Related papers: Time-dependent Probability Density Functions and I…
We trace with analytical methods and in a model parameter independent manner the independent bits of Fisher information of each of the moments of the lognormal distribution, as a now standard prescription for the distribution of the…
Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…
The probability density function (PDF) of the logarithmic density contrast, $s=\ln (\rho/\rho_0)$, with gas density $\rho$ and mean density $\rho_0$, for hydrodynamical supersonic turbulence is well-known to have significant non-Gaussian…
The Velocity Gradients Technique (VGT) and the Probability Density Functions (PDFs) of mass density are tools to study turbulence, magnetic fields, and self-gravity in molecular clouds. However, self-absorption can significantly make the…
Eulerian-Lagrangian models of particle-laden (multiphase) flows describe fluid flow and particle dynamics in the Eulerian and Lagrangian frameworks respectively. Regardless of whether the flow is turbulent or laminar, the particle dynamics…
Uncertainties on parton distribution functions (PDFs) compromise discovery at the LHC for any new physics which can be described as a contact-interaction. PDF uncertainties also limit our ability to use W and Z cross-sections as an accurate…
Analytical studies based on perturbative theory have shown that the moments of the Probability Distribution Function (PDF) of the local smoothed velocity divergence are expected to have a very specific dependence on the density parameter…
Line-intensity mapping (LIM) is quickly attracting attention as an alternative technique to probe large-scale structure and galaxy formation and evolution at high redshift. LIM one-point statistics are motivated because they provide access…
The thermodynamics of phase transitions between phases that are size-mismatched but coherent differs from conventional stress-free thermodynamics. Most notably, in open systems such phase transitions are always associated with hysteresis.…
Physics-based simulation for fluid flow in porous media is a computational technology to predict the temporal-spatial evolution of state variables (e.g. pressure) in porous media, and usually requires high computational expense due to its…
Modern analysis on parton distribution functions (PDFs) requires calculations of the log-likelihood functions from thousands of experimental data points, and scans of multi-dimensional parameter space with tens of degrees of freedom. In…
A core feature of complex systems is that the interactions between elements in the present causally constrain each-other as the system evolves through time. To fully model all of these interactions (between elements, as well as ensembles of…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials…
Inter-scale kinetic energy transfer in turbulent flows is accompanied by very intense and intermittent spatial-temporal fluctuations. Such intermittency is expected to be particularly prominent in premixed flames, where heat release,…
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…
Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…
Two numerical strategies based on the Wang-Landau and Lee entropic sampling schemes are implemented to investigate the first-order transition features of the 3D bimodal ($\pm h$) random-field Ising model at the strong disorder regime. We…
We investigate the time behavior of the fragmentation model with Kolmogorov time scales and space contraction resembling the random $\beta$-model of turbulence. The space averages computed at any instant using the entire spatial realization…