A Variational Assimilation Method for Satellite and Conventional Data: a Revised Basic Model 2B

A variational objective analysis technique that modifies observations of temperature, height, and wind on the cyclone scale to satisfy the five 'primitive' model forecast equations is presented. This analysis method overcomes all of the problems that hindered previous versions, such as over-determination, time consistency, solution method, and constraint decoupling. A preliminary evaluation of the method shows that it converges rapidly, the divergent part of the wind is strongly coupled in the solution, fields of height and temperature are well-preserved, and derivative quantities such as vorticity and divergence are improved. Problem areas are systematic increases in the horizontal velocity components, and large magnitudes of the local tendencies of the horizontal velocity components. The preliminary evaluation makes note of these problems but detailed evaluations required to determine the origin of these problems await future research

A Monte Carlo Evaluation of the Efficiency of the PCSE Estimator

Panel data characterized by groupwise heteroscedasticity, cross-sectional correlation, and AR(1) serial correlation pose problems for econometric analyses. It is well known that the asymptotically efficient, FGLS estimator (Parks) sometimes performs poorly in finite samples. In a widely cited paper, Beck and Katz (1995) claim that their estimator (PCSE) is able to produce more accurate coefficient standard errors without any loss in efficiency in ¡°practical research situations.¡± This study disputes that claim. We find that the PCSE estimator is usually less efficient than Parks -- and substantially so -- except when the number of time periods is close to the number of cross-sections.Panel data estimation; Monte Carlo analysis; FGLS; Parks; PCSE; finite sample

Another Look At What To Do With Time-Series Cross-Section Data

Our study revisits Beck and Katz’ (1995) comparison of the Parks and PCSE estimators using time-series, cross-sectional data (TSCS). Our innovation is that we construct simulated statistical environments that are designed to closely match “real-world,” TSCS data. We pattern our statistical environments after income and tax data on U.S. states from 1960-1999. While PCSE generally does a better job than Parks in estimating standard errors, it too can be unreliable, sometimes producing standard errors that are substantially off the mark. Further, we find that the benefits of PCSE can come at a substantial cost in estimator efficiency. Based on our study, we would give the following advice to researchers using TSCS data: Given a choice between Parks and PCSE, we recommend that researchers use PCSE for hypothesis testing, and Parks if their primary interest is accurate coefficient estimates.Panel Data, Panel Corrected Standard Errors, Monte Carlo analysis

Another Look at what to do with Time-series Cross-section Data

Our study revisits Beck and Katz' (1995) comparison of the Parks and PCSE estimators using time-series, cross-sectional data (TSCS). Our innovation is that we construct simulated statistical environments that are designed to approximate actual TSCS data. We pattern our statistical environments after income and tax data on U.S. states from 1960-1999. While PCSE generally does a better job than Parks in estimating standard errors/confidence intervals, it too can be unreliable, sometimes producing standard errors/confidence intervals that are substantially off the mark. Further, we find that the benefits of PCSE can come at a large cost in estimator efficiency.Panel data, Parks model; PCSE estimator; Monte Carlo methods

A Variational Assimilation Method for Satellite and Conventional Data: Development of Basic Model for Diagnosis of Cyclone Systems

A summary is presented of the progress toward the completion of a comprehensive diagnostic objective analysis system based upon the calculus of variations. The approach was to first develop the objective analysis subject to the constraints that the final product satisfies the five basic primitive equations for a dry inviscid atmosphere: the two nonlinear horizontal momentum equations, the continuity equation, the hydrostatic equation, and the thermodynamic equation. Then, having derived the basic model, there would be added to it the equations for moist atmospheric processes and the radiative transfer equation

A random version of shepp's urn scheme

[[abstract]]In this paper, we consider the following random version of Shepp’s urn scheme: A player is given an urn with n balls. p of these balls have value +1 and n − p have value −1. The player is allowed to draw balls randomly, without replacement, until he or she wants to stop. The player knows n, the total number of balls, but knows only that p, the number of balls of value +1, is a number selected randomly from the set {0,1,2,...,n}. The player wishes to maximize the expected value of the sum of the balls drawn. We first derive the player’s optimal drawing policy and an algorithm to compute the player’s expected value at the stopping time when he or she uses the optimal drawing policy. Since the optimal drawing policy is rather intricate and the computation of the player’s optimal expected value is quite cumbersome, we present a very simple drawing policy, which is asymptotically optimal. We also show that this random urn scheme is equivalent to a random coin tossing problem.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[booktype]]紙本[[countrycodes]]US

Seismic attenuation structure in central Mexico: Image of a focused high-attenuation zone in the mantle wedge

Velocity spectra from moderate-sized earthquakes were used to investigate the P wave attenuation structure in central Mexico. In particular, we included regional events with magnitudes in the range of 4.5 to 6.1 recorded from 2005 to 2007 on the Middle American Subduction Experiment (MASE) array, which consists of 100 broadband sensors across central Mexico from Acapulco to Tempoal, near the Gulf of Mexico. By assuming a Brune-type source, a frequency-independent t* value was obtained for each seismogram in the frequency band 1 to 30 Hz. These measurements were then inverted for two-dimensional spatial variations in Q_p in the cross section along the MASE array, perpendicular to the trench. The model has uniform 20 km vertical grid spacing down to a depth of 200 km and 50 km or 100 km horizontal grid spacing depending on ray coverage. The inversion results show low attenuation in the subducting slab and high attenuation in the mantle wedge and the crust below and to the north of the volcanic belt. The focused high-attenuation zone (Q_p < 200) in the mantle wedge lies away from the top of the slab, between depths of 80 km and 120 km beneath the volcanic belt, and is likely to be related to relatively high temperature, fluids, and partial melts produced in subduction process. The high-attenuation region in the lower crust correlates with the low-resistivity and low-velocity region and could be caused by partial melts and fluids from dehydration and magmatic processes

Random walks on Z2n

AbstractFor each positive integer n ≥ 1, let Z2n be the direct product of n copies of Z2, i.e., Z2n = {(a1, a2, …, an)∥ai = 0 or 1 for all i = 1, 2, …, n} and let {Wtn}t≥0 be a random walk on Z2n such that P{W0n = A} = 2−n for all A's in Z2n and P{Wj+1n = (a2, a3, …, an, 0)∥Wjn = (a1, a2, …, an)} = P{Wj+1n = (a2, a3, …, an, 1)∥Wjn = (a1, a2, …, an)} = 12 for all j = 0, 1, 2, …, and all (a1, a2, …, an)'s in Z2n. For each positive integer n ≥ 1, let Cn denote the covering time taken by the random walk Wtn on Z2n to cover Z2n, i.e., to visit every element of Z2n. In this paper, we prove that, among other results, P{except finitely many n, c2nln(2n) < Cn < d2nln(2n)} = 1 if c < 1 < d

Wigner distribution of twisted photons

We present the first experimental characterization of the azimuthal Wigner distribution of a photon. Our protocol fully characterizes the transverse structure of a photon in conjugate bases of orbital angular momentum (OAM) and azimuthal angle (ANG). We provide a test of our protocol by characterizing pure superpositions and incoherent mixtures of OAM modes in a seven-dimensional space. The time required for performing measurements in our scheme scales only linearly with the dimension size of the state under investigation. This time scaling makes our technique suitable for quantum information applications involving a large number of OAM states