal population. These results are supplemented by the effect of correlations on the mutual information of the system. Our analysis provides an estimate of the effective number of statistically independent degrees of freedom, denoted N(eff), that a large correlated system can have. According to our theory N(eff) remains finite in the limit of a large N. Estimating the parameters of the correlations and tuning curves from experimental data in some cortical areas that code for angles, we predict that the number of effective degrees of freedom embedded in localized populations in these areas is less than or of the order of approximately 10(2).
TL;DR: It is shown that by proper spatial arrangement of magnetic and dielectric components one can construct a magnetic photonic crystal with strong spectral asymmetry (nonreciprocity) omega(k-->) not equal omega(-k-->).
Abstract: We study band dispersion relations omega(k-->) of a photonic crystal with at least one of the constitutive components being a magnetically ordered material. It is shown that by proper spatial arrangement of magnetic and dielectric components one can construct a magnetic photonic crystal with strong spectral asymmetry (nonreciprocity) omega(k-->) not equal omega(-k-->). The spectral asymmetry, in turn, results in a number of interesting phenomena, in particular, one-way transparency when the magnetic photonic crystal, being perfectly transparent for a Bloch wave of frequency omega, "freezes" the radiation of the same frequency omega propagating in the opposite direction. The frozen radiation corresponds to a Bloch wave with zero group velocity partial differential omega(k)/ partial differential k=0 and, in addition, with partial differential(2)omega(k)/ partial differential k(2)=0.