Fluctuating Fronts as Correlated Extreme Value Problems: An Example of Gaussian Statistics

In this paper, we view fluctuating fronts made of particles on a one-dimensional lattice as an extreme value problem. The idea is to denote the configuration for a single front realization at time $t$ by the set of co-ordinates $\{k_i(t)\}\equiv[k_1(t),k_2(t),...,k_{N(t)}(t)]$ of the constituent particles, where $N(t)$ is the total number of particles in that realization at time $t$. When $\{k_i(t)\}$ are arranged in the ascending order of magnitudes, the instantaneous front position can be denoted by the location of the rightmost particle, i.e., by the extremal value $k_f(t)=\text{max}[k_1(t),k_2(t),...,k_{N(t)}(t)]$. Due to interparticle interactions, $\{k_i(t)\}$ at two different times for a single front realization are naturally not independent of each other, and thus the probability distribution $P_{k_f}(t)$ [based on an ensemble of such front realizations] describes extreme value statistics for a set of correlated random variables. In view of the fact that exact results for correlated extreme value statistics are rather rare, here we show that for a fermionic front model in a reaction-diffusion system, $P_{k_f}(t)$ is Gaussian. In a bosonic front model however, we observe small deviations from the Gaussian.Comment: 6 pages, 3 figures, miniscule changes on the previous version, to appear in Phys. Rev.

Renormalization group study of the two-dimensional random transverse-field Ising model

The infinite disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to $L=2048$. We have calculated sample dependent pseudo-critical points and studied their distribution, which is found to be characterized by the same shift and width exponent: $\nu=1.24(2)$. For different types of disorder the infinite disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: $x=0.982(15)$ and $\psi=0.48(2)$. We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases

Brainstem auditory evoked responses in man. 1: Effect of stimulus rise-fall time and duration

Short latency (under 10 msec) evoked responses elicited by bursts of white noise were recorded from the scalp of human subjects. Response alterations produced by changes in the noise burst duration (on-time) inter-burst interval (off-time), and onset and offset shapes are reported and evaluated. The latency of the most prominent response component, wave V, was markedly delayed with increases in stimulus rise-time but was unaffected by changes in fall-time. The amplitude of wave V was insensitive to changes in signal rise-and-fall times, while increasing signal on-time produced smaller amplitude responses only for sufficiently short off-times. It is concluded that wave V of the human auditory brainstem evoked response is solely an onset response

Strong Griffiths singularities in random systems and their relation to extreme value statistics

We consider interacting many particle systems with quenched disorder having strong Griffiths singularities, which are characterized by the dynamical exponent, z, such as random quantum systems and exclusion processes. In several d=1 and d=2 dimensional problems we have calculated the inverse time-scales, t^{-1}, in finite samples of linear size, L, either exactly or numerically. In all cases, having a discrete symmetry, the distribution function, P(t^{-1},L), is found to depend on the variable, u=t^{-1}L^{z/d}, and to be universal given by the limit distribution of extremes of independent and identically distributed random numbers. This finding is explained in the framework of a strong disorder renormalization group approach when, after fast degrees of freedom are decimated out the system is transformed into a set of non-interacting localized excitations. The Frechet distribution of P(t^{-1},L) is expected to hold for all random systems having a strong disorder fixed point, in which the Griffiths singularities are dominated by disorder fluctuations.Comment: 11 pages, 11 figure

Extreme statistics for time series: Distribution of the maximum relative to the initial value

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/f^alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRH_I). The exact MRH_I distribution is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random acceleration), and alpha=infinity (single sinusoidal mode). For other, intermediate values of alpha, the distribution is determined from simulations. We find that the MRH_I distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all alpha. The two main distinguishing features of the MRH_I distribution are the much larger weight for small relative heights and the divergence at zero height for alpha>3. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some non-periodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the MRH_I distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.Comment: 29 pages, 4 figure

