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This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…
This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…
Galactic disks lie at the heart of many of the most pressing astrophysical puzzles. There are sophisticated kinetic theories that describe some aspects of galaxy disk dynamics, but extracting quantitative predictions from those theories has…
We cover some useful techniques in computational aspects of analytic number theory, with specific emphasis on ideas relevant to the evaluation of L-functions. These techniques overlap considerably with basic methods from analytic number…
Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice…
We survey several results known on sampling in computational geometry.
Two fundamental research tasks in science and engineering are forward predictions and data inversion. This article introduces a recent R package RobustCalibration for Bayesian data inversion and model calibration by experiments and field…
We obtain an explicit formula for the number of rational cuspidal curves of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This enumerative problem is expressed as an Euler…
This is a survey describing recents developments in enumerative geometry of curves on projective varieties. Various methods to arrive at results such as Kontsevich's formula for plane rational curves, or Caporaso-Harris's formula for plane…
The purpose of the present review is to discuss the role of Soft Computing techniques in understanding the complexity associated with atmospheric phenomena and thus developing predictive models. Problems in atmospheric data analysis are…
Astronomical data have shown that the galaxy rotation curves are mostly flat in the far distance of the galactic cores, which reveals the insufficiency of our knowledges about how gravity works in these regimes. In this paper we introduce a…
High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed…
I present here a review of past and present multi-disciplinary research of the Pittsburgh Computational AstroStatistics (PiCA) group. This group is dedicated to developing fast and efficient statistical algorithms for analysing huge…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.
In this short note we briefly review some recent mathematical results relevant to the classical Regge Calculus evolution problem.
The time evolution of models for an isolated disk of highly flattened galaxies of stars is investigated by direct integration of the Newtonian equations of motion of N=30,000 identical stars over a time span of many galactic rotations.…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the…
We derive efficient, closed form, differentiable, and numerically stable solutions for the flux measured from a spherical planet or moon seen in reflected light, either in or out of occultation. Our expressions apply to the computation of…