The positive partial transpose conjecture for n=3

We present the PPT square conjecture introduced by M. Christandl. We prove the conjecture in the case $n=3$ as a consequence of the fact that two-qutrit PPT states have Schmidt at most two. Our result in Lemma 3 is independent from the proof found M\"uller-Hermes. M\"uller-Hermes announced that this conjecture is true for the states on $\mathbb{C}_3\otimes\mathbb{C}_3$ \cite{hermes} recently. The PPT square conjecture in the case $n\ge4$ is still open

Standardization, Distance, Host Galaxy Extinction of Type Ia Supernova and Hubble Diagram from the Flux Ratio Method

In this paper we generalize the flux ratio method Bailey et al. (2009) to the case of two luminosity indicators and search the optimal luminosity-flux ratio relations on a set of spectra whose phases are around not only the date of bright light but also other time. With these relations, a new method is proposed to constrain the host galaxy extinction of SN Ia and its distance. It is first applied to the low redshift supernovas and then to the high redshift ones. The results of the low redshift supernovas indicate that the flux ratio method can indeed give well constraint on the host galaxy extinction parameter E(B-V), but weaker constraints on R_{V}. The high redshift supernova spectra are processed by the same method as the low redshift ones besides some differences due to their high redshift. Among 16 high redshift supernovas, 15 are fitted very well except 03D1gt. Based on these distances, Hubble diagram is drew and the contents of the Universe are analyzed. It supports an acceleration behavior in the late Universe. Therefore, the flux ratio method can give constraints on the host galaxy extinction and supernova distance independently. We believe, through further studies, it may provide a precise tool to probe the acceleration of the Universe than before.Comment: 33 pages, 9 figures and 6 table

Doubly Stochastic Primal-Dual Coordinate Method for Bilinear Saddle-Point Problem

We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates of the primal and dual solutions to update. The linear convergence of our method could be established in terms of 1) the distance from the current iterate to the optimal solution and 2) the primal-dual objective gap. We show that the proposed method has a lower overall complexity than existing coordinate methods when either the data matrix has a factorized structure or the proximal mapping on each block is computationally expensive, e.g., involving an eigenvalue decomposition. The efficiency of the proposed method is confirmed by empirical studies on several real applications, such as the multi-task large margin nearest neighbor problem

Energy-efficient Analytics for Geographically Distributed Big Data

Big data analytics on geographically distributed datasets (across data centers or clusters) has been attracting increasing interests from both academia and industry, but also significantly complicates the system and algorithm designs. In this article, we systematically investigate the geo-distributed big-data analytics framework by analyzing the fine-grained paradigm and the key design principles. We present a dynamic global manager selection algorithm (GMSA) to minimize energy consumption cost by fully exploiting the system diversities in geography and variation over time. The algorithm makes real-time decisions based on the measurable system parameters through stochastic optimization methods, while achieving the performance balances between energy cost and latency. Extensive trace-driven simulations verify the effectiveness and efficiency of the proposed algorithm. We also highlight several potential research directions that remain open and require future elaborations in analyzing geo-distributed big data

Chemical Bondings Induced Rich Electronic Properties of Oxygen Absorbed Few-layer Graphenes

Electronic properties of graphene oxides enriched by the strong chemical bondings are investigated using first-principle calculations. They are very sensitive to the changes in the number of graphene layer, stacking configuration, and distribution of oxygen. The feature-rich electronic structures exhibit the destruction or distortion of Dirac cone, opening of band gap, anisotropic energy dispersions, O- and (C,O)-dominated energy dispersions, and extra critical points. All the few-layer graphene oxides are semi-metals except for the semiconducting monolayer ones. For the former, the distorted Dirac-cone structures and the O-dominated energy bands near the Fermi level are revealed simultaneously. The orbital-projected density of states (DOS) have many special structures mainly coming from a composite energy band, the parabolic and partially flat ones. The DOS and spatial charge distributions clearly indicate the critical bondings in O-O, C-O and C-C bonds, being responsible for the diversified properties

Secrecy Energy Efficiency Maximization for UAV-Enabled Mobile Relaying

This paper investigates the secrecy energy efficiency (SEE) maximization problem for unmanned aerial vehicle enabled mobile relaying system, where a high-mobility UAV is exploited to assist delivering the confidential information from a ground source to a legitimate ground destination with the direct link blocked, in the presence of a potential eavesdropper. We aim to maximize SEE of the UAV by jointly optimizing the communication scheduling, power allocation, and UAV trajectory over a finite time horizon. The formulated problem is a mixed-integer non-convex optimization problem that is challenging to be solved optimally. To make the problem tractable, we decompose the problem into three subproblems, and propose an efficient iterative algorithm that alternately optimizes the subproblems. In addition, two special cases are considered as benchmarks in this paper. Simulation results show that the proposed design significantly improves the SEE of the UAV, as compared to the benchmarksComment: 22pages 7figures for possible journal submissio

L∞L^\infty-variational problems associated to measurable Finsler structures

We study $L^\infty$-variational problems associated to measurable Finsler structures in Euclidean spaces. We obtain existence and uniqueness results for the absolute minimizers.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1305.6130 by other author

Singlet States Preparation for Three Λ\Lambda-type Atoms with Rydberg Blockade Mechanism

A proposal for the generation of singlet states of three $\Lambda$-type Rydberg atoms is presented. The singlet state is prepared through the combination of a Rydberg state and an EPR pair, and the scheme relies on the Rydberg blockade effect which prevents the simultaneous excitation of the two atoms to a Rydberg state. In addition, some frequency detuning between lasers and atomic transitions is set to eliminate the degenerate of the two ground states. And finally, a series of numerical simulations are made to show the feasibility of the scheme.Comment: 8 pages,5 figure

Fluorination-Enriched Electronic and Magnetic Properties in Graphene Nanoribbons

The feature-rich electronic and magnetic properties of fluorine-doped graphene nanoribbons are investigated by the first-principles calculations. They arise from the cooperative or competitive relations among the significant chemical bonds, finite-size quantum confinement and edge structure. There exist C-C, C-F, and F-F bonds with the multi-orbital hybridizations. Fluorine adatoms can create the p-type metals or the concentration- and distribution-dependent semiconductors, depending on whether the $\pi$ bonding is seriously suppressed by the top-site chemical bonding. Furthermore, five kinds of spin-dependent electronic and magnetic properties cover the non-magnetic and ferromagnetic metals, the non-magnetic semiconductors, and the anti-ferromagnetic semiconductors with/without the spin splitting. The diverse essential properties are clearly revealed in the spatial charge distribution, the spin density, and the orbital-projected density of states

Master equation approach to transient quantum transport incorporating with initial correlations

In this paper, the exact transient quantum transport of non-interacting nanostructures is investigated in the presence of initial system-lead correlations and initial lead-lead correlations for a device system coupled to general electronic leads. The exact master equation incorporating with initial correlations is derived through the extended quantum Langevin equation. The effects of the initial correlations are manifested through the time-dependent fluctuations contained explicitly in the exact master equation. The transient transport current incorporating with initial correlations is obtained from the exact master equation. The resulting transient transport current can be expressed in terms of the single-particle propagating and correlation Green functions of the device system. We show that the initial correlations can affect quantum transport not only in the transient regime, but also in the steady-state limit when system-lead couplings are strong enough so that electron localized bound states occur in the device system.Comment: 13pages, 4figure