A novel method of measuring cosmological distances using broad-line regions of quasars

The absolute distance scale measurements in cosmology have always been an important mission. In particular, in recent years, the Hubble constant tension between the measurements from early and late universe has become a new crisis for cosmology, which calls for new, independent absolute cosmological distance measurements. Recently, a result of measuring the parallax distance to 3C 273 through spectroastrometry and reverberation mapping was reported. We comment on this novel method in this News & Views paper.Comment: 3 pages; News & Views, published online in Science Bulleti

Global existence of solutions of the Liquid Crystal flow for the Oseen-Frank model

In the first part of this paper, we establish global existence of solutions of the liquid crystal (gradient) flow for the well-known Oseen-Frank model. The liquid crystal flow is a prototype of equations from the Ericksen-Leslie system in the hydrodynamic theory and generalizes the heat flow for harmonic maps into the 2-sphere. The Ericksen-Leslie system is a system of the Navier-Stokes equations coupled with the liquid crystal flow. In the second part of this paper, we also prove global existence of solutions of the Ericksen-Leslie system for a general Oseen-Frank model in $\Bbb R^2$.Comment: 39 page

Universal properties of many-body localization transitions in quasiperiodic systems

Precise nature of MBL transitions in both random and quasiperiodic (QP) systems remains elusive so far. In particular, whether MBL transitions in QP and random systems belong to the same universality class or two distinct ones has not been decisively resolved. Here we investigate MBL transitions in one-dimensional ($d\!=\!1$) QP systems as well as in random systems by state-of-the-art real-space renormalization group (RG) calculation. Our real-space RG shows that MBL transitions in 1D QP systems are characterized by the critical exponent $\nu\!\approx\!2.4$, which respects the Harris-Luck bound ($\nu\!>\!1/d$) for QP systems. Note that $\nu\!\approx\! 2.4$ for QP systems also satisfies the Harris-CCFS bound ($\nu\!>\!2/d$) for random systems, which implies that MBL transitions in 1D QP systems are stable against weak quenched disorder since randomness is Harris irrelevant at the transition. We shall briefly discuss experimental means to measure $\nu$ of QP-induced MBL transitions.Comment: Accepted version by Phys. Rev. Let

Ambiguity set and learning via Bregman and Wasserstein

Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing appropriate probability distributions based on observed data is critical for approximating the true distribution. To improve the performance of machine learning models, there has recently been interest in designing objective functions based on Lp-Wasserstein distance rather than the classical Kullback-Leibler (KL) divergence. In this paper, we derive concentration and asymptotic results using Bregman divergence. We propose a novel asymmetric statistical divergence called Wasserstein-Bregman divergence as a generalization of L2-Wasserstein distance. We discuss how these results can be applied to the construction of ambiguity set in robust optimization

Convergence of the Generalized Alternating Projection Algorithm for Compressive Sensing

The convergence of the generalized alternating projection (GAP) algorithm is studied in this paper to solve the compressive sensing problem \yv = \Amat \xv + \epsilonv. By assuming that \Amat\Amat\ts is invertible, we prove that GAP converges linearly within a certain range of step-size when the sensing matrix \Amat satisfies restricted isometry property (RIP) condition of $\delta_{2K}$, where $K$ is the sparsity of \xv. The theoretical analysis is extended to the adaptively iterative thresholding (AIT) algorithms, for which the convergence rate is also derived based on $\delta_{2K}$ of the sensing matrix. We further prove that, under the same conditions, the convergence rate of GAP is faster than that of AIT. Extensive simulation results confirm the theoretical assertions.Comment: 12 pages, 11 figure

Molecular ordering of glycine on Cu(100): the p(2×42\times4) superstructure

Glycine molecules deposited on Cu(100) surface give rise to an anisotropic free-electron-like (FEL) electronic dispersion in its p(2$\times$4) superstructure, as reported in recent experiments [Phys. Rev. Lett. {\bf 99}, 216102 (2007); J. Am. Chem. Soc. {\bf 129}, 740 (2007)]. Using density functional theory and exhaustively calculating sixteen possible structures, we have determined the molecular arrangement that can give the experimentally observed FEL behavior. Eight configurations, among the sixteen, were not investigated before in the literature and one of them (denoted Str-3) is able to provide the FEL behavior in excellent agreement with the experiments. In addition, the particular configuration Str-3 satisfies other criteria of the observed p(2$\times$4) superstructure, e.g. chirality and cleavable orientation.Comment: 7 pages, 4 figures, 3 table

Lyapunov indices with two nearby trajectories in a curved spacetime

We compare three methods for computing invariant Lyapunov exponents (LEs) in general relativity. They involve the geodesic deviation vector technique (M1), the two-nearby-orbits method with projection operations and with coordinate time as an independent variable (M2), and the two-nearby-orbits method without projection operations and with proper time as an independent variable (M3). An analysis indicates that M1 and M3 do not need any projection operation. In general, the values of LEs from the three methods are almost the same. As an advantage, M3 is simpler to use than M2. In addition, we propose to construct the invariant fast Lyapunov indictor (FLI) with two-nearby-trajectories and give its algorithm in order to quickly distinguish chaos from order. Taking a static axisymmetric spacetime as a physical model, we apply the invariant FLIs to explore the global dynamics of phase space of the system where regions of chaos and order are clearlyidentified.Comment: 12 pages, 5 figure

Stability of non-constant equilibrium solutions for two-fluid non-isentropic Euler-Maxwell systems arising in plasmas

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy estimates, the global smooth solution with small amplitude is established near a non-constant equilibrium solution with asymptotic stability properties. This improves the results obtained in \cite{LWF16a} for models with temperature diffusion terms by using the pressure functions $p^\nu$ in place of the unknown variables densities $n^\nu$

Vibration-assisted coherent excitation energy transfer in a detuning system

The roles of the vibration motions played in the excitation energy transfer process are studied. It is found that a strong coherent transfer in the hybrid system emerges when the detuning between the donor and the acceptor equals the intrinsic frequency of the vibrational mode, and as a result the energy can be transferred into the acceptor much effectively. Three cases of the donor and the acceptor coupling with vibrational modes are investigated respectively. We find that the quantum interference between the two different transfer channels via the vibrational modes can affects the dynamics of the system significantly.Comment: 7 pages, 8 figure

Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite NN

Many key features of the higher-dimensional Sachdev-Ye-Kitaev (SYK) model at {\it finite} $N$ remain unknown. Here we study the SYK chain consisting of $N$ ($N$$\ge$$2$) fermions per site with random interactions and hoppings between neighboring sites. In the limit of vanishing SYK interactions, from both supersymmetric field theory analysis and numerical calculations we find that the random hopping model exhibits Anderson localization at finite $N$, irrespective of the parity of $N$. Moreover, the localization length scales linearly with N, implying no Anderson localization \textit{only} at $N\!=\!\infty$. For finite SYK interaction $J$ , from the exact diagonalization we show that there is a dynamic phase transition between many-body localization and thermal diffusion as $J$ exceeds a critical value $J_c$. In addition, we find that the critical value $J_c$ decreases with the increase of $N$, qualitatively consistent with the analytical result of $J_c/t \!\propto\! \frac{1}{N^{5/2}\log N}$ derived from the weakly interacting limit.Comment: Published versio