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Tao Yang

Publications and source records attributed to Tao Yang.

At least 397 records · Page 22Linked to original sources
arXiv2016

Thermodynamic limit and boundary energy of the SU(3) spin chain with non-diagonal boundary fields

We investigate the thermodynamic limit of the su(n)-invariant spin chain models with unparallel boundary fields. It is found that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy does vanish in the thermodynamic limit. This fact allows us to calculate the boundary energy of the system. Taking the su(2) (or the XXX) spin chain and the su(3) spin chain as concrete examples, we have studied the corresponding boundary energies of the models. The method used in this paper can be generalized to study the thermodynamic properties and boundary energy of other high rank models with non-diagonal boundary fields.

math-ph↗
arXiv2016

Experimental Test of Irreducible Four-Qubit Greenberger-Horne-Zeilinger Paradox

Bell's theorem shows a profound contradiction between local realism and quantum mechanics on the level of statistical predictions. It does not involve directly Einstein-Podolsky-Rosen (EPR) correlations. The paradox of Greenberger-Horne-Zeilinger (GHZ) disproves directly the concept of EPR elements of reality, based on the EPR correlations, in an all-versus-nothing way. A three-qubit experimental demonstration of the GHZ paradox was achieved nearly twenty years ago, and followed by demonstrations for more qubits. Still, the GHZ contradictions underlying the tests can be reduced to three-qubit one. We show an irreducible four-qubit GHZ paradox, and report its experimental demonstration. The reducibility loophole is closed. The bound of a three-setting per party Bell-GHZ inequality is violated by $7σ$. The fidelity of the GHZ state was around $81\%$, and an entanglement witness reveals a violation of the separability threshold by $19σ$.

quant-ph↗
arXiv2016

Bethe ansatz solution of the $τ_2$-model with arbitrary boundary fields

The quantum $τ_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an inhomogeneous T-Q relation, which is based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices. Moreover, the associated Bethe Ansatz equations are also obtained.

math-ph↗
arXiv2016

Dynamics of vortex quadrupoles in nonrotating trapped Bose-Einstein condensate

Dynamics of vortex clusters is essential for understanding diverse superfluid phenomena. In this paper, we examine the dynamics of vortex quadrupoles in a trapped two-dimensional (2D) Bose-Einstein condensate. We find that the movement of these vortex-clusters fall into three distinct regimes which are fully described by the radial positions of the vortices in a 2D isotropic harmonic trap, or by the major radius (minor radius) of the elliptical equipotential lines decided by the vortex positions in a 2D anisotropic harmonic trap. In the "recombination" and "exchange" regimes the quadrupole structure maintains, while the vortices annihilate each other permanently in the "annihilation" regime. We find that the mechanism of the charge flipping in the "exchange" regime and the disappearance of the quadrupole structure in the "annihilation" regime are both through an intermediate state where two vortex dipoles connected through a soliton ring. We give the parameter ranges for these three regimes in coordinate space for a specific initial configuration and phase diagram of the vortex positions with respect to the Thomas-Fermi radius of the condensate. We show that the results are also applicable to systems with quantum fluctuations for the short-time evolution.

cond-mat.quant-gas↗
arXiv2016

Large-scale Collaborative Imaging Genetics Studies of Risk Genetic Factors for Alzheimer's Disease Across Multiple Institutions

Genome-wide association studies (GWAS) offer new opportunities to identify genetic risk factors for Alzheimer's disease (AD). Recently, collaborative efforts across different institutions emerged that enhance the power of many existing techniques on individual institution data. However, a major barrier to collaborative studies of GWAS is that many institutions need to preserve individual data privacy. To address this challenge, we propose a novel distributed framework, termed Local Query Model (LQM) to detect risk SNPs for AD across multiple research institutions. To accelerate the learning process, we propose a Distributed Enhanced Dual Polytope Projection (D-EDPP) screening rule to identify irrelevant features and remove them from the optimization. To the best of our knowledge, this is the first successful run of the computationally intensive model selection procedure to learn a consistent model across different institutions without compromising their privacy while ranking the SNPs that may collectively affect AD. Empirical studies are conducted on 809 subjects with 5.9 million SNP features which are distributed across three individual institutions. D-EDPP achieved a 66-fold speed-up by effectively identifying irrelevant features.

