Single-Elimination Brackets Fail to Approximate Copeland Winner

Single-elimination (SE) brackets appear commonly in both sports tournaments and the voting theory literature. In certain tournament models, they have been shown to select the unambiguously-strongest competitor with optimum probability. By contrast, we reevaluate SE brackets through the lens of approximation, where the goal is to select a winner who would beat the most other competitors in a round robin (i.e., maximize the Copeland score), and find them lacking. Our primary result establishes the approximation ratio of a randomly-seeded SE bracket is 2^{- Theta(sqrt{log n})}; this is underwhelming considering a 1/2 ratio is achieved by choosing a winner uniformly at random. We also establish that a generalized version of the SE bracket performs nearly as poorly, with an approximation ratio of 2^{- Omega(sqrt[4]{log n})}, addressing a decade-old open question in the voting tree literature

Dynamical zeta functions and Kummer congruences

We establish a connection between the coefficients of Artin-Mazur zeta-functions and Kummer congruences. This allows to settle positively the question of the existence of a map T such that the number of fixed points of the n-th iterate of T is equal to the absolute value of the 2n-th Euler number. Also we solve a problem of Gabcke related to the coefficients of Riemann-Siegel formula.Comment: 12 pages, AMS-LaTe

Bivalvia, Veneroidea, Corbiculidae, Corbicula largillierti (Philippi, 1844): New distribution record in the Del Valle Central basin, Catamarca Province, Argentina

Corbicula largillierti (Philippi 1844), an invasive freshwater bivalve, accidentally reached Argentina from Asia presumably in the 1960s. Since then, records of its presence from the Rio de la Plata River to the northeast and northwest Argentinian freshwater systems have been documented. A new record in Del Valle River, part of the Del Valle Central basin in Catamarca Province of northwest Argentina, makes evident that the species is still spreading through Argentina.Fil: Torre, Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Diversidad y Ecología Animal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Diversidad y Ecología Animal; ArgentinaFil: Reyna, Paola Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Diversidad y Ecología Animal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Diversidad y Ecología Animal; Argentin