Related papers: Algebraic Curves for Factorized String Solutions
The work is devoted to constructing a wide class of differential-functional dynamical systems, whose rich algebraic structure makes their integrability analytically effective. In particular, there is analyzed in detail the operator Lax type…
Suffix trees are an important data structure at the core of optimal solutions to many fundamental string problems, such as exact pattern matching, longest common substring, matching statistics, and longest repeated substring. Recent lines…
Modules over a vertex operator algebra V give rise to sheaves of coinvariants on moduli of stable pointed curves. If V satisfies finiteness and semi-simplicity conditions, these sheaves are vector bundles. This relies on factorization, an…
We investigate string graphs through the lens of graph product structure theory, which describes complicated graphs as subgraphs of strong products of simpler building blocks. A graph $G$ is called a string graph if its vertices can be…
We study the generalized Lam\'e equation on an elliptic curve $E$ with multiple singularities. By restricting to the locus admitting solutions with quasi-periodic properties, we construct two curves: (i) The generalized Lam'e curve: with…
Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…
High-order methods gain more and more attention in computational fluid dynamics. However, the potential advantage of these methods depends critically on the availability of efficient elliptic solvers. With spectral-element methods, static…
Braid matrices $\hat{R}(\theta)$, corresponding to vector representations, are spectrally decomposed obtaining a ratio $f_{i}(\theta)/f_{i}(-\theta)$ for the coefficient of each projector $P_{i}$ appearing in the decomposition. This…
We present the OSp(2,2|6) symmetric algebraic curve for the AdS4/CFT3 duality recently proposed in arXiv:0806.1218. It encodes all classical string solutions at strong t'Hooft coupling and the full two loop spectrum of long single trace…
For a boundary CFT to give a good approximation to the bulk flat-space S-matrix, a number of conditions need to be satisfied: some of those are investigated here. In particular, one would like to identify an appropriate set of approximate…
The generalized composition graph is used by Cardoso and some researchers for factorization of the adjacency spectrum and Laplacian of a simple graph. Because the generalized composition graph is an example of a set-theoretic linear operad,…
Factorization of statistical language models is the task that we resolve the most discriminative model into factored models and determine a new model by combining them so as to provide better estimate. Most of previous works mainly focus on…
New algorithms for prime factorization that outperform the existing ones or take advantage of particular properties of the prime factors can have a practical impact on present implementations of cryptographic algorithms that rely on the…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…
The matrix chain problem consists in finding the parenthesization of a matrix product $M := A_1 A_2 \cdots A_n$ that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated…
Connected components of real algebraic sets are semi-algebraic, i.e. they are described by a boolean formula whose atoms are polynomial constraints with real coefficients. Computing such descriptions finds topical applications in optical…
The boundary correlation functions for a QFT in a fixed AdS background should reduce to S-matrix elements in the flat-space limit. We consider this procedure in detail for four-point functions. With minimal assumptions we rigorously show…
Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category C with a distinguished object, a symmetric special…
Just as knowing some roots of a polynomial allows one to factor it, a well-known result provides a factorization of any scalar differential operator given a set of linearly independent functions in its kernel. This note provides a…
Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…