arXiv research

Proof of Gromov's theorem on convex polytopes with acute angles.

Let $C(L)$ be the right-angled Coxeter group defined by an abstract triangulation $L$ of $\mathbb{S}^2$. We show that $C(L)$ is isomorphic to a hyperbolic right-angled reflection group if and only if $L$ can be realized as an acute triangulation. The proof relies on the theory of CAT(-1) spaces. A corollary is that an …

The study finds minimal hypersurfaces in wedge-shaped manifolds with boundary.

Improved volume estimates for right-angled polyhedra in hyperbolic space.

Maps between acute triangles with minimal stretch found and studied.

Paper finds optimal shapes for minimizing average lengths of billiard trajectories in specific polygons.

On a compact Riemannian manifold with boundary, the absolute and relative cohomology groups appear as certain subspaces of harmonic forms. DeTurck and Gluck showed that these concrete realizations of the cohomology groups decompose into orthogonal subspaces corresponding to cohomology coming from the interior and bound…

Study on Teichmüller space of acute triangles using explicit calculations.

In a 2013 paper, Gromov proves that if smooth Riemannian metrics $g_i$ converge to a smooth Riemannian metric $g$ uniformly, and $g_i$ have scalar curvature uniformly bounded below, then $g$ shares the same scalar curvature lower bound. In some places in the paper, the proofs are only sketched. In this paper we explain…

The paper explores Kähler and anti-Kähler structures on quasi-statistical manifolds.

Improved rigidity of Delaunay triangulated plane.

We developed an explainable artificial intelligence (AI) early warning score (xAI-EWS) system for early detection of acute critical illness. While maintaining a high predictive performance, our system explains to the clinician on which relevant electronic health records (EHRs) data the prediction is grounded. Acute cri…

Bayesian optimization improves classifier selection for acute infection and mortality.

In this paper, the development of a probabilistic network for the diagnosis of acute cardiopulmonary diseases is presented. This paper is a draft version of the article published after peer review in 2018 (https://doi.org/10.1002/bimj.201600206). A panel of expert physicians collaborated to specify the qualitative part…

Study developed phenotypes for ICU patients' brain dysfunction states.

Background: Fluctuating hearing loss is characteristic of Meniere's Disease (MD) during acute episodes. However, no reliable audiometric hallmarks are available for counselling the hearing recovery possibility. Aims/Objectives: To find parameters for predicting MD hearing outcomes. Material and Methods: We applied mach…

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such directions, eliminating the need for the user to tune the learning rate. The pro…

The paper classifies Poincaré complexes as topological manifolds.

It has been shown that the Alvarez-Gaum$\mathrm{\acute{e}}$-Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain characteristic forms. In this paper, we show that the Green-Schwarz formula and the Schwarz-Witten formula i…

Large vessel occlusion (LVO) plays an important role in the diagnosis of acute ischemic stroke. Identifying LVO of patients in the early stage on admission would significantly lower the probabilities of suffering from severe effects due to stroke or even save their lives. In this paper, we utilized both structural and …

Plane triangulations remain rigid under discrete conformal changes.

We construct discrete and faithful representations into the isometry group of a hyperbolic space of the fundamental groups of acute negatively curved even-sided polygons of finite groups.

In critical care, intensivists are required to continuously monitor high dimensional vital signs and lab measurements to detect and diagnose acute patient conditions. This has always been a challenging task. In this study, we propose a novel self-correcting deep learning prediction approach to address this challenge. W…

Let $Σ$ be a complete Riemannian manifold with the volume doubling property and the uniform Neumann-Poincar$\mathrm{\acute{e}}$ inequality. We show that any positive minimal graphic function on $Σ$ is a constant.

The paper examines properties of self-affine Sierpiński sponges using metric invariants.

Timely prediction of clinically critical events in Intensive Care Unit (ICU) is important for improving care and survival rate. Most of the existing approaches are based on the application of various classification methods on explicitly extracted statistical features from vital signals. In this work, we propose to elim…

Proposes a framework for personalized treatment recommendations using observational data.

