Miracle-dz/UniFAR-FTUs huggingface dataset:
A method for estimating the number of components in a normal mixture density function

A criticism of using the Gaussian density function to model the classes in multispectral remote sensing data is that the classes may be multimodal, and therefore, not well represented by the Gaussian density function. The normal mixture density function, which is the sum of one or more weighted Gaussian components, is a compromise between Gaussian and non-parametric density functions. It can model multimodal density functions, yet requires fewer parameters to be estimated than non-parametric density functions, which is an advantage in remote sensing applications where training samples are difficult and expensive to obtain. Usually in practice, the number of components is not known, and must be estimated from the training samples. A new approach for estimating the appropriate number of components in a normal mixture density is described. The approach is to divide the data from each class into various numbers of clusters using the nearest means algorithm, compute a measure of fit which measures how well the training data are represented by the clusters, and to select the number of clusters that best fits the data. The measure of fit is computed by leaving one sample out and estimating the mean vectors and covariance matrices of the mixture density with the rest of the samples. Then the likelihood of the left-out sample is computed, and the process is repeated, each time leaving out a different sample. In this way, the samples used to test the estimates are independent of the samples used to compute estimates, and so the measure of fit, which is the average log likelihood of the left-out samples, does not increase monotonically like the joint likelihood, but will reach a maximum. The number of clusters that results in the maximum value of the measure of fit is selected as the estimate of the number of components in the mixture density.
Ultra flat supercontinuum generation in silicate dual core microstructured fiber

In this paper we report on ultra flat supercontinuum generation in dual core photonic crystal fiber pumped in the normal dispersion regime. The fiber cladding is fabricated from custom NC21 borosilicate glass while the fiber cores is made of commercially available F2 high index lead-silicate glass from Schott Corp. We investigated the supercontinuum characteristics for single and double core excitation by a Ti:Sapphire oscillator delivering 100 fs pulses centered at 800 nm with an energy of 4.2 nJ. Dual core pumping resulted in appreciable flattening of the supercontinuum spectra in the range 875 – 950 nm.
Implementing time-frequency representations for non-Cohen classes

Time-frequency representations (TFRs) of Cohen's class are not always the best TFRs for analyzing a given signal. Using algorithms to find Cohen's-class TFRs, it is possible to find TFRs of an infinite number of classes, including the hyperbolic class. Optimal TFRs of various signals illustrate that for many signals, certain optimum TFRs outside of Cohen's class outperform optimal Cohen's-class TFRs in analysing these signals. <<ETX>>
Transport properties and origin of ferromagnetism in (Ga,Mn)As

Magnetotransport properties of $p$-type ferromagnetic (Ga,Mn)As, a diluted magnetic semiconductor based on III-V semiconductors, are measured and the $p\ensuremath{-}d$ exchange between holes and Mn $3d$ spins is determined. The ferromagnetic transition temperatures calculated based on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction using the exchange reproduce remarkably well the observed ferromagnetic transition temperatures, demonstrating that ferromagnetism of (Ga,Mn)As has its origin in the RKKY interaction mediated by holes.
Kriging a soil variable with a simple nonstationary variance model

Kriging is a standard tool in the environmental sciences for spatial prediction from limited sample data, subject to the assumption of intrinsic stationarity, made about the underlying spatially correlated random function. It is generally well understood how the assumption of stationarity in the mean can be relaxed within the linear mixed model framework, using residual maximum likelihood to estimate variance parameters for the random effects. The Best Linear Unbiased Predictor (BLUP) is equivalent to the kriging predictor in these circumstances. However, nonstationarity in the variance is a harder problem to solve. Stationarity assumptions are necessary if the spatial covariance of a random process is to be estimated from the single realization which nature provides. However, they are not always plausible for variables arising from processes in complex landscapes across contrasting topography and geology.This article shows how a relatively simple extension of the random effects variance model in a Linear Mixed Model (LMM) for the slope of the soil surface across 10 km in western England allows nonstationarity in the variance to be modeled. Tests on the log-likelihood ratio provide evidence in favor of the nonstationary model, and the results of prediction at validation sites show that it characterizes the uncertainty of these predictions better than does a stationary equivalent. More complex models of nonstationary covariance may sometimes be needed, but the case study reported here shows that a relatively minor relaxation of the stationarity assumptions can lead to improved spatial modeling and prediction of a quite complex environmental variable.
Intermethod agreement and body fat estimates using skinfolds and a footpad-style bioelectrical impedance device

