Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions

A pair of dual frames with almost exponentially localized elements (needlets) are constructed on \RR_+^d based on Laguerre functions. It is shown that the Triebel-Lizorkin and Besov spaces induced by Laguerre expansions can be characterized in terms of respective sequence spaces that involve the needlet coefficients.Comment: 42 page

Effects of Ru Substitution on Dimensionality and Electron Correlations in Ba(Fe_{1-x}Ru_x)_2As_2

We report a systematic angle-resolved photoemission spectroscopy study on Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ for a wide range of Ru concentrations (0.15 $\leq$ \emph{x} $\leq$ 0.74). We observed a crossover from two-dimension to three-dimension for some of the hole-like Fermi surfaces with Ru substitution and a large reduction in the mass renormalization close to optimal doping. These results suggest that isovalent Ru substitution has remarkable effects on the low-energy electron excitations, which are important for the evolution of superconductivity and antiferromagnetism in this system.Comment: 4 pages, 4 figure

A Herschel Study of 24 micron-Selected AGNs and Their Host Galaxies

We present a sample of 290 24-micron-selected active galactic nuclei (AGNs) mostly at z ~ 0.3 -- 2.5, within 5.2 square degrees distributed as 25' X 25' fields around each of 30 galaxy clusters in the Local Cluster Substructure Survey (LoCuSS). The sample is nearly complete to 1 mJy at 24 microns, and has a rich multi-wavelength set of ancillary data; 162 are detected by Herschel. We use spectral templates for AGNs, stellar populations, and infrared emission by star forming galaxies to decompose the spectral energy distributions (SEDs) of these AGNs and their host galaxies, and estimate their star formation rates (SFRs), AGN luminosities, and host galaxy stellar masses. The set of templates is relatively simple: a standard Type-1 quasar template; another for the photospheric output of the stellar population; and a far infrared star-forming template. For the Type-2 AGN SEDs, we substitute templates including internal obscuration, and some Type-1 objects require a warm component (T > 50 K). The individually Herschel- detected Type-1 AGNs and a subset of 17 Type-2 ones typically have luminosities > 10^{45} ergs/s, and supermassive black holes of ~ 3 X 10^8 Msun emitting at ~ 10% of the Eddington rate. We find them in about twice the numbers of AGN identified in SDSS data in the same fields, i.e., they represent typical high luminosity AGN, not an infrared-selected minority. These AGNs and their host galaxies are studied further in an accompanying paper

A Unifying Perspective: Solitary Traveling Waves As Discrete Breathers And Energy Criteria For Their Stability

In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a co-traveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and based on this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) $H$ of the model on the wave velocity $c$ changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian $H"(c_0)$ evaluated at the critical velocity $c_0$. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers

Learning-aided Stochastic Network Optimization with Imperfect State Prediction

We investigate the problem of stochastic network optimization in the presence of imperfect state prediction and non-stationarity. Based on a novel distribution-accuracy curve prediction model, we develop the predictive learning-aided control (PLC) algorithm, which jointly utilizes historic and predicted network state information for decision making. PLC is an online algorithm that requires zero a-prior system statistical information, and consists of three key components, namely sequential distribution estimation and change detection, dual learning, and online queue-based control. Specifically, we show that PLC simultaneously achieves good long-term performance, short-term queue size reduction, accurate change detection, and fast algorithm convergence. In particular, for stationary networks, PLC achieves a near-optimal $[O(\epsilon)$, $O(\log(1/\epsilon)^2)]$ utility-delay tradeoff. For non-stationary networks, \plc{} obtains an $[O(\epsilon), O(\log^2(1/\epsilon)$ $+ \min(\epsilon^{c/2-1}, e_w/\epsilon))]$ utility-backlog tradeoff for distributions that last $\Theta(\frac{\max(\epsilon^{-c}, e_w^{-2})}{\epsilon^{1+a}})$ time, where $e_w$ is the prediction accuracy and $a=\Theta(1)>0$ is a constant (the Backpressue algorithm \cite{neelynowbook} requires an $O(\epsilon^{-2})$ length for the same utility performance with a larger backlog). Moreover, PLC detects distribution change $O(w)$ slots faster with high probability ($w$ is the prediction size) and achieves an $O(\min(\epsilon^{-1+c/2}, e_w/\epsilon)+\log^2(1/\epsilon))$ convergence time. Our results demonstrate that state prediction (even imperfect) can help (i) achieve faster detection and convergence, and (ii) obtain better utility-delay tradeoffs