Correlation entropy of synaptic input-output dynamics

The responses of synapses in the neocortex show highly stochastic and nonlinear behavior. The microscopic dynamics underlying this behavior, and its computational consequences during natural patterns of synaptic input, are not explained by conventional macroscopic models of deterministic ensemble mean dynamics. Here, we introduce the correlation entropy of the synaptic input-output map as a measure of synaptic reliability which explicitly includes the microscopic dynamics. Applying this to experimental data, we find that cortical synapses show a low-dimensional chaos driven by the natural input pattern.Comment: 7 pages, 6 Figures (7 figure files

Topological properties and fractal analysis of recurrence network constructed from fractional Brownian motions

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the relationship between $H$ and $$can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e. the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension$$ of recurrence networks decreases with the Hurst index $H$ of the associated FBMs, and their dependence approximately satisfies the linear formula $\approx 2 - H$. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index $H=0.5$ possess the strongest multifractality. In addition, the dependence relationships of the average information dimension $$and the average correlation dimension$$ on the Hurst index $H$ can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.Comment: 25 pages, 1 table, 15 figures. accepted by Phys. Rev.

Granger Causality and Cross Recurrence Plots in Rheochaos

Our stress relaxation measurements on wormlike micelles using a Rheo-SALS (rheology + small angle light scattering) apparatus allow simultaneous measurements of the stress and the scattered depolarised intensity. The latter is sensitive to orientational ordering of the micelles. To determine the presence of causal influences between the stress and the depolarised intensity time series, we have used the technique of linear and nonlinear Granger causality. We find there exists a feedback mechanism between the two time series and that the orientational order has a stronger causal effect on the stress than vice versa. We have also studied the phase space dynamics of the stress and the depolarised intensity time series using the recently developed technique of cross recurrence plots (CRPs). The presence of diagonal line structures in the CRPs unambiguously proves that the two time series share similar phase space dynamics.Comment: 10 pages, 7 figure

On the fraction of dark matter in charged massive particles (CHAMPs)

From various cosmological, astrophysical and terrestrial requirements, we derive conservative upper bounds on the present-day fraction of the mass of the Galactic dark matter (DM) halo in charged massive particles (CHAMPs). If dark matter particles are neutral but decay lately into CHAMPs, the lack of detection of heavy hydrogen in sea water and the vertical pressure equilibrium in the Galactic disc turn out to put the most stringent bounds. Adopting very conservative assumptions about the recoiling velocity of CHAMPs in the decay and on the decay energy deposited in baryonic gas, we find that the lifetime for decaying neutral DM must be > (0.9-3.4)x 10^3 Gyr. Even assuming the gyroradii of CHAMPs in the Galactic magnetic field are too small for halo CHAMPs to reach Earth, the present-day fraction of the mass of the Galactic halo in CHAMPs should be < (0.4-1.4)x 10^{-2}. We show that redistributing the DM through the coupling between CHAMPs and the ubiquitous magnetic fields cannot be a solution to the cuspy halo problem in dwarf galaxies.Comment: 21 pages, 2 figures. To appear in JCA

The KLN Theorem and Soft Radiation in Gauge Theories: Abelian Case

We present a covariant formulation of the Kinoshita, Lee, Nauenberg (KLN) theorem for processes involving the radiation of soft particles. The role of the disconnected diagrams is explored and a rearrangement of the perturbation theory is performed such that the purely disconnected diagrams are factored out. The remaining effect of the disconnected diagrams results in a simple modification of the usual Feynman rules for the S-matrix elements. As an application, we show that when combined with the Low theorem, this leads to a proof of the absense of the $1/Q$ corrections to inclusive processes (like the Drell-Yan process). In this paper the abelian case is discussed to all orders in the coupling.Comment: 27 pages, LaTeX, 14 figure

Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data

The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias

Recurrence quantification analysis as a tool for the characterization of molecular dynamics simulations

A molecular dynamics simulation of a Lennard-Jones fluid, and a trajectory of the B1 immunoglobulin G-binding domain of streptococcal protein G (B1-IgG) simulated in water are analyzed by recurrence quantification, which is noteworthy for its independence from stationarity constraints, as well as its ability to detect transients, and both linear and nonlinear state changes. The results demonstrate the sensitivity of the technique for the discrimination of phase sensitive dynamics. Physical interpretation of the recurrence measures is also discussed.Comment: 7 pages, 8 figures, revtex; revised for review for Phys. Rev. E (clarifications and expansion of discussion)-- addition of the 8 postscript figures previously omitted, but unchanged from version

The Interstellar Environment of our Galaxy

We review the current knowledge and understanding of the interstellar medium of our galaxy. We first present each of the three basic constituents - ordinary matter, cosmic rays, and magnetic fields - of the interstellar medium, laying emphasis on their physical and chemical properties inferred from a broad range of observations. We then position the different interstellar constituents, both with respect to each other and with respect to stars, within the general galactic ecosystem.Comment: 39 pages, 12 figures (including 3 figures in 2 parts

Scaling Patterns for QCD Jets

Jet emission at hadron colliders follows simple scaling patterns. Based on perturbative QCD we derive Poisson and staircase scaling for final state as well as initial state radiation. Parton density effects enhance staircase scaling at low multiplicities. We propose experimental tests of our theoretical findings in Z+jets and QCD gap jets production based on minor additions to current LHC analyses.Comment: 36 pages, 16 figure