Comments on the non-conformal gauge theories dual to Ypq manifolds

We study the infrared behavior of the entire class of Y(p,q) quiver gauge theories. The dimer technology is exploited to discuss the duality cascades and support the general belief about a runaway behavior for the whole family. We argue that a baryonic classically flat direction is pushed to infinity by the appearance of ADS-like terms in the effective superpotential. We also study in some examples the IR regime for the L(a,b,c) class showing that the same situation might be reproduced in this more general case as well.Comment: 48 pages, 27 figures; updated reference

Non-commutative polynomials with convex level slices

Let a and x denote tuples of (jointly) freely noncommuting variables. A square matrix valued polynomial p in these variables is naturally evaluated at a tuple (A,X) of symmetric matrices with the result p(A,X) a square matrix. The polynomial p is symmetric if it takes symmetric values. Under natural irreducibility assumptions and other mild hypothesis, the article gives an algebraic certificate for symmetric polynomials p with the property that for sufficiently many tuples A, the set of those tuples X such that p(A,X) is positive definite is convex. In particular, p has degree at most two in x. The case of noncommutative quasi-convex polynomials is of particular interest. The problem analysed here occurs in linear system engineering problems. There the A tuple corresponds to the parameters describing a system one wishes to control while the X tuple corresponds to the parameters one seeks in designing the controller. In this setting convexity is typically desired for numerical reasons and to guarantee that local optima are in fact global. Further motivation comes from the theories of matrix convexity and operator systems

Towards a New Extracting and Querying Approach of Fuzzy Summaries

Diversification of DB applications highlighted the limitations of relational database management system (RDBMS) particularly on the modeling plan. In fact, in the real world, we are increasingly faced with the situation where applications need to handle imprecise data and to offer a flexible querying to their users. Several theoretical solutions have been proposed. However, the impact of this work in practice remained negligible with the exception of a few research prototypes based on the formal model GEFRED. In this chapter, the authors propose a new approach for exploitation of fuzzy relational databases (FRDB) described by the model GEFRED. This approach consists of 1) a new technique for extracting summary fuzzy data, Fuzzy SAINTETIQ, based on the classification of fuzzy data and formal concepts analysis; 2) an approach of assessing flexible queries in the context of FDB based on the set of fuzzy summaries generated by our fuzzy SAINTETIQ system; 3) an approach of repairing and substituting unanswered query.Comment: 22 pages, 6 figures, 8 tables. Multidisciplinary Approaches to Service-Oriented Engineering, 2018. arXiv admin note: text overlap with arXiv:1401.049

Counting Markov Types

International audienceThe method of types is one of the most popular techniques in information theory and combinatorics. Two sequences of equal length have the same type if they have identical empirical distributions. In this paper, we focus on Markov types, that is, sequences generated by a Markov source (of order one). We note that sequences having the same Markov type share the same so called $\textit{balanced frequency matrix}$ that counts the number of distinct pairs of symbols. We enumerate the number of Markov types for sequences of length $n$ over an alphabet of size $m$. This turns out to coincide with the number of the balanced frequency matrices as well as with the number of special $\textit{linear diophantine equations}$, and also balanced directed multigraphs. For fixed $m$ we prove that the number of Markov types is asymptotically equal to $d(m) \frac{n^{m^{2-m}}}{(m^2-m)!}$, where $d(m)$ is a constant for which we give an integral representation. For $m \to \infty$ we conclude that asymptotically the number of types is equivalent to $\frac{\sqrt{2}m^{3m/2} e^{m^2}}{m^{2m^2} 2^m \pi^{m/2}} n^{m^2-m}$ provided that $m=o(n^{1/4})$ (however, our techniques work for $m=o(\sqrt{n})$). These findings are derived by analytical techniques ranging from multidimensional generating functions to the saddle point method

Noncentral Student distributed LS and IV Estimators

The distribution of the least squares and the instrumental variable estimators of the coefficients in a linear relation is noncentral student when the data are normally distributed around possibly non-constant means. This is the claim of the paper and we show for what definition of a noncentral student density this claim to compact summary of the vast literature is justified. Unfortunately, the definition of the noncentral student density is as complicated as its parent, the noncentral Wishart density. Both are defined in terms of infinite series of zonal polynomials of all orders. We have developed however a recursive online method that generates these polynomials sequentially ad infinitum for bivariate and trivariate densities. The time is here that the practicality of the theory can be widened considerably.

Boletín oficial de la provincia de León: Boletín oficial de la provincia de León: Número 147 - 1951 julio 3 (03/07/1951)

Copia digital. Valladolid : Junta de Castilla y León. Consejería de Cultura y Turismo, 2011-201