Scaling behaviour in probabilistic neuronal cellular automata

We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective temperature). There are avalanches of neuronal activity, namely spatially and temporally contiguous sites of activity; a detailed numerical study of these activity avalanches is presented, and single, joint and marginal probability distributions are computed. At the critical point, we find that the scaling exponents for the variables are in good agreement with a mean--field theory.Comment: 7 pages, 4 figures Accepted for publication in Physical Review

Memoryless nonlinear response: A simple mechanism for the 1/f noise

Discovering the mechanism underlying the ubiquity of $"1/f^{\alpha}"$ noise has been a long--standing problem. The wide range of systems in which the fluctuations show the implied long--time correlations suggests the existence of some simple and general mechanism that is independent of the details of any specific system. We argue here that a {\it memoryless nonlinear response} suffices to explain the observed non--trivial values of $\alpha$: a random input noisy signal $S(t)$ with a power spectrum varying as $1/f^{\alpha'}$, when fed to an element with such a response function $R$ gives an output $R(S(t))$ that can have a power spectrum $1/f^{\alpha}$ with $\alpha < \alpha'$. As an illustrative example, we show that an input Brownian noise ($\alpha'=2$) acting on a device with a sigmoidal response function R(S)= \sgn(S)|S|^x, with $x<1$, produces an output with $\alpha = 3/2 +x$, for $0 \leq x \leq 1/2$. Our discussion is easily extended to more general types of input noise as well as more general response functions.Comment: 5 pages, 5 figure

Power spectrum of mass and activity fluctuations in a sandpile

We consider a directed abelian sandpile on a strip of size $2\times n$, driven by adding a grain randomly at the left boundary after every $T$ time-steps. We establish the exact equivalence of the problem of mass fluctuations in the steady state and the number of zeroes in the ternary-base representation of the position of a random walker on a ring of size $3^n$. We find that while the fluctuations of mass have a power spectrum that varies as $1/f$ for frequencies in the range $3^{-2n} \ll f \ll 1/T$, the activity fluctuations in the same frequency range have a power spectrum that is linear in $f$.Comment: 8 pages, 10 figure

A cutoff time scaling of 1/f noise in a sandpile

We show that for fluctuations in a sandpile with $1/f^{\alpha}$ spectrum, the power may also exhibit a scaling with its cutoff time. Despite significant progress, this generic behaviour remains so far overlooked and poorly understood. An intriguing example is the power spectrum of a simple random walk (normal diffusive process) on a ring with L sites, showing $L/f^{3/2}$ behaviour instead of $1/f^2$ (Brownian noise) in the frequency regime $1/L^2 \ll f \ll 1/2$ . We address the intriguing problem by scaling method and discuss its relevance in the context of the sandpile system and a class of stochastic processes

A Response of Snow Cover to the Climate in the Northwest Himalaya (NWH) Using Satellite Products

