相关论文: Proof of the impossibility of probabilistic induct…

In earlier work the authors obtained integral formulas for probabilities for a single particle in the asymmetric simple exclusion process. Here formulas are obtained for joint probabilities for several particles. In the case of a single…

Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…

This note is an extended read of my read of Laplace's book Theorie Analytique des Probabilites, when considered from a Bayesian viewpoint but without historical nor comparative pretentions. A deeper analysis is provided in Dale (1999).

In the article [PR1] {\it On Hrushovski's proof of the Manin-Mumford conjecture} (Proceedings of the ICM 2002), R. Pink and the author gave a short proof of the Manin-Mumford conjecture, which was inspired by an earlier model-theoretic…

We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.

Based on the general thought that mechanics cannot be absolutely exact, supported by pulsed nuclear magnetic resonance (NMR) experiments on the reversal of time in spin systems, we postulate existence of a probability which do not follow…

We present a computable algorithm that assigns probabilities to every logical statement in a given formal language, and refines those probabilities over time. For instance, if the language is Peano arithmetic, it assigns probabilities to…

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

We give a short Wiener measure proof of the Riemann hypothesis based on a surprising, unexpected and deep relation between the Riemann zeta $\zeta(s)$ and the trivial zeta $\zeta_{t}(s):=Im(s)(2Re(s)-1)$.

Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

The no-supervenience theorem limits the capacity of physicalist theories to provide a comprehensive account of human consciousness. The proof of the theorem is difficult to formalize because it relies on both alethic and epistemic notions…

In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.

The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

We present a short and self-contained proof of the choosability version of Brooks' theorem.

In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].

A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In…

A simple heuristic proof of an integral identity recently derived (Glasser ML 2011 J. Phys. A: Math. Theor. 44 225202) is presented.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.