Related papers: Reflected diffusions defined via the extended Skor…
In this paper, we establish an existence and uniqueness result for system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a convex domain in R^k by analytical approach. The method is based on…
This paper presents existence and uniqueness results for reflected system of quasilinear stochastic partial differential equations in a convex domain D from Rk. The method is based on the probabilistic interpretation of the solution by…
This paper presents investigations on the generalized laws of refraction and reflection for metasurfaces made of diffractive elements. It introduces a phenomenological model that reproduces all the features of the experiments dedicated to…
Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, proliferation and death to depend upon whether the agents are…
A generalisation of Takens' delay-coordinate embedding theorem to stochastic systems, the Stochastic Embedding Sufficiency Theorem, is an inverse methodology enabling non-parametric recovery of both drift and diffusion fields from scalar…
Deep segmentation models often face the failure risks when the testing image presents unseen distributions. Improving model robustness against these risks is crucial for the large-scale clinical application of deep models. In this study,…
Deep convolutional neural networks achieve remarkable performance by exhaustively processing dense spatial feature maps, yet this brute-force strategy introduces significant computational redundancy and encourages reliance on spurious…
In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and…
The incoherent regime of Multiple Andreev Reflections (MAR) is studied in long diffusive SNS junctions at applied voltages larger than the Thouless energy. Incoherent MAR is treated as a transport problem in energy space by means of a…
After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
In this paper, we establish propagation of chaos (POC) for doubly mean reflected backward stochastic differential equations (MRBSDEs). MRBSDEs differentiate the typical RBSDEs in that the constraint is not on the paths of the solution but…
In this paper we consider the Skorokhod embedding problem for target distributions with non-zero mean. In the zero-mean case, uniform integrability provides a natural restriction on the class of embeddings, but this is no longer suitable…
We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of…
Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…
Measured exponents associated with Stretched Exponential Relaxation (SER) are widely scattered in microscopically inhomogeneous glasses, but accurately bifurcate into two "magic" values, 3/5 and 3/7, in a wide variety of microscopically…
Although EDM aims to unify the design space of diffusion models, its reliance on fixed Gaussian noise prevents it from explaining emerging flow-based methods that diffuse arbitrary noise. Moreover, our study reveals that EDM's forcible…
We consider embedded ring-type surfaces (that is, compact, connected, orientable surfaces with two boundary components and Euler-Poincar\'{e} characteristic zero) in ${\bold R}^3$ of constant mean curvature which meet planes $\Pi_1$ and…
Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant…
Semi-discrete Runge-Kutta schemes for nonlinear diffusion equations of parabolic type are analyzed. Conditions are determined under which the schemes dissipate the discrete entropy locally. The dissipation property is a consequence of the…