Marcel Grossmann and his contribution to the general theory of relativity

This article reviews the biography of the Swiss mathematician Marcel Grossmann (1878-1936) and his contributions to the emergence of the general theory of relativity. The first part is his biography, while the second part reviews his collaboration with Einstein in Zurich which resulted in the Einstein-Grossmann theory of 1913. This theory is a precursor version of the final theory of general relativity with all the ingredients of that theory except for the correct gravitational field equations. Their collaboration is analyzed in some detail with a focus on the question of exactly what role Grossmann played in it.Comment: 52pp, 7 figs, to appear in Proceedings of 13th Marcel Grossmann meeting; revised version with some minor stylistic emendation

EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis

Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical properties and to the existence of maximum-likelihood estimators based on expectation-maximization (EM). In this paper we propose a new mixture model that associates a weight with each observed point. We introduce the weighted-data Gaussian mixture and we derive two EM algorithms. The first one considers a fixed weight for each observation. The second one treats each weight as a random variable following a gamma distribution. We propose a model selection method based on a minimum message length criterion, provide a weight initialization strategy, and validate the proposed algorithms by comparing them with several state of the art parametric and non-parametric clustering techniques. We also demonstrate the effectiveness and robustness of the proposed clustering technique in the presence of heterogeneous data, namely audio-visual scene analysis.Comment: 14 pages, 4 figures, 4 table

Design of engineering systems in Polish mines in the third quarter of the 20th century

Participation of mathematicians in the implementation of economic projects in Poland, in which mathematics-based methods played an important role, happened sporadically in the past. Usually methods known from publications and verified were adapted to solving related problems. The subject of this paper is the cooperation between mathematicians and engineers in Wroc{\l}aw in the second half of the twentieth century established in the form of an analysis of the effectiveness of engineering systems used in mining. The results of this cooperation showed that at the design stage of technical systems it is necessary to take into account factors that could not have been rationally controlled before. The need to explain various aspects of future exploitation was a strong motivation for the development of mathematical modeling methods. These methods also opened research topics in the theory of stochastic processes and graph theory. The social aspects of this cooperation are also interesting.Comment: 45 pages, 11 figures, 116 reference

Spartan Daily, September 29, 2005

Volume 125, Issue 20https://scholarworks.sjsu.edu/spartandaily/10163/thumbnail.jp

The Minimal Modal Interpretation of Quantum Theory

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory asserts that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture of states and Hilbert-space trajectories to the case of open quantum systems as well. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure---which we call subsystem space---that we believe merits further study. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text.Comment: 73 pages + references, 9 figures; cosmetic changes, added figure, updated references, generalized conditional probabilities with attendant changes to the sections on the EPR-Bohm thought experiment and Lorentz invariance; for a concise summary, see the companion letter at arXiv:1405.675