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In order to obtain a good understanding of astrochemistry, it is crucial to better understand the key parameters that govern grain-surface chemistry. For many chemical networks, these crucial parameters are the binding energies of the…
In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…
We apply the finite element cell-centered (FECC) scheme [2] to the solution of the nearly incompressible elasticity problem. By applying a technique of dual mesh, such a low-order finite element scheme can be constructed from any given mesh…
In this paper, we introduce the notion of motif closure and describe higher-order ranking and link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and…
We present a novel method for designing higher-order Control Barrier Functions (CBFs) that guarantee convergence to a safe set within a user-specified finite. Traditional Higher Order CBFs (HOCBFs) ensure asymptotic safety but lack…
Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn--Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn--Sham wavefunctions but also…
In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such…
In this paper, we consider the problem of model order reduction of stochastic biochemical networks. In particular, we reduce the order of (the number of equations in) the Linear Noise Approximation of the Chemical Master Equation, which is…
Flow Matching (FM) models achieve remarkable results in generative tasks. Building upon diffusion models, FM's simulation-free training paradigm enables simplicity and efficiency but introduces a train-inference gap: model outputs cannot be…
We propose a Kron-based model-order reduction method for mass-action kinetics chemical reaction networks (CRN) with constant inflow and proportional outflow. The reduced-order models preserve the CRN structure and we establish that the…
We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that…
We study decentralized markets for goods whose utility perishes in time, with compute as a primary motivation. Recent advances in reproducible and verifiable execution allow jobs to pause, verify, and resume across heterogeneous hardware,…
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…
We study the acceleration of steady-state computation for microflow, which is modeled by the high-order moment models derived recently from the steady-state Boltzmann equation with BGK-type collision term. By using the lower-order model…
Mutual exclusion is one of the most commonly used techniques to handle contention in concurrent systems. Traditionally, mutual exclusion algorithms have been designed under the assumption that a process does not fail while…
Finite element model updating is challenging because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield responses that are similar with respect to…
Gaining insights from realistic dynamical models of biochemical systems can be challenging given their large number of state variables. Model reduction techniques can mitigate this by decreasing complexity by mapping the model onto a…
A reaction network consists of a finite number of species, which interact through predefined reaction channels. Traditionally such networks were modeled deterministically, but it is now well-established that when reactant copy numbers are…
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…