Anti-lecture Hall Compositions and Overpartitions

We show that the number of anti-lecture hall compositions of n with the first entry not exceeding k-2 equals the number of overpartitions of n with non-overlined parts not congruent to $0,\pm 1$ modulo k. This identity can be considered as a refined version of the anti-lecture hall theorem of Corteel and Savage. To prove this result, we find two Rogers-Ramanujan type identities for overpartition which are analogous to the Rogers-Ramanjan type identities due to Andrews. When k is odd, we give an alternative proof by using a generalized Rogers-Ramanujan identity due to Andrews, a bijection of Corteel and Savage and a refined version of a bijection also due to Corteel and Savage.Comment: 16 page

The Rogers-Ramanujan-Gordon Theorem for Overpartitions

Let $B_{k,i}(n)$ be the number of partitions of $n$ with certain difference condition and let $A_{k,i}(n)$ be the number of partitions of $n$ with certain congruence condition. The Rogers-Ramanujan-Gordon theorem states that $B_{k,i}(n)=A_{k,i}(n)$. Lovejoy obtained an overpartition analogue of the Rogers-Ramanujan-Gordon theorem for the cases $i=1$ and $i=k$. We find an overpartition analogue of the Rogers-Ramanujan-Gordon theorem in the general case. Let $D_{k,i}(n)$ be the number of overpartitions of $n$ satisfying certain difference condition and $C_{k,i}(n)$ be the number of overpartitions of $n$ whose non-overlined parts satisfy certain congruences condition. We show that $C_{k,i}(n)=D_{k,i}(n)$. By using a function introduced by Andrews, we obtain a recurrence relation which implies that the generating function of $D_{k,i}(n)$ equals the generating function of $C_{k,i}(n)$. We also find a generating function formula of $D_{k,i}(n)$ by using Gordon marking representations of overpartitions, which can be considered as an overpartition analogue of an identity of Andrews for ordinary partitions.Comment: 26 page

An efficient protocol for the problem of secure two-party vector dominance

The problem of secure two-party vector dominance requires the comparison of two vectors in an "all-or-nothing" way. In this paper we provide a solution to this problem based on the semi-honest model. It is reduced to the problem of privacy preserving prefix test, and an additive threshold homomorphic encryption is used to protect those privacies while computing the results of all of the prefix tests. Our solution has advantages of efficiency and security in comparison with other solutions.Yingpeng Sang, Hong Shen, Zonghua Zhan

Secure data aggregation in wireless sensor networks: A survey

Data aggregation is a widely used technique in wireless sensor networks. The security issues, data confidentiality and integrity, in data aggregation become vital when the sensor network is deployed in a hostile environment. There has been many related work proposed to address these security issues. In this paper we survey these work and classify them into two cases: hop-by-hop encrypted data aggregation and end-to-end encrypted data aggregation. We also propose two general frameworks for the two cases respectively. The framework for end-to-end encrypted data aggregation has higher computation cost on the sensor nodes, but achieves stronger security, in comparison with the framework for hop-by-hop encrypted data aggregation.Yingpeng Sang, Hong Shen, Yasushi Inoguchi, Yasuo Tan, Naixue Xion

Spontaneous phase oscillation induced by inertia and time delay

We consider a system of coupled oscillators with finite inertia and time-delayed interaction, and investigate the interplay between inertia and delay both analytically and numerically. The phase velocity of the system is examined; revealed in numerical simulations is emergence of spontaneous phase oscillation without external driving, which turns out to be in good agreement with analytical results derived in the strong-coupling limit. Such self-oscillation is found to suppress synchronization and its frequency is observed to decrease with inertia and delay. We obtain the phase diagram, which displays oscillatory and stationary phases in the appropriate regions of the parameters.Comment: 5 pages, 6 figures, to pe published in PR