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Our experience of web access slowing down is a consequence of the aggregated web access pattern of web users. This is just one example among several human oriented services which are strongly affected by human activity patterns. Recent…
Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal…
Complexity researchers view burstiness--fluctuating levels of activity--as evidence of hidden interactions within the system generating the activity signal. Yet, current burstiness metrics miss evidence of burstiness in some moderately…
Information processing in the brain requires integration of information over time. Such an integration can be achieved if signals are maintained in the network activity for the required period, as quantified by the intrinsic timescale.…
Noise-induced population bursting has been widely identified to play important roles in the information process. We constructed a mathematical model for a random and sparse neural network where bursting can be induced from the resting state…
Diffusion processes are studied theoretically for the case where the diffusion coefficient is itself a time and position dependent random function. We investigate how inhomogeneities and fluctuations of the diffusion coefficient affect the…
The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance…
Human behaviour is dictated by past experiences via cumulative inertia (CI): the longer a certain behaviour has been going on, the less likely changes becomes. This is a well-known sociological phenomenon observed in employment, residence,…
Quantification of neuronal correlations in neuron populations helps us to understand neural coding rules. Such quantification could also reveal how neurons encode information in normal and disease conditions like Alzheimer's and…
Stimulus from the environment that guides behavior and informs decisions is encoded in the firing rates of neural populations. Each neuron in the populations, however, does not spike independently: spike events are correlated from cell to…
Many natural and physical processes display long memory and extreme events. In these systems, the measured time series is invariably contaminated by noise. As the extreme events display large deviation from the mean behaviour, the noise…
Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…
Gene expression is inherently a noisy process which manifests as cell-to-cell variability in time evolution of proteins. Consequently, events that trigger at critical threshold levels of regulatory proteins exhibit stochasticity in their…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
This paper describes limiting behaviour of tail empirical process associated with long memory stochastic volatility models. We show that such process has dichotomous behaviour, according to an interplay between a Hurst parameter and a tail…
The signaling capacity of a neural population depends on the scale and orientation of its covariance across trials. Estimating this "noise" covariance is challenging and is thought to require a large number of stereotyped trials. New…
Temporal hypergraphs capture time-resolved group interactions among nodes. Empirical data support that time-stamped group interactions show bursty event sequences and non-trivial temporal correlations. In the present study, we introduce…
We define a metric, mutual information in frequency (MI-in-frequency), to detect and quantify the statistical dependence between different frequency components in the data, referred to as cross-frequency coupling and apply it to…
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…
With heightened mining intensity, the incidence of coal bursts is escalating, necessitating advanced understanding and prediction techniques. This research delves into the intricacies of coal burst mechanisms, proposing a novel theoretical…