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The study of cataclysmic variable stars has long been a fruitful area of co-operation between amateur and professional astronomers. In this Presidential Address, I shall take stock of our current understanding of these fascinating binary…
One of the most important topics in geophysics is to study convection in a sea. Based on the algebraic characteristics of the equations of dynamic convection in a sea, we introduce various schemes with multiple parameter functions to solve…
This paper provides an overview of the birth and early development of Indian astronomy. Taking account of significant new findings from archaeology and literary analysis, it is shown that early mathematical astronomy arose in India in the…
We assess the accuracy with which Omega and Lambda can be measured by combining various types of upcoming experiments. Useful expressions for the Fisher information matrix are derived for classical cosmological tests involving luminosity…
We present a collection of new, open-source computational tools for numerically modeling recent large-scale observational data sets using modern cosmology theory. Specifically, these tools will allow both students and researchers to…
Details for known solutions of some geometric and algebraic problems with the help of origami are presented: two theorems of Haga, the general cubic equation, especially the heptagon equation, doubling the cube as well as the trisection of…
We review results of papers written on the topic of polynomial amoebas with an emphasis on computational aspects of the topic. The polynomial amoebas have a lot of applications in various domains of science. Computation of the amoeba for a…
This article briefly summarizes the increasingly precise observational estimates of the cosmological parameters. After three years on the stump, the Lambda-CDM model is still the leading candidate. Although the Universe is expanding, our…
Cosmology contributes a good deal to the investigation of variation of fundamental physical constants. High resolution data is available and allows for detailed analysis over cosmological distances and a multitude of methods were developed.…
Presents a history of the evolution of the author's ideas on program-size complexity and its applications to metamathematics over the course of more than four decades. Includes suggestions for further work.
The arithmetic mean is the mean for addition and the geometric mean is that for multiplication. Then what kind of binary operation is associated with the arithmetic-geometric mean (AGM) due to C. F. Gauss? If it is possible to construct an…
Today, the operating TAIGA (Tunka Advanced Instrument for cosmic rays and Gamma Astronomy) experiment continuously produces and accumulates a large volume of raw astroparticle data. To be available for the scientific community these data…
Functionals of the meta-generalized gradient approximation (MGGA) are nowadays widely used in chemistry and solid-state physics for the simulation of electronic systems like molecules, solids, or surfaces. Due to their dependency on the…
With the recent advent of a sound mathematical theory for extreme events in dynamical systems, new ways of analyzing a system's inherent properties have become available: Studying only the probabilities of extremely close Poincar\'{e}…
Several methods have been recently proposed for estimating sparse Gaussian graphical models using $\ell_{1}$ regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
We present a Mathematica package for doing computations with gamma matrices, spinors, tensors and other objects, in any dimension and signature. The approach we use is based on defining the commutation relations of the relevant matrices,…
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Anonymizing the GPS locations of observations can bias a spatial model's parameter estimates and attenuate spatial predictions when improperly accounted for, and is relevant in applications from public health to paleoseismology. In this…
Diffusion Models have become very popular for Semantic Image Synthesis (SIS) of human faces. Nevertheless, their training and inference is computationally expensive and their computational requirements are high due to the quadratic…