We study the logarithmic and ratio asymptotic of linear forms constructed from a Nikishin system which satisfy orthogonality conditions with respect to a system of measures generated from another Nikishin system. This construction combines type I and type II multiple orthogonal polynomials. The logarithmic asymptotic of the linear forms is expressed in terms of the extremal solution of an assoc...

Let G be a connected non-regular graph with n vertices, maximum degree ∆ and minimum degree δ, and let λ1 be the greatest eigenvalue of the adjacency matrix of G. In this paper, by studying the Perron vector of G, it is shown that type-I-a graphs and type-I-b (resp. type-II-a) graphs with some specified properties are not λ1-extremal graphs. Moreover, for each connected non-regular graph some l...

Five-dimensional stringy rotating black holes are embedded into N=2 supergravity interacting with one vector multiplet. The existence of an unbroken supersymmetry of the rotating solution is proved directly by solving the Killing spinor equations. The asymptotic enhancement of supersymmetry near the horizon in the presence of rotation is established via the calculation of the super-curvature. T...

We study the recently discovered phenomenon [1] of existence of comparative probability orderings on finite sets that violate Fishburn hypothesis [2, 3] — we call such orderings and the discrete cones associated with them extremal. Conder and Slinko constructed an extremal discrete cone on the set of n = 7 elements and showed that no extremal cones exist on the set of n ≤ 6 elements. In this pa...

REACT estimators use ideas from signal processing, model-selection, and shrinkage to achieve much smaller risk in one-way layouts and other linear models than does the classical least squares estimator. The REACT method can generate automatic scatterplot smoothers that compete well on standard data sets with the best fits obtained by other methods. This paper addresses two further questions: Wh...

This paper introduces a novel combinatorial algorithm to compute a hierarchy of discrete gradient vector fields for three-dimensional scalar fields. The hierarchy is defined by an importance measure and represents the combinatorial gradient flow at different levels of detail. The presented algorithm is based on Forman’s discrete Morse theory, which guarantees topological consistency and algorit...

Let G be a connected non-regular graph with n vertices, maximum degree ∆ and minimum degree δ, and let λ1 be the greatest eigenvalue of the adjacency matrix of G. In this paper, by studying the Perron vector of G, it is shown that type-I-a graphs and type-I-b (resp. type-II-a) graphs with some specified properties are not λ1-extremal graphs. Moreover, for each connected non-regular graph some l...

We consider general black holes in D = 5, N = 2 supergravity coupled to vector multiplets, and discuss the issue of microstate counting from various viewpoints. The statistical entropy is computed for the near-extremal case using the central charge of the AdS2 factor appearing in the near-horizon geometry. Furthermore, we explicitly construct the duality transformation connecting electrically c...

We use the boundary state formalism to study the interaction of two moving identical D-branes in the Type II superstring theory compactified on orbifolds. By computing the velocity dependence of the amplitude in the limit of large separation we can identify the nature of the different forces between the branes. In particular, in the Z3 orbifold case we find a boundary state which is coupled onl...

The issue of microstate counting for general black holes in D = 5, N = 2 supergravity coupled to vector multiplets is discussed from various viewpoints. The statistical entropy is computed for the near-extremal case by using the central charge appearing in the asymptotic symmetry algebra of AdS2. Furthermore, we show that the considered supergravity theory enjoys a duality invariance which conn...