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Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both…
The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…
One of the presuppositions of science since the times of Galileo, Newton, Laplace, and Descartes has been the predictability of the world. This idea has strongly influenced scientific and technological models. However, in recent decades,…
We study cosmological solutions for the very early universe beginning at the Planck scale for a universe containing radiation, curvature and, as a simplification of a possible scalar field potential, a cosmological constant term. The…
The realization that string theory gives rise to a huge landscape of vacuum solutions has recently prompted a statistical approach towards extracting phenomenological predictions from string theory. Unfortunately, for most classes of string…
Evolution of scalar perturbations in a universe containing solid matter with positive pressure is studied. Solution for pure solid is found and matched with solution for ideal fluid, including the case when the pressure to energy density…
In spite of the phenomenological successes of the inflationary universe scenario, the current realizations of inflation making use of scalar fields lead to serious conceptual problems which are reviewed in this lecture. String theory may…
Based on the theory of invariant sets of descending flow, we give a new proof of the existence of three nontrivial solutions and some remarks on it.
All sciences need and many arts apply mathematics whereas mathematics seems to be independent of all of them, but only based upon logic. This conservative concept, however, needs to be revised because, contrary to Platonic idealism…
We consider two questions in string ``phenomenology.'' First, are there any generic string predictions? Second, are there any general lessons which string theory suggests for thinking about low energy models, particularly in the framework…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
An overview is given of the formulation of low-energy string cosmologies together with examples of particular solutions, successes and problems of the theory.
Many mathematical models of statistical physics in two dimensions are either known or conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions of various exponents describing the behavior of these models.…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
Multiple solutions exist in various experimental situations whenever the sum of several amplitudes is used to fit the experimentally measured distributions, such as the cross section, the mass spectrum, or the angular distribution. We show…
Varying physical constant cosmologies were claimed to solve standard cosmological problems such as the horizon, the flatness and the $\Lambda$-problem. In this paper, we suggest yet another possible application of these theories: solving…
We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for…
Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many…
Quantum theory can be derived from purely informational principles. Five elementary axioms-causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning-define a broad class of theories of…
Mathematicians invented Mathematics to escape from words, but at last they depend on them just as much as everybody else. At the end, all basic definitions will be reliant on words, yet the mathematician believes that he's elevated from…