Double Chargino Production in e−e−e^{-}e^{-} scattering

We point out the production of the charginos and neutralinos in electron-electron process in several supersymmetric models, in order to show that the International Linear Collider can discover double charged charginos if these particles really exist in nature.Comment: 9 pages, 9 figures, Talk given at CTP symposium on Supersymmetry at LHC: Theoretical and Experimental Perspectives, The British University in Egypt, Cairo, Egypt, 11-14 March 200

On the relation between hyperrings and fuzzy rings

We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings and explicitly characterize the essential image --- it fails to be essentially surjective in a very minor way. This embedding provides an identification of Baker's theory of matroids over hyperfields with Dress's theory of matroids over fuzzy rings (provided one restricts to those fuzzy rings in the essential image). The embedding functor extends from hyperfields to hyperrings, and we study this extension in detail. We also analyze the relation between hyperfields and Baker's partial demifields

A matroid associated with a phylogenetic tree

A (pseudo-)metric D on a finite set X is said to be a `tree metric' if there is a finite tree with leaf set X and non-negative edge weights so that, for all x,y ∈X, D(x,y) is the path distance in the tree between x and y. It is well known that not every metric is a tree metric. However, when some such tree exists, one can always find one whose interior edges have strictly positive edge weights and that has no vertices of degree 2, any such tree is 13; up to canonical isomorphism 13; uniquely determined by D, and one does not even need all of the distances in order to fully (re-)construct the tree's edge weights in this case. Thus, it seems of some interest to investigate which subsets of X, 2 suffice to determine (`lasso') these edge weights. In this paper, we use the results of a previous paper to discuss the structure of a matroid that can be associated with an (unweighted) X-tree T defined by the requirement that its bases are exactly the `tight edge-weight lassos' for T, i.e, the minimal subsets of X, 2 that lasso the edge weights of T

Lassoing and corraling rooted phylogenetic trees

The construction of a dendogram on a set of individuals is a key component of a genomewide association study. However even with modern sequencing technologies the distances on the individuals required for the construction of such a structure may not always be reliable making it tempting to exclude them from an analysis. This, in turn, results in an input set for dendogram construction that consists of only partial distance information which raises the following fundamental question. For what subset of its leaf set can we reconstruct uniquely the dendogram from the distances that it induces on that subset. By formalizing a dendogram in terms of an edge-weighted, rooted phylogenetic tree on a pre-given finite set X with |X|>2 whose edge-weighting is equidistant and a set of partial distances on X in terms of a set L of 2-subsets of X, we investigate this problem in terms of when such a tree is lassoed, that is, uniquely determined by the elements in L. For this we consider four different formalizations of the idea of "uniquely determining" giving rise to four distinct types of lassos. We present characterizations for all of them in terms of the child-edge graphs of the interior vertices of such a tree. Our characterizations imply in particular that in case the tree in question is binary then all four types of lasso must coincide

Les Pavages d'Anges et de Diables

On utilise la méthode des symboles de Delaney pour classifier à l’aide de I’ordinateur, à homéomorphisme équivariant près, tous les pavages périodiques du plan dont les pavés peuvent être colories de noir et de blanc de telle manière que les pavés se partageant une arête soient de couleurs différentes, que le groupe de symétrie agisse de faGon transitive sur les pavés noirs, que tout pavé possède au moins trois arêtes et que de chaque sommet soient issues au moins trois arêtes.The method of Delaney symbols is used to classify by a computer program all periodic tilings of the Euclidean plane up to equivariant homeomorphisms for which the tiles can be coloured by black and white such that tiles sharing an edge have different colours, the symmetry group acts transitively on the black tiles, every tile has at least three edges and from every vertex at least three edges originate.Peer Reviewe

k-Spectra of weakly-c-Balanced Words

A word $u$ is a scattered factor of $w$ if $u$ can be obtained from $w$ by deleting some of its letters. That is, there exist the (potentially empty) words $u_1,u_2,..., u_n$, and $v_0,v_1,..,v_n$ such that $u = u_1u_2...u_n$ and $w = v_0u_1v_1u_2v_2...u_nv_n$. We consider the set of length-$k$ scattered factors of a given word w, called here $k$-spectrum and denoted \ScatFact_k(w). We prove a series of properties of the sets \ScatFact_k(w) for binary strictly balanced and, respectively, $c$-balanced words $w$, i.e., words over a two-letter alphabet where the number of occurrences of each letter is the same, or, respectively, one letter has $c$-more occurrences than the other. In particular, we consider the question which cardinalities n= |\ScatFact_k(w)| are obtainable, for a positive integer $k$, when $w$ is either a strictly balanced binary word of length $2k$, or a $c$-balanced binary word of length $2k-c$. We also consider the problem of reconstructing words from their $k$-spectra

Геохимия твердой фазы снежного покрова в окрестностях цементного завода (на примере г. Топки Кемеровской области)

Dress A, RUCH E, TRIESCH E. Extremals of the cone of norms and the cohomology of c3-stratifications. Advances in Applied Mathematics. 1992;13(1):1-47

Minimum triplet covers of binary phylogenetic X-trees

Trees with labelled leaves and with all other vertices of degree three play an important role in systematic biology and other areas of classification. A classical combinatorial result ensures that such trees can be uniquely reconstructed from the distances between the leaves (when the edges are given any strictly positive lengths). Moreover, a linear number of these pairwise distance values suffices to determine both the tree and its edge lengths. A natural set of pairs of leaves is provided by any `triplet cover' of the tree (based on the fact that each non-leaf vertex is the median vertex of three leaves). In this paper we describe a number of new results concerning triplet covers of minimum size. In particular, we characterize such covers in terms of an associated graph being a 2-tree. Also, we show that minimum triplet covers are `shellable' and thereby provide a set of pairs for which the inter-leaf distance values will uniquely determine the underlying tree and its associated branch lengths

Counting, generating and sampling tree alignments

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical sets of matches between identical pairs of trees. This ambiguity is uninformative, and detrimental to any probabilistic analysis.In this work, we consider tree alignments up to equivalence. Our first result is a precise asymptotic enumeration of tree alignments, obtained from a context-free grammar by mean of basic analytic combinatorics. Our second result focuses on alignments between two given ordered trees $S$ and $T$. By refining our grammar to align specific trees, we obtain a decomposition scheme for the space of alignments, and use it to design an efficient dynamic programming algorithm for sampling alignments under the Gibbs-Boltzmann probability distribution. This generalizes existing tree alignment algorithms, and opens the door for a probabilistic analysis of the space of suboptimal RNA secondary structures alignments.Comment: ALCOB - 3rd International Conference on Algorithms for Computational Biology - 2016, Jun 2016, Trujillo, Spain. 201

1/fα1/f^\alpha spectra in elementary cellular automata and fractal signals

We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays $1/f$ spectra though considered as trivial, and on the other hand that various automata classified as chaotic/complex display no $1/f$ spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce $1/f^{\alpha}$ spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics and computer sciences, there are various candidates to show spectra similar to our results.Comment: 4 pages (3 figs included