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We investigate a supersymmetric generalisation of topological recursion from two perspectives: algebraic and geometric. The algebraic side concerns a recursive structure encoded in modules of a super Virasoro algebra, and the geometric…
This paper concerns extension of the classical Lagrange theorem, on the eventual periodicity of continued fraction expansions of quadratic surds, and the versions of it found in the literature in the case of complex numbers. In this…
Schur's transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we…
In well-studied graph modification problems, adding and deleting vertices and edges are used as graph editing operations. We propose a model for graph modification on geometric intersection graphs called Geometric Graph Edit Distance that…
This paper presents an algorithm for the efficient approximation of the saddle-extremum persistence diagram of a scalar field. Vidal et al. introduced recently a fast algorithm for such an approximation (by interrupting a progressive…
A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with…
The text deals with generalizations of the Markoff equation in number theory, arising from continued fractions. It gives the method for the complete resolution of such new equations, and their interpretation in algebra and algebraic…
In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…
For each of the eight $n$-th derivative parameter changing formulas for Gauss hypergeometric functions a corresponding fractional integration formula is given. For both types of formulas the differential or integral operator is intertwining…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
A new graphical calculus for operating with isometries of low dimensional spaces of classical geometries is proposed. It is similar to a well-known graphical representation for vectors and translations in an affine space. Instead of arrows,…
We give an approximation algorithm for MaxCut and provide guarantees on the average fraction of edges cut on $d$-regular graphs of girth $\geq 2k$. For every $d \geq 3$ and $k \geq 4$, our approximation guarantees are better than those of…
This paper deals with (globally) random substitutions on a finite set of prototiles. Using renormalization tools applied to objects from operator algebras we establish upper and lower bounds on the rate of deviations of ergodic averages for…
This paper presents an enhanced version of our previous work, hybrid non-uniform subdivision surfaces [19], to achieve optimal convergence rates in isogeometric analysis. We introduce a parameter $\lambda$ ($\frac{1}{4}<\lambda<1$) to…
Symmetry under a particular class of non-strictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant…
Quasi-periodic motions on invariant tori of an integrable system of dimension smaller than half the phase space dimension may continue to exists after small perturbations. The parametric equations of the invariant tori can often be computed…
Graph Shift (GS) algorithms are recently focused as a promising approach for discovering dense subgraphs in noisy data. However, there are no theoretical foundations for proving the convergence of the GS Algorithm. In this paper, we propose…
We prove an effective version of a celebrated result of Eskin and Masur: for any affine invariant manifold of translation surfaces, almost every translation surface has quadratic growth for the saddle connection holonomy vectors, with an…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
A basic feature of Teichm\"uller theory of Riemann surfaces is the interplay of two dimensional hyperbolic geometry, the behavior of geodesic-length functions and Weil-Petersson geometry. Let $\mathcal{T}_g$ $(g\geq 2)$ be the Teichm\"uller…