Improving the condition number of estimated covariance matrices

High dimensional error covariance matrices and their inverses are used to weight the contribution of observation and background information in data assimilation procedures. As observation error covariance matrices are often obtained by sampling methods, estimates are often degenerate or ill-conditioned, making it impossible to invert an observation error covariance matrix without the use of techniques to reduce its condition number. In this paper we present new theory for two existing methods that can be used to ‘recondition’ any covariance matrix: ridge regression, and the minimum eigenvalue method. We compare these methods with multiplicative variance inflation, which cannot alter the condition number of a matrix, but is often used to account for neglected correlation information. We investigate the impact of reconditioning on variances and correlations of a general covariance matrix in both a theoretical and practical setting. Improved theoretical understanding provides guidance to users regarding method selection, and choice of target condition number. The new theory shows that, for the same target condition number, both methods increase variances compared to the original matrix, with larger increases for ridge regression than the minimum eigenvalue method. We prove that the ridge regression method strictly decreases the absolute value of off-diagonal correlations. Theoretical comparison of the impact of reconditioning and multiplicative variance inflation on the data assimilation objective function shows that variance inflation alters information across all scales uniformly, whereas reconditioning has a larger effect on scales corresponding to smaller eigenvalues. We then consider two examples: a general correlation function, and an observation error covariance matrix arising from interchannel correlations. The minimum eigenvalue method results in smaller overall changes to the correlation matrix than ridge regression, but can increase off-diagonal correlations. Data assimilation experiments reveal that reconditioning corrects spurious noise in the analysis but underestimates the true signal compared to multiplicative variance inflation

Hadronization of massive quark matter

We present a fast hadronization model for the constituent quark plasma (CQP) produced in relativistic heavy ion collisions at SPS. The model is based on rate equations and on an equation of state inspired by the string phenomenology. This equation of state has a confining character. We display the time evolution of the relevant physical quantities during the hadronization process and the final hadron multiplicities. The results indicate that the hadronization of CQP is fast.Comment: 12 pages, Latex, 2 EPS figures, contribution to the Proceedings of the 4th International Conference on Strangeness in Quark Matter (SQM'98), Padova, Italy, 20-24 July 199

Estimation of properties of low-lying excited states of Hubbard models : a multi-configurational symmetrized projector quantum Monte Carlo approach

We present in detail the recently developed multi-configurational symmetrized projector quantum Monte Carlo (MSPQMC) method for excited states of the Hubbard model. We describe the implementation of the Monte Carlo method for a multi-configurational trial wavefunction. We give a detailed discussion of issues related to the symmetry of the projection procedure which validates our Monte Carlo procedure for excited states and leads naturally to the idea of symmetrized sampling for correlation functions, developed earlier in the context of ground state simulations. It also leads to three possible averaging schemes. We have analyzed the errors incurred in these various averaging procedures and discuss and detail the preferred averaging procedure for correlations that do not have the full symmetry of the Hamiltonian. We study the energies and correlation functions of the low-lying excited states of the half-filled Hubbard model in 1-D. We have used this technique to study the pair-binding energies of two holes in $4n$ and $4n+2$ systems, which compare well the Bethe ansatz data of Fye, Martins and Scalettar. We have also studied small clusters amenable to exact diagonalization studies in 2-D and have reproduced their energies and correlation functions by the MSPQMC method. We identify two ways in which a multiconfigurational trial wavefunction can lead to a negative sign problem. We observe that this effect is not severe in 1-D and tends to vanish with increasing system size. We also note that this does not enhance the severity of the sign problem in two dimensions.Comment: 29 pages, 2 figures available on request, submitted to Phys. Rev.

The climate sensitivity of carbon, timber, and species richness covaries with forest age in boreal–temperate North America

Climate change threatens the provisioning of forest ecosystem services and biodiversity (ESB). The climate sensitivity of ESB may vary with forest development from young to old-growth conditions as structure and composition shift over time and space. This study addresses knowledge gaps hindering implementation of adaptive forest management strategies to sustain ESB. We focused on a number of ESB indicators to (a) analyze associations among carbon storage, timber growth rate, and species richness along a forest development gradient; (b) test the sensitivity of these associations to climatic changes; and (c) identify hotspots of climate sensitivity across the boreal–temperate forests of eastern North America. From pre-existing databases and literature, we compiled a unique dataset of 18,507 forest plots. We used a full Bayesian framework to quantify responses of nine ESB indicators. The Bayesian models were used to assess the sensitivity of these indicators and their associations to projected increases in temperature and precipitation. We found the strongest association among the investigated ESB indicators in old forests (\u3e170 years). These forests simultaneously support high levels of carbon storage, timber growth, and species richness. Older forests also exhibit low climate sensitivity of associations among ESB indicators as compared to younger forests. While regions with a currently low combined ESB performance benefitted from climate change, regions with a high ESB performance were particularly vulnerable to climate change. In particular, climate sensitivity was highest east and southeast of the Great Lakes, signaling potential priority areas for adaptive management. Our findings suggest that strategies aimed at enhancing the representation of older forest conditions at landscape scales will help sustain ESB in a changing world

Phase Transitions Driven by Vortices in 2D Superfluids and Superconductors: From Kosterlitz-Thouless to 1st Order

