Distributed Event Localization via Alternating Direction Method of Multipliers

This paper addresses the problem of distributed event localization using noisy range measurements with respect to sensors with known positions. Event localization is fundamental in many wireless sensor network applications such as homeland security, law enforcement, and environmental studies. However, most existing distributed algorithms require the target event to be within the convex hull of the deployed sensors. Based on the alternating direction method of multipliers (ADMM), we propose two scalable distributed algorithms named GS-ADMM and J-ADMM which do not require the target event to be within the convex hull of the deployed sensors. More specifically, the two algorithms can be implemented in a scenario in which the entire sensor network is divided into several clusters with cluster heads collecting measurements within each cluster and exchanging intermediate computation information to achieve localization consistency (consensus) across all clusters. This scenario is important in many applications such as homeland security and law enforcement. Simulation results confirm effectiveness of the proposed algorithms.Comment: accepted to IEEE Transactions on Mobile Computin

A Simple, Efficient, High-order Accurate Sliding-Mesh Interface Approach to the Spectral Difference Method on Coupled Rotating and Stationary Domains

This paper presents a simple, efficient, and high-order accurate sliding-mesh interface approach to the spectral difference (SD) method. We demonstrate the approach by solving the two-dimensional compressible Navier-Stokes equations on quadrilateral grids. This approach is an extension of the straight mortar method originally designed for stationary domains by Kopriva, it employs curved dynamic mortars on sliding-mesh interfaces to couple rotating and stationary domains. On the nonconforming sliding-mesh interfaces, the related variables are first projected from cell faces to mortars to compute common fluxes, and then the common fluxes are projected back from the mortars to the cell faces to ensure conservation. To verify the spatial order of accuracy of the sliding-mesh spectral difference (SSD) method, both inviscid and viscous flow cases are tested. It is shown that the SSD method preserves the high-order accuracy of the SD method. Meanwhile, the SSD method is found to be very efficient in terms of computational cost. This novel sliding-mesh interface method is very suitable for parallel processing with domain decomposition. It can be applied to a wide range of problems, such as the aerodynamics of rotorcraft, wind turbines, and oscillating wing wind power generators, etc

Dynamical spin-density waves in a spin-orbit-coupled Bose-Einstein condensate

Synthetic spin-orbit (SO) coupling, an important ingredient for quantum simulation of many exotic condensed matter physics, has recently attracted considerable attention. The static and dynamic properties of a SO coupled Bose-Einstein condensate (BEC) have been extensively studied in both theory and experiment. Here we numerically investigate the generation and propagation of a \textit{dynamical} spin-density wave (SDW) in a SO coupled BEC using a fast moving Gaussian-shaped barrier. We find that the SDW wavelength is sensitive to the barrier's velocity while varies slightly with the barrier's peak potential or width. We qualitatively explain the generation of SDW by considering a rectangular barrier in a one dimensional system. Our results may motivate future experimental and theoretical investigations of rich dynamics in the SO coupled BEC induced by a moving barrier.Comment: 8 pages, 8 figure

1D topological chains with Majorana fermions in 2D non-topological optical lattices

The recent experimental realization of 1D equal Rashba-Dresselhaus spin-orbit coupling (ERD-SOC) for cold atoms provide a disorder-free platform for the implementation and observation of Majorana fermions (MFs), similar to the well studied solid state nanowire/superconductor heterostructures. However, the corresponding 1D chains of cold atoms possess strong quantum fluctuation, which may destroy the superfluids and MFs. In this Letter, we show that such 1D topological chains with MFs may be on demand generated in a 2D non-topological optical lattice with 1D ERD-SOC by modifying local potentials on target locations using experimentally already implemented atomic gas microscopes or patterned (e.g., double or triple well) optical lattices. All ingredients in our scheme have been experimentally realized and the combination of them may pave the way for the experimental observation of MFs in a clean system.Comment: 6 pages, 6 figure

FFLO or Majorana superfluids: The fate of fermionic cold atoms in spin-orbit coupled optical lattices

The recent experimental realization of spin-orbit coupling (SOC) for ultra-cold atoms opens a completely new avenue for exploring new quantum matter. In experiments, the SOC is implemented simultaneously with a Zeeman field. Such spin-orbit coupled Fermi gases are predicted to support Majorana fermions with non-Abelian exchange statistics in one dimension (1D). However, as shown in recent theory and experiments for 1D spin-imbalanced Fermi gases, the Zeeman field can lead to the long-sought Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids with non-zero momentum Cooper pairings, in contrast to the zero momentum pairing in Majorana superfluids. Therefore a natural question to ask is which phase, FFLO or Majorana superfluids, will survive in spin-orbit coupled Fermi gases in the presence of a large Zeeman field. In this paper, we address this question by studying the mean field quantum phases of 1D (quasi-1D) spin-orbit coupled fermionic cold atom optical lattices.Comment: 7 pages, 7 figures, results for quasi-1D lattices were adde

