Related papers: Modelling bursty time series
We analyze the coherent quantum evolution of a many-particle system after slowly sweeping a power-law confining potential. The amplitude of the confining potential is varied in time along a power-law ramp such that the many-particle system…
On-line communities offer a great opportunity to investigate human dynamics, because much information about individuals is registered in databases. In this paper, based on data statistics of online comments on Blog posts, we first present…
Recently a number of empirical "universal" scaling law papers have been published, most notably by OpenAI. `Scaling laws' refers to power-law decreases of training or test error w.r.t. more data, larger neural networks, and/or more compute.…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
We propose a dynamical mechanism for a scale dependent error growth rate, by the introduction of a class of hierarchical models. The coupling of time scales and length scales is motivated by atmospheric dynamics. This model class can be…
Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling $p$) and deterministic critical…
We describe a chain of unidirectionally coupled adaptive excitable elements slowly driven by a stochastic process from one end and open at the other end, as a minimal toy model of unresolved irreducible uncertainty in a system performing…
Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a…
The interevent time distribution characterizes the temporal occurrence in seismic catalogs. Universal scaling properties of this distribution have been evidenced for entire catalogs and seismic sequences. Recently, these universal features…
Self-exciting point processes describe the manner in which every event facilitates the occurrence of succeeding events. By increasing excitability, the event occurrences start to exhibit bursts even in the absence of external stimuli. We…
We derive the most basic dynamical properties of random hyperbolic graphs (the distributions of contact and intercontact durations) in the hot regime (network temperature $T > 1$). We show that for sufficiently large networks the contact…
We rigorously analyze the low temperature non-equilibrium dynamics of the East model, a special example of a one dimensional oriented kinetically constrained particle model, when the initial distribution is different from the reversible one…
A project schedule contains a network of activities, the activity durations, the early and late finish dates for each activity, and the associated total float or slack times, the difference between the late and early dates. Here I show that…
A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda…
A new model, called "Human Dynamics", has been recently proposed that individuals execute activities based on a perceived priority of tasks, which can be characterized by a power-law distribution of waiting time between consecutive tasks…
Power spectral density scaling with frequency $f$ as $1/f^\beta$ and $\beta \approx 1$ is widely found in natural and socio-economic systems. Consequently, it has been suggested that such self-similar spectra reflect the universal dynamics…
We study analytically the dynamics of a ball bouncing inelastically on a randomly vibrating platform, as a simple toy model of inelastic collapse. Of principal interest are the distributions of the number of flights n_f till the collapse…
Inhomogeneous temporal processes in natural and social phenomena have been described by bursts that are rapidly occurring events within short time periods alternating with long periods of low activity. In addition to the analysis of…
This paper proposes a method for modeling event sequences with ambiguous timestamps, a time-discounting convolution. Unlike in ordinary time series, time intervals are not constant, small time-shifts have no significant effect, and…
Dynamic spin correlation functions $<S_i^x (t)S_j^x>$ for the 1D $S=1/2$ $XX$ model $H = -J\Sigma_i \{S_i^x S_{i+1}^x + S_i^y S_{i+1}^y \}$ are calculated exactly for finite open chains with up to N=10000 spins. Over a certain time range…