Local polynomial method for ensemble forecast of time series

International audienceWe present a nonparametric approach based on local polynomial regression for ensemble forecast of time series. The state space is first reconstructed by embedding the univariate time series of the response variable in a space of dimension (D) with a delay time (?). To obtain a forecast from a given time point t, three steps are involved: (i) the current state of the system is mapped on to the state space, known as the feature vector, (ii) a small number (K=?*n, ?=fraction (0,1] of the data, n=data length) of neighbors (and their future evolution) to the feature vector are identified in the state space, and (iii) a polynomial of order p is fitted to the identified neighbors, which is then used for prediction. A suite of parameter combinations (D, ?, ?, p) is selected based on an objective criterion, called the Generalized Cross Validation (GCV). All of the selected parameter combinations are then used to issue a T-step iterated forecast starting from the current time t, thus generating an ensemble forecast which can be used to obtain the forecast probability density function (PDF). The ensemble approach improves upon the traditional method of providing a single mean forecast by providing the forecast uncertainty. Further, for short noisy data it can provide better forecasts. We demonstrate the utility of this approach on two synthetic (Henon and Lorenz attractors) and two real data sets (Great Salt Lake bi-weekly volume and NINO3 index). This framework can also be used to forecast a vector of response variables based on a vector of predictors

Local polynomial method for ensemble forecast of time series

We present a nonparametric approach based on local polynomial regression for ensemble forecast of time series. The state space is first reconstructed by embedding the univariate time series of the response variable in a space of dimension (<i>D</i>) with a delay time (&tau;). To obtain a forecast from a given time point <i>t</i>, three steps are involved: (i) the current state of the system is mapped on to the state space, known as the feature vector, (ii) a small number (<i>K</i>=&alpha;*<i>n</i>, &alpha;=fraction (0,1] of the data, <i>n</i>=data length) of neighbors (and their future evolution) to the feature vector are identified in the state space, and (iii) a polynomial of order <i>p</i> is fitted to the identified neighbors, which is then used for prediction. A suite of parameter combinations (<i>D</i>, &tau;, &alpha;, <i>p</i>) is selected based on an objective criterion, called the Generalized Cross Validation (GCV). All of the selected parameter combinations are then used to issue a T-step iterated forecast starting from the current time <i>t</i>, thus generating an ensemble forecast which can be used to obtain the forecast probability density function (PDF). The ensemble approach improves upon the traditional method of providing a single mean forecast by providing the forecast uncertainty. Further, for short noisy data it can provide better forecasts. We demonstrate the utility of this approach on two synthetic (Henon and Lorenz attractors) and two real data sets (Great Salt Lake bi-weekly volume and NINO3 index). This framework can also be used to forecast a vector of response variables based on a vector of predictors

Efficacy of single and double SiNx interlayers on defect reduction in GaN overlayers grown by organometallic vapor-phase epitaxy

We report on the growth of and evolution of defects in GaN epilayers having single- and double-layer SiNx nanoporous insertion layers. The SiNx was formed in situ in the growth chamber of an organometallic vapor-phase epitaxy system by simultaneous flow of diluted silane and ammonia. The GaN epilayers and SiNx interlayers were grown on 6H-SiC substrates using three different nucleation layers, namely, low-temperature GaN, high-temperature GaN, and high-temperature AlN nucleation layers. X-ray-diffraction rocking curves and cross-sectional and plan-view transmission electron microscope analyses indicated that a nanoporous SiNx layer can reduce the dislocations density in the GaN overgrown layer to ∼3×108cm−2 range; below this level the defect blocking effect of SiNx would saturate. Therefore the insertion of a second SiNx layer becomes much less effective in reducing dislocations, although it continues to reduce the point defects, as suggested by time-resolved photoluminescence measurements. The insertion of SiNx interlayers was found to improve significantly the mechanical strength of the GaN epilayers resulting in a much lower crack line density

Equilibration and Dynamic Phase Transitions of a Driven Vortex Lattice

We report on the observation of two types of current driven transitions in metastable vortex lattices. The metastable states, which are missed in usual slow transport measurements, are detected with a fast transport technique in the vortex lattice of undoped 2H-NbSe$_2$. The transitions are seen by following the evolution of these states when driven by a current. At low currents we observe an equilibration transition from a metastable to a stable state, followed by a dynamic crystallization transition at high currents.Comment: 5 pages, 4 figure

