1,721,025 research outputs found
Sensor networks that are provably resilient
No full textWe give, for the first time, a precise mathematical analysis of the connectivity and security properties of sensor networks that make use of the random pre-distribution of keys. We also show how to set the parameters- pool and keyring size- in such a way that the network is not only connected with high probability via secure links, but also provably resilient, in the following sense: we formally show that any attacker that captures sensors at random with the aim of compromising a constant fraction of the secure links, must capture at least a constant fraction of the nodes of the network. In the context of wireless sensor networks where random pre-distribution of keys is employed, we are the first to provide a mathematically precise proof, with a clear indication of parameter choice, that two crucial properties - connectivity via secure links and resilience against malicious attacks- can be obtained simultaneously. Our theoretical results are complemented by extensive simulations that reinforce our main conclusions. ©2006 IEEE
An improved bound on the zero-error list-decoding capacity of the 4/3 channel
No full textWe prove a new, improved upper bound on the size of codes C ⊆{1, 2, 3, 4}n with the property that every four distinct codewords in C have a coordinate where they all differ. Specifically, we show that such a code has size at most 26n/19 +o(n), or equivalently has rate bounded by 6/19 ≤ 0.3158 (measured in bits). This improves the previous best upper bound of 0.3512 due to (Arikan 1994), which in turn improved the 0.375 bound that followed from general bounds for perfect hashing due to (Fredman and Komlos, 1984) and (Korner and Marton, 1988). The context for this problem is two-fold: zero-error list decoding capacity, where such codes give a way to communicate with no error on the “4/3 channel” when list-of-3 decoding is employed, and perfect hashing, where such codes give a perfect hash family of size n mapping C to {1, 2, 3, 4}
Better Lower Bounds for Monotone Threshold Formulas
No full textAbstractWe show that every monotone formula that computes the threshold function THk, n, 2⩽k⩽n/2, has size at least ⌊k/2⌋nlog(n/(k−1)). The same lower bound is shown to hold in the stronger monotone directed contact networks model
Set membership with two bit probes
Full text linkWe will consider the bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form Is x in S? by adaptively probing the bit vector at t places. Let s(m,n,t) be the minimum number of bits of storage needed for such a scheme. Alon and Feige showed that for t=2 (two bit probes), such schemes can be obtained from dense graphs with large girth. In particular, they showed that for n \u3c \log m,
s(m,n,2) = O(m n \log((\log m) / n) / \log m).
We improve their analysis and obtain a better upper bound and a corresponding lower bound.
Upper bound: There is a constant C\u3e0, such that for all large m,
s(m,n,2) \leq C \cdot m^{1-\frac{1}{(4n+1)}}.
Lower bound: There is a constant D\u3e0, such that for n\geq 4 and all large m, we have
s(m,n,2) \geq D \cdot m^{1-\frac{1}{\lfloor n/4 \rfloor}}.
(This is joint work with Mohit Garg.)
Download the attached PDF to see the abstract with proper math formatting
An Entropy Proof of Bregman's Theorem
No full textAbstractLetA=(ai, j) be ann×n0-1 matrix. LetSbe the set of permutationsσof [n] such thatai, σ(i)=1 fori=1, 2, …, n. Then, the permanent ofAis perm(A)=def|S|. Theorem(Brégman,Soviet Math. Dokl.14(1973), 945–949). If the number of 1's in rowiofAisri, then[formula]A short proof of this theorem was given by Schrijver (J. Combin. Theory Ser. A25(1978), 80–83); Alon and Spencer (“The Probabilistic Method,” Wiley/Interscience, New York, 1992), obtained a similar proof by analyzing a randomized procedure for estimating the permanent. In this note we present a proof based on entropy
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
A note on scrambling permutations
No full textA family F of permutations of [n] is completelyk-scrambling [Spencer,1972] if for every sequence
<p1, p2,...,pk > of k distinct elements of [n], there is a
permutation π ∈ F with π(p1) < π(p2) <
,..,< π(pk). We show that the size of the smallest completely k-scrambling family of
permutations of [n] is at least 1+(2/log2e)(n/2n−k+1)(k+1)log2(n-k+2).
This improves the previous best lower bound, due to Füredi 1996, by a factor of approximately
2/log2e
Variations on the Author
Full text link“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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