cs.LG↗
arXiv2016

Dodging the cosmic curvature to probe the constancy of the speed of light

We develop a new model-independent method to probe the constancy of the speed of light $c$. In our method, the degeneracy between the cosmic curvature and the speed of light can be eliminated, which makes the test more natural and general. Combining the independent observations of Hubble parameter $H(z)$ and luminosity distance $d_L(z)$, we use the model-independent smoothing technique, Gaussian processes, to reconstruct them and then detect variation of the speed of light. We find no signal of deviation from the present value of the speed of light $c_0$. Moreover, to demonstrate the improvement in probing the constancy of the speed of light from future experiments, we produce a series of simulated data. The Dark Energy Survey will be able to detect $Δc /c_0 \sim 1\%$ at $\sim 1.5σ$ confidence level and $Δc /c_0 \sim 2\%$ at $\sim 3σ$ confidence level. If the errors are reduced to one-tenth of the expected DES ones, it can detect a $Δc /c_0 \sim 0.1\%$ variation at $\sim 2σ$ confidence level.

astro-ph.CO↗
arXiv2016

Heisenberg double as braided commutative Yetter-Drinfel'd module algebra over Drinfel'd double in multiplier Hopf algebra case

Based on a pairing of two regular multiplier Hopf algebras $A$ and $B$, Heisenberg double $\mathscr{H}$ is the smash product $A \# B$ with respect to the left regular action of $B$ on $A$. Let $\mathscr{D}=A\bowtie B$ be the Drinfel'd double, then Heisenberg double $\mathscr{H}$ is a Yetter-Drinfel'd $\mathscr{D}$-module algebra, and it is also braided commutative by the braiding of Yetter-Drinfel'd module, which generalizes the results in [10] to some infinite dimensional cases.

math.RA↗
arXiv2016

Another construction of the braided $T$-category

This paper introduces group-cograded monoidal Hom-Hopf algebras, and shows that this kind of group-cograded monoidal Hom-Hopf algebras are monoidal Hom-Hopf algebras in the Turaev category $\mathcal{J}_{k}$ introduced by Canepeel and De Lombaerde. Then we define the $p$-Yetter-Drinfeld category over a group-cograded monoidal Hom-Hopf algebra, and construct a new kind of braided $T$-categories.

math.RA↗
arXiv2016

Representation Crossed Category of Group-cograded Multiplier Hopf Algebras

Let $A=\bigoplus_{p\in G}A_{p}$ be a multiplier Hopf $T$-coalgebra over a group $G$, in this paper we give the definition of the crossed left $A$-$G$-modules and show that the category of crossed left $A$-$G$-modules is a monoidal category. Finally we show that a family of multipliers $R = \{R_{p, q} \in M(A_{p}\otimes A_{q})\}_{p, q\in G}$ is a quasitriangular structure of a multiplier $T$-coalgebra $A$ if and only if the crossed left $A$-$G$-module category over $A$ is a braided monoidal category with the braiding $c$ defined by $R$, generalizing the main results in \cite{ZCL11} to the more general framework of multiplier Hopf algebras.

math.RA↗
arXiv2016

Experimental quantum coding against photon loss error

A significant obstacle for practical quantum computation is the loss of physical qubits in quantum computers, a decoherence mechanism most notably in optical systems. Here we experimentally demonstrate, both in the quantum circuit model and in the one-way quantum computer model, the smallest non-trivial quantum codes to tackle this problem. In the experiment, we encode single-qubit input states into highly-entangled multiparticle codewords, and we test their ability to protect encoded quantum information from detected one-qubit loss error. Our results prove the in-principle feasibility of overcoming the qubit loss error by quantum codes.

quant-ph↗
arXiv2016

QoE-Aware Proactive Caching of Scalable Videos Over Small Cell Networks

The explosion of mobile video traffic imposes tremendous challenges on present cellular networks. To alleviate the pressure on backhaul links and to enhance the quality of experience (QoE) of video streaming service, small cell base stations (SBS) with caching ability are introduced to assist the content delivery. In this paper, we present the first study on the optimal caching strategy of scalable video coding (SVC) streaming in small cell networks with the consideration of channel diversity and video scalability. We formulate an integer programming problem to maximize the average SVC QoE under the constraint of cache size at each SBS. By establishing connections between QoE and caching state of each video, we simplify the proactive caching of SVC as a multiple-choice knapsack problem (MCKP), and propose a low-complexity algorithm using dynamic programming. Our proactive caching strategy reveals the structural properties of cache allocation to each video based on their popularity profiles. Simulation results manifest that the SBSs with caching ability can greatly improve the average QoE of SVC streaming service, and that our proposed caching strategy acquires significant performance gain compared with other conventional caching policies.

cs.NI↗
arXiv2016

Cobraided Smash Product Hom-Hopf Algebras

Let $(A,\a)$ and $(B,\b)$ be two Hom-Hopf algebras. In this paper, we construct a class of new Hom-Hopf algebras: $R$-smash product $(A\natural_R B,\aø\b)$. Moreover, necessary and sufficient conditions for $(A\natural_R B,\aø\b)$ to be a cobraided Hom-Hopf algebra are given.

