相关论文: Spectral networks for polynomial cubic differentia…

Non-Hermitian random matrices with symplectic symmetry provide examples for Pfaffian point processes in the complex plane. These point processes are characterised by a matrix valued kernel of skew-orthogonal polynomials. We develop their…

In recent years, many useful applications of the polynomial method have emerged in finite geometry. Indeed, algebraic curves, especially those defined by R\'edei-type polynomials, are powerful in studying blocking sets. In this paper, we…

2D image representations are in regular grids and can be processed efficiently, whereas 3D point clouds are unordered and scattered in 3D space. The information inside these two visual domains is well complementary, e.g., 2D images have…

The embedding of a Taub-NUT space in the directions transverse to the world volume of branes describes branes at (spherical) orbifold singularities. Similarly, the embedding of a pp-wave in the brane world volume yields an AdS orbifold. In…

The irreducible representations of symmetric groups can be realized as certain graded pieces of invariant rings, equivalently as global sections of line bundles on partial flag varieties. There are various ways to choose useful bases of…

Polynomial neural networks (PNNs) have been recently shown to be particularly effective at image generation and face recognition, where high-frequency information is critical. Previous studies have revealed that neural networks demonstrate…

This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds…

The goal of the paper is two-fold. At first, we attempt to give a survey of some recent applications of symmetric polynomials and divided differences to intersection theory. We discuss: polynomials universally supported on degeneracy loci;…

In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We classify all configurations of singularities occurring for a projection of a smooth curve embedded by a…

We study the possible BPS domain wall junction configurations for general polynomial superpotentials of N=1 supersymmetric Wess-Zumino models in D=4. We scan the parameter space of the superpotential and find different possible BPS states…

It is possible to understand whether a given BPS spectrum is generated by a relevant deformation of a 4D N=2 SCFT or of an asymptotically free theory from the periodicity properties of the corresponding quantum monodromy. With the aim of…

We consider the hermitian random matrix model with external source and general polynomial potential, when the source has two distinct eigenvalues but is otherwise arbitrary. All such models studied so far have a common feature: an…

We propose a novel derived cohomological framework for the Birch and Swinnerton-Dyer (BSD) conjecture for elliptic curves. In our approach, local arithmetic data are encoded in derived sheaves which, when glued via a mapping cone…

Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by…

Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…

A conformal map from a Riemann surface to a Euclidean space of dimension greater than or equal to three is explained by using the Clifford algebra, in a similar fashion to quaternionic holomorphic geometry of surfaces in the Euclidean…

Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of a properly constructed matrix, and has found applications throughout science and technology. Many networks are multipartite, meaning…

We construct a family of self-adjoint operators on the prime numbers whose entries depend on pairwise arithmetic divergences, replacing geometric distance with number-theoretic dissimilarity. The resulting spectra encode how coherence…

We investigate the spectrum of the principal chiral model (PCM) on odd-dimensional superspheres as a function of the curvature radius R. For volume-filling branes on S^{3|2}, we compute the exact boundary spectrum as a function of R. The…

In this paper, we construct polynomial growth harmonic maps from once-punctured Riemann surfaces of any finite genus to any even-sided, regular, ideal polygon in the hyperbolic plane. We also establish their uniqueness within a class of…