J.J.L. Vel$\acute{a}$zquez in 1994 used the degree theory to show that there is a perturbation of Simons' cone, starting from which the mean curvature flow develops a type $\mathrm{II}$ singularity at the origin. He also showed that under a proper time-dependent rescaling of the solution around the origin, the rescaled…

Cluster analysis aims at separating patients into phenotypically heterogenous groups and defining therapeutically homogeneous patient subclasses. It is an important approach in data-driven disease classification and subtyping. Acute coronary syndrome (ACS) is a syndrome due to sudden decrease of coronary artery blood f…

Deep Learning can significantly benefit cancer proteomics and genomics. In this study, we attempt to determine a set of critical proteins that are associated with the FLT3-ITD mutation in newly-diagnosed acute myeloid leukemia patients. A Deep Learning network consisting of autoencoders forming a hierarchical model fro…

We explore how Deep Learning (DL) can be utilized to predict prognosis of acute myeloid leukemia (AML). Out of TCGA (The Cancer Genome Atlas) database, 94 AML cases are used in this study. Input data include age, 10 common cytogenetic and 23 most common mutation results; output is the prognosis (diagnosis to death, DTD…

This project was motivated by a dialysis study in northern Taiwan. Dialysis patients, after shunt implantation, may experience two types ("acute" or "non-acute") of shunt thrombosis, both of which may recur. We formulate the problem under the framework of recurrent events data in the presence of competing risks. In par…

Logistic regression (LR) is widely used in clinical prediction because it is simple to deploy and easy to interpret. Nevertheless, being a linear model, LR has limited expressive capability and often has unsatisfactory performance. Generalized additive models (GAMs) extend the linear model with transformations of input…

Acute kidney injury (AKI) in critically ill patients is associated with significant morbidity and mortality. Development of novel methods to identify patients with AKI earlier will allow for testing of novel strategies to prevent or reduce the complications of AKI. We developed data-driven prediction models to estimate…

Heart disease remains the leading cause of death in the United States. Compared with risk assessment guidelines that require manual calculation of scores, machine learning-based prediction for disease outcomes such as mortality can be utilized to save time and improve prediction accuracy. This study built and evaluated…

Predicting the risk of mortality for patients with acute myocardial infarction (AMI) using electronic health records (EHRs) data can help identify risky patients who might need more tailored care. In our previous work, we built computational models to predict one-year mortality of patients admitted to an intensive care…

Patients who suffer an acute coronary syndrome are at elevated risk for adverse cardiovascular events such as myocardial infarction and cardiovascular death. Accurate assessment of this risk is crucial to their course of care. We focus on estimating a patient's risk of cardiovascular death after an acute coronary syndr…

Study reviews machine learning techniques for stress monitoring.

Defines Kahler angle for a broader context.

We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant complex angle with respect to a fixed spacelike plane. This notion is the natural Lo…

Study angle structures on pseudo 3-manifolds, proving existence for some cases.

In this paper we study the right-angled Coxeter groups that acts geometrically on the Salvetti complex of a certain right-angled Artin group, which we refer to as Croke-Kleiner spaces. We prove that any right-angled Coxeter group that acts geometrically on the Croke-Kleiner spaces acts with $π/2$ angles between reflect…

Deep Rule Forests identifies drug-drug and drug-disease interactions causing AKI.

Introduces a new geometry based on difference angles, showing unique properties.

The paper analyzes skewness and kurtosis measures for skew-elliptical distributions.

Stiefel-Whitney classes of moment-angle manifolds are trivial.

In this paper, we discuss the Lagrangian angle and the Kähler angle of immersed surfaces in $\mathbb C^2$. Firstly, we provide an extension of Lagrangian angle, Maslov form and Maslov class to more general surfaces in $\mathbb C^2$ than Lagrangian surfaces, and then naturally extend a theorem by J.-M. Morvan to surface…

Improves feature selection in high-dimensional data using LLM-generated weights.