Related papers: PC4 at Age 40
Exponentiation makes the difference between the bit-size of this line and the number (<< 2^{300}) of particles in the known Universe. The expulsion of exponential time algorithms from Computer Theory in the 60's broke its umbilical cord…
Triggered by a recent interesting New Scientist article on the too frequent incorrect use of probabilistic evidence in courts, I introduce the basic concepts of probabilistic inference with a toy model, and discuss several important issues…
With rising life expectancies around the world and an older scientific workforce than ever before, what does aging mean for individual scientists, and what do aging scientists mean for scientific progress as a whole? Here we examine how…
During the 80's, some experiments and the repetitions of old ones, lead to the hypothesis of a fifth force. Nevertheless, a more accurate research was not able to confirm this hypothesis. This article wants to go over again the most…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
In a recently launched research program for developing logic as a formal theory of (interactive) computability, several very interesting logics have been introduced and axiomatized. These fragments of the larger Computability Logic aim not…
Ball lightning is a very rarely observed phenomenon that makes it extremely difficult to characterize scientifically. Eye-witness accounts of ball lightning that describe many features in common have been variously recorded for centuries.…
The comments relate to the often overlooked, if not in fact intentionally disregarded depths of what the so called internal aspects of mathematical knowledge may involve, depths concerning among others issues such as its unreasonable…
The brain is very often viewed as a network, be it at small scale made of cells, mostly neurons, or at larger scale made of neuronal assemblies. Here we introduce a conjecture, in the spirit of a philosophical though experiment, which…
The plausibility of uncommon events and miracles based on testimony of such an event has been much discussed. When analyzing the probabilities involved, it has mostly been assumed that the common events can be taken as data in the…
One of the important questions in statistical mechanics is how irreversibility (time's arrow) occurs when Newton equations of motion are time reversal invariant. One objection to irreversibility is based on Poincar\'e's recursion theorem: a…
Spitzer's identity describes the position of a reflected random walk over time in terms of a bivariate transform. Among its many applications in probability theory are congestion levels in queues and random walkers in physics. We present a…
In memory of the famous physicist Bruno Pontecorvo, whereof is just occurred the centenary anniversary of the birth and the twentieth anniversary of the death, this paper traces the scientific and human adventure of the italian scientist,…
Several years ago the second author playing with different "recognizers of real constants", e.g., the LLL algorithm, the Plouffe inverter, etc. found empirically the following formula. Let $p_n/q_n$ denote the $n$th convergent of the…
The concept of only One-dimensional time is wrong, time is Four-dimensional. The light refraction emerges directly that time is four-dimensional to us perfectly. It translates some thing incomprehensible into easily comprehensible in…
This is, with minor modifications, a text read at the 114th Statistical Mechanics meeting, in honor of D.Ruelle and Y.Sinai, at Rutgers, Dec.13-15, 2015. It does not attempt to analyze, or not even just quote, all works of David Ruelle; I…
Covariantly we reformulate the description of a spinning particle in terms of the Poincar\'{e} group. We also construct a Lagrangian which entails all possible constraints explicitly; all constraints can be obtained just from the…
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
In this paper we presents results of research about elderly users of Stack Overflow (Question and Answer portal for programmers). They have different roles, different main activities and different habits. They are an important part of the…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…