An efficient threshold scheme is proposed in this paper. It overcomes the weakness of Asmuth et al.’s scheme. The (r, n)-threshold scheme proposed below only takes O(r) operations to recover the shared secret while Shamir’s scheme takes O(rlogr) operations. We show that our scheme is perfect. Further, we also propose a method to generate a pairwise relatively prime integer set which satisfies t...

We discuss the Cucker-Smale’s (C-S) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasov-type kinetic model for the C-S particle model and prove it exhibits time-asymptotic flocking behavior for arbitrary compactly supported initial data. Finally, we introduce a hydrodynamic descript...

We show how to design secure authentication protocols for a non-standard class of scenarios. In these authentication is not bootstrapped from a PKI, shared secrets or trusted third parties, but rather using a minimum of work by human user(s) implementing the low-bandwidth unspoofable channels between them. We develop both pairwise and group protocols which are essentially optimal in human effor...

Conditions under which pairwise dissimilarity ratings should reflect manipulations of the stimulus distribution were outlined by a model that proposed these effects. These conditions arise from either a context dependent process for constructing implicit scale values or a process that uses previously established stimulus-response associates. Consistent with the model, results from 3 experiments...

In [K–K–S] it was shown that fields of generalized power series cannot admit an exponential function. In this paper, we construct fields of generalized power series with bounded support which admit an exponential. We give a natural definition of an exponential, which makes these fields into models of real exponentiation. The method allows to construct for every κ regular uncountable cardinal, 2...

We propose a randomized relax-and-round inference algorithm that samples near-MAP configurations of a binary pairwise Markov random field. We experiment on MAP inference tasks in several restricted Boltzmann machines. We also use our underlying sampler to estimate the log-partition function of restricted Boltzmann machines and compare against other sampling-based methods. 1. Background and setu...

We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or pe...

We analyze the structure of the imaginary part of the two-loop Euler-Heisenberg QED effective Lagrangian for a constant self-dual background. The novel feature of the two-loop result, compared to one-loop, is that the prefactor of each exponential (instanton) term in the imaginary part has itself an asymptotic expansion. We also perform a high-precision test of Borel summation techniques applie...

Current research proposes a natural environment for the space-time codes and in this context it is obtained a new design criterion for space-time codes in multi-antenna communication channels. The objective of this criterion is to minimize the pairwise error probability of the maximum likelihood decoder, endowed with the matrix spectrum norm. The random matrix theory is used and an approximatio...

in this paper, the use of weighted pairwise likelihood instead of the full likelihood in estimating the parameters of the multivariate ar(1) is investigated. a closed formula for typical elements of the godambe information(sandwich information) is presented. some efficiency calculations are also given to discuss the feasibility andcomputational advantages of the weighted pairwise likelihood app...