On uncertainty versus size in branching programs

AbstractWe propose an information-theoretic approach to proving lower bounds on the size of branching programs. The argument is based on Kraft type inequalities for the average amount of uncertainty about (or entropy of) a given input during the various stages of computation. The uncertainty is measured by the average depth of so-called ‘splitting trees’ for sets of inputs reaching particular nodes of the program.We first demonstrate the approach for read-once branching programs. Then, we introduce a strictly larger class of so-called ‘balanced’ branching programs and, using the suggested approach, prove that some explicit Boolean functions cannot be computed by balanced programs of polynomial size. These lower bounds are new since some explicit functions, which are known to be hard for most previously considered restricted classes of branching programs, can be easily computed by balanced branching programs of polynomial size

Real-time and Probabilistic Temporal Logics: An Overview

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

The Ratio of W + N jets To Z/gamma + N jets As a Precision Test of the Standard Model

We suggest replacing measurements of the individual cross-sections for the production of W + N jets and Z/gamma + N jets in searches for new high-energy phenomena at hadron colliders by the precision measurement of the ratios (W+0 jet)/(Z+0 jet), (W+1 jet)/(Z+1 jet), (W+2 jets)/(Z+2 jets),... (W+N jets)/(Z+N jets), with N as large as 6 (the number of jets in ttbarH). These ratios can also be formed for the case where one or more of the jets is tagged as a b or c quark. Existing measurements of the individual cross sections for Wenu + N jets at the Tevatron have systematic uncertainties that grow rapidly with N, being dominated by uncertainties in the identification of jets and the jet energy scale. These systematics, and also those associated with the luminosity, parton distribution functions (PDF's), detector acceptance and efficiencies, and systematics of jet finding and b-tagging, are expected to substantially cancel in calculating the ratio of W to Z production in each N-jet channel, allowing a greater sensitivity to new contributions in these channels in Run II at the Tevatron and at the LHC.Comment: 10 pages, 8 figures, added reference

A Multivariate Training Technique with Event Reweighting

An event reweighting technique incorporated in multivariate training algorithm has been developed and tested using the Artificial Neural Networks (ANN) and Boosted Decision Trees (BDT). The event reweighting training are compared to that of the conventional equal event weighting based on the ANN and the BDT performance. The comparison is performed in the context of the physics analysis of the ATLAS experiment at the Large Hadron Collider (LHC), which will explore the fundamental nature of matter and the basic forces that shape our universe. We demonstrate that the event reweighting technique provides an unbiased method of multivariate training for event pattern recognition.Comment: 20 pages, 8 figure

Element Distinctness, Frequency Moments, and Sliding Windows

We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. We develop a randomized algorithm for the element distinctness problem whose time T and space S satisfy T in O (n^{3/2}/S^{1/2}), smaller than previous lower bounds for comparison-based algorithms, showing that element distinctness is strictly easier than sorting for randomized branching programs. This algorithm is based on a new time and space efficient algorithm for finding all collisions of a function f from a finite set to itself that are reachable by iterating f from a given set of starting points. We further show that our element distinctness algorithm can be extended at only a polylogarithmic factor cost to solve the element distinctness problem over sliding windows, where the task is to take an input of length 2n-1 and produce an output for each window of length n, giving n outputs in total. In contrast, we show a time-space tradeoff lower bound of T in Omega(n^2/S) for randomized branching programs to compute the number of distinct elements over sliding windows. The same lower bound holds for computing the low-order bit of F_0 and computing any frequency moment F_k, k neq 1. This shows that those frequency moments and the decision problem F_0 mod 2 are strictly harder than element distinctness. We complement this lower bound with a T in O(n^2/S) comparison-based deterministic RAM algorithm for exactly computing F_k over sliding windows, nearly matching both our lower bound for the sliding-window version and the comparison-based lower bounds for the single-window version. We further exhibit a quantum algorithm for F_0 over sliding windows with T in O(n^{3/2}/S^{1/2}). Finally, we consider the computations of order statistics over sliding windows.Comment: arXiv admin note: substantial text overlap with arXiv:1212.437

Report of the QCD Working Group

The activities of the QCD working group concentrated on improving the understanding and Monte Carlo simulation of multi-jet final states due to hard QCD processes at LEP, i.e. quark-antiquark plus multi-gluon and/or secondary quark production, with particular emphasis on four-jet final states and b-quark mass effects. Specific topics covered are: relevant developments in the main event generators PYTHIA, HERWIG and ARIADNE; the new multi-jet generator APACIC++; description and tuning of inclusive (all-flavour) jet rates; quark mass effects in the three- and four-jet rates; mass, higher-order and hadronization effects in four-jet angular and shape distributions; b-quark fragmentation and gluon splitting into b-quarks.Comment: 95 pages, 48 figures, contribution to Proceedings of the LEP2 Monte Carlo Workshop. References for NLO 4-jet matrix elements adde