On permanents of Sylvester Hadamard matrices

It is well-known that the evaluation of the permanent of an arbitrary $(-1,1)$-matrix is a formidable problem. Ryser's formula is one of the fastest known general algorithms for computing permanents. In this paper, Ryser's formula has been rewritten for the special case of Sylvester Hadamard matrices by using their cocyclic construction. The rewritten formula presents an important reduction in the number of sets of $r$ distinct rows of the matrix to be considered. However, the algorithm needs a preprocessing part which remains time-consuming in general

On an inequivalence criterion for cocyclic Hadamard matrices

Given two Hadamard matrices of the same order, it can be quite difficult to decide whether or not they are equivalent. There are some criteria to determine Hadamard inequivalence. Among them, one of the most commonly used is the 4-profile criterion. In this paper, a reformulation of this criterion in the cocyclic framework is given. The improvements obtained in the computation of the 4-profile of a cocyclic Hadamard matrix are indicated.Ministerio de Ciencia e Innovación MTM2008-06578Junta de Andalucía FQM–296Junta de Andalucía P07-FQM-0298

Self-Dual codes from (−1,1)(-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

Generalized binary arrays from quasi-orthogonal cocycles

Generalized perfect binary arrays (GPBAs) were used by Jedwab to construct perfect binary arrays. A non-trivial GPBA can exist only if its energy is 2 or a multiple of 4. This paper introduces generalized optimal binary arrays (GOBAs) with even energy not divisible by 4, as analogs of GPBAs. We give a procedure to construct GOBAs based on a characterization of the arrays in terms of 2-cocycles. As a further application, we determine negaperiodic Golay pairs arising from generalized optimal binary sequences of small length.Junta de Andalucía FQM-01

On quasi-orthogonal cocycles

We introduce the notion of quasi-orthogonal cocycle. This is motivated in part by the maximal determinant problem for square {±1}-matrices of size congruent to 2 modulo 4. Quasi-orthogonal cocycles are analogous to the orthogonal cocycles of algebraic design theory. Equivalences with new and known combinatorial objects afforded by this analogy, such as quasi-Hadamard groups, relative quasi-difference sets, and certain partially balanced incomplete block designs, are proved.Junta de Andalucía FQM-01

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

Boolean Functions and Permanents of Sylvester Hadamard Matrices

One of the fastest known general techniques for computing permanents is Ryser’s formula. On this note, we show that this formula over Sylvester Hadamard matrices of order 2m, Hm, can be carried out by enumerating m-variable Boolean functions with an arbitrary Walsh spectrum. As a consequence, the quotient per(Hm)/22m might be a measure of the “density” of m-variable Boolean functions with high nonlinearity

Severe Atopic Dermatitis In Spain: A Real-Life Observational Study

Objective: To determine the epidemiology and characterize the treatment prescribed for severe atopic dermatitis (AD) in children/adults in usual clinical practice. Methods: Observational, retrospective study made through review of medical records of Spanish patients aged >= 6 years. Patients diagnosed with severe AD who required care between 2013 and 2017 were included. The study groups were: 6-12 years; 13-18 years; and > 18 years. Patients were followed for 5 years. The main measurements were the prevalence of AD, comorbidity and treatment duration. Statistical significance was established as p <0.05. Results: We included 2323 patients with severe AD. The overall prevalence was 0.10% (95% CI: 0.09-0.11%) and was 0.39%, 0.23% and 0.07% in the 6-12 years, 13-18 years and >18 years age groups, respectively (p <0.001), the percentage of males was 58%, 48.6% and 39%, respectively, and general comorbidity was 0.1, 0.2 and 0.9 points, respectively (p <0.001).The most frequent comorbidities were asthma in 49.0%, 44.9% and 20.8%, respectively (p <0.001), and anxiety in 79.7%, 65.8% and 67.3%, respectively (p <0.001). Oral corticosteroids were administered in 97.3%, 90.9% and 81.7%, respectively (concomitant-medication). Cyclosporine (45.3%), azathioprine (15.9%) and methotrexate (9.0%) were the most frequently prescribed drugs; biologic agents were administered in 5.8% of patients (for AD). Conclusion: In AD the presence of comorbidities was significant, especially in the psychological, immunoallergic and cardiovascular areas. Cyclosporine was the most widely used immunosuppressant. There was a degree of variability in the use and duration of the treatments prescribed

Quasi-Hadamard Full Propelinear Codes

In this paper, we give a characterization of quasi-Hadamard groups in terms of propelinear codes. We define a new class of codes that we call quasi-Hadamard full propelinear codes. Some structural properties of these codes are studied and examples are provided.Junta de Andalucía FQM-016Ministerio de Economía y Competitividad TIN2016-77918-

Análisis de la rentabilidad en el sector de la distribución en Europa

This empine study aims at stablishing which are the main factors that explain profitability in companies operating in the european distribution sector and their reiative importance. Methodology is based on an analysis of variance and its components. Although this type of analysis has been frequently applied on the industrial sector, its use in the distribution business is very innovative, above all when we consider the country as one of the key factors.Au travers de ce travail empirique on veut analyser quels sont les facteurs qui expliquent la rentabilité des entreprises dans le secteur de la distribution en Europe. On veut également connaftre l'importance reiative de chacun de ees facteurs. La méthodologie employée a été l'Analyse de la Variance et lAnalyse des Composants de la Variance. Mime si ce type d'analyse a été appliquée avec une fréquence reiative dans quelques secteurs industriéis, dans celui de la distribution c'est nouveau, surtout si on prend en compte le pays comme facteur explicati