Related papers: Mutation of theta functions
Commutative hypercomplex algebras offer significant advantages over traditional quaternions due to their compatibility with linear algebra techniques and efficient computational implementation, which is crucial for broad applicability. This…
We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use of quantum approximate counting, and all of…
We describe some configurations of conjugate permutations which may be used as a mathematical model of some genetical processes and crystal growth.
Mutation is an operation on 3-manifolds containing an embedded surface of genus 2. It is defined by cutting along the surface and regluing using the `hyperelliptic' involution, and is known to preserve many 3-manifold invariants. I show…
Cluster algebras, introduced by Fomin and Zelevinsky through the process of quiver mutation, have become central objects in modern algebra and geometry, linking combinatorial constructions with diverse mathematical domains such as…
Details of quantum knot invariant calculations using a specific SU(3)_q-module are given which distinguish the Conway and Kinoshita-Teresaka pair of mutant knots. Features of Kuperberg's skein-theoretic techniques for SU(3)_q invariants in…
We construct the scattering matrices for an arbitrary Weyl group in terms of elementary operators which obey the generalised Yang-Baxter equation. We use this construction to obtain the affine Hecke algebras. The center of the affine Hecke…
A set of n points in low dimensions takes Theta(n w) bits to store on a w-bit machine. Surface reconstruction and mesh refinement impose a requirement on the distribution of the points they process. I show how to use this assumption to…
In this paper we study the characters of N=3 superconformal modules by using the Zwegers' theory on modification of mock theta functions.
It oftens occurs that Taylor coefficients of (dimensionally regularized) Feynman amplitudes $I$ with rational parameters, expanded at an integral dimension $D= D_0$, are not only periods (Belkale, Brosnan, Bogner, Weinzierl) but actually…
Inequalities for the transformation operator kernel $A(x,y)$ in terms of $F$-function are given, and vice versa. These inequalities are applied to inverse scattering on half-line. Characterization of the scattering data corresponding to the…
Mutation of compact silting objects is a fundamental operation in the representation theory of finite-dimensional algebras due to its connections to cluster theory and to the lattice of torsion pairs in module or derived categories. In this…
By applying the property of Ext-symmetry and the affine space structure of certain fibers, we introduce the notion of weighted quantum cluster functions and prove their multiplication formulas associated to abelian categories with…
We study theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We…
We present a numerically efficient and accurate Multiple Scattering formalism, which is a generalization of the Multiple Scattering method with a truncated basis set [X. -G. Zhang and W. H. Butler, Phys. Rev. B 46,7433 (1992)]. Compared to…
We describe a general construction principle which allows to add colour values to a coupling constant dependent scattering matrix. As a concrete realization of this mechanism we provide a new type of S-matrix which generalizes the one of…
The objective functions used in spectral clustering are usually composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
We explore the Mellin representation of conformal correlation functions recently proposed by Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes and scattering amplitudes. We conjecture a simple formula…
Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…