Local matching indicators for transport problems with concave costs

In this paper, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of N demands and M supplies in R in the case where the cost function is concave. The computational cost of these indicators is small and independent of N. A hierarchical use of them enables to obtain an efficient algorithm

Remarks on the Generalized Chaplygin Gas

We have developed an action formulation for the Generalized Chaplygin Gas (GCG). The most general form for the nonrelativistic GCG action is derived consistent with the equation of state. We have also discussed a relativistic formulation for GCG by providing a detailed analysis of the Poincare algebra.Comment: References addede

How unprovable is Rabin's decidability theorem?

We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree. We first show that the complementation theorem for tree automata, which forms the technical core of typical proofs of Rabin's theorem, is equivalent over the moderately strong second-order arithmetic theory $\mathsf{ACA}_0$ to a determinacy principle implied by the positional determinacy of all parity games and implying the determinacy of all Gale-Stewart games given by boolean combinations of ${\bf \Sigma^0_2}$ sets. It follows that complementation for tree automata is provable from $\Pi^1_3$- but not $\Delta^1_3$-comprehension. We then use results due to MedSalem-Tanaka, M\"ollerfeld and Heinatsch-M\"ollerfeld to prove that over $\Pi^1_2$-comprehension, the complementation theorem for tree automata, decidability of the MSO theory of the infinite binary tree, positional determinacy of parity games and determinacy of $\mathrm{Bool}({\bf \Sigma^0_2})$ Gale-Stewart games are all equivalent. Moreover, these statements are equivalent to the $\Pi^1_3$-reflection principle for $\Pi^1_2$-comprehension. It follows in particular that Rabin's decidability theorem is not provable in $\Delta^1_3$-comprehension.Comment: 21 page

Practical End-to-End Verifiable Voting via Split-Value Representations and Randomized Partial Checking

We describe how to use Rabin's "split-value" representations, originally developed for use in secure auctions, to efficiently implement end-to-end verifiable voting. We propose a simple and very elegant combination of split-value representations with "randomized partial checking" (due to Jakobsson et al. [16])

Practical Provably Correct Voter Privacy Protecting End-to-End Voting Employing Multiparty Computations and Split Value Representations of Votes

Continuing the work of Rabin and Rivest we present another simple and fast method for conducting end to end voting and allowing public verification of correctness of the announced vote tallying results. This method was referred to in as the SV/VCP method. In the present note voter privacy protection is achieved by use of a simple form of Multi Party Computations (MPC). At the end of vote tallying process, random permutations of the cast votes are publicly posted in the clear, without identification of voters or ballot ids. Thus vote counting and assurance of correct form of cast votes are directly available. Also, a proof of the claim that the revealed votes are a permutation of the concealed cast votes is publicly posted and verifiable by any interested party. Advantages of this method are: Easy understandability by non-­‐cryptographers, implementers and ease of use by voters and election officials. Direct handling of complicated ballot forms. Independence from any specialized primitives. Speed of vote-­‐tallying and correctness proving: elections involving a million voters can be tallied and proof of correctness of results posted within a few minutes

Aspects of Diffeomorphism and Conformal invariance in classical Liouville theory

The interplay between the diffeomorphism and conformal symmetries (a feature common in quantum field theories) is shown to be exhibited for the case of black holes in two dimensional classical Liouville theory. We show that although the theory is conformally invariant in the near horizon limit, there is a breaking of the diffeomorphism symmetry at the classical level. On the other hand, in the region away from the horizon, the conformal symmetry of the theory gets broken with the diffeomorphism symmetry remaining intact.Comment: Accepted in Euro. Phys. Letters., Title changed, abstract modified, major modifications made in the pape

Verifiable Random Functions

We efficiently combine unpredictability and verifiability by extending the Goldreich-Goldwasser-Micali notion of pseudorandom functions $f_s$ from a secret seed s, so that knowledge of $s$ not only enables one to evaluate $f_s$ at any point x, but also to provide an NP-proof that the value $f{_s}(x)$ is indeed correct without compromising the unpredictability of $f_s$ at any other point for which no such a proof was provided.Engineering and Applied Science

How To Exchange Secrets with Oblivious Transfer

The original paper does not have an abstract. This is a scanned version of the original hand written manuscript of this paper. It appeared in print as a Harvard University Technical Report, but at some point the university ran out of copies. At that time copies of the hand written version started to circulate, and were the only ones available. As access to these copies has become difficult I have scanned my copy of the paper and I\u27m posting it on the web for others to read. *Note that the manuscript has a different title, but the paper is most commonly (if not only) cited with this title. Thus, I assume that it should continue to be cited in this manner with reference to the original technical report