This study sought to determine whether body fat percentage estimates using an inexpensive bioelectrical impedance analysis (BIA) device (Tanita TBF-521, Tanita Corp, of America, Arlington Heights, IL) could be freely substituted for those obtained utilizing skinfolds (method equivalence). Data were analyzed from measurements on 38 children age 6 to 12 years. Random effect intraclass correlation (r = .930; 95% confidence interval [CI] = .87 to .96), fixed effect intraclass correlation (r = .932; 95% CI = .87 to .96), and least-products regression supported the equivalence of the 2 methods. The technical error between the 2 methods (3.7; coefficient of variation = 12.2%) was small and also supported the equivalence of the two methods. The ability of the BIA device to categorize into normal and obese categories when compared to the skinfold technique was also impressive (κ = .95; 95% CI = .73 to .99). However, the results of the limits of agreement analysis showed that the approximate 95% CI for the differen.
Effects of thermal cycling on mechanical properties of graphite polyimide

An experimental study to determine the effects of thermal cycling on residual mechanical properties of a graphite/polyimide composite has been conducted. Interlaminar shear, flexure, and compression strengths were measured at room temperature and 316 °C on unidirectional and quasi-isotropic laminates subjected to 150 and 500 thermal cycles between -156 and 316°C. Thermal cycling produced transverse microcracks and delaminations in the laminates. The linear density of the microcracks (35 per cm) was about the same after 150 and 500 cycles. Although the crack density did not change from 150 to 500 cycles, crack growth did occur with intralamina cracks growing into adjacent lamina. The matrix controlled properties of the quasi-isotropic laminate at both room temperature and 316°C were reduced significantly by thermal cycling. However, the properties of the unidirectional laminate were reduced significantly only at 316°C.
Bayesian Spatial Prediction of Random Space-Time Fields With Application to Mapping PM2.5 Exposure

This article presents a multivariate spatial prediction methodology in a Bayesian framework. The method is especially suited for use in environmetrics, where vector-valued responses are observed at a small set of ambient monitoring stations “(gauged sites)” at successive time points. However, the stations may have varying start-up times so that the data have a “staircase” pattern (“monotone” pattern in the terminology of Rubin and Shaffer). The lowest step corresponds to the newest station in the monitoring network. We base our approach on a hierarchical Bayes prior involving a Gaussian generalized inverted Wishart model. For given hyperparameters, we derive the predictive distribution for currently gauged sites at times before their start-up when no measurements were taken. The resulting predictive distribution is a matric t distribution with appropriate covariance parameters and degrees of freedom. We estimate the hyperparameters using the method of moments (MOM) as an easy-to-implement alternative to the more complex EM algorithm. The MOM in particular gives exact parameter estimates and involves less cumbersome calculations than the EM algorithm. Finally, we obtain the predictive distribution for unmeasured responses at “ungauged” sites. The results obtained here allow us to pool the data from different sites that measure different pollutants and also to treat cases where the observed data monitoring stations have a monotonic “staircaserldquo; structure. We demonstrate the use of this methodology by mapping PM2.5 fields for Philadelphia during the period of May 1992 to September 1993. Large amounts of data missing by design make this application particularly challenging. We give empirical evidence that the method performs well.
Study on Snow Depth Anomaly over Eurasia, Indian Rainfall and Circulations

