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In this paper we introduce 1-$D$ and 2-$D$ discrete models for the dynamic granular matter formation process in the form of a system of difference equations. This approach allows us to differentiate between the influx of the rolling layer…
Dual-energy X-ray Computed Tomography (DECT) constitutes an advanced technology which enables automatic decomposition of materials in clinical images without manual segmentation using the dependency of the X-ray linear attenuation with…
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…
The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles…
In [math-ph/0107005] we have proven that the generating function for self-avoiding branched polymers in D+2 continuum dimensions is proportional to the pressure of the hard-core continuum gas at negative activity in D dimensions. This…
A diffusion probabilistic model (DPM), which constructs a forward diffusion process by gradually adding noise to data points and learns the reverse denoising process to generate new samples, has been shown to handle complex data…
A deep generative model is developed for representation and analysis of images, based on a hierarchical convolutional dictionary-learning framework. Stochastic {\em unpooling} is employed to link consecutive layers in the model, yielding…
Event skeleton generation, aiming to induce an event schema skeleton graph with abstracted event nodes and their temporal relations from a set of event instance graphs, is a critical step in the temporal complex event schema induction task.…
Mode separation, namely how sharply a distribution fragments into barrier-separated clusters, is a fundamental geometric property of densities, difficult to quantify in high dimensions. It is structurally distinct from dispersion, yet…
Talking head generation is a significant research topic that still faces numerous challenges. Previous works often adopt generative adversarial networks or regression models, which are plagued by generation quality and average facial shape…
Discrete Element Method (DEM) simulations of granular media are computationally intensive, particularly during initialization phases dominated by large displacements and kinetic energy. This paper presents a novel generative pipeline based…
We present a robust method to find region-level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…
We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…
We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical…
Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…
In this paper, we propose DDPM-Polycube, a generative polycube creation approach based on denoising diffusion probabilistic models (DDPM) for generating high-quality hexahedral (hex) meshes and constructing volumetric splines. Unlike…