arXiv research

The study examines singularities and geometric properties of surfaces derived from frontals with specific singular points.

Study behavior of curvatures near singular points of frontals.

Study on singularities of frontal surfaces, classifying under equivalence.

The paper studies singularities of pedal curves of hyperbolic frontals.

Solves recognition problem of frontal singularities.

Study helicoidal surfaces with singular points using frontals.

Abstract: Characterizes frontals and wavefronts with formulas.

The study examines vertices in curves with singular points in the Euclidean plane.

Develops a Thom-Mather theory for corank 1 frontals.

In this survey article we introduce the notion of frontals, which provides a class of generalised submanifolds with singularities but with well-defined tangent spaces. We present a review of basic theory and known studies on frontals in several geometric problems from singularity theory viewpoints. In particular, in th…

Study helicoidal surfaces from frontals, revealing geometric rigidity and stability of singularities.

The paper studies singularities on parallels of tangent developable surfaces of frontal curves.

The paper generalizes curvature bounds for submanifolds with singularities.

The paper studies helicoidal surfaces of non-lightlike frontals in Lorentz-Minkowski 3-space.

The paper improves Zakalyukin's lemma for frontals and applies it to surface singularities.

The paper generalizes Fenchel's theorem for curves with singularities.

Study surfaces of revolution from frontals in Euclidean space.

Geometric study of cuspidal $S_1$ singularities using diffeomorphisms and isometries.

The paper derives new Gauss-Bonnet formulas for frontal bundles over surfaces with boundary.

We study a generalization of constant Gauss curvature -1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyze the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods for constructing all n…

Extends Kummer's theory to singular surfaces for line congruences.

Proves fundamental theorem for singular surfaces with limiting tangent planes.

Defines axial curvatures for corank 1 singular manifolds in higher dimensions.

We give the complete solution to the local diffeomorphism classification problem of generic singularities which appear in tangent surfaces, in as wider situations as possible. We interpret tangent geodesics as tangent lines whenever a (semi-)Riemannian metric, or, more generally, an affine connection is given in an amb…

In a joint work with Saji, the second and the third authors gave an intrinsic formulation of wave fronts and proved a realization theorem of wave fronts in space forms. As an application, we show that the following four objects are essentially same; * conformally flat n-manifolds (n>=3) with admissible singular points …

Study of normal and tangent maps to frontals.

Generalized Frenet frames for singular space curves

We consider developable surfaces along the singular set of a swallowtail which are considered to be flat approximations of the swallowtail. For the study of singularities of such developable surfaces, we introduce the notion of Darboux frames along swallowtails and invariants. As a by-product, we give a new example of …

The paper extends equiaffine structure to frontals and defines Blaschke vector fields.

New curvature defined for corank 1 singular surfaces in 3D.

Defines horocyclic evolutes, parallels, and involutes of spacelike frontals in hyperbolic 2-space.

We give the complete solution to the local diffeomorphism classification problem of generic singularities which appear in tangent surfaces, in as wider situations as possible. We interpret tangent geodesics as tangent lines whenever a (semi-)Riemannian metric, or, more generally, an affine connection is given in an amb…

Characterizes the Legendre involution on generic frontals.

The paper studies parallel surfaces of cuspidal cross caps and their degeneracy.

The paper defines and explores anti-orthotomics of frontals and their applications.

The paper studies circular evolutes and involutes of framed curves in Euclidean space.

The MIMIC-CXR dataset is (to date) the largest released chest x-ray dataset consisting of 473,064 chest x-rays and 206,574 radiology reports collected from 63,478 patients. We present the results of training and evaluating a collection of deep convolutional neural networks on this dataset to recognize multiple common t…

It is classically known that complete flat surfaces in Euclidean 3-space are cylinders over space curves. This implies that the study of global behaviour of flat surfaces requires the study of singular points as well. If a flat surface $f$ admits singularities but its Gauss map $ν$ can be smoothly extended across the s…

In this work we consider the Taylor expansion of the exponential map of a submanifold immersed in R^n up to order three, in order to introduce the concepts of lateral and frontal deviation. We compute the directions of extreme lateral and frontal deviation for surfaces in R^3. Also we compute, by using the Taylor expan…

Introduces cofrontal mappings and studies their properties.

A geometric construction is provided that associates to a given flat front in $\mathbb{H}^3$ a pair of minimal surfaces in $\mathbb{R}^3$ which are related by a Ribaucour transformation. This construction is generalized associating to a given frontal in $\mathbb{H}^3$ , a pair of frontals in $\mathbb{R}^3$ that are env…

We present a method for synthesizing a frontal, neutral-expression image of a person's face given an input face photograph. This is achieved by learning to generate facial landmarks and textures from features extracted from a facial-recognition network. Unlike previous approaches, our encoding feature vector is largely…

Understanding the functional architecture of the brain in terms of networks is becoming increasingly common. In most fMRI applications functional networks are assumed to be stationary, resulting in a single network estimated for the entire time course. However recent results suggest that the connectivity between brain …

Study reveals biases in facial landmark detection methods for dementia patients.

Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image s…

Evaluating human brain potentials during watching different images can be used for memory evaluation, information retrieving, guilty-innocent identification and examining the brain response. In this study, the effects of watching images, with different levels of familiarity, on subjects' Electroencephalogram (EEG) have…

Proposes a bilinear form to efficiently represent high-order temporal action information.

We developed an automated deep learning system to detect hip fractures from frontal pelvic x-rays, an important and common radiological task. Our system was trained on a decade of clinical x-rays (~53,000 studies) and can be applied to clinical data, automatically excluding inappropriate and technically unsatisfactory …