The Himalayan region is one of the most crucial mountain systems across the globe, which has significant importance in terms of the largest depository of snow and glaciers for fresh water supply, river runoff, hydropower, rich biodiversity, climate, and many more socioeconomic developments. This region directly or indirectly affects millions of lives and their livelihoods but has been considered one of the most climatically sensitive parts of the world. This study investigates the spatiotemporal variation in maximum extent of snow cover area (SCA) and its response to temperature, precipitation, and elevation over the northwest Himalaya (NWH) during 2000–2019. The analysis uses Moderate Resolution Imaging Spectroradiometer (MODIS)/Terra 8-day composite snow Cover product (MOD10A2), MODIS/Terra/V6 daily land surface temperature product (MOD11A1), Climate Hazards Infrared Precipitation with Station data (CHIRPS) precipitation product, and Shuttle Radar Topography Mission (SRTM) DEM product for the investigation. Modified Mann-Kendall (mMK) test and Spearman’s correlation methods were employed to examine the trends and the interrelationships between SCA and climatic parameters. Results indicate a significant increasing trend in annual mean SCA (663.88 km2/year) between 2000 and 2019. The seasonal and monthly analyses were also carried out for the study region. The Zone-wise analysis showed that the lower Himalaya (184.5 km2/year) and the middle Himalaya (232.1 km2/year) revealed significant increasing mean annual SCA trends. In contrast, the upper Himalaya showed no trend during the study period over the NWH region. Statistically significant negative correlation (−0.81) was observed between annual SCA and temperature, whereas a nonsignificant positive correlation (0.47) existed between annual SCA and precipitation in the past 20 years. It was also noticed that the SCA variability over the past 20 years has mainly been driven by temperature, whereas the influence of precipitation has been limited. A decline in average annual temperature (−0.039 °C/year) and a rise in precipitation (24.56 mm/year) was detected over the region. The results indicate that climate plays a vital role in controlling the SCA over the NWH region. The maximum and minimum snow cover frequency (SCF) was observed during the winter (74.42%) and monsoon (46.01%) season, respectively, while the average SCF was recorded to be 59.11% during the study period. Of the SCA, 54.81% had a SCF above 60% and could be considered as the perennial snow. The elevation-based analysis showed that 84% of the upper Himalaya (UH) experienced perennial snow, while the seasonal snow mostly dominated over the lower Himalaya (LH) and the middle Himalaya (MH)

Emergent organization in a model market

We study the collective behaviour of interacting agents in a simple model of market economics that was originally introduced by Norrelykke and Bak. A general theoretical framework for interacting traders on an arbitrary network is presented, with the interaction consisting of buying (namely consumption) and selling (namely production) of commodities. Extremal dynamics is introduced by having the agent with least profit in the market readjust prices, causing the market to self-organize. In addition to examining this model market on regular lattices in two-dimensions, we also study the cases of random complex networks both with and without community structures. Fluctuations in an activity signal exhibit properties that are characteristic of avalanches observed in models of self-organized criticality, and these can be described by power-law distributions when the system is in the critical state. (C) 2017 Elsevier B.V. All rights reserved

Sub-diffusion and trapped dynamics of neutral and charged probes in DNA-protein coacervates

The physical mechanism leading to the formation of large intermolecular DNA-protein complexes has been studied. Our study aims to explain the occurrence of fast coacervation dynamics at the charge neutralization point, followed by the appearance of smaller complexes and slower coacervation dynamics as the complex experiences overcharging. Furthermore, the electrostatic potential and probe mobility was investigated to mimic the transport of DNA / DNA-protein complex in a DNA-protein complex coacervate medium [N. Arfin and H. B. Bohidar, J. Phys. Chem. B 116, 13192 (2012)] by assigning neutral, negative, or positive charge to the probe particle. The mobility of the neutral probe was maximal at low matrix concentrations and showed random walk behavior, while its mobility ceased at the jamming concentration of c = 0.6, showing sub-diffusion and trapped dynamics. The positively charged probe showed sub-diffusive random walk followed by trapped dynamics, while the negatively charged probe showed trapping with occasional hopping dynamics at much lower concentrations. Sub-diffusion of the probe was observed in all cases under consideration, where the electrostatic interaction was used exclusively as the dominant force involved in the dynamics. For neutral and positive probes, the mean square displacement ⟨R2⟩ exhibits a scaling with time as ⟨R2⟩ ∼ tα, distinguishing random walk and trapped dynamics at α = 0.64 ± 0.04 at c = 0.12 and c = 0.6, respectively. In addition, the same scaling factors with the exponent β = 0.64 ± 0.04 can be used to distinguish random walk and trapped dynamics for the neutral and positive probes using the relation between the number of distinct sites visited by the probe, S(t), which follows the scaling, S(t) ∼ tβ/ln (t). Our results established the occurrence of a hierarchy of diffusion dynamics experienced by a probe in a dense medium that is either charged or neutral