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A learning algorithm combining functional discriminant coordinates and functional principal components

Tomasz Górecki, Mirosław Krzyśko (2014)

Discussiones Mathematicae Probability and Statistics

A new type of discriminant space for functional data is presented, combining the advantages of a functional discriminant coordinate space and a functional principal component space. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 35 functional data sets (time series). Experiments show that constructed combined space provides a higher quality of classification of LDA method compared with component spaces.

A learning paradigm for motion control of mobile manipulators

Foudil Abdessemed, Eric Monacelli, Khier Benmahammed (2006)

International Journal of Applied Mathematics and Computer Science

Motion control of a mobile manipulator is discussed. The objective is to allow the end-effector to track a given trajectory in a fixed world frame. The motion of the platform and that of the manipulator are coordinated by a neural network which is a kind of graph designed from the kinematic model of the system. A learning paradigm is used to produce the required reference variables for each of the mobile platform and the robot manipulator for an overall coordinate behavior. Simulation results are...

A length bound for binary equality words

Jana Hadravová (2011)

Commentationes Mathematicae Universitatis Carolinae

Let w be an equality word of two binary non-periodic morphisms g , h : { a , b } * → Δ * with unique overflows. It is known that if w contains at least 25 occurrences of each of the letters a and b , then it has to have one of the following special forms: up to the exchange of the letters a and b either w = ( a b ) i a , or w = a i b j with gcd ( i , j ) = 1 . We will generalize the result, justify this bound and prove that it can be lowered to nine occurrences of each of the letters a and b .

A Linear Time Algorithm for Computing Longest Paths in Cactus Graphs

Markov, Minko, Ionut Andreica, Mugurel, Manev, Krassimir, Tapus, Nicolae (2012)

Serdica Journal of Computing

ACM Computing Classification System (1998): G.2.2.We propose an algorithm that computes the length of a longest path in a cactus graph. Our algorithm can easily be modified to output a longest path as well or to solve the problem on cacti with edge or vertex weights. The algorithm works on rooted cacti and assigns to each vertex a two-number label, the first number being the desired parameter of the subcactus rooted at that vertex. The algorithm applies the divide-and-conquer approach and computes...

A little more about morphic Sturmian words

Isabelle Fagnot (2006)

RAIRO - Theoretical Informatics and Applications

Among Sturmian words, some of them are morphic, i.e. fixed point of a non-identical morphism on words. Berstel and Séébold (1993) have shown that if a characteristic Sturmian word is morphic, then it can be extended by the left with one or two letters in such a way that it remains morphic and Sturmian. Yasutomi (1997) has proved that these were the sole possible additions and that, if we cut the first letters of such a word, it didn't remain morphic. In this paper, we give an elementary and combinatorial...

A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs

Viviane Baladi, Aïcha Hachemi (2008)

Annales de l'I.H.P. Probabilités et statistiques

For large N, we consider the ordinary continued fraction of x=p/q with 1≤p≤q≤N, or, equivalently, Euclid’s gcd algorithm for two integers 1≤p≤q≤N, putting the uniform distribution on the set of p and qs. We study the distribution of the total cost of execution of the algorithm for an additive cost function c on the set ℤ+* of possible digits, asymptotically for N→∞. If c is nonlattice and satisfies mild growth conditions, the local limit theorem was proved previously by the second named author....

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