arXiv research

The opioid epidemic in the United States claims over 40,000 lives per year, and it is estimated that well over two million Americans have an opioid use disorder. Over-prescription and misuse of prescription opioids play an important role in the epidemic. Individuals who are prescribed opioids, and who are diagnosed wit…

The study identifies patient subgroups with enhanced or diminished opioid treatment effects.

Deep learning predicts opioid use disorder risk in patients.

CASTNet forecasts opioid overdoses using crime patterns.

Computational chemists typically assay drug candidates by virtually screening compounds against crystal structures of a protein despite the fact that some targets, like the $μ$ Opioid Receptor and other members of the GPCR family, traverse many non-crystallographic states. We discover new conformational states of $μOR$…

Opioid addiction is a severe public health threat in the U.S, causing massive deaths and many social problems. Accurate relapse prediction is of practical importance for recovering patients since relapse prediction promotes timely relapse preventions that help patients stay clean. In this paper, we introduce a Generati…

Model predicts drug overdose hotspots using EMS and toxicology data.

Study uses machine learning to analyze state drug policies and reduce overdose deaths.

Enhanced framework selects features for unbiased causal inference.

Identifying anomalous patterns in real-world data is essential for understanding where, when, and how systems deviate from their expected dynamics. Yet methods that separately consider the anomalousness of each individual data point have low detection power for subtle, emerging irregularities. Additionally, recent dete…

We introduce a machine learning approach for extracting fine-grained representations of protein evolution from molecular dynamics datasets. Metastable switching linear dynamical systems extend standard switching models with a physically-inspired stability constraint. This constraint enables the learning of nuanced repr…

Study on the convergence rate of prescribed scalar curvature flow.

Proves optimal regularity for sphere minimizers in 3-sphere.

Develops variational approach for Kähler-Einstein metrics with prescribed singularities on Fano manifolds.

Proves existence and uniqueness of Killing graphs with prescribed curvature.

Paper estimates curvature of convex hypersurfaces with prescribed curvature.

Theory proves existence of hypersurfaces with prescribed curvature.

Introduce a flow for prescribed Hermitian-Yang-Mills tensors

We develop a compactness result near the boundary for families of locally convex immersions. We also develop a mod 2 degree theory for immersion of constant (and prescribed) Gaussian curvature with prescribed boundary. These are then used to solve the Plateau problem for immersions of constant (and prescribed) Gaussian…

Utilizing a weight matrix we study surfaces of prescribed weighted mean curvature which yield a natural generalisation to critical points of anisotropic surface energies. We first derive a differential equation for the normal of immersions with prescribed weighted mean curvature, generalising a result of Clarenz and vo…

Study convex capillary hypersurfaces with prescribed curvature in a spherical cap.

Paper solves degenerated circle pattern metric problem in spherical geometry.

Paper solves Dirichlet problem for $p$-convex hypersurfaces with curvature constraints.

Study on prescribing Ricci curvature on compact Lie groups.

We describe two recently proposed machine learning approaches for discovering emerging trends in fatal accidental drug overdoses. The Gaussian Process Subset Scan enables early detection of emerging patterns in spatio-temporal data, accounting for both the non-iid nature of the data and the fact that detecting subtle p…

Study on $t$-graphs with prescribed mean curvature in Heisenberg groups.

We prove that on any compact complex manifold one can find Gauduchon metrics with prescribed volume form. This is equivalent to prescribing the Chern-Ricci curvature of the metrics, and thus solves a conjecture of Gauduchon from 1984.

The paper studies prescribed angle surfaces in Riemannian manifolds with torse-forming vector fields.

The paper constructs surfaces with prescribed mean curvature in a specific space.

The paper solves a curvature problem on a ball's surface near constant values.

Study of prescribed mean curvature flow on noncompact hypersurfaces in Lorentz manifolds.

In his paper "Shapes of Polyhedra and Triangulations of the Sphere", Thurston found that the set of shapes of convex polyhedra with prescribed cone-deficits has a complex hyperbolic structure. Inspired by his work, this paper studies the set of shapes of centrally symmetric octahedra with prescribed cone-deficits. We s…

In this work we study solutions of the prescribed mean curvature equation over a general domain that do not necessarily attain the given boundary data. To such a solution, we can naturally associate a current with support in the closed cylinder above the domain and with boundary given by the prescribed boundary data an…

Proves existence of graph on torus with prescribed curvature.

In this work, we study the Yamabe flow corresponding to the prescribed scalar curvature problem on compact Riemannian manifolds with negative scalar curvature. The long time existence and convergence of the flow are proved under appropriate conditions on the prescribed scalar curvature function.

Study local curvature estimates and existence of conformal metrics on noncompact manifolds.

The paper defines and proves the existence of curves in Riemannian manifolds with prescribed angles to torse-forming vector fields.

We construct a twin correspondence between graphs with prescribed mean curvature in three-dimensional Riemannian Killing submersions and spacelike graphs with prescribed mean curvature in three-dimensional Lorentzian Killing submersions. Our duality extends the Calabi correspondence between minimal graphs in the Euclid…

Existence of convex body with prescribed generalized curvature measures is discussed, this result is obtained by making use of Guan-Li-Li's innovative techniques. In surprise, that methods has also brought us to promote Ivochkina's $C^2$ estimates for prescribed curvature equation in \cite{I1, I}.

Classification of surfaces with prescribed mean curvature in Heisenberg space and SL2(R).

Study finds loops with specific curvature exist using Hardy's inequality.

We use a phase space analysis to give some classification results for rotational hypersurfaces in $\mathbb{R}^{n+1}$ whose mean curvature is given as a prescribed function of its Gauss map. For the case where the prescribed function is an even function in $\mathbb{S}^n$, we show that a Delaunay-type classification hold…

We prove a uniqueness theorem for immersed spheres of prescribed (non-constant) mean curvature in homogeneous three-manifolds. In particular, this uniqueness theorem proves a conjecture by A.D. Alexandrov about immersed spheres of prescribed Weingarten curvature in R3 for the special but important case of prescribed me…

Study solves complex Hessian equations with prescribed singularities on compact Kähler manifolds.

Study of metrics with prescribed curvature and geodesic curvature on a disc.

The paper solves curvature measure problem in hyperbolic space.

Proves Chen-Lin conjecture for sphere scalar curvature problem.

Study eigenvalues for special curvature equations on star-shaped surfaces.