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Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
Study of charged particle multiplicity distribution in high energy interactions of particles helps in revealing the dynamics of particle production and the underlying statistical patterns, which these distributions follow. Several…
This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…
We consider a particular class of n-dimensional homogeneous diffusions all of which have an identity diffusion matrix and a drift function that is piecewise constant and scale invariant. Abstract stochastic calculus immediately gives us…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
Diffusion of particles in velocity space undergoing turbulent field was extensively studied in the problem of warm beam relaxation. Under low field intensities the diffusion is described by the Fokker-Planck equation with the diffusion…
Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…
Noise is one of the primary sources of interference in seismic exploration. Many authors have proposed various methods to remove noise from seismic data; however, in the face of strong noise conditions, satisfactory results are often not…
This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…
Recently, a new formalism describing the anomalous diffusion processes, based on the Onsager-Machlup fluctuation theory, has been suggested \cite{Smain, Spub}. We study particles performing this new type of motion, under the action of…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
Recovering the turbulence-degraded point spread function from a single intensity image is important for a variety of imaging applications. Here, a deep learning model based on a convolutional neural network is applied to intensity images to…
The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis…
Much effort has been put into developing theories for dense fluids, as a result of these efforts many theories work for a certain type of particle or in a certain concentration regime. Rosenfeld proposed a dependence of the self-diffusion…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material,…
Diffusion-based motion planners are becoming popular due to their well-established performance improvements, stemming from sample diversity and the ease of incorporating new constraints directly during inference. However, a primary…
In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…