相关论文: Computing Instanton Numbers of Curve Singularities

Analogue computers use continuous properties of physical system for modeling. In the paper is described possibility of modeling by analogue quantum computers for some model of data analysis. It is analogue associative memory and a formal…

Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…

This paper dwells in developing a general algorithm for constructing a piecewise Ball Curve with curvature continuity (GC2). The proposed algorithm requires GC2 data in which the designer must define unit tangent vectors and signed…

There are thirteen types of singular points for irreducible real quartic curves and seventeen types of singular points for reducible real quartic curves. This classification is originally due to D.A. Gudkov. There are nine types of singular…

Measuring the similarity of curves is a fundamental problem arising in many application fields. There has been considerable interest in several such measures, both in Euclidean space and in more general setting such as curves on Riemannian…

There have been two distinct schemes studied in the literature for instanton counting in A_{p-1} asymptotically locally Euclidean (ALE) spaces. We point out that the two schemes---namely the counting of orbifolded instantons and instanton…

Understanding intermittency of turbulent systems from the underlying differential equations is an outstanding problem in fluid dynamics. Here, in the example of Burgers turbulence as a stringent test, we introduce a method that yields…

A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.

We generalize two classical formulas for complete intersection curves by introducing the the complete intersection discrepancy of a curve as a correction term. The first is a well-known multiplicity formula in singularity theory, due to…

We give a computational algorithm for computing Ext groups between bounded complexes of coherent sheaves on a projective variety, and we describe an implementation of this algorithm in Macaulay2. In particular, our results yield methods for…

A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…

We find exact multi-instanton solutions to the selfdual Yang-Mills equation on a large class of curved spaces with $SO(3)$ isometry, generalizing the results previously found on $\mathbb{R}^4$. The solutions are featured with explicit…

Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…

We study N=2 supersymmetric Abelian gauge model with the Fayet-Iliopoulos term and an arbitrary number of chiral matter multiplets in two dimensions. By analyzing the instanton contribution we compute the non-perturbative corrections to the…

We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…

We look into computational aspects of two classical knot invariants. We look for ways of simplifying the computation of the coloring invariant and of the Alexander module. We support our ideas with explicit computations on pretzel knots.

Two curves are affinely equivalent if there exists an affine mapping transforming one of them onto the other. Thus, detecting affine equivalence comprises, as important particular cases, similarity, congruence and symmetry detection. In…

An outstanding problem in quantum computing is the calculation of entanglement, for which no closed-form algorithm exists. Here we solve that problem, and demonstrate the utility of a quantum neural computer, by showing, in simulation, that…

In these lectures we describe the use of Monte Carlo simulations in understanding the role of tunneling events, instantons, in a quantum mechanical toy model. We study, in particular, a variety of methods that have been used in the QCD…

We discuss an algorithm computing the push-forward to projective space of several classes associated to a (possibly singular, reducible, nonreduced) projective scheme. For example, the algorithm yields the topological Euler characteristic…