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Recovering pixel-wise geometric properties from a single image is fundamentally ill-posed due to appearance ambiguity and non-injective mappings between 2D observations and 3D structures. While discriminative regression models achieve…
Embedded random matrix ensembles with $k$-body interactions are well established to be appropriate for many quantum systems. For these ensemble the two point correlation function is not yet derived though these ensembles are introduced 50…
Quantitative structure-property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure…
In this paper, we study the truncated two-particle correlation function in particle systems with long range interactions. For Coulombian and soft potentials, we define and give well-posedness results for the equilibrium correlations. In the…
We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…
This note describes a method for detecting dense random texture using fully connected points sampled on image edges. An edge image is randomly sampled with points, the standard L2 distance is calculated between all connected points in a…
We consider correlation functions of topologically twisted, $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group ${\rm SU}(2)$ and $N_f\leq 3$ massive hypermultiplets in the fundamental representation. For a smooth, compact,…
We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…
The simple entropic method to statistical reconstructing of heterogeneous three-dimensional media from a single two-dimensional image is briefly reported. We apply the entropic descriptor quantifying spatial inhomogeneity that depends on…
We introduce a general framework for generating diverse visual content, including ambiguous images, panorama images, mesh textures, and Gaussian splat textures, by synchronizing multiple diffusion processes. We present exhaustive…
On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…
Text-to-image (T2I) diffusion models have achieved widespread success due to their ability to generate high-resolution, photorealistic images. These models are trained on large-scale datasets, like LAION-5B, often scraped from the internet.…
The normal forms up to the third order for a Hopf-steady state bifurcation of a general system of partial functional differential equations (PFDEs) is derived based on the center manifold and normal form theory of PFDEs. This is a…
Density matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency,…
This work introduces InJecteD, a framework for interpreting Denoising Diffusion Probabilistic Models (DDPMs) by analyzing sample trajectories during the denoising process of 2D point cloud generation. We apply this framework to three…
SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…
Rayleigh-L\'evy flights are simplified cosmological tools which capture certain essential statistical properties of the cosmic density field, including hierarchical structures in higher-order correlations, making them a valuable reference…
We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
In this paper, we propose a improved 2D-PEH based on double prediction-error. First,different from previous 2D-PEH, the proposed 2D-DPEH is established by selecting two distinct predictors with low correlation to calculate double prediction…