Related papers: Time-dependent probability density functions and i…
The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a…
We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that MSD relaxes to a constant only when the distribution of reset times possess finite mean and variance. In this case, the leading…
We study a single-field inflation model in which the inflaton potential has an upward step between two slow-roll regimes by taking into account the finite width of the step. We calculate the probability distribution function (PDF) of the…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations…
We suggest a mechanism based on spike time dependent plasticity (STDP) of synapses to store, retrieve and predict temporal sequences. The mechanism is demonstrated in a model system of simplified integrate-and-fire type neurons densely…
In complex systems such as turbulent flows and financial markets, the dynamics in long and short time-lags, signaled by Gaussian and fat-tailed statistics, respectively, calls for a unified description. To address this issue we analyze a…
Distance measurements have long provided the primary observational constraints on the expansion history of the Universe and the properties of dark energy. However, because such observables depend on cumulative line-of-sight integrals over…
We consider one-dimensional hyperbolic PDEs, linear and nonlinear, with random initial data. Our focus is the {\em pointwise statistics,} i.e., the probability measure of the solution at any fixed point in space and time. For linear…
Logarithmic growth-rates are fundamental observables for describing ecological systems and the characterization of their distributions with analytical techniques can greatly improve their comprehension. Here a neutral model based on a…
This paper presents a speech enhancement method, where an adaptive threshold is statistically determined based on Gaussian modeling of Teager energy (TE) operated perceptual wavelet packet (PWP) coefficients of noisy speech. In order to…
We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance $c(t)$ depending on time. We find that for $c(t)\propto t^{-\alpha}$ there is a transition at $\alpha=1/2$. When $\alpha>1/2$, the solution…
Under ideal conditions, the probability density function (PDF) of a random variable, such as a sensor measurement, would be well known and amenable to computation and communication tasks. However, this is often not the case, so the user…
The rainflow counting algorithm for material fatigue is both simple to implement and extraordinarily successful for predicting material failure times. However, it neglects memory effects and time-ordering dependence, and therefore runs into…
We study analytically and by means of an off-lattice bead-spring dynamic Monte Carlo simulation model the adsorption kinetics of a single macromolecule on a structureless flat substrate in the regime of strong physisorption. The underlying…
The article derives some novel independence measures and contrast functions for Blind Source Separation (BSS) application. For the $k^{th}$ order differentiable multivariate functions with equal hyper-volumes (region bounded by…
The Tsallis entropy and Fisher information entropy (matrix) are very important quantities expressing information measures in nonextensive systems. Stationary and dynamical properties of the information entropies have been investigated in…
We present the first detailed analysis of the statistical properties of jump processes bounded by a saturation function and driven by Poisson white noise, being a random sequence of delta pulses. The Kolmogorov-Feller equation for the…
We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhibit very interesting time-evolving…
In the large-momentum expansion for parton distribution functions (PDFs), the natural physics scale is the longitudinal momentum ($p_z$) of the quarks (or gluons) in a large-momentum hadron. We show how to expose this scale dependence…