Self-Dual codes from (−1,1)-matrices of skew symmetric type

Previously, self-dual codes have been constructed from weighing matrices, and in particular from conference matrices (skew and symmetric). In this paper, codes constructed from matrices of skew symmetric type whose determinants reach the Ehlich- Wojtas’ bound are presented. A necessary and sufficient condition for these codes to be self-dual is given, and examples are provided for lengths up to 52.Ministerio de Ciencia e Innovación MTM2008-06578Junta de Andalucía FQM-016Junta de Andalucía P07-FQM-0298

Modificacions neuroendocrinològiques amb l'estrès

Sota el terme estrès s'engloben una àmplia gamma de canvis orgànics que tenen lloc en resposta a tot un ventall d'estímuls i situacions que no podrien ser afrontats satisfactòriament mitjancant els mecanismes homeostàtics normals. Tant el component físic i psicòlogic dels estímuls estressants, la seva intensitat , com la forma en que els organismes hi són exposats, determinen el tipus de resposta que es posarà en marxa. Els estímuls estressants són processats a nivell del sistema nerviós central. Però els centres, les vies i els neurotransmissors implicats són encara lluny d'estar ben caracteritzats, si bé les vies noradrenèrgiques procedents del tronc encefàlic podrien tenir un paper rellevant. Per la seva banda, l'hipotàlem i la corticoliberina tenen un paper clau en la integració de tot aquest proces, i aixi, l'activació subsegüent de 1'eix neuroendocrí hipotalamico - pituitario - adrenal (HPA) constitueix un dels puntals de la resposta d'estrès. En situacions cròniques d'estrès, malgrat que la capacitat potencial de resposta de 1'eix HPA està notablement incrementada, la resposta de 1'adrenocorticotropina (ACTH) al mateix estímul (homotípic) està freqüentment atenuada (habituació), mentre que davant d' un estímul estressant nou (heterotípic) es troba, almenys en alguns casos, exacerbada (facilitació). Les perspectives de recerca es dirigeixen cap a l'estudi de la relació entre estrès i sistema immunitari, cada dia més clara.The term of stress comprises a myriad of organic changes occurring in response to a wide range of stimuli and situations which could not be satisfactorily faced by means of normal homeostatic mechanisms. Both the physical and psychological components of stressors, their intensity and the way the organisms are exposed to them, determine the type of response that will be triggered. Stressors are processed within the central nervous system, but the centers, pathways and neurotransmitters involved are far from being well understood. Nevertheless, brainstern noradrenergic system might be of relevance. Similarly, the hypothalamus and the corticotropin -releasing factor play a pivotal role in integrating this process, and thus, the subsequent activation of the neuroendocrine hypothalamicpituitary-adrenal (HPA) axis, one of the crucial components of the stress response. During chronic stress situations, despite the fact that the potential response of the HPA axis is increased, the adrenocorticotropin (ACTH) response to the same (homotypic) stimulus has usually been found to be attenuated (habituation) and that to novel (heterotypic) stressors to be exacerbated, at least in some cases (facilitation). The growing body of evidence about the close relationship between stress and the immune system opens a universe of research perspectives in this field

Error correcting codes from quasi-Hadamard matrices

Levenshtein described in [5] a method for constructing error correcting codes which meet the Plotkin bounds, provided suitable Ha- damard matrices exist. Uncertainty about the existence of Hadamard matrices on all orders multiple of 4 is a source of difficulties for the prac- tical application of this method. Here we extend the method to the case of quasi-Hadamard matrices. Since efficient algorithms for constructing quasi-Hadamard matrices are potentially available from the literature (e.g. [7]), good error correcting codes may be constructed in practise. We illustrate the method with some examples.Junta de Andalucía FQM–29

Determinants of (–1,1)-matrices of the skew-symmetric type: a cocyclic approach

An n by n skew-symmetric type (−1, 1)-matrix K = [ki,j ] has 1’s on the main diagonal and ±1’s elsewhere with ki,j = −kj,i. The largest possible determinant of such a matrix K is an interesting problem. The literature is extensive for n 0 mod 4 (skew- Hadamard matrices), but for n 2 mod 4 there are few results known for this question. In this paper we approach this problem constructing cocyclic matrices over the dihedral group of 2t elements, for t odd, which are equivalent to (−1, 1)-matrices of skew type. Some explicit calculations have been done up to t = 11. To our knowledge, the upper bounds on the maximal determinant in orders 18 and 22 have been improved.Junta de Andalucía FQM-01

