相关论文: Orthogonal invariant sets of the diffusion tensor …

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

We propose a novel method for testing isotropy of a three-dimensional distribution using Shannon entropy. We test the method on some Monte Carlo simulations of isotropic and anisotropic distributions and find that the method can effectively…

Invariant manifolds are one of the key features that organize the dynamics of a differential equation. We introduce a novel approach to visualizing and studying invariant manifolds by using 3D printing technology, combining advanced…

The loading of a granular material induces anisotropies of the particle arrangement (fabric) and of the material's strength, incremental stiffness, and permeability. Thirteen measures of fabric anisotropy are developed, which are arranged…

The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping…

Motivated by population studies of Diffusion Tensor Imaging, the paper investigates the use of mean-based and dispersion-based permutation tests to define and compute the significance of a statistical test for data taking values on…

Anisotropy in crystals plays a pivotal role in many technological applications. For example, anisotropic electronic and thermal transport are thought to be beneficial for thermoelectric applications, while anisotropic mechanical properties…

We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the…

This work concerns the modeling of radiative transfer in anisotropic turbid media using diffusion theory. A theory for the relationship between microscopic scattering properties (i.e., an arbitrary differential scattering cross-section) and…

Anisotropic diffusion is a well recognized tool in digital image processing, including edge detection and denoising. We present here a particular nonlinear time-dependent operator together with an appropriate high-order discretization for…

Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…

The aim of this paper is to explore the relationship between invariant cones and nonlinear normal modes in piecewise linear mechanical systems. As a key result, we extend the invariant cone concept, originally established for homogeneous…

This paper improves a previously established test involving only coefficients to decide a priori whether or not non-trivial symmetries of a large class of space-time dependent diffusion processes on the real line exist. When the existence…

Ill-posed imaging inverse problems remain challenging due to the ambiguity in mapping degraded observations to clean images. Diffusion-based generative priors have recently shown promise, but typically rely on computationally intensive…

This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…

An indentation testing method, which utilizes lateral contact of a long cylindrical indenter, is developed for a thin transversely isotropic incompressible elastic film deposited onto a smooth rigid substrate. It is assumed that the…

Tensor interpolation is an essential step for tensor data analysis in various fields of application and scientific disciplines. In the present work, novel interpolation schemes for general, i.e., symmetric or non-symmetric, invertible…

A new method to investigate anomalous diffusion in human brain is proposed. The method has been inspired by both the stretched-exponential model proposed by Hall and Barrick (HB) and DTI. Quantities extracted using HB method were able to…

We propose a novel method for non-rigid 3-D motion correction of orthogonally raster-scanned optical coherence tomography angiography volumes. This is the first approach that aligns predominantly axial structural features like retinal…

We studied the self-diffusion of colloidal ellipsoids in a monolayer near a flat wall by video microscopy. The image processing algorithm can track the positions and orientations of ellipsoids with sub-pixel resolution. The translational…