Research
Research
Research
Research
5,734+ open-access research outputs.
We consider the problem of finding the (unique) minimal Walrasian equilibrium price in multi-item, multi-unit auction models: there are multiple indivisible items for sale, with several units of each …
Let $\mathcal{R}$ be an association scheme with nontrivial relations $A_1,\ldots,A_d$. We call $\mathcal{R}$ amorphic if every possible fusion of its nontrivial relations gives rise to a fusion scheme…
In renewable power-to-ammonia (ReP2A) systems, the intermittency of wind and solar generation propagates through electrolytic hydrogen production and induces thermal instability in the ammonia synthes…
This article presents a partial differential equation (PDE) of Keller-Segel (KS) type that reproduces patterns commonly observed during the growth of brain microvasculature. We provide mathematical in…
The existence of global weak solutions to the compressible Navier-Stokes equations for the density of endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentrati…
In a seminal work, Chatterjee and Durrett (2009) established that for the SIS epidemic process on random graphs with power-law degree distributions, the infection survives for an exponentially long ti…
We consider an incompressible magnetohydrodynamics (MHD) model in which the classical first-order time derivatives in the momentum and magnetic induction equations are replaced by variable-order Caput…
Randomized neural networks (RaNNs) are attractive for partial differential equations (PDEs) because they replace expensive end-to-end training with a linear least-squares solve over randomized hidden …
Fully decentralized Muon is difficult because its nonlinear matrix-sign operator does not commute with linear gossip averaging. This makes decentralized Muon a structural design problem: in designing …
Column generation is a widely used decomposition technique for large-scale linear programs, but it often suffers from slow convergence due to poor initial dual estimates and dual oscillations. Stabili…
In 1965 Kraichnan pointed out that a sufficiently strong background magnetic field, i.e. the case of small Alfv\'en number, will reduce the nonlinear interaction and inhibit the formation of strong gr…
Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and ad…
High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intr…
Graph burning is a discrete-time process that models the spread of social contagion. Initially, all vertices are unburned. In each round, one unburned vertex is selected and burned, while any unburned…
ReLU neural networks trained as surrogate models can be embedded exactly in mixed-integer linear programs (MILPs), enabling global optimization over the learned function. The tractability of the resul…
In this paper, we propose and analyze a novel one-dimensional inhomogeneous random walk model that combines spatial decay of transition probabilities with a temporal renewal structure for each excursi…
For $k$-graphs $F$ and $H_0$ the $F$-bootstrap percolation process (or $F$-process) starting with $H_0$ is a sequence $(H_i)_{i\geq0}$ of $k$-graphs such that $H_{i+1}$ is obtained from $H_i$ by addin…
Experimental designs that are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean …
Transient instability in nonlinear stochastic dynamical systems is a fundamental limitation in safety-critical aerospace applications, particularly during powered descent and landing where failure is …
Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essent…
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