A monte carlo method for factorization

We describe briefly a novel factorization method involving probabilistic ideas.     

A new version of algorithmic information theory

We present a much more concrete version of algorithmic information theory in which one can actually run on a computer the algorithms in the proofs of a number of key information-theoretic incompleteness theorems.     

Bayesian nonparametrie inference and monte carlo optimization

As global or combinatorial optimization problems are not effectively tractable by means of deterministic techniques, Monte Carlo methods are used in practice for obtaining ”good“ approximations to the optimum. In order to test the accuracy achieved after a sample of finite size, the Bayesian nonparametric approach is proposed as a suitable context, and the theoretical as well as computational implications of prior distributions in the class of neutral to the right distributions are examined. The feasibility of the approach relatively to particular Monte Carlo procedures is finally illustrated both for the global optimization problem and the {0 - 1} programming problem.     

A monte carlo model for simulation of tank battles

A Monte Carlo model for simulation of company-level tank battles is described. The simulation is started with an observation phase. The probability of discovery is dependent upon properties of the terrain etc. Target selection is simulated deterministically with priority rules. Every unit belongs to one of the following states of fight: undamaged, able to shoot only, able to move only, shocked and out of action.It is possible to simulate surprise attacks and battles after a sudden contact if the units are assumed to fight from the same position during the whole battle. In a later version of the model, the units are permitted to show as much of themselves as they wish during the battle. Thus it is possible to simulate (small) changes of position, initiated by the current events.     

Implementation of sensitivity calculations on a monte carlo experiment

A new approach to the optimization of discrete-event dynamic systems has recently been developed (Refs. 1–4). The implementation of this approach requires answering the following question: given an observed value of the outcome of a random variable, what would have been the outcome if the parameters of the random variable had been different? The answer to this question would traditionally involve the value of an outcome in an underlying sample space. However, this underlying value cannot normally be observed. In this note, we give a framework for answering this question, in terms of the observed value alone. This point had not been considered rigorously in the new approach of Refs. 1–4, and our note derives a basic equation required for that approach.     

Elliptic curve primality tests for Fermat and related primes

We use elliptic curves with complex multiplication to develop primality tests for Fermat primes and for primes of the form ?²³−²?−1³+1 and ?²²−²?−1²+1.     

A note on extrapolation theory

We show some explicit computations on extrapolation of L^p spaces.     

A note on estimation and information topologies

A relation between uniformly consistent density estimates and information topologies is described. Specifically, the Hellinger metric topology is the strongest metric topology in which uniformly consistent estimation is possible     

A note on the elimination theory

We consider certain generalisation of the resultant of two polynomials in one variable. Using the Schur symmetricfunctions we describe the ideal of all polynomials in the coefficients of two equations, which vanish if these equations haver+1 roots in common, where r≥0. We discuss also related (classical)criterions giving the conditions when two equations have r+1 roots in common, where r≥0.     

A note on the modified two-way MANOVA tests

For heteroscedastic two-way MANOVA, the so-called modified MANOVA tests proposed recently are too conservative, not powerful and not affine-invariant. In this note, we show how they can be improved and can be made affine-invariant. A real data example and some simulation studies are used to illustrate and demonstrate the methodologies.     

A new method for probabilistic assessments in power systems,combining monte carlo and stochastic‐algebraic methods

This article discusses a new methodology, which combines two efficient methods known as Monte Carlo (MC) and Stochastic‐algebraic (SA) methods for stochastic analyses and probabilistic assessments in electric power systems. The main idea is to use the advantages of each former method to cover the blind spots of the other. This new method is more efficient and more accurate than SA method and also faster than MC method while is less dependent of the sampling process. In this article, the proposed method and two other ones are used to obtain the probability density function of different variables in a power system. Different examples are studied to show the effectiveness of the hybrid method. The results of the proposed method are compared to the ones obtained using the MC and SA methods. © 2014 Wiley Periodicals, Inc. Complexity 21: 100–110, 2015