Q-ary Ulam-Renyi game with weighted constrained lies

Cicalese F, Deppe C, Mundici D. Q-ary Ulam-Renyi game with weighted constrained lies. In: COMPUTING AND COMBINATORICS, PROCEEDINGS. Vol 3106. SPRINGER-VERLAG BERLIN; 2004: 82-91.The Ulam-Renyi game is a classical model for the problem of determining the minimum number of queries to find an unknown number in a finite set when up to a finite number of the answers may be erroneous/mendacious. In the variant considered in this paper, questions with q many possible answers are allowed, with q fixed and known beforehand; further, lies are constrained by a weighted bipartite graph (the "channel"). We provide a tight asymptotic estimate for the number of questions needed to solve the problem. Our results are constructive, and the appropriate searching strategies are actually provided. As an extra bonus, all our strategies use the minimum amount of adaptiveness: they ask a first batch of nonadaptive questions, and then, only depending on the answers to these questions, they ask a second nonadaptive batch

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

Errata and Addenda to Mathematical Constants

We humbly and briefly offer corrections and supplements to Mathematical Constants (2003) and Mathematical Constants II (2019), both published by Cambridge University Press. Comments are always welcome.Comment: 162 page

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal