Towards Mixed Gr{\"o}bner Basis Algorithms: the Multihomogeneous and Sparse Case

One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of unmixed polynomial systems, that is systems with polynomials having the same support, using the approach of Faug{\`e}re, Spaenlehauer, and Svartz [ISSAC'14]. We present two algorithms for sparse Gr{\"o}bner bases computations for mixed systems. The first one computes with mixed sparse systems and exploits the supports of the polynomials. Under regularity assumptions, it performs no reductions to zero. For mixed, square, and 0-dimensional multihomogeneous polynomial systems, we present a dedicated, and potentially more efficient, algorithm that exploits different algebraic properties that performs no reduction to zero. We give an explicit bound for the maximal degree appearing in the computations

Statistically Stable Estimates of Variance in Radioastronomical Observations as Tools for RFI Mitigation

A selection of statistically stable (robust) algorithms for data variance calculating has been made. Their properties have been analyzed via computer simulation. These algorithms would be useful if adopted in radio astronomy observations in the presence of strong sporadic radio frequency interference (RFI). Several observational results have been presented here to demonstrate the effectiveness of these algorithms in RFI mitigation

Correlates of tourist vacation behavior: a combination of CHAID and Loglinear Logit Analysis

The aim of study is to examine the relationships between vacation choice behavior and socioeconomic variables. A sequence alignment method is used to classify respondents into homogeneous clusters, based on temporal and spatial aspects of their vacation histories. The relationship between this clustering and a set of socioeconomic variables is then examined using a combination of CHAID and loglinear analysis. The results suggest some interpretable, consistent patterns.

Integrable Quasiclassical Deformations of Cubic Curves

A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and characterize these deformations.Comment: 24 page

P.A.M. Dirac and the Discovery of Quantum Mechanics

Dirac's contributions to the discovery of non-relativistic quantum mechanics and quantum electrodynamics, prior to his discovery of the relativistic wave equation, are described