Related papers: Fingerprints, lemniscates and quadratic differenti…

This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem's solution to more general cases is investigated, based on which a discussion is…

The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…

We propose Material Fingerprinting, a new method for the rapid discovery of mechanical material models from direct or indirect data that avoids solving potentially non-convex optimization problems. The core assumption of Material…

The thesis studies linear and semilinear Dirichlet problems driven by different fractional Laplacians. The boundary data can be smooth functions or also Radon measures. The goal is to classify the solutions which have a singularity on the…

We study Lefschetz pencils on symplectic four-manifolds via the associated spheres in the moduli spaces of curves, and in particular their intersections with certain natural divisors. An invariant defined from such intersection numbers can…

Latent fingerprints are important for identifying criminal suspects. However, recognizing a latent fingerprint in a collection of reference fingerprints remains a challenge. Most, if not all, of existing methods would extract representation…

For a second-order elliptic equation in divergence form we investigate conditions on the coefficients which imply that all solutions are Lipschitz continuous or differentiable at a given point. We assume the coefficients have modulus of…

For several congruence subgroups of low levels and their conjugates, we derive differential equations satisfied by the Eisenstein series of weight 4 and relate them to elliptic curves, whose associated new forms of weight 2 constitute the…

The Deligne-Ogus-Shioda theorem guarantees the existence of isomorphisms between products of supersingular elliptic curves over finite fields. In this paper, we present methods for explicitly computing these isomorphisms in polynomial time,…

We give two algorithms to compute linear determinantal representations of smooth plane curves of any degree over any field. As particular examples, we explicitly give representatives of all equivalence classes of linear determinantal…

Molecular fingerprints are widely used for predicting chemical properties, and selecting appropriate fingerprints is important. We generate new fingerprints based on the assumption that a performance of prediction using a more effective…

Motivated by the study of hammock (aka brick-wall) networks, we introduce in this paper the notion of X-path. Using the Jordan Curve Theorem for piecewise smooth curves, we prove duality properties for hammock networks. Consequences for…

A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger…

We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…

Protecting a fingerprint database against attackers is very vital in order to protect against false acceptance rate or false rejection rate. A key property in distinguishing fingerprint images is by exploiting the characteristics of these…

Precise asymptotics for Christoffel functions are established for power type weights on unions of Jordan curves and arcs. The asymptotics involve the equilibrium measure of the support of the measure. The result at the endpoints of arc…

The world is abundant with diverse materials, each possessing unique surface appearances that play a crucial role in our daily perception and understanding of their properties. Despite advancements in technology enabling the capture and…

Our goal is to provide a novel method of representing 2D shapes, where each shape will be assigned a unique fingerprint - a computable approximation to a conformal map of the given shape to a canonical shape in 2D or 3D space (see page 22…

In this paper we consider Jordan curves on the Riemann sphere passing through $n \ge 3$ given points. We show that in each relative isotopy class of such curves, there exists a unique curve that minimizes the Loewner energy. These curves…

In order to utilize identification to the best extent, we need robust and fast algorithms and systems to process the data. Having palmprint as a reliable and unique characteristic of every person, we extract and use its features based on…