Coherence Enhancement Based on Recursive Anisotropic Scale-Space with Adaptive Kernels

The reduction of unnecessary details is important in a variety of imaging tasks. Image denoising can be generally formulated as a diffusion process that iteratively suppresses undesirable image features with high variance. We propose a recursive diffusion process that simultaneously computes the local geometrical property of the image features and determines the size and shape of the diffusion kernel, leading to an anisotropic scale-space. In the construction of the proposed anisotropic scale-space, image features due to undesirable noise are suppressed while significant geometrical image features such as edges and corners are preserved across the scale-space. The diffusion kernels are iteratively determined based on the local geometrical properties of the image features. We demonstrate the effectiveness and robustness of the proposed algorithm in the detection of curvilinear features using simple yet effective synthetic and real images. The algorithm is quantitatively evaluated based on the identification of fissures in lung CT imagery. The experimental results indicate that the proposed algorithm can be used for the detection of linear or curvilinear structures in a variety of images ranging from satellite to medical images.

Heat Diffusion Kernel Algorithm-Based Interpretation of the Disease Intervention Mechanism for DHA

Docosahexaenoic acid (DHA) is effective in the prevention and treatment of cancer, congenital disorders, and various chronic diseases. According to the omnigenic hypothesis, these complex diseases are caused by disordered gene regulatory networks comprising dozens to hundreds of core genes and a mass of peripheral genes. However, conventional research on the disease intervention mechanism of DHA only focused on specific types of genes or pathways instead of examining genes at the network level, resulting in conflicting conclusions. In this study, we used HotNet2, a heat diffusion kernel algorithm, to calculate the gene regulatory networks of connectivity map (cMap)-derived agents (including DHA) based on gene expression profiles, aiming to interpret the disease intervention mechanism of DHA at the network level. As a result, significant gene regulatory networks for DHA and 676 cMap-derived agents were identified respectively. The biological functions of the DHA-regulated gene network provide preliminary insights into the mechanism by which DHA intervenes in disease. In addition, we compared the gene regulatory networks of DHA with those of cMap-derived agents, which allowed us to predict the pharmacological effects and disease intervention mechanism of DHA by analogy with similar agents with clear indications and mechanisms. Some of our analysis results were supported by experimental observations. Therefore, this study makes a significant contribution to research on the disease intervention mechanism of DHA at the regulatory network level, demonstrating the potential application value of this methodology in clarifying the mechanisms about nutrients influencing health.

Searching for rewards in graph-structured spaces

How do people generalize and explore structured spaces? We study human behavior on a multi-armed bandit task, where rewards are influenced by the connectivity structure of a graph. A detailed predictive model comparison shows that a Gaussian Process regression model using a diffusion kernel is able to best describe participant choices, and also predict judgments about expected reward and confidence. This model unifies psychological models of function learning with the Successor Representation used in reinforcement learning, thereby building a bridge between different models of generalization.

Transport dynamics of complex fluids

Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate subdiffusive, and long-time diffusive motion, unless interrupted. Despite its relevance to numerous dynamical processes of interest in modern science, a unified, quantitative understanding of thermal motion in complex fluids remains a challenging problem. Here, we present a transport equation and its solutions, which yield a unified quantitative explanation of the mean-square displacement (MSD), the non-Gaussian parameter (NGP), and the displacement distribution of complex fluids. In our approach, the environment-coupled diffusion kernel and its time correlation function (TCF) are the essential quantities that determine transport dynamics and characterize mobility fluctuation of complex fluids; their time profiles are directly extractable from a model-free analysis of the MSD and NGP or, with greater computational expense, from the two-point and four-point velocity autocorrelation functions. We construct a general, explicit model of the diffusion kernel, comprising one unbound-mode and multiple bound-mode components, which provides an excellent approximate description of transport dynamics of various complex fluidic systems such as supercooled water, colloidal beads diffusing on lipid tubes, and dense hard disk fluid. We also introduce the concepts of intrinsic disorder and extrinsic disorder that have distinct effects on transport dynamics and different dependencies on temperature and density. This work presents an unexplored direction for quantitative understanding of transport and transport-coupled processes in complex disordered media.