Reflexive Monte-Carlo search uses the Monte-Carlo search of a given level to improve the search of the upper level. We describe the application to Morpion Solitaire. For the non touching version, reflexive Monte-Carlo search breaks the current record and establishes a new record of 78 moves.

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a suffici...

In the history of cybernetics there have been several attempts by cyberneticians to put themselves into the circularities of their theories and designs, invoking a shift from the cybernetics of mechanisms to a cybernetics of cybernetics. The latter is the title of a book chapter by Margaret Mead (1968) and of Heinz von Foerster’s (1974) edited compilation of articles on cybernetics. Foerster in...

In the synchronous discrete model, the average memory capacity of bidirectional associative memories (BAMs) is compared with that of Hopfield memories, by means of a calculat10n of the percentage of good recall for 100 random BAMs of dimension 64x64, for different numbers of stored vectors. The memory capac1ty Is found to be much smal1er than the Kosko upper bound, which Is the lesser of the tw...

In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of t...

The main results of the paper: (1) The dual Banach space X∗ contains a linear subspace A ⊂ X∗ such that the set A of all limits of weak∗ convergent bounded nets in A is a proper norm-dense subset of X∗ if and only if X is a non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual. (2) Let X be a non-reflexive Banach space. Then there exists a convex subse...

Maximal monotone operators on a Banach space into its dual can be represented by convex functions bounded below by the duality product. It is natural to ask under which conditions a convex function represents a maximal monotone operator. A satisfactory answer, in the context of reflexive Banach spaces, has been obtained some years ago. Recently, a partial result on non-reflexive Banach spaces w...

A two-beam coupling interaction of an information-bearing beam with a copy of itself in a photorefractive medium changes the spatiotemporal nature of the beam. We analyze the reflexive coupling of an informationbearing beam carrying two or more spatiotemporal signals, using a one-dimensional model. We find that the statistical information content of the beam can be increased or decreased by use...