Anomalous Exponent of the Spin Correlation Function of a Quantum Hall Edge

The charge and spin correlation functions of partially spin-polarized edge electrons of a quantum Hall bar are studied using effective Hamiltonian and bosonization techniques. In the presence of the Coulomb interaction between the edges with opposite chirality we find a different crossover behavior in spin and charge correlation functions. The crossover of the spin correlation function in the Coulomb dominated regime is characterized by an anomalous exponent, which originates from the finite value of the effective interaction for the spin degree of freedom in the long wavelength limit. The anomalous exponent may be determined by measuring nuclear spin relaxation rates in a narrow quantum Hall bar or in a quantum wire in strong magnetic fields.Comment: 4 pages, Revtex file, no figures. To appear in Physical Revews B, Rapid communication

Dynamic transition in driven vortices across the peak effect in superconductors

We study the zero-temperature dynamic transition from the disordered flow to an ordered flow state in driven vortices in type-II superconductors. The transition current $I_{p}$ is marked by a sharp kink in the $V(I)$ characteristic with a concomitant large increase in the defect concentration. On increasing magnetic field $B$, the $I_{p}(B)$ follows the behaviour of the critical current $I_{c}(B)$. Specifically, in the peak effect regime $I_{p}(B)$ increases rapidly along with $I_{c}$. We also discuss the effect of varying disorder strength on $I_{p}$.Comment: 4 pages, 4 figure

Isotropic and anisotropic surface wave cloaking techniques

In this paper we compare two different approaches for surface waves cloaking. The first technique is a unique application of Fermat's principle and requires isotropic material properties, but owing to its derivation is limited in its applicability. The second technique utilises a geometrical optics approximation for dealing with rays bound to a two dimensional surface and requires anisotropic material properties, though it can be used to cloak any smooth surface. We analytically derive the surface wave scattering behaviour for both cloak techniques when applied to a rotationally symmetric surface deformation. Furthermore, we simulate both using a commercially available full-wave electromagnetic solver and demonstrate a good level of agreement with their analytically derived solutions. Our analytical solutions and simulations provide a complete and concise overview of two different surface wave cloaking techniques

Spin Degeneracy and Conductance Fluctuations in Open Quantum Dots

The dependence of mesoscopic conductance fluctuations on parallel magnetic field is used as a probe of spin degeneracy in open GaAs quantum dots. The variance of fluctuations at high parallel field is reduced from the low-field variance (with broken time-reversal symmetry) by factors ranging from roughly two in a 1 square-micron dot at low temperature, to four or greater in 8 square-micron dots. The factor of two is expected for simple Zeeman splitting of spin degenerate channels. A possible explanation for the unexpected larger factors in terms of field-dependent spin orbit scattering is proposed.Comment: Includes new reference to related theoretical work, cond-mat/0010064. Other minor changes. Related papers at http://marcuslab.harvard.ed

Exchange Instabilities in Semiconductor Double Quantum Well Systems

We consider various exchange-driven electronic instabilities in semiconductor double-layer systems in the absence of any external magnetic field. We establish that there is no exchange-driven bilayer to monolayer charge transfer instability in the double-layer systems. We show that, within the unrestricted Hartree-Fock approximation, the low density stable phase (even in the absence of any interlayer tunneling) is a quantum ``pseudospin rotated'' spontaneous interlayer phase coherent spin-polarized symmetric state rather than the classical Ising-like charge-transfer phase. The U(1) symmetry of the double quantum well system is broken spontaneously at this low density quantum phase transition, and the layer density develops quantum fluctuations even in the absence of any interlayer tunneling. The phase diagram for the double quantum well system is calculated in the carrier density--layer separation space, and the possibility of experimentally observing various quantum phases is discussed. The situation in the presence of an external electric field is investigated in some detail using the spin-polarized-local-density-approximation-based self-consistent technique and good agreement with existing experimental results is obtained.Comment: 24 pages, figures included. Also available at http://www-cmg.physics.umd.edu/~lzheng/preprint/ct.uu/ . Revised final version to appear in PR