Polarized Fermi gases in asymmetric optical lattices

The zero-temperature phase diagrams of imbalanced two-species Fermi gases are investigated in asymmetric optical lattices with arbitrary potential depths, based on the exact spectrum instead of the Fermi-Hubbard model. We study the effect of lattice potentials and atomic densities to the fully paired Bardeen-Cooper-Schrieffer (BCS) state and particularly the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. It is found that the increasing lattice potential favors BCS at low densities because of the enhanced effective coupling; whereas FFLO is favored at intermediate densities when the system undergoes a dimensional crossover. Finally using local density approximation we study the evolution of phase profile in the presence of external harmonic traps by merely tuning the lattice potentials.Comment: 7 pages, 6 figures, published versio

On the asymptotic stability of wave equations coupled by velocities of anti-symmetric type

In this paper, we study the asymptotic stability of two wave equations coupled by velocities of anti-symmetric type via only one damping. We adopt the frequency domain method to prove that the system with smooth initial data is logarithmically stable, provided that the coupling domain and the damping domain intersect each other. Moreover, we show, by an example, that this geometric assumption of the intersection is necessary for 1-D case

A Necessary Condition for Power Flow Insolvability in Power Distribution Systems with Distributed Generators

This paper proposes a necessary condition for power flow insolvability in power distribution systems with distributed generators (DGs). We show that the proposed necessary condition indicates the impending singularity of the Jacobian matrix and the onset of voltage instability. We consider different operation modes of DG inverters, e.g., constant-power and constant-current operations, in the proposed method. A new index based on the presented necessary condition is developed to indicate the distance between the current operating point and the power flow solvability boundary. Compared to existing methods, the operating condition-dependent critical loading factor provided by the proposed condition is less conservative and is closer to the actual power flow solution space boundary. The proposed method only requires the present snapshots of voltage phasors to monitor the power flow insolvability and voltage stability. Hence, it is computationally efficient and suitable to be applied to a power distribution system with volatile DG outputs. The accuracy of the proposed necessary condition and the index is validated by simulations on a distribution test system with different DG penetration levels

Counterexample to Equivalent Nodal Analysis for Voltage Stability Assessment

Existing literature claims that the L-index for voltage instability detection is inaccurate and proposes an improved index quantifying voltage stability through system equivalencing. The proposed stability condition is claimed to be exact in determining voltage instability.We show the condition is incorrect through simple arguments accompanied by demonstration on a two-bus system counterexample.Comment: 3 pages, 3 figure

Partial Penalized Likelihood Ratio Test under Sparse Case

This work is concern with testing the low-dimensional parameters of interest with divergent dimensional data and variable selection for the rest under the sparse case. A consistent test via the partial penalized likelihood approach, called the partial penalized likelihood ratio test statistic is derived, and its asymptotic distributions under the null hypothesis and the local alternatives of order $n^{-1/2}$ are obtained under some regularity conditions. Meanwhile, the oracle property of the partial penalized likelihood estimator also holds. The proposed partial penalized likelihood ratio test statistic outperforms the full penalized likelihood ratio test statistic in term of size and power, and performs as well as the classical likelihood ratio test statistic. Moreover, the proposed method obtains the variable selection results as well as the p-values of testing. Numerical simulations and an analysis of Prostate Cancer data confirm our theoretical findings and demonstrate the promising performance of the proposed partial penalized likelihood in hypothesis testing and variable selection.Comment: 26 pages, 3 figures,6 table

A Note on ∗*-Clean Rings

A $*$-ring $R$ is called (strongly) $*$-clean if every element of $R$ is the sum of a projection and a unit (which commute with each other). In this note, some properties of $*$-clean rings are considered. In particular, a new class of $*$-clean rings which called strongly $\pi$-$*$-regular are introduced. It is shown that $R$ is strongly $\pi$-$*$-regular if and only if $R$ is $\pi$-regular and every idempotent of $R$ is a projection if and only if $R/J(R)$ is strongly regular with $J(R)$ nil, and every idempotent of $R/J(R)$ is lifted to a central projection of $R.$ In addition, the stable range conditions of $*$-clean rings are discussed, and equivalent conditions among $*$-rings related to $*$-cleanness are obtained.Comment: 16 page

Biosignal Analysis with Matching-Pursuit Based Adaptive Chirplet Transform

Chirping phenomena, in which the instantaneous frequencies of a signal change with time, are abundant in signals related to biological systems. Biosignals are non-stationary in nature and the time-frequency analysis is a viable tool to analyze them. It is well understood that Gaussian chirplet function is critical in describing chirp signals. Despite the theory of adaptive chirplet transform (ACT) has been established for more than two decades and is well accepted in the community of signal processing, application of ACT to bio-/biomedical signal analysis is still quite limited, probably because that the power of ACT, as an emerging tool for biosignal analysis, has not yet been fully appreciated by the researchers in the field of biomedical engineering. In this paper, we describe a novel ACT algorithm based on the "coarse-refinement" scheme. Namely, the initial estimate of a chirplet is implemented with the matching-pursuit (MP) algorithm and subsequently it is refined using the expectation-maximization (EM) algorithm, which we coin as MPEM algorithm. We emphasize the robustness enhancement of the algorithm in face of noise, which is important to biosignal analysis, as they are usually embedded in strong background noise. We then demonstrate the capability of our algorithm by applying it to the analysis of representative biosignals, including visual evoked potentials (bioelectrical signals), audible heart sounds and bat ultrasonic echolocation signals (bioacoustic signals), and human speech. The results show that the MPEM algorithm provides more compact representation of signals under investigation and clearer visualization of their time-frequency structures, indicating considerable promise of ACT in biosignal analysis. The MATLAB code repository is hosted on GitHub for free download (https://github.com/jiecui/mpact).Comment: 27 pages, 8 figure

Asymptotic stability of wave equations coupled by velocities

This paper is devoted to study the asymptotic stability of wave equations with constant coefficients coupled by velocities. By using Riesz basis approach, multiplier method and frequency domain approach respectively, we find the sufficient and necessary condition, that the coefficients satisfy, leading to the exponential stability of the system. In addition, we give the optimal decay rate in one dimensional case

Stochastic Configuration Networks Ensemble for Large-Scale Data Analytics

This paper presents a fast decorrelated neuro-ensemble with heterogeneous features for large-scale data analytics, where stochastic configuration networks (SCNs) are employed as base learner models and the well-known negative correlation learning (NCL) strategy is adopted to evaluate the output weights. By feeding a large number of samples into the SCN base models, we obtain a huge sized linear equation system which is difficult to be solved by means of computing a pseudo-inverse used in the least squares method. Based on the group of heterogeneous features, the block Jacobi and Gauss-Seidel methods are employed to iteratively evaluate the output weights, and a convergence analysis is given with a demonstration on the uniqueness of these iterative solutions. Experiments with comparisons on two large-scale datasets are carried out, and the system robustness with respect to the regularizing factor used in NCL is given. Results indicate that the proposed ensemble learning techniques have good potential for resolving large-scale data modelling problems.Comment: 20 pages, 7 figures, 9 tables; this paper has been submitted to Information Sciences for publication in December 2016, and accepted on July 3, 201

Framed Cord Algebra Invariant of Knots in S1×S2S^1 \times S^2

We generalize Ng's two-variable algebraic/combinatorial $0$-th framed knot contact homology for framed oriented knots in $S^3$ to knots in $S^1 \times S^2$, and prove that the resulting knot invariant is the same as the framed cord algebra of knots. Actually, our cord algebra has an extra variable, which potentially corresponds to the third variable in Ng's three-variable knot contact homology. Our main tool is Lin's generalization of the Markov theorem for braids in $S^3$ to braids in $S^1 \times S^2$. We conjecture that our framed cord algebras are always finitely generated for non-local knots.Comment: 37 pages, 14 figure