Based on Historical Soviet Daily Snow Depth (HSDSD-II) data for the period 1941-1995, it is found that winter/spring snow depth anomalies over east Eurasia (70 E-160 E, 35 N-65 N) is positively correlated, while west Eurasia (25 E-70 E, 35 N-65 N) is negatively correlated with subsequent Indian summer monsoon rainfall (ISMR). The correlations become stronger and negative with winter snow depth anomaly over west Eurasia during the recent period of study (1975-1995). Four years of high snow (1966, 1968, 1979 and 1986) and two years of low snow (1961 and 1975) are selected on the basis of standardized winter snow depth anomaly over west Eurasia. The Pentad (Fivedays average) analysis of snow depth during the above contrasting snow years show that high/low snow is associated with late/early snow disappearance. NCEP/NCAR reanalyzed data are used for the study of some important atmospheric characteristics of seasonal monsoon circulation during high/low snow years, followed by deficient/excess ISMR.The important findings ofthis study are: (1) the anomalous persistence of winter/spring snow delays the spring time continental heating, results in weak thermal low and weak monsoon westerlies over India, (2) the difference fields of Velocity Potential shows complete phase reversal in the dipole structure from high to low snow years and (3) the temperature and related circulation fields show that low level jet over east Asia is also considerably influenced by Eurasian snow anomaly.
Transport and Thermodynamic Studies of Stripe and Checkerboard Ordering in Layered Nickel Oxides R 2− x Sr x NiO 4 (R = La and Nd)

We have investigated the Sr-doped layered nickelates Nd2−xSrxNiO4 and La2−xSrxNiO4 to elucidate qualitative differences between the stripe-type and checkerboard (CB)-type charge/spin ordered phases. From electrical resistivity, specific heat, magnetic susceptibility and inelastic neutron-scattering measurements, we construct a revised phase diagram around the border of the stripe and CB phases in Nd2−xSrxNiO4, and show the marked difference in the hole-concentration dependence of physical properties between two phases. These results strongly indicate that the CB order is not a simple structural limit of the stripe order.
Dynamic dislocation behavior in ``pure'' magnesium oxide single crystals

Edge‐ and screw‐dislocation velocities in ``pure'' MgO single crystals have been measured as a function of stress, temperature, and valence state of the iron impurities in order to identify the rate‐controlling drag mechanism for dislocation mobility. Edge dislocations have been observed to move faster than screw dislocations in both the valence states over the stress and the temperature regimes investigated. Both the edge and screw dislocations move faster in reduced (Fe+2) samples than in oxidized (Fe+3) samples. From the analysis of the edge‐ and screw‐dislocation velocity data in terms of the activation parameters (activation volume, activation enthalpy, total activation enthalpy, and the stress exponent of dislocation velocity) it is suggested that the edge‐ and screw‐dislocation mobilities in ``pure'' MgO single crystals in the reduced state are controlled by Peierls mechanism with thermally activated double‐kink nucleation as the rate limiting step. The total activation barriers for edge‐ and screw.
Design principles for particle plasmon enhanced solar cells

We develop fundamental design principles for increasing the efficiency of solar cells using light trapping by scattering from metal nanoparticles. We show that cylindrical and hemispherical particles lead to much higher path length enhancements than spherical particles, due to enhanced near-field coupling, and that the path length enhancement for an electric point dipole is even higher than the Lambertian value. Silver particles give much higher path length enhancements than gold particles. The scattering cross section of the particles is very sensitive to the thickness of a spacer layer at the substrate, which provides additional tunability in the design of particle arrays.
Gauge-invariant theory of the Hall effect in a weak magnetic field

An exact expression is obtained for the off-diagonal part of the conductivity tensor of a man-body electron system up to the first order in an applied magnetic field. The formalism includes all types of electron scattering mechanism and is independent of the choice of the gauge describing the magnetic field. The resulting formula is expressed in terms of the three-body correlation function and includes the Lorentz force in an explicit operator form.
Interpreting an evaluation of the ECMWF global model with CloudSat observations: ambiguities due to radar reflectivity forward operator uncertainties

