arXiv research

Deep learning predicts preterm birth risk with improved accuracy.

The precise diagnosis is of great significance in developing precise treatment plans to restore neck function and reduce the burden posed by the cervical spondylosis (CS). However, the current available neck function assessment method are subjective and coarse-grained. In this paper, based on the relationship among CS,…

There are various algorithms and methodologies used for automated screening of cervical cancer by segmenting and classifying cervical cancer cells into different categories. This study presents a critical review of different research papers published that integrated AI methods in screening cervical cancer via different…

Cervical cancer is the leading gynecological malignancy worldwide. This paper presents diverse classification techniques and shows the advantage of feature selection approaches to the best predicting of cervical cancer disease. There are thirty-two attributes with eight hundred and fifty-eight samples. Besides, this da…

Cervical spondylosis (CS) is a common chronic disease that affects up to two-thirds of the population and poses a serious burden on individuals and society. The early identification has significant value in improving cure rate and reducing costs. However, the pathology is complex, and the mild symptoms increase the dif…

Adversarial method improves pneumonia classifier's performance across hospitals.

We investigate conformal actions of cocompact lattices in higher-rank simple Lie groups on compact pseudo-Riemannian manifolds. Our main result gives a general bound on the real-rank of the lattice, which was already known for the action of the full Lie group by a result of Zimmer. When the real-rank is maximal, we pro…

Given a simple Lie group G of rank 1, we consider compact pseudo-Riemannian manifolds (M,g) of signature (p,q) on which G can act conformally. Precisely, we determine the smallest possible value for the index min(p,q) of the metric. When the index is optimal and G non-exceptional, we prove that the metric must be confo…

Deep learning improves MRI analysis of MSK disorders.

Study explores solvable Lie groups' actions on closed Lorentzian manifolds.

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.

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

The paper examines rigidity in geometric actions of Coxeter groups on Croke-Kleiner spaces.

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…

Uniqueness of quasi-roots explored in right-angled Artin groups.

This note generalizes the visual angle to convex sets in 3D space.

Study proves existence of weak mean curvature flow with contact angle.

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

New model improves cancer screening prediction accuracy.

This paper explores historical and philosophical aspects of angles and solid angles, inspired by Euler's work.

Real moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic.

Defines Lorentzian angles for null vectors in geometry.

Agol recently introduced the notion of a veering triangulation, and showed that such triangulations naturally arise as layered triangulations of fibered hyperbolic 3-manifolds. We prove, by a constructive argument, that every veering triangulation admits positive angle structures, recovering a result of Hodgson, Rubins…

We provide a congruence theorem for minimal surfaces in $S^5$ with constant contact angle using Gauss-Codazzi-Ricci equations. More precisely, we prove that Gauss-Codazzi-Ricci equations for minimal surfaces in $S^5$ with constant contact angle satisfy an equation for the Laplacian of the holomorphic angle. Also, we wi…

Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational fans, the manifold Z is the total space of a holomorphic bundle over a toric variet…

Surveying connections between graph combinatorics and algebraic right-angled Artin groups.

We give a new notion of angle in general metric spaces; more precisely, given a triple a points $p,x,q$ in a metric space $(X,d)$, we introduce the notion of angle cone ${\angle_{pxq}}$ as being an interval ${\angle_{pxq}}:=[\angle^-_{pxq},\angle^+_{pxq}]$, where the quantities $\angle^\pm_{pxq}$ are defined in terms o…

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

In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle property. Moreover, the natural extension to normal and binormal constant angle sur…

We survey the role of right-angled Artin groups in the theory of diffeomorphism groups of low dimensional manifolds. We first describe some of the subgroup structure of right-angled Artin groups. We then discuss the interplay between algebraic structure, compactness, and regularity for group actions on one--dimensional…

Study on null hypersurfaces with constant angle in Lorentzian manifolds.

The paper solves a geometric problem involving points in a triangle's plane.

Establishes a boundary maximum principle for varifolds with fixed contact angle.

This notes explores angle structures on ideally triangulated compact $3$-manifolds with high genus boundary. We show that the existence of angle structures implies the existence of a hyperbolic metric with totally geodesic boundary, and conversely each hyperbolic $3$-manifold with totally geodesic boundary has an ideal…

The paper studies the face angles of tetrahedra with a fixed base.

We consider the question of determining whether a given group (especially one generated by involutions) is a right-angled Coxeter group. We describe a group invariant, the involution graph, and we characterize the involution graphs of right-angled Coxeter groups. We use this characterization to describe a process for c…

This paper characterizes a specific type of twisted Artin groups embedded in knot groups.

The angle defect, which is the standard way to measure curvature at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the literature an axiomatic characterization of the angle defect. We give a characterization …

Hyperbolic links in thickened torus decompose into angled tetrahedra.

In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to study attributes of triangles. Using the new definition, this paper investigates the existence of the incenter and the isogonal conjugate of a…

Fixed angles of convex polygons lead to combinatorially rich polytopes.

We study surfaces in $\R^4$ whose tangent spaces have constant principal angles with respect to a plane. Using a PDE we prove the existence of surfaces with arbitrary constant principal angles. The existence of such surfaces turns out to be equivalent to the existence of a special local symplectomorphism of $\R^2$. We …

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

Paper shows examples of hyperbolic cone structures degenerating with decreasing cone angles.

Predict steering angles of self-driving cars from images.