Embedding cocylic D-optimal designs in cocylic Hadamard matrices

A method for embedding cocyclic submatrices with “large” determinants of orders 2t in certain cocyclic Hadamard matrices of orders 4t is described (t an odd integer). If these determinants attain the largest possible value, we are embedding D-optimal designs. Applications to the pivot values that appear when Gaussian elimination with complete pivoting is performed on these cocyclic Hadamard matrices are studied.Ministerio de Ciencia e Innovación MTM2008-06578Junta de Andalucía FQM-016Junta de Andalucía P07-FQM-0298

On the Krein–Milman Property and the Bade Property

AbstractThroughout this paper a study on the Krein–Milmam Property and the Bade Property is entailed reaching the following conclusions: If a real topological vector space satisfies the Krein–Milmam Property, then it is Hausdorff; if a real topological vector space satisfies the Krein–Milmam Property and is locally convex and metrizable, then all of its closed infinite dimensional vector subspaces have uncountable dimension; if a real pseudo-normed space has the Bade Property, then it is Hausdorff as well but could allow closed infinite dimensional vector subspaces with countable dimension. On other hand, we show the existence of infinite dimensional closed subspaces of ℓ∞ with the Bade Property that are not the space of convergence associated to any series in a real topological vector space. Finally, we characterize unconditionally convergent series in real Banach spaces by means of a new concept called uniform convergence of series

Rooted Trees Searching for Cocyclic Hadamard Matrices over D4t

A new reduction on the size of the search space for cocyclic Hadamard matrices over dihedral groups D4t is described, in terms of the so called central distribution. This new search space adopt the form of a forest consisting of two rooted trees (the vertices representing subsets of coboundaries) which contains all cocyclic Hadamard matrices satisfying the constraining condition. Experimental calculations indicate that the ratio between the number of constrained cocyclic Hadamard matrices and the size of the constrained search space is greater than the usual ratio.Ministerio de Ciencia e Innovación MTM2008-06578Junta de Andalucía FQM–296Junta de Andalucía P07-FQM-0298

Searching for partial Hadamard matrices

Three algorithms looking for pretty large partial Hadamard ma- trices are described. Here “large” means that hopefully about a third of a Hadamard matrix (which is the best asymptotic result known so far, [8]) is achieved. The first one performs some kind of local exhaustive search, and consequently is expensive from the time consuming point of view. The second one comes from the adaptation of the best genetic algorithm known so far searching for cliques in a graph, due to Singh and Gupta [21]. The last one consists in another heuristic search, which prioritizes the required processing time better than the final size of the partial Hadamard matrix to be obtained. In all cases, the key idea is characterizing the adjacency properties of vertices in a particular subgraph Gt of Ito’s Hadamard Graph (4t) [18], since cliques of order m in Gt can be seen as (m + 3) × 4t partial Hadamard matrices.Ministerio de Ciencia e Innovación MTM2008-06578Junta de Andalucía FQM-016Junta de Andalucía P07-FQM-0298

ACS Searching for D4t-Hadamard Matrices

An Ant Colony System (ACS) looking for cocyclic Hadamard matrices over dihedral groups D4t is described. The underlying weighted graph consists of the rooted trees described in [1], whose vertices are certain subsets of coboundaries. A branch of these trees defines a D4t- Hadamard matrix if and only if two conditions hold: (i) Ii = i − 1 and, (ii) ci = t, for every 2 ≤ i ≤ t, where Ii and ci denote the number of ipaths and i-intersections (see [3] for details) related to the coboundaries defining the branch. The pheromone and heuristic values of our ACS are defined in such a way that condition (i) is always satisfied, and condition (ii) is closely to be satisfied.Ministerio de Ciencia e Innovación MTM2008-06578Junta de Andalucía FQM–296Junta de Andalucía P07-FQM-0298

GA Based Robust Blind Digital Watermarking

A genetic algorithm based robust blind digital watermarking scheme is presented. The experimental results show that our scheme keeps invisibility, security and robustness more likely than other proposals in the literature, thanks to the GA pretreatment.Junta de Andalucía FQM-01