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A lower bound for the length of a partial transversal in a Latin square
No full textAbstractIt is proved that every n×n Latin square has a partial transversal of length at least n−O(log2n). The previous papers proving these results (including one by the second author) not only contained an error, but were sloppily written and quite difficult to understand. We have corrected the error and improved the clarity
On the Structure of Quintic Polynomials
Get PDFWe study the structure of bounded degree polynomials over finite fields. Haramaty and Shpilka [STOC 2010] showed that biased degree three or four polynomials admit a strong structural property. We confirm that this is the case for degree five polynomials also. Let F=F_q be a prime field. Suppose f:F^n to F is a degree five polynomial with bias(f)=delta. We prove the following two structural properties for such f.
1. We have f= sum_{i=1}^{c} G_i H_i + Q, where G_i and H_is are nonconstant polynomials satisfying deg(G_i)+deg(H_i)<= 5 and Q is a degree <5 polynomial. Moreover, c does not depend on n.
2. There exists an Omega_{delta,q}(n) dimensional affine subspace V subseteq F^n such that f|_V is a constant.
Cohen and Tal [Random 2015] proved that biased polynomials of degree at most four are constant on a subspace of dimension Omega(n). Item 2.]extends this to degree five polynomials. A corollary to Item 2. is that any degree five affine disperser for dimension k is also an affine extractor for dimension O(k). We note that Item 2. cannot hold for degrees six or higher.
We obtain our results for degree five polynomials as a special case of structure theorems that we prove for biased degree d polynomials when d<|\F|+4. While the d<|F|+4 assumption seems very restrictive, we note that prior to our work such structure theorems were only known for d<|\F| by Green and Tao [Contrib. Discrete Math. 2009] and Bhowmick and Lovett [arXiv:1506.02047]. Using algorithmic regularity lemmas for polynomials developed by Bhattacharyya, et al. [SODA 2015], we show that whenever such a strong structure exists, it can be found algorithmically in time polynomial in n
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
An approximation algorithm for the total covering problem
No full textWe introduce a 2-factor approximation algorithm for the minimum total covering number problem
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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Derandomizing space-bounded computation via pseudorandom generators and their generalizations
Get PDFTo what extent is randomness necessary for efficient computation? We study the problem of deterministically simulating randomized algorithms with low space overhead. The traditional approach to this problem is to try to design sufficiently powerful pseudorandom generators (PRGs). PRG constructions often provide deep insights into models of computation and have applications beyond derandomization. There are other approaches based on generalizations of the PRG concept that are potentially easier to construct yet still valuable for derandomization. One such generalization is a hitting set generator (HSG), a standard "one-sided" version of a PRG. Another such generalization, introduced recently by Braverman, Cohen, and Garg [BCG20], is a weighted pseudorandom generator (WPRG), which is similar to a PRG except probability distributions are replaced by "pseudodistributions." In this dissertation, we present new results (obtained jointly with collaborators) regarding all three of these approaches to derandomizing space-bounded algorithms.
Regarding the PRG approach, we present improved PRGs for interesting models of computation including unbounded-width permutation branching programs, read-once AC⁰ formulas, and superlinear-size constant-depth threshold circuits. The first two PRGs are unconditionally near-optimal; substantially improving the third would require a breakthrough in circuit lower bounds. Each PRG is in some way connected to derandomizing space-bounded algorithms.
Regarding generalizations of PRGs, we present new constructions and applications of HSGs and WPRGs for read-once branching programs (ROBPs), the nonuniform model that directly corresponds to randomized space-bounded algorithms. In particular, we construct explicit HSGs and WPRGs with an optimal dependence on the error parameter ε. In terms of applications, we show that optimal HSGs for polynomial-width ROBPs could be used to derandomize decision algorithms with two-sided error (BPL, not just RL). Unconditionally, we explain how to use recent WPRG constructions to deterministically simulate randomized space-S decision algorithms in space O (S [superscript 3/2] / [square root of log S]), a slight improvement over Saks and Zhou's celebrated O (S [superscript 3/2]) bound [SZ99]. Finally, using the techniques underlying our HSG construction, we give an improved unconditional derandomization of log-space algorithms that have one-sided error and low success probability.Computer Scienc
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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