Lookahead Strategies for Sequential Monte Carlo

Based on the principles of importance sampling and resampling, sequential Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with complex stochastic dynamic systems. Many of these systems possess strong memory, with which future information can help sharpen the inference about the current state. By providing theoretical justification of several existing algorithms and introducing several new ones, we study systematically how to construct efficient SMC algorithms to take advantage of the "future" information without creating a substantially high computational burden. The main idea is to allow for lookahead in the Monte Carlo process so that future information can be utilized in weighting and generating Monte Carlo samples, or resampling from samples of the current state.Comment: Published in at http://dx.doi.org/10.1214/12-STS401 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Symmetry Reduction and Boundary Modes for Fe-Chains on an s-wave Superconductor

We investigate the superconducting phase diagram and boundary modes for a quasi-1D system formed by three Fe-Chains on an s-wave superconductor, motivated by the recent Princeton experiment. The $\vec l\cdot\vec s$ onsite spin-orbit term, inter-chain diagonal hopping couplings, and magnetic disorders in the Fe-chains are shown to be crucial for the superconducting phases, which can be topologically trivial or nontrivial in different parameter regimes. For the topological regime a single Majorana and multiple Andreew bound modes are obtained in the ends of the chain, while for the trivial phase only low-energy Andreev bound states survive. Nontrivial symmetry reduction mechanism induced by the $\vec l\cdot\vec s$ term, diagonal hopping couplings, and magnetic disorder is uncovered to interpret the present results. Our study also implies that the zero-bias peak observed in the recent experiment may or may not reflect the Majorana zero modes in the end of the Fe-chains.Comment: 5 pages, 4 figures; some minor errors are correcte

Peer to Peer Mobile Coupons: Adding Incentives without Sacrificing Security

Mobile commerce is flourishing today due to the advance of the mobile technology. Many conventional marketing activities are moving their ways to the mobile environment. Efficient marketing instruments such as the paper coupons and the electronic coupons are also evolving into the mobile coupons. In comparison with conventional coupons, mobile coupons are personalized and suitable for peer to peer delivery. Coupons are commonly issued by the merchants, used by the interested customers, and discarded by the uninterested receivers. Raising the redemption rate of the coupon will increase the sales of the promoted items. The raise can be accomplished by forwarding coupons from uninterested receivers to potentially interested customers. The ease-of-use exchange mechanism in mobile devices pushes the delivery in the peer to peer environment. Moreover, the characteristic of personalization inspires trust into mobile coupons. Thus, adding the incentives of coupon forwarding, such as a reward bonus, may activate the movement of stationary coupons and eventually increase the redemption rate of mobile coupons. Nevertheless, the incentives adding may bring the threats of alterations and forgery; if the adding mechanism is improperly made. Additionally, complicated security means are hindered by the limitations of storage space, computation power, and communication bandwidth of mobile devices. Therefore, we propose a scheme that uses digital signatures for verifying the incentive-added coupons and design a hash chain to detect possible forgery. The proposed scheme may increase the use of peer to peer mobile coupons without sacrificing the security

Magic wavelengths for the 6s^2\,^1S_0-6s6p\,^3P_1^o transition in ytterbium atom

The static and dynamic electric-dipole polarizabilities of the 6s^2\,^1S_0 and 6s6p\,^3P_1^o states of Yb are calculated by using the relativistic ab initio method. Focusing on the red detuning region to the 6s^2\,^1S_0-6s6p\,^3P_1^o transition, we find two magic wavelengths at 1035.7(2) nm and 612.9(2) nm for the 6s^2\,^1S_0-6s6p\,^3P_1^o, M_J=0 transition and three magic wavelengthes at 1517.68(6) nm, 1036.0(3) nm and 858(12) nm for the 6s^2\,^1S_0-6s6p\,^3P_1^o, M_J=\pm1 transitions. Such magic wavelengths are of particular interest for attaining the state-insensitive cooling, trapping, and quantum manipulation of neutral Yb atom.Comment: 13 pages, 3 figure