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Large-scale diffusion neural networks represent a substantial milestone in text-to-image generation, but they remain poorly understood, lacking interpretability analyses. In this paper, we perform a text-image attribution analysis on Stable…
Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a…
The investigation of thermal convection of a fluid with the dependence of thermal diffusivity on temperature in a vertical Hele Shaw cell heated from below has been fulfilled theoretically.The expression for equilibrium temperature…
Alzheimer's disease (AD) emerges from a complex interplay of molecular, cellular, and network-level disturbances that are not easily captured by traditional reductionist frameworks. Conventional analyses of gene expression often rely on…
Human close-range proximity interactions are the key determinant for spreading processes like knowledge diffusion, norm adoption, and infectious disease transmission. These dynamical processes can be modeled with time-respecting paths on…
The development of simple and fast hypergraph spectral methods has been hindered by the lack of numerical algorithms for simulating heat diffusions and computing fundamental objects, such as Personalized PageRank vectors, over hypergraphs.…
Alzheimer's disease (AD) is a progressive neurodegenerative disorder in which pathological changes begin many years before the onset of clinical symptoms, making early detection essential for timely intervention. T1-weighted (T1w) Magnetic…
Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here, we consider multiple levels of abstraction via a…
Diffusion probabilistic models have achieved remarkable success in generative tasks across diverse data types. While recent studies have explored alternative degradation processes beyond Gaussian noise, this paper bridges two key diffusion…
Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…
The dynamic heat transfer between two half-spaces separated by a vacuum gap due to coupling of their surface modes is modelled using the theory that describes the dynamic energy transfer between two coupled harmonic oscillators each…
Autism Spectrum Disorder (ASD) is a prevalent neurological disorder. However, the multi-faceted symptoms and large individual differences among ASD patients are hindering the diagnosis process, which largely relies on subject descriptions…
Anthropogenic climate change has increased the probability, severity, and duration of heat waves and droughts, subsequently escalating the risk of wildfires. Mathematical and computational models can enhance our understanding of wildfire…
In this work, we introduce novel algorithms for label propagation and self-training using fractional heat kernel dynamics with a source term. We motivate the methodology through the classical correspondence of information theory with the…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
The temperature-dependence of dynamical properties (e.g., the asymptotic diffusion coefficient and the sub-diffusive exponent) are calculated for charges and excitons in one-dimensional systems subject to static and dynamic disorder. These…
Graph models provide efficient tools to capture the underlying structure of data defined over networks. Many real-world network topologies are subject to change over time. Learning to model the dynamic interactions between entities in such…
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a…
A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…