95 research outputs found

    Probabilistic existence of regular combinatorial structures

    Full text link
    We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise permutations. In all cases, the sizes of the objects are optimal up to polynomial overhead. The proof of existence is probabilistic. We show that a randomly chosen structure has the required properties with positive yet tiny probability. Our method allows also to give rather precise estimates on the number of objects of a given size and this is applied to count the number of orthogonal arrays, t-designs and regular hypergraphs. The main technical ingredient is a special local central limit theorem for suitable lattice random walks with finitely many steps.Comment: An extended abstract of this work [arXiv:1111.0492] appeared in STOC 2012. This version expands the literature discussio

    Estimating Product Characteristics and Spatial Competition in the Network Television Industry

    Get PDF
    Assessing the demand for products with characteristics that are unobservable or difficult to measure is becoming increasingly important with the growing proliferation and value of such products. Analyzing industry performance and firm competition in these sectors is hindered by the failure of traditional empirical methods to estimate demand for the products of these sectors. This paper focuses on the network television industry to present: (a) an empirical analysis of spatial competition, and (b) a structural approach to estimating product characteristics and consumer preferences in such industries, and (c) optimal network programming and scheduling given the estimated demand system. We use maximum simulated likelihood to estimate a structural model of viewer choice, yielding estimates of the latent characteristics of each show, the distribution of consumers' preferences for these characteristics, and the state dependence of choices. Results indicate the attribute space spans four dimensions of horizontal differentiation and one vertically differentiated dimension. Interpretations of these dimensions reflect the traditional show labels. For example, one of the dimensions represents the degree of realism in a show. Furthermore, the clustering of shows based on the estimated characteristics corresponds to traditional show labels. We identify four clusters --- sitcoms for mature viewers, sitcoms for younger viewers, reality based dramas, and fictional dramas. Regarding strategic behavior, our model suggests the networks should use counter-programming (i.e., differentiated products) within each time slot and homogeneous programming through each night. The estimated show locations reveal an extensive use of these strategies, as well as a limited degree of branding. Nonetheless, by unilaterally changing their schedules to increase both counter-programming and homogeneity, ABC, CBS, and NBC are able to increase their weekly ratings by 16%, 12%, and 15%, respectively. In a Nash equilibrium of the static scheduling game, these gains are reduced to 15%, 6%, and 12% increases.

    The Effectiveness and Targeting of Television Advertising

    Full text link

    An Additive Combinatorics Approach Relating Rank to Communication Complexity

    Full text link
    Identifying complexity measures that bound the communication complexity of a {0,1}-valued matrix M is one the most fundamental problems in communication complexity. Mehlhorn and Schmidt [1982] were the first to suggest matrix-rank as one such measure. Among other things, they showed log rankF(M)≤CC(M) ≤rankF2(M), where CC(M) denotes the (deterministic) communication complexity of the function associated with M, and the rank on the left-hand side is over any field F and on the right-hand side it is over the two-element field F2. For certain matrices M, communication complexity equals the right-hand side, and this completely settles the question of "communication complexity vs. F2-rank". Here we reopen this question by pointing out that, when M has an additional natural combinatorial property-high discrepancy with respect to distributions which are uniform over submatrices-then communication complexity can be sublinear in F2-rank. Assuming the Polynomial Freiman-Ruzsa (PFR) conjecture in additive combinatorics, we show that CC(M)≤O(rankF2M)/log rankF2 (M)) for any matrix M which satisfies this combinatorial property. We also observe that if M has low rank over the reals, then it has low rank over F2 and it additionally satisfies this combinatorial property. As a corollary, our results also give the first (conditional) sublinear bound on communication complexity in terms of rank over the reals, a result improved later by Lovett [2014]. Our proof is based on the study of the "approximate duality conjecture" which was suggested by Ben-Sasson and Zewi [2011] and studied there in connection to the PFR conjecture. First, we improve the bounds on approximate duality assuming the PFR conjecture. Then, we use the approximate duality conjecture (with improved bounds) to get our upper bound on the communication complexity of low-rank matrices. © 2014 ACM 0004-5411/2014/07-ART20 $15.00

    FORGETFULNESS AND THE POLITICAL CYCLE

    No full text
    This paper examines a mechanism that underlies both the political business cycle and the cycle in non-economic policies executed by politicians. We show that if rational voters suffer from forgetfulness (a noise in the memory). then government expenditure on the production of public good increases as elections approach. Hence, the model describes a cycle that is observed in the government expenditures of democratic societies. Unlike previous models, this model does not require that the government have information superiority over rational voters with respect to its competency. According to this model, incumbents transfer resources from the beginning of their terms of service and use them near the end of their terms. We also find that the less concave the production function, the wider the cycle. Copyright 1993 Blackwell Publishers Ltd..
    corecore