Related papers: Fractional differential entropy and its applicatio…
The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage…
It is well known that to estimate the Shannon entropy for symbolic sequences accurately requires a large number of samples. When some aspects of the data are known it is plausible to attempt to use this to more efficiently compute entropy.…
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
We study a spatial diffusion process generated by velocity fluctuations of intermittent nature. We note that intermittence reduces the entropy production rate while enhancing the diffusion strength. We study a case of space-dependent…
We consider a fractional porous medium equation that extends the classical porous medium and fractional heat equations. The flow is studied in the space of periodic probability measures endowed with a non-local transportation distance…
In this paper, we investigate new procedures for statistical testing based on Tsallis entropy, a parametric generalization of Shannon entropy. Focusing on multivariate generalized Gaussian and $q$-Gaussian distributions, we develop…
Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
We present here a new stochastic modelling in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
For studies in reliability, biometry, and survival analysis, the length-biased distribution is often well-suited for certain natural sampling plans. In this paper, we study the strong uniform consistency of two nonparametric estimators for…
We describe an approach to improving model fitting and model generalization that considers the entropy of distributions of modelling residuals. We use simple simulations to demonstrate the observational signatures of overfitting on ordered…
Non-Newtonian fluid flow might be driven by spatially nonlocal velocity, the dynamics of which can be described by promising fractional derivative models. This short communication proposes a space FrActional-order Constitutive Equation…
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
We present experimental observations of the velocity and spatial distribution of inertial particles dispersed in the turbulent downward flow through a vertical channel at $Re_{\tau} = 235$ and $335$. The working fluid is air laden with…
Despite the popular of multimodal statistical models, there lacks rigorous statistical inference tools for inferring the significance of a single modality within a multimodal model, especially in high-dimensional models. For…
In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure…