Related papers: Fractal geometry-governed oxygen diffusion: Tumors…
Neural networks transform data through learned representations whose geometry affects separation, contraction, and generalization. Recent work studies this geometry using discrete curvature on neighborhood graphs, suggesting Ricci-flow-like…
A three-dimensional cell culture called a spheroid serves as a foundational entity in a wide variety of modern tissue engineering applications, including 3D-bioprinting and preclinical drug testing. Lack of oxygen within tissue spheroids…
Objective: This study aims to investigate the influence of organ architecture (specifically the distinction between serial and parallel tissue) on the protective FLASH effect when organs are irradiated with inhomogeneous dose distributions.…
Evidence is presented that the galaxy distribution can be described as a fractal system in the redshift range of the FDF galaxy survey. The fractal dimension $D$ was derived using the FDF galaxy volume number densities in the spatially…
Diffusion generative models have emerged as a powerful framework for addressing problems in structural biology and structure-based drug design. These models operate directly on 3D molecular structures. Due to the unfavorable scaling of…
Heterogeneous dynamics commonly emerges in anomalous diffusion with intermittent transitions of diffusion states but proves challenging to identify using conventional statistical methods. To effectively capture these transient changes of…
We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from super-diffusion to normal diffusion, as a function of the distance…
High-dimensional images, known for their rich semantic information, are widely applied in remote sensing and other fields. The spatial information in these images reflects the object's texture features, while the spectral information…
The generalized Taylor's Formula is used to derive a fractional radial-cylindrical diffusivity model via a fractional conservation of mass in radial geometry in a petroleum reservoir. The result is a space-fractional generalization of the…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
With the growing interest in foundation models for brain signals, graph-based pretraining has emerged as a promising paradigm for learning transferable representations from connectome data. However, existing contrastive and masked…
Molecular dynamics (MD) has long been the de facto choice for simulating complex atomistic systems from first principles. Recently deep learning models become a popular way to accelerate MD. Notwithstanding, existing models depend on…
Musculoskeletal disorders represent a significant global health burden and are a leading cause of disability worldwide. While MRI is essential for accurate diagnosis, its interpretation remains exceptionally challenging. Radiologists must…
Anatomical atlases are widely used for population studies and analysis. Conditional atlases target a specific sub-population defined via certain conditions, such as demographics or pathologies, and allow for the investigation of…
Most earlier 3D structure-based molecular generation approaches follow an atom-wise paradigm, incrementally adding atoms to a partially built molecular fragment within protein pockets. These methods, while effective in designing tightly…
Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of…
Diffusion Transformers (DiTs) have demonstrated strong performance in generative modeling, particularly in image synthesis, making them a compelling choice for molecular conformer generation. However, applying DiTs to molecules introduces…
Anomalous diffusion, in particular subdiffusion, is frequently invoked as a mechanism of motion in dense biological media, and may have a significant impact on the kinetics of binding/unbinding events at the cellular level. In this work we…
Motivated by a problem in heterogeneous catalysis, we study a model for irreversible first-order reactions in which gas transport occurs only by diffusion, and reaction occurs only at a small number of well-localized sites. The main problem…
The dynamics of two-phase flow within the cathode of a proton exchange membrane fuel cell, particularly in Gas Diffusion Layers (GDLs) with varying fiber curvatures, remain underexplored. Using a periodic surface model, we stochastically…