Related papers: Fluctuation scaling in neural spike trains
It is known that after scaling a random Motzkin path converges to a Brownian excursion. We prove that the fluctuations of the counting processes of the ascent steps, the descent steps and the level steps converge jointly to linear…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
Converging research suggests that the resting brain operates at the cusp of dynamic instability signified by scale-free temporal correlations. We asked if the scaling properties of these correlations differ between amplitude and phase…
Physical kinetic roughening processes are well known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available…
Non-equilibrium random fluctuations of non-thermal nature are a salient feature of active matter. In this work, we consider the collective excitations of active systems at high density, focusing on a one-dimensional chain of elastically…
Learning in neural systems occurs through change in synaptic connectivity that is driven by neural activity. Learning performance is influenced by both neural activity and the task to be learned. Experimental studies suggest a link between…
Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder,…
We study the dynamics of an elastic chain driven on a disordered substrate and analyze numerically the statistics of force fluctuations at the depinning transition. The probability distribution function of the amplitude of the slip events…
In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…
Human motor activities are known to exhibit scale-free long-term correlated fluctuations over a wide range of timescales, from few to thousands of seconds. The fundamental processes originating such fractal-like behavior are not yet…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
We address the problem of finding patterns from multi-neuronal spike trains that give us insights into the multi-neuronal codes used in the brain and help us design better brain computer interfaces. We focus on the synchronous firings of…
In this paper we combine statistical analysis of large text databases and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. Besides the sublinear scaling of the vocabulary size with…
Human motor activity is constrained by the rhythmicity of the 24 hours circadian cycle, including the usual 12-15 hours sleep-wake cycle. However, activity fluctuations also appear over a wide range of temporal scales, from days to a few…
We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…
Neural activity fluctuates over a wide range of timescales within and across brain areas. Experimental observations suggest that diverse neural timescales reflect information in dynamic environments. However, how timescales are defined and…
In this paper, the diffusion entropy technique is applied to investigate the scaling behavior of stride interval fluctuations of human gait. The scaling behavior of the stride interval of human walking at normal, slow and fast rate are…
The "critical brain hypothesis" posits that neural circuitry may be tuned close to a "critical point" or "phase transition" -- a boundary between different operating regimes of the circuit. The renormalization group and theory of critical…
Intermittent transitions, associated with critical dynamics and characterized by power-law distributions, are commonly observed during sleep. These critical behaviors are evident at the microscopic level through neuronal avalanches and at…
A statistical model for describing the scaling of the distribution of inter-event times is described. By considering the diverse region seismicity (natural and induced) at different scale levels the self-similarity of the distribution has…