The Landau-Ginzburg-Wilson hamiltonian is studied for different values of the parameter $\lambda$ which multiplies the quartic term (it turns out that this is equivalent to consider different values of the coherence length $\xi$ in units of the lattice spacing $a$). It is observed that amplitude fluctuations can change dramatically the nature of the phase transition: for small values of $\lambda$ ($\xi/a > 0.7$), instead of the smooth Kosterlitz-Thouless transition there is a {\em first order} transition with a discontinuous jump in the vortex density $v$ and a larger non-universal drop in the helicity modulus. In particular, for $\lambda$ sufficiently small ($\xi/a \cong 1$), the density of bound pairs of vortex-antivortex below $T_c$ is so low that, $v$ drops to zero almost for all temperature $T<Tc$.Comment: 8 pages, 5 .eps figure

First Order Transition in the Ginzburg-Landau Model

The d-dimensional complex Ginzburg-Landau (GL) model is solved according to a variational method by separating phase and amplitude. The GL transition becomes first order for high superfluid density because of effects of phase fluctuations. We discuss its origin with various arguments showing that, in particular for d = 3, the validity of our approach lies precisely in the first order domain.Comment: 4 pages including 2 figure

Attosecond control of electrons emitted from a nanoscale metal tip

Attosecond science is based on steering of electrons with the electric field of well-controlled femtosecond laser pulses. It has led to, for example, the generation of XUV light pulses with a duration in the sub-100-attosecond regime, to the measurement of intra-molecular dynamics by diffraction of an electron taken from the molecule under scrutiny, and to novel ultrafast electron holography. All these effects have been observed with atoms or molecules in the gas phase. Although predicted to occur, a strong light-phase sensitivity of electrons liberated by few-cycle laser pulses from solids has hitherto been elusive. Here we show a carrier-envelope (C-E) phase-dependent current modulation of up to 100% recorded in spectra of electrons laser-emitted from a nanometric tungsten tip. Controlled by the C-E phase, electrons originate from either one or two sub-500as long instances within the 6-fs laser pulse, leading to the presence or absence of spectral interference. We also show that coherent elastic re-scattering of liberated electrons takes place at the metal surface. Due to field enhancement at the tip, a simple laser oscillator suffices to reach the required peak electric field strengths, allowing attosecond science experiments to be performed at the 100-Megahertz repetition rate level and rendering complex amplified laser systems dispensable. Practically, this work represents a simple, exquisitely sensitive C-E phase sensor device, which can be shrunk in volume down to ~ 1cm3. The results indicate that the above-mentioned novel attosecond science techniques developed with and for atoms and molecules can also be employed with solids. In particular, we foresee sub-femtosecond (sub-) nanometre probing of (collective) electron dynamics, such as plasmon polaritons, in solid-state systems ranging in size from mesoscopic solids via clusters to single protruding atoms.Comment: Final manuscript version submitted to Natur

Thermal analysis of hadron multiplicities from relativistic quantum molecular dynamics

Some questions arising in the application of the thermal model to hadron production in heavy ion collisions are studied. We do so by applying the thermal model of hadron production to particle yields calculated by the microscopic transport model RQMD(v2.3). We study the bias of incomplete information about the final hadronic state on the extraction of thermal parameters.It is found that the subset of particles measured typically in the experiments looks more thermal than the complete set of stable particles. The hadrons which show the largest deviations from thermal behaviour in RQMD(v2.3) are the multistrange baryons and antibaryons. We also looked at the influence of rapidity cuts on the extraction of thermal parameters and found that they lead to different thermal parameters and larger disagreement between the RQMD yields and the thermal model.Comment: 12 pages, 2 figures, uses REVTEX, only misprint and stylistic corrections, to appear in Physical Review

Coulomb Effect: A Possible Probe for the Evolution of Hadronic Matter

Electromagnetic field produced in high-energy heavy-ion collisions contains much useful information, because the field can be directly related to the motion of the matter in the whole stage of the reaction. One can divide the total electromagnetic field into three parts, i.e., the contributions from the incident nuclei, non-participating nucleons and charged fluid, the latter consisting of strongly interacting hadrons or quarks. Parametrizing the space-time evolution of the charged fluid based on hydrodynamic model, we study the development of the electromagnetic field which accompanies the high-energy heavy-ion collisions. We found that the incident nuclei bring a rather strong electromagnetic field to the interaction region of hadrons or quarks over a few fm after the collision. On the other hand, the observed charged hadrons' spectra are mostly affected (Coulomb effect) by the field of the charged fluid. We compare the result of our model with experimental data and found that the model reproduces them well. The pion yield ratio pi^-/pi+ at a RHIC energy, Au+Au 100+100 GeV/nucleon, is also predicted.Comment: 23 pages, RevTex, 19 eps figures, revised versio

Strange hyperon and antihyperon production from quark and string-rope matter

Hyperon and antihyperon production is investigated using two microscopical models: {\bf (1)} the fast hadronization of quark matter as given by the ALCOR model; {\bf (2)} string formation and fragmentation as in the HIJING/B model. We calculate the particle numbers and momentum distributions for Pb+Pb collisions at CERN SPS energies in order to compare the two models with each other and with the available experimental data. We show that these two theoretical approaches give similar yields for the hyperons, but strongly differ for antihyperons.Comment: 11 pages, Latex, 3 EPS figures, contribution to the Proceedings of the 4th International Conference on Strangeness in Quark Matter (SQM'98), Padova, Italy, 20-24 July 199