This article explores the uncertainties associated with evaluating a global atmospheric model with radar reflectivity observations. A forward operator for radar reflectivity (ZmVar) is described and used for the comparison of the ECMWF global numerical weather prediction model short‐range forecasts with radar data from CloudSat. A sensitivity study is performed to determine which differences can be attributed to either specific radar forward operator assumptions or to deficiencies in the global model. The results show that model‐derived reflectivities are particularly sensitive to the definition of subgrid precipitation fraction, as precipitation dominates the radar reflectivity signal, but also to the choice of particle size distribution and scattering properties of the different hydrometeor categories. However, there are a number of consistent differences in the reflectivity comparison that are significantly larger than can be explained by the sensitivity tests. This suggests that these discrepancies are due to deficiencies in the model cloud and precipitation frequency of occurrence and hydrometeor water contents. These include too frequent occurrence at high altitudes, too low occurrence in the Southern Hemisphere storm track and an overestimate of rain in warm‐phase low cloud. The study shows the value of CloudSat for evaluating the model in terms of radar reflectivity and highlights the importance of taking into account forward operator uncertainties for both model evaluation and data assimilation applications. Copyright © 2012 Royal Meteorological Society
Numerical simulations on thermocapillary migrations of nondeformable droplets with large Marangoni numbers

In this paper, the study on isolated spherical drops in thermocapillary migrations in zero gravity is carried out with a novel numerical scheme to accomplish long-tank simulations in a very short computing domain, and the full migrating phenomena with fairly large Marangoni numbers (up to 400) are discussed in detail. Larger Marangoni numbers lead to more complicated migrating processes, and longer distances for the drops to reach their final stable migrating velocities (U-F). There is nontrivial difference between the U-F values in theoretical analysis, numerical simulations, and space experiments, and the most possible reason is the assumed different migrating distances to reach steady states in different investigations.
Simulations of the turbulent channel flow at Reτ = 180 with projection‐based finite element variational multiscale methods

Projection‐based variational multiscale (VMS) methods, within the framework of an inf–sup stable second order finite element method for the Navier–Stokes equations, are studied in simulations of the turbulent channel flow problem at Reτ = 180. For comparison, the Smagorinsky large eddy simulation (LES) model with van Driest damping is included into the study. The simulations are performed on very coarse grids. The VMS methods give often considerably better results. For second order statistics, however, the differences to the reference values are sometimes rather large. The dependency of the results on parameters in the eddy viscosity model is much weaker for the VMS methods than for the Smagorinsky LES model with van Driest damping. It is shown that one uniform refinement of the coarse grids allows an underresolved direct numerical simulations (DNS). Copyright © 2007 John Wiley & Sons, Ltd.
The inverse Goldbach problem

Improved upper and lower bounds of the counting functions of the conceivable additive decomposition sets of the set of primes are established. Suppose that A + B = P', where P' differs from the set of primes in finitely many elements only and |A|, |B| ≥ 2. It is shown that the counting functions A(x) of A and B(x) of B, for sufficiently large x, satisfy x 1/2 (log x) -5 «A(x) « x 1/2 (log x) 4 . The same bounds hold for B(x). This immediately solves the ternary inverse Goldbach problem: there is no ternary additive decomposition A + B + C = P', where P' is as above and |A|, |B|, |C| ≥ 2. This considerably improves upon the previously known bounds: for any r ≥ 2, there exist positive constants c 1 and c 2 such that, for sufficiently large x, the following bounds hold: formula math. (Here log r x denotes the rth iterated logarithm.) The proof makes use of a combination of Montgomery's large sieve method and of Gallagher's larger sieve. This combined large sieve method may be of interest in its own right.
On the efficient numerical simulation of directionally spread surface water waves

