Research
Research
Research
Research
12,714+ open-access research outputs.
We survey recent progress on the birational geometry of foliations on complex varieties. We focus on the MMP viewpoint: singularities, adjunction and applications to the MMP for foliations on surfaces…
We study the Wasserstein projection of a compactly supported probability measure onto the class of measures whose density ratio is bounded, and we place this projection in a broader program connecting…
The concept of input-independent computational time for chemistry-based analog computers was introduced in Anderson-Joshi (2025), where it was shown that arithmetic operations can be computed in a fix…
Asymptotic properties of discrete, stochastic approximations to hybrid systems, modeled as hybrid inclusions, are studied. First, the internal chain transitivity of omega-limits of solutions is conclu…
We introduce the concept of deck transformations within the category of developable complexes of groups. Drawing inspiration from classical covering theory for topological spaces, we propose an altern…
The mathematical representation of uncertainty has led to a proliferation of preference structures, such as interval-valued fuzzy sets, intuitionistic fuzzy sets, and various granular models. While th…
Quantitative systems pharmacology (QSP) models are increasingly applied to inform decision making across drug development and to support regulatory interactions within model informed drug development …
We establish Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear anisotropic elliptic equations exhibiting non-standard growth conditions. A primary example of such o…
A key problem in approximation theory is the recovery of high-dimensional functions from samples. In many cases, the functions of interest exhibit anisotropic smoothness, and, in many practical settin…
We present a formalization in Lean of the core interior De Giorgi--Nash--Moser theory for uniformly elliptic divergence-form equations with bounded measurable coefficients. The formalized results incl…
By extending the Johnson--Barron projection method from one dimension to high dimensions and utilizing a Wang type dimension-free Harnack inequality, we obtain a new quantitative bound for the entropi…
We give an alternative proof of the existence of the anticanonical minimal model program for potentially klt pairs, assuming the anticanonical divisor admits a birational Zariski decomposition. Moreov…
Kinetic transport models are mesoscopic mathematical descriptions of the transport of particles as well as their interactions with the background media or among themselves, and they have wide applicat…
We present a Lean 4 Mathlib formalization of Nagata's factoriality theorem: if R is a noetherian domain and S <= R is a prime-generated submonoid such that S^{-1}R is a UFD, then R itself is a UFD. Th…
Floating-point arithmetic is error-prone and unintuitive. Floating-point debuggers instrument programs to monitor floating-point arithmetic at run time and flag numerical issues. They estimate residue…
This article proposes a category-theoretic formalization of Greimasian narrative programs (NPs) that makes their compositional structure mathematically precise. Building on a reconstruction of the act…
We develop a novel primal heuristic for nonconvex Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQPs). The method is built around a convex approximation that is dynamically adjusted w…
We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our frame…
This paper presents a smooth parameterization of continuous-time Signal Temporal Logic (CT-STL) specifications for nonconvex trajectory optimization that is sound and complete up to the accuracy of th…
Let $(Y,g_0)$ be a compact K\"ahler space with a finite number of singular points, where the metric at each singular point is modelled on an admissible K\"ahler cone. We show that the K\"ahler-Ricci f…
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