We study the large-coalition asymptotics of fingerprinting and group testing and derive explicit decoders that provably achieve capacity for many of the considered models. We do this both for simple decoders (which are fast but commonly require larger code lengths) and for joint decoders (which may be slower but achieve the best code lengths). We further make the distinction between informed decoding, where the pirate strategy is exactly known, and uninformed decoding, and we design decoding schemes for both settings. For fingerprinting, we show that if the pirate strategy is known, the Neyman-Pearson-based log-likelihood decoders provably achieve capacity, regardless of the strategy. The decoder built against the interleaving attack is further shown to be a universal decoder, able to deal with arbitrary attacks and achieving the uninformed capacity. This universal decoder is shown to be closely related to the Lagrange-optimized decoder of and the empirical mutual information decoder of Moulin. Joint decoders are also proposed, and we conjecture that these also achieve the corresponding joint capacities. For group testing, the simple decoder for the classical model is shown to be more efficient than the one of and it provably achieves the simple group testing capacity. For generalizations of this model such as noisy group testing, the resulting simple decoders also achieve the corresponding simple capacities.
Based on channel capacities, Amiri and Tardos @cite_1 and Huang and Moulin @cite_11 independently derived the optimal leading constant to be @math (i.e. an asymptotic code length of @math ) and many improvements to Tardos's original scheme were made @cite_13 @cite_26 @cite_21 @cite_22 to reduce the leading constant from @math to @math . Recently it was shown that with Tardos' original score function' one cannot achieve capacity @cite_4 , which lead to the study of different score functions. Based on a result of Abbe and Zheng @cite_20 , Meerwald and Furon @cite_31 noted that a score function designed against the worst-case attack achieves capacity against arbitrary attacks. This also lead to a proposal for a capacity-achieving score function in @cite_38 , which achieves the lower bound on the leading constant of @math .
@cite_38 @cite_26 @cite_4 @cite_22 @cite_21 @cite_1 @cite_31 @cite_13 @cite_20 @cite_11
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We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . We study the asymptotic-capacity-achieving score function that was recently proposed by for bias-based traitor tracing codes. For the bias function, we choose the Dirichlet distribution with a cutoff. Using Bernstein's inequality and Bennett's inequality, we upper bound the false-positive and false-negative error probabilities. From these bounds we derive sufficient conditions for the scheme parameters. We solve these conditions in the limit of large coalition size c0 and obtain asymptotic solutions for the cutoff, the sufficient code length, and the corresponding accusation threshold. We find that the code length converges to its asymptote approximately as c0?1 2 @math , which is faster than the c0?1 3 @math of Tardos' score function. MSC:94B60 A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. The Tardos scheme is a well-known traitor tracing scheme to protect copyrighted content against collusion attacks. The original scheme contained some suboptimal design choices, such as the score function and the distribution function used for generating the biases. previously showed that a symbol-symmetric score function leads to shorter codes, while obtained the optimal distribution functions for arbitrary coalition sizes. Later, showed that combining these results leads to even shorter codes when the coalition size is small. We extend their analysis to the case of large coalitions and prove that these optimal distributions converge to the arcsine distribution, thus showing that the arcsine distribution is asymptotically optimal in the symmetric Tardos scheme. We also present a new, practical alternative to the discrete distributions of and give a comparison of the estimated lengths of the fingerprinting codes for each of these distributions.