We consider the subclass of linear programs that formulate Markov Decision Processes (mdps). We show that the Simplex algorithm with the GassSaaty shadow-vertex pivoting rule is strongly polynomial for a subclass of mdps, called controlled random walks (CRWs); the running time is O(|S| · |U |), where |S| denotes the number of states and |U | denotes the number of actions per state. This result ...

A happy number N is defined by the condition S(N ) = 1 for some number n of iterations of the function S, where S(N ) is the sum of the squares of the digits of N . Up to 10, the longest known string of consecutive happy numbers was length five. We find the smallest string of consecutive happy numbers of length 6, 7, 8, . . . , 13. For instance, the smallest string of six consecutive happy numb...

In this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proved that, under some conditions, these iterations have a chaotic behavior in the meaning of Devaney. This chaotic behavior allows us to propose a way to generate new hash functions. An illustration example is detailed in ...

We introduce a method of constructing a forcing along a simplified (κ, 1)-morass such that the forcing satisfies the κ-chain condition. Alternatively, this may be seen as a method to thin out a larger forcing to get a chain condition. As an application, we construct a ccc forcing that adds an ω2-Suslin tree. Related methods are Shelah’s historic forcing and Todorcevic’s ρ-functions.

The n-localization property is preserved under the countable support iteration of suitably definable forcings. This solves a question of Ros lanowski and greatly simplifies the proofs in the area.

This paper presents a new method for fitting an ellipse to a point sequence extracted from images. It is widely known that the best fit is obtained by maximum likelihood. However, it requires iterations, which may not converge in the presence of large noise. Our approach is algebraic distance minimization; no iterations are required. Exploiting the fact that the solution depends on the way the ...

Chaotic iterations have been introduced on the one hand by Chazan, Miranker [5] and Miellou [9] in a numerical analysis context, and on the other hand by Robert [11] and Pellegrin [10] in the discrete dynamical systems framework. In both cases, the objective was to derive conditions of convergence of such iterations to a fixed state. In this paper, a new point of view is presented, the goal her...

In the setting of hyperbolic spaces, we show that convergence Browder-type sequences and Halpern iterations respectively entail their viscosity version with a Rakotch map. We also hybrid Krasnoselskii-Mann iteration follows from Browder type sequence. Our results follow proof-theoretic techniques (proof mining). From an analysis theorems due to T. Suzuki, extract transformation rates for origin...

In this paper, several $Delta$ and strong convergence theorems are established for the Ishikawa iterations for nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and improve the corresponding results

When a loop in a sequential program is parallelized, it is normally guaranteed that all ow dependencies and anti-dependencies are respected so that the result of parallel execution is always the same as sequential execution. In some cases, however, the algorithm implemented by the loop allows the iterations to be executed in a di erent sequential order than the one speci ed in the program. This...