Related papers: Dispersive Lineshape Theory
We formulate a new model for transport in stochastic media with long-range spatial correlations where exponential attenuation (controlling the propagation part of the transport) becomes power law. Direct transmission over optical distance…
A general non-linear response theory is derived for an arbitrary time-dependent Hamiltonian, not necessarily obeying time-reversal symmetry. This allows us to obtain a greatly generalized Kubo type formula. Applied to a mesoscopic system…
We show that a meaningful statistical description is possible in conservative and mixing systems with zero Lyapunov exponent in which the dynamical instability is only linear in time. More specifically, (i) the sensitivity to initial…
Some stochastic systems are particularly interesting as they exhibit critical behavior without fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of driven-dissipative steady states, one of the main…
We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
We look into the fluctuations caused by disturbances in power systems. In the linearized system of the power systems, the disturbance is modeled by a Brownian motion process, and the fluctuations are described by the covariance matrix of…
Spectral line-shapes provide a window into the local environment coupled to a quantum transition in the condensed phase. In this paper, we build upon a stochastic model to account for non-stationary background processes produced by…
Our investigation is specially motivated by the stochastic version of a common model of potential spread in a dendritic tree. We do not assume the noise in the junction points to be Markovian. In fact, we allow for long-range dependence in…
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…
We investigate the process of random sequential adsorption of polydisperse particles whose size distribution exhibits a power-law dependence in the small size limit, $P(R)\sim R^{\alpha-1}$. We reveal a relation between pattern formation…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
Transformers have achieved state-of-the-art results across a range of domains, but their quadratic attention mechanism poses significant challenges for long-sequence modelling. Recent efforts to design linear-time attention mechanisms have…
We consider simple examples illustrating some new features of the linear response theory developed by Ruelle for dissipative and chaotic systems [{\em J. of Stat. Phys.} {\bf 95} (1999) 393]. In this theory the concepts of linear response,…
We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each…
This paper presents a comprehensive review of stochastic processes, with a particular focus on Markov chains and jump processes. The main results related to queuing systems are analyzed. Additionally, conditions that ensure the stability,…
A stochastic model is presented for a super-position of uncorrelated pulses with a random distribution of amplitudes, sizes, velocities and arrival times. The pulses are assumed to move radially with fixed shape and amplitudes decaying…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…