In-depth analysis of the Naming Game dynamics: the homogeneous mixing case

Language emergence and evolution has recently gained growing attention through multi-agent models and mathematical frameworks to study their behavior. Here we investigate further the Naming Game, a model able to account for the emergence of a shared vocabulary of form-meaning associations through social/cultural learning. Due to the simplicity of both the structure of the agents and their interaction rules, the dynamics of this model can be analyzed in great detail using numerical simulations and analytical arguments. This paper first reviews some existing results and then presents a new overall understanding.Comment: 30 pages, 19 figures (few in reduced definition). In press in IJMP

Correlator Bank Detection of GW chirps. False-Alarm Probability, Template Density and Thresholds: Behind and Beyond the Minimal-Match Issue

The general problem of computing the false-alarm rate vs. detection-threshold relationship for a bank of correlators is addressed, in the context of maximum-likelihood detection of gravitational waves, with specific reference to chirps from coalescing binary systems. Accurate (lower-bound) approximants for the cumulative distribution of the whole-bank supremum are deduced from a class of Bonferroni-type inequalities. The asymptotic properties of the cumulative distribution are obtained, in the limit where the number of correlators goes to infinity. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a gaussian-correlation inequality. The result is used to estimate the optimum template density, yielding the best tradeoff between computational cost and detection efficiency, in terms of undetected potentially observable sources at a prescribed false-alarm level, for the simplest case of Newtonian chirps.Comment: submitted to Phys. Rev.

Griffiths-McCoy singularities in random quantum spin chains: Exact results

We consider random quantum (tight-binding, XX and Ising) spin chains in the off-critical region and study their Griffiths-McCoy singularities. These are obtained from the density of states of the low-energy excitations, which is calculated exactly by the Dyson-Schmidt method. In large finite systems the low-energy excitations are shown to follow the statistics of extremes and their distribution is given by the Fr\'echet form. Relation between the Dyson-Schmidt technique and the strong disorder renormalization group method is also discussed.Comment: 7 pages, accepted for publication in Phys. Rev.

Humic acid enhances the growth of tomato promoted by endophytic bacterial strains through the activation of hormone-, growth-, and transcription-related processes

Plant growth-promoting bacteria (PGPB) are promising alternatives in the reduction of the use of chemical fertilizers. Likewise, humic acid (HA) can improve plant growth and/or the establishment of endophytic PGPB. Although the effects of PGPB colonization or HA treatment have been studied separately, little information is available on plant response to the combined applications of PGPB and HA. Thus, the aim of this work was to understand the physiological effects, bacterial colonization and transcriptional responses activated by endophytic bacterial strains in tomato roots and shoots in the absence (control condition) and presence of HA (HA condition). Tomato shoot length was promoted by seed inoculation with Paraburkholderia phytofirmans PsJN, Pantoea agglomerans D7G, or Enterobacter sp. 32A in the presence of HA, indicating a possible complementation of PGPB and HA effects. Tomato colonization by endophytic bacterial strains was comparable in the control and HA condition. The main transcriptional regulations occurred in tomato roots and the majority of differentially expressed genes (DEGs) was upregulated by endophytic bacterial strains in the HA condition. Half of the DEGs was modulated by two or three strains as possible common reactions to endophytic bacterial strains, involving protein metabolism, transcription, transport, signal transduction, and defense. Moreover, strain-specific tomato responses included the upregulation of signal transduction, transcription, hormone metabolism, protein metabolism, secondary metabolism, and defense processes, highlighting specific traits of the endophyte-tomato interaction. The presence of HA enhanced the upregulation of genes related to signal transduction, hormone metabolism, transcription, protein metabolism, transport, defense, and growth-related processes in terms of number of involved genes and fold change values. This study provides detailed information on HA-dependent enhancement of growth-related processes stimulated by endophytic bacterial strains in tomato plants and reports the optimized dosages, complementation properties and gene markers for the further development of efficient PGPB- and HA-based biostimulant