Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

CP-rays in simplicial cones

An interior point of a triangle is called CP-point if its orthogonal projection on the line containing each side lies in the relative interior of that side. In classical mathematics, interest in the concept of regularity of a triangle is mainly centered on the property of every interior point of the triangle being a CP-point. We generalize the concept of regularity using this property, and extend this work to simplicial cones in ℝ n , and derive necessary and sufficient conditions for this property to hold in them. These conditions highlight the geometric properties of Z-matrices. We show that these concepts have important ramifications in algorithmic studies of the linear complementarity problem. We relate our results to other well known properties of square matrices.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47921/1/10107_2005_Article_BF01582265.pd

Pivoting in Linear Complementarity: Two Polynomial-Time Cases

We study the behavior of simple principal pivoting methods for the P-matrix linear complementarity problem (P-LCP). We solve an open problem of Morris by showing that Murty’s least-index pivot rule (under any fixed index order) leads to a quadratic number of iterations on Morris’s highly cyclic P-LCP examples. We then show that on K-matrix LCP instances, all pivot rules require only a linear number of iterations. As the main tool, we employ unique-sink orientations of cubes, a useful combinatorial abstraction of the P-LCP

Splenectomy for splenomegaly and secondary hypersplenism

Splenomegaly and secondary hypersplenism may be associated with acute and chronic infections, autoimmune states, portal hypertension or splenic vein thrombosis, and a number of infiltrative and neoplastic conditions involving the spleen. Our experience and that of others with these various conditions demonstrates that the decision to perform splenectomy should be based on well-defined and often strictly limited indications. Except for idiopathic splenomegaly, the presence and severity of secondary hypersplenism or severely symptomatic splenomegaly should be well documented. In each case, the potential for palliation and known mean duration of expected response must be weighed against the increased morbidity and mortality of splenectomy (as compared to operation for “primary” hypersplenism) . La splénomégalie avec hypersplénisme secondaire relève de multiples causes: infection aigue ou chronique, états autoimmunologiques, hypertension portale, thrombose de la veine splénique, lésions tumorales spléniques. L'expérience de l'auteur qui rejoint celle de nombreux collègues lui permet d'affirmer que les indications de la splénectomie doivent être bien définies et sont strictement limitées. A l'exception de la splénomégalie idiopathique, l'existence et l'intensité de l'hypersplénisme, l'importance des symptomes provoqués par la splénomégalie doivent être aprréciées avec précision. Dans chaque cas le potentiel de la rémission de l'affection et la durée de la rémission doivent être pris en considération en fonction de l'éventuelle morbidité et de l'éventuelle mortalité de la splénectomie (par comparaison avec la splénectomie pour hypersplénisme primaire). Eplenomegalia e hiperesplenismo secundario pueden estar asociados con infecciones agudas y crónicas, estados autoinmunes (síndrome de Felty, lupus eritematoso sistémico), “esplenomegalia congestiva” por hipertensión portal o trombosis de la vena esplénica y con una variedad de entidades de tipo infiltrativo y neoplásico que afectan al bazo (sarcoidosis, enfermedad de Gaucher, varios desórdenes mieloproliferativos y linfomas). Nuestra experiencia, y aquella de otros autores, con tales condiciones demuestra que la decisión de realizar esplenectomía debe estar fundamentada en indicaciones bien definidas y estrictamente limitadas. Excepto en casos de esplenomegalia idiopática, la presencia y severidad del hiperesplenismo secundario o de esplenomegalia severamente sintomática debe ser bien documentada. En cada caso debe determinarse el potencial de paliación y la duración de la respuesta que se espera obtener frente a la incrementada morbilidad y mortalidad de la esplenectomía (en comparación con la operación que se realiza por hiperesplenismo “primario”).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41318/1/268_2005_Article_BF01655279.pd

Search for bottom-squark pair production with the ATLAS detector in final states containing Higgs bosons, b -jets and missing transverse momentum

Abstract: The result of a search for the pair production of the lightest supersymmetric partner of the bottom quark b˜1 using 139 fb−1 of proton-proton data collected at s = 13 TeV by the ATLAS detector is reported. In the supersymmetric scenarios considered both of the bottom-squarks decay into a b-quark and the second-lightest neutralino, b˜1→b+χ˜20. Each χ˜20 is assumed to subsequently decay with 100% branching ratio into a Higgs boson (h) like the one in the Standard Model and the lightest neutralino: χ˜20→h+χ˜10. The χ˜10 is assumed to be the lightest supersymmetric particle (LSP) and is stable. Two signal mass configurations are targeted: the first has a constant LSP mass of 60 GeV; and the second has a constant mass difference between the χ˜20 and χ˜10 of 130 GeV. The final states considered contain no charged leptons, three or more b-jets, and large missing transverse momentum. No significant excess of events over the Standard Model background expectation is observed in any of the signal regions considered. Limits at the 95% confidence level are placed in the supersymmetric models considered, and bottom-squarks with mass up to 1.5 TeV are excluded