Quantify Entanglement for Multipartite Quantum States

In this paper, we consider the problem of how to quantify entanglement for any multipartite quantum states. For bipartite pure states partial entropy is a good entanglement measure. By using partial entropy, we firstly introduce the Combinatorial Entropy of Fully entangled states (CEF) which can be used to quantify entanglement for any fully entangled pure states. In order to quantify entanglement for any multipartite states we also need another concept the Entanglement Combination (EC) which can be used to completely describe the entanglement between any parties of the given quantum states. Combining CEF with EC, we define the Combinatorial Entropy (CE) for any multipartite pure states and present some nice properties which indicate CE is a good entanglement measure. Finally, we point out the feasibility of extending these three concepts to mixed quantum states.Comment: 5 page

Quantum phases of Bose-Einstein condensates with synthetic spin - orbital-angular-momentum coupling

The experimental realization of emergent spin-orbit coupling through laser-induced Raman transitions in ultracold atoms paves the way for exploring novel superfluid physics and simulating exotic many-body phenomena. A recent proposal with the use of Laguerre-Gaussian lasers enables another fundamental type of coupling between spin and orbital angular momentum (SOAM) in ultracold atoms. We hereby study quantum phases of a realistic Bose-Einstein condensate (BEC) with this synthetic SOAM coupling in a disk-shaped geometry, respecting radial inhomogeneity of the Raman coupling. We find that the experimental system naturally resides in a strongly interacting regime in which the phase diagram significantly deviates from the single-particle picture. The interplay between SOAM coupling and interaction leads to rich structures in spin-resolved position and momentum distributions, including a stripe phase and various types of immiscible states. Our results would provide a guide for an experimental investigation of SOAM-coupled BECs.Comment: 8 pages, 7 figure

Large Sets of Orthogonal Sequences Suitable for Applications in CDMA Systems

In this paper, we employ the so-called semi-bent functions to achieve significant improvements over currently known methods regarding the number of orthogonal sequences per cell that can be assigned to a regular tessellation of hexagonal cells, typical for certain code-division multiple-access (CDMA) systems. Our initial design method generates a large family of orthogonal sets of sequences derived from vectorial semi-bent functions. A modification of the original approach is proposed to avoid a hard combinatorial problem of allocating several such orthogonal sets to a single cell of a regular hexagonal network, while preserving the orthogonality to adjacent cells. This modification increases the number of users per cell by starting from shorter codewords and then extending the length of these codewords to the desired length. The specification and assignment of these orthogonal sets to a regular tessellation of hexagonal cells have been solved regardless of the parity and size of $m$ (where $2^m$ is the length of the codewords). In particular, when the re-use distance is $D=4$ the number of users per cell is $2^{m-2}$ for almost all $m$, which is twice as many as can be obtained by the best known methods.Comment: 24 pages, 4 figures, 5 tables. IEEE Transactions on Information Theory,vol.62, no.6, 201

Privacy-preserving Decentralized Optimization via Decomposition

This paper considers the problem of privacy-preservation in decentralized optimization, in which $N$ agents cooperatively minimize a global objective function that is the sum of $N$ local objective functions. We assume that each local objective function is private and only known to an individual agent. To cooperatively solve the problem, most existing decentralized optimization approaches require participating agents to exchange and disclose estimates to neighboring agents. However, this results in leakage of private information about local objective functions, which is undesirable when adversaries exist and try to steal information from participating agents. To address this issue, we propose a privacy-preserving decentralized optimization approach based on proximal Jacobian ADMM via function decomposition. Numerical simulations confirm the effectiveness of the proposed approach.Comment: submitted to American control conferenc

ADMM Based Privacy-preserving Decentralized Optimization

Privacy preservation is addressed for decentralized optimization, where $N$ agents cooperatively minimize the sum of $N$ convex functions private to these individual agents. In most existing decentralized optimization approaches, participating agents exchange and disclose states explicitly, which may not be desirable when the states contain sensitive information of individual agents. The problem is more acute when adversaries exist which try to steal information from other participating agents. To address this issue, we propose a privacy-preserving decentralized optimization approach based on ADMM and partially homomorphic cryptography. To our knowledge, this is the first time that cryptographic techniques are incorporated in a fully decentralized setting to enable privacy preservation in decentralized optimization in the absence of any third party or aggregator. To facilitate the incorporation of encryption in a fully decentralized manner, we introduce a new ADMM which allows time-varying penalty matrices and rigorously prove that it has a convergence rate of $O(1/t)$. Numerical and experimental results confirm the effectiveness and low computational complexity of the proposed approach.Comment: accepted to IEEE Transactions on Information Forensics and Securit