Related papers: Singularity degree of non-facially exposed faces

Given a simplicial complex we associate to it a squarefree monomial ideal which we call the face ideal of the simplicial complex, and show that it has linear quotients. It turns out that its Alexander dual is a whisker complex. We apply…

An essential factor to achieve high performance in face recognition systems is the quality of its samples. Since these systems are involved in daily life there is a strong need of making face recognition processes understandable for humans.…

Robert Bryant (Theorie des varietes minimales et applications, 1988, 154: 321-347) proved that an isolated singularity of a conformal metric of positive constant curvature on a Riemann surface is a conical one. Using Complex Analysis, we…

Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…

Let $S = K[x_1, ..., x_n ]$ be a polynomial ring over a field $K$, and $E = K < y_1, ..., y_n >$ an exterior algebra. The "linearity defect" $ld_E(N)$ of a finitely generated graded $E$-module $N$ measures how far $N$ departs from…

A convex optimization problem in conic form involves minimizing a linear functional over the intersection of a convex cone and an affine subspace. In some cases, it is possible to replace a conic formulation using a certain cone, with a…

Neural networks with high performance can still be biased towards non-relevant features. However, reliability and robustness is especially important for high-risk fields such as clinical pain treatment. We therefore propose a verification…

The degree of a map between orientable manifolds is a fundamental concept in topology, providing deep insights into the structure of manifolds and the behavior of maps between them. Recently, this notion has been extensively studied,…

Face recognition is a biometric which is attracting significant research, commercial and government interest, as it provides a discreet, non-intrusive way of detecting, and recognizing individuals, without need for the subject's knowledge…

We enumerate the number of surfaces of degree $d$ in $P^3$ having a singular line of order $k$, passing through $\delta$ generic points (where $\delta$ is the dimension of moduli space of such surfaces).

In the beginning stage, face verification is done using easy method of geometric algorithm models, but the verification route has now developed into a scientific progress of complicated geometric representation and matching process. In…

Data cleaning, architecture, and loss function design are important factors contributing to high-performance face recognition. Previously, the research community tries to improve the performance of each single aspect but failed to present a…

The objective of this work is to study weak infeasibility in second order cone programming. For this purpose, we consider a relaxation sequence of feasibility problems that mostly preserve the feasibility status of the original problem.…

Assessing the similarity of matrices is valuable for analyzing the extent to which data sets exhibit common features in tasks such as data clustering, dimensionality reduction, pattern recognition, group comparison, and graph analysis.…

Shape complexity is a hard-to-quantify quality, mainly due to its relative nature. Biased by Euclidean thinking, circles are commonly considered as the simplest. However, their constructions as digital images are only approximations to the…

Conventional subspace learning approaches based on image gradient orientations only employ the first-order gradient information. However, recent researches on human vision system (HVS) uncover that the neural image is a landscape or a…

We show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de…

The paper presents an algorithm for topological classification of nondegenerate saddle-focus singularities of integrable Hamiltonian systems with three degrees of freedom up to semi-local equivalence. In particular, we prove that any…

We introduce the notion of radical parametrization of a surface, and we provide algorithms to compute such type of parametrizations for families of surfaces, like: Fermat surfaces, surfaces with a high multiplicity (at least the degree…

We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of categoricity is $\bf{0^{(\alpha)}}$ for…