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Lie group methods are applied to the time-dependent, monoenergetic neutron diffusion equation in materials with spatial and time dependence. To accomplish this objective, the underlying 2nd order partial differential equation (PDE) is…
The Debye-Stokes-Einstein (DSE) model of rotational diffusion predicts that the rotational correlation times $\tau_{l}$ vary as $[l(l+1)]^{-1}$, where $l$ is the rank of the orientational correlation function (given in terms of the Legendre…
We measure different contributions to entropy production in a living functional epithelial tissue. We do this by extracting the functional dynamics of development while at the same time quantifying fluctuations. Using the translucent…
In healthcare, clinical risks are crucial for treatment decisions, yet the analysis of their associations is often overlooked. This gap is particularly significant when balancing risks that are weighed against each other, as in the case of…
Thermophoresis is the process of particles moving along a temperature gradient in thermodynamic systems. Even though it has been studied for over 150 years, there is neither a complete theoretical description of thermophoresis in liquids…
Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system, are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by…
Computer simulations and scaling theory are used to investigate the damping of oscillations during epitaxial growth on high-symmetry surfaces. The crossover from smooth to rough growth takes place after the deposition of (D/F)^\delta…
Discrete empirical interpolation method (DEIM) is a popular technique for nonlinear model reduction and it has two main ingredients: an interpolating basis that is computed from a collection of snapshots of the solution and a set of indices…
We propose a dual scale drift-diffusion model for interfacial growth and etching processes. The two scales are: (i) a depletion layer width surrounding the aggregate and (ii) a drift length.The interplay between these two antithetical…
In a feedforward network, Transfer Entropy (TE) can be used to measure the influence that one layer has on another by quantifying the information transfer between them during training. According to the Information Bottleneck principle, a…
The large-time asymptotics of the solutions to a class of degenerate parabolic cross-diffusion systems is analyzed. The equations model the interaction of an arbitrary number of population species in a bounded domain with no-flux boundary…
We present a mechanism to steer the sampling diversity of denoising diffusion and flow matching models, allowing users to sample from a sharper or broader distribution than the training distribution. We build on the observation that these…
Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved…
Significance: The depolarization of circularly polarized light caused by scattering in turbid media reveals structural information about the dispersed particles, such as their size, density, and distribution, which is useful for…
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling…
Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…
Artifact detection algorithms are crucial to correcting the output generated by diffusion models. However, because of the variety of artifact forms, existing methods require substantial annotated data for training. This requirement limits…
We present a modification to the diffusion entropy analysis method for detecting temporal scaling. Diffusion entropy analysis detects temporal scaling in a data set by converting a time-series into a diffusion trajectory and using the…
We introduce a broadly applicable statistical procedure for testing which parametric distribution family generated a random sample of data. The method, termed the Difference in Differential Entropy (DDE) test, provides a unified framework…
The training process of ranking models involves two key data selection decisions: a sampling strategy, and a labeling strategy. Modern ranking systems, especially those for performing semantic search, typically use a ``hard negative''…