math.RA↗
arXiv2016

Modeling QoE of Video Streaming in Wireless Networks with Large-Scale Measurement of User Behavior

Unraveling quality of experience (QoE) of video streaming is very challenging in bandwidth shared wireless networks. It is unclear how QoE metrics such as starvation probability and buffering time interact with dynamics of streaming traffic load. In this paper, we collect view records from one of the largest streaming providers in China over two weeks and perform an in-depth measurement study on flow arrival and viewing time that shed light on the real traffic pattern. Our most important observation is that the viewing time of streaming users fits a hyper-exponential distribution quite well. This implies that all the views can be categorized into two classes, short and long views with separated time scales. We then map the measured traffic pattern to bandwidth shared cellular networks and propose an analytical framework to compute the closed-form starvation probability on the basis of ordinary differential equations (ODEs). Our framework can be naturally extended to investigate practical issues including the progressive downloading and the finite video duration. Extensive trace-driven simulations validate the accuracy of our models. Our study reveals that the starvation metrics of the short and long views possess different sensitivities to the scheduling priority at base station. Hence, a better QoE tradeoff between the short and long views has a potential to be leveraged by offering them different scheduling weights. The flow differentiation involves tremendous technical and non-technical challenges because video content is owned by content providers but not the network operators and the viewing time of each session is unknown beforehand. To overcome these difficulties, we propose an online Bayesian approach to infer the viewing time of each incoming flow with the "least" information from content providers.

cs.NI↗
arXiv2016

Null test of the cosmic curvature using $H(z)$ and supernovae data

We introduce a model-independent approach to the null test of the cosmic curvature which is geometrically related to the Hubble parameter $H(z)$ and luminosity distance $d_L(z)$. Combining the independent observations of $H(z)$ and $d_L(z)$, we use the model-independent smoothing technique, Gaussian processes, to reconstruct them and determine the cosmic curvature $Ω_K^{(0)}$ in the null test relation. The null test is totally geometrical and without assuming any cosmological model. We show that the cosmic curvature $Ω_K^{(0)}=0$ is consistent with current observational data sets, falling within the $1σ$ limit. To demonstrate the effect on the precision of the null test, we produce a series of simulated data of the models with different $Ω_K^{(0)}$. Future observations in better quality can provide a greater improvement to constrain or refute the flat universe with $Ω_K^{(0)}=0$.

astro-ph.CO↗
arXiv2015

Explicit Realization of Hopf Cyclic Cohomology Classes of Bicrossed Product Hopf Algebras

We construct a Hopf action, with an invariant trace, of a bicrossed product Hopf algebra $\cH=\big( \cU(\Fg_1) \acr \cR(G_2) \big)^{\cop}$ constructed from a matched pair of Lie groups $G_1$ and $G_2$, on a convolution algebra $\cA=C_c^{\ify}(G_1)\rtimes G_2^δ$. We give an explicit way to construct Hopf cyclic cohomology classes of our Hopf algebra $\cH$ and then realize these classes in terms of explicit representative cocycles in the cyclic cohomology of the convolution algebra $\cA$.

math.DG↗
arXiv2015

Drinfel'd twist of multiplier Hopf algebras

This paper generalizes the Drinfel'd twist to the multiplier Hopf algebra case. For a multiplier Hopf algebra $A$ with a twist $J$, we construct a new multiplier Hopf algebra $A^{J}$. Furthermore, if $A$ is quasitriangular, then $A^{J}$ is also. Finally, for a counimodular algebraic quantum group $A$, $A^{J}$ is an algebraic quantum group.

math.RA↗
arXiv2015

Network Synchronization with Nonlinear Dynamics and Switching Interactions

This paper considers the synchronization problem for networks of coupled nonlinear dynamical systems under switching communication topologies. Two types of nonlinear agent dynamics are considered. The first one is non-expansive dynamics (stable dynamics with a convex Lyapunov function $φ(\cdot)$) and the second one is dynamics that satisfies a global Lipschitz condition. For the non-expansive case, we show that various forms of joint connectivity for communication graphs are sufficient for networks to achieve global asymptotic $φ$-synchronization. We also show that $φ$-synchronization leads to state synchronization provided that certain additional conditions are satisfied. For the globally Lipschitz case, unlike the non-expansive case, joint connectivity alone is not sufficient for achieving synchronization. A sufficient condition for reaching global exponential synchronization is established in terms of the relationship between the global Lipschitz constant and the network parameters. We also extend the results to leader-follower networks.

eess.SY↗