Abstract This paper concerns the description of transient and highly nonlinear, near-breaking, surface water waves that are characterized by a spread of wave energy in both frequency and direction. A new spectral wave model is described that allows both the unsteadiness and the directionality of a wave field to be described in a fully nonlinear sense. The methodology underlying the scheme is similar to the unidirectional model developed previously by Craig and Sulem [13]. An approximation of the Dirichlet–Neumann operator is made that transforms the boundary values of the velocity potential, φ, at the water surface into values of φ z . This allows an initial spatial representation of the water surface elevation and the velocity potential on this surface to be time marched using fast Fourier transforms. The advantages of this technique lie in both its efficiency and its robustness. These are of fundamental importance when seeking to model extreme ocean waves, involving broad-banded frequency spectra and realistic directional spreads, since they incorporate a large range of horizontal length scales. In its present form, the model is appropriate to waves propagating on water of constant depth; it runs on a PC and is sufficiently stable to predict the evolution of near-breaking waves. Indeed, the only significant restriction arises due to the Fourier series representation. This requires the water surface elevation to be a single-valued function of the horizontal coordinates and therefore limits the model to non-overturning waves. The new numerical scheme is validated against a fifth-order Stokes solution for regular waves and the recent experimental observations provided by Johannessen and Swan [3]. These latter comparisons are particularly important, confirming that the model is able to describe the rapid and highly significant energy transfers that occur across the wavenumber spectrum in the vicinity of an extreme event. These are strongly dependent upon the directionality of the wavefield and critically important when seeking to define the characteristics of an extreme, near-breaking, wave. The paper concludes with an example of the formation of a realistic, fully nonlinear and directionally spread wave group in the open ocean.
Commuting families of symmetric differential operators

Many commuting families of differential operators or completely integrable quantum systems have been constructed in connection with root systems (cf. [OP2] and references therein). Such families often have a certain symmetry in coordinates. The radial parts of invariant differential operators on symmetric spaces give a good example of a commuting family of differential operators (cf. [HC]). In this case some parameters take only some discrete values determined by the dimensions of the root spaces for the symmetric spaces. On the other hand, [Sj] generalized them to complex parameters for the root system of type An. The same generalization was given by [H1], [H2], [HO], [Op1], [Op2] for general root systems. If the root system is of classical type, their operators give examples of the commuting families studied in this note (cf. Remark 3 iii)). Namely we shall determine all the families under the assumption of a symmetry in coordinates. Let W be the Weyl group of type An−1 with n ≥ 3 or of type Bn with n ≥ 2 or of type Dn with n ≥ 4. We identify W with the group of the coordinate transformations (x1, . . . , xn) 7→ (ε1xσ(1), . , εnxσ(n)) of R, where σ are the elements of the n-th symmetric group Sn and  ε1 = · · · = εn = 1 if W is of type An−1, ε1 = ±1, · · · , εn = ±1 if W is of type Bn, ε1 = ±1, · · · , εn = ±1 and #{i ; εi = −1} is even if W is of type Dn.
Energy-containing scales of turbulence in the ocean

From measurements of the energy-containing scales of turbulence in the ocean thermocline, two new formulations are examined: (1) an inviscid estimate for the viscous dissipation rate of turbulent kinetic energy and (2) a mixing length estimate for the turbulent heat flux. These formulations are tested using coincident measurements of the relevant properties of both energy-containing and dissipation scales of stratified turbulence in the ocean's main thermocline obtained from a vertical microstructure profiler. It is found that energy-containing scale estimates of both dissipation rate and heat flux compare favorably with dissipation scale estimates. Since the energy-containing scales are many times greater than the dissipation scales, the measurement constraints on these new estimates are considerably less strict than for dissipation scale estimates of the same quantities. These observations also suggest that the timescale for viscous decay of turbulent motions is greater than that for diffusive smoothing of scalar fluctuations. It is argued that this is consistent with current estimates of mixing efficiencies.