We study the action of derived Hecke algebra in setting dihedral weight one forms and prove a conjecture second- fourth- named authors relating this to certain Stark units associated symmetric square L-function. The proof exploits theta correspondence between various modules as well ideas Merel Lecouturier on higher Eisenstein elements.

Zero-knowledge set is a primitive introduced by Micali, Rabin, and Kilian (FOCS 2003)which enables a prover to commit a set to a verifier, without revealing even the size of the set.Later the prover can give zero-knowledge proofs to convince the verifier of membership/non-membership of elements in/not in the committed set.We present a new primitive called Statistically Hiding Se...

In this paper, we propose an alternate approach to ad-hoc networking called Best Effort multi-Hop Geographical Routing (BEHGR). BEHGR does not fit under the current classifications of on-demand or table-based approaches to ad-hoc routing, but instead statistically attempts to dynamically route packets to a central location in a “best effort” manner. The basis of such a protocol assumes that a s...

A hitherto neglected form of explanation is explored, especially its role in population genetics. “Statistically abstractive explanation” (SA explanation) mandates the suppression of factors probabilistically relevant to an explanandum when these factors are extraneous to the theoretical project being pursued. When these factors are suppressed, the explanandum is rendered uncertain. But this un...

Service oriented computing o ers a new approach to programming. To be useful for large and diverse sets of problems, e ective service selection and composition is crucial. While current frameworks offer tools and methods for selecting services based on various user-de ned criteria, little attention has been paid to how such services act and interact. Similarly, the patterns of interaction might...

Fortunately, the probability that the process was simply a chance encounter can be calculated, and a minimum threshold of statistical significance can be set. If the results are obtained such that the probability that they are simply a chance process is less than this threshold of significance, then we can say the results have a high probability of not being due to chance. Note that the probabi...

In this paper we present a method for constraining the deformations of Snakes (Active Contour Models) when segmenting a known class of objects. The method we propose is similar to both Active Shape Models (ASM) but without the landmark identification and correspondence requirement, and to Active Contour Models (ACM), but armed with a priori information about shape variation. Rather than represe...