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We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.
A global offensive alliance in a graph $G$ is a set $S$ of vertices with the property that every vertex not belonging to $S$ has at least one more neighbor in $S$ than it has outside of $S$. The globa...
On computing the generalized Lambert series     computing  generalized Lambert series  Theta convergence  ODEs       font style='font-size:12px;'> 2012/3/1
We show how the generalized Lambert series sum(n>=1, x*q^n/(1-x*q^n)) can be computed with Theta convergence. This allows the computation of the sum of the inverse Fibonacci numbers without splitting ...
Structural equation model has become a very popular data-analytic technique. It is widely applied in Psychology and Sociology as well as other fields, especially in Customer Satisfaction Index (CSI) m...
This paper presents a recursive procedure to compute the Moore-Penrose inverse of a matrix A. The method is based on the expression for the Moore-Penrose inverse of rank-one modified matrix. The compu...
Computing the Singularities of Rational Surfaces     Singularities of Rational Surfaces  Algebraic Geometry       font style='font-size:12px;'> 2011/9/21
Abstract: Given a rational projective parametrization $\cP(\ttt,\sss,\vvv)$ of a rational projective surface $\cS$ we present an algorithm such that, with the exception of a finite set (maybe empty) $...
Computing the obstacle number of a plane graph     obstacle number of a plane graph  Computational Geometry       font style='font-size:12px;'> 2011/10/9
Abstract: An obstacle representation of a plane graph G is V(G) together with a set of opaque polygonal obstacles such that G is the visibility graph on V(G) determined by the obstacles. We investigat...
Abstract: We provide an algorithm for computing the centered Hausdorff measure of self-similar sets satisfying the strong separation condition. We prove the convergence of the algorithm and test its u...
Computing the homology of groups: the geometric way     homology of groups  the geometric way  Algebraic Topology       font style='font-size:12px;'> 2011/9/14
Abstract: In this paper we present several algorithms related with the computation of the homology of groups, from a geometric perspective (that is to say, carrying out the calculations by means of si...
Abstract: In this paper, we show how to use stochastic approximation to compute hitting time of a stochastic process, based on the study of the time for a fluid approximation of this process to be at ...
Abstract: The evaluation of long-range potentials in periodic, many-body systems arises as a necessary step in the numerical modeling of a multitude of interesting physical problems. Direct evaluation...
Abstract: We consider the "Method of particular solutions" for numerically computing eigenvalues and eigenfunctions of the Laplacian $\Delta$ on a smooth, bounded domain Omega in RR^n with either Diri...
Abstract: We provide an overview of the Macaulay2 package VersalDeformations, which algorithmically computes versal deformations of isolated singularities, as well as local (multi)graded Hilbert schem...
Abstract: The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers a...
Abstract: Given a chain complex with the only modi?cation that each cell of the complex has a probability distribution assigned. We will call this complex - a random complex and what should be underst...

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