Spectral Gradient Research Articles

THE RADIO PROPERTIES AND MAGNETIC FIELD CONFIGURATION IN THE CRAB-LIKE PULSAR WIND NEBULA G54.1+0.3

We present a multifrequency radio investigation of the Crab-like pulsar wind nebula (PWN) G54.1+0.3 using the Very Large Array. The high resolution of the observations reveals that G54.1+0.3 has a complex radio structure which includes filamentary and loop-like structures that are magnetized, a diffuse extent similar to the associated diffuse X-ray emission. But the radio and X-ray structures in the central region differ strikingly, indicating that they trace very different forms of particle injection from the pulsar and/or particle acceleration in the nebula. No spectral index gradient is detected in the radio emission across the PWN, whereas the X-ray emission softens outward in the nebula. The extensive radio polarization allows us to image in detail the intrinsic magnetic field, which is well-ordered and reveals that a number of loop-like filaments are strongly magnetized. In addition, we determine that there are both radial and toroidal components to the magnetic field structure of the pulsar wind nebula. Strong mid-IR emission detected in Spitzer Space Telescope data is closely correlated with the radio emission arising from the southern edge of G54.1+0.3. In particular, the distributions of radio and X-ray emission compared with the mid-IR emission suggest that the PWN may be interacting with this interstellar cloud. This may be the first PWN where we are directly detecting its interplay with an interstellar cloud that has survived the impact of the supernova explosion associated with the pulsar's progenitor.

The simulated sea ice thermal microwave emission at window and sounding frequencies

Although the sea ice microwave emissivity is well defined in terms of brightness temperature and the effective temperature it is difficult to derive in practice and its link to physical processes in the snow and sea ice cover is not understood in detail. Future applications of assessing the sea ice microwave emission potentially include atmospheric sounding over sea ice for channels peaking near the surface. Here the microwave emission processes from sea ice are simulated using the combination of a one-dimensional thermodynamic snow and sea ice model and a microwave emission model. The emission model is a sea ice version of the Microwave Emission Model for Layered Snow-packs (MEMLS). It is demonstrated that the simulated seasonal variability of the emissivity, the spectral gradient and the polarization are comparable to satellite measurements. The spectral gradient ratio defined as the difference over the sum of the 18 and 36 GHz at vertical polarization is related to the emissivity at the atmospheric temperature sounding channels at around 50 GHz. Further the brightness temperature at neighbouring channels is highly correlated. However, the effective temperature at lower frequencies (18, 23, 36 and 50 GHz) is poorly correlated with the surface or air temperature.

A CLASS OF NONMONOTONE SPECTRAL MEMORY GRADIENT METHOD

In this paper, we develop a nonmonotone spectral memory gradient method for unconstrained optimization, where the spectral stepsize and a class of memory gradient direction are combined efficiently. The global convergence is obtained by using a nonmonotone line search strategy and the numerical tests are also given to show the efficiency of the proposed algorithm.

Comet dust as a mixture of aggregates and solid particles: Model consistent with ground-based and space-mission results

The most successful model of comet dust presents comet particles as aggregates of submicron grains. It qualitatively explains the spectral and angular change in the comet brightness and polarization and is consistent with the thermal infrared data and composition of the comet dust obtained {\it in situ} for comet 1P/Halley. However, it experiences some difficulties in providing a quantitative fit to the observational data. Here we present a model that considers comet dust as a mixture of aggregates and compact particles. The model is based on the Giotto and Stardust mission findings that both aggregates (made mainly of organics, silicates, and carbon) and solid silicate particles are present in the comet dust. We simulate aggregates as {\bf Ballistic Cluster-Cluster Aggregates (BCCA)} and compact particles as polydisperse spheroids with some distribution of the aspect ratio. The particles follow a power-law size distribution with the power -3 that is close to the one obtained for comet dust {\it in situ}, at studies of the Stardust returned samples, and the results of ground-based observations of comets. The model provides a good fit to the angular polarization curve. It also reproduces the positive spectral gradient of polarization, red color of the dust, and {\bf low albedo. It also has the ratio of compact to fluffy particles close to the one found {\it in situ} for comet 1P/Halley} and the mass ratio of silicate to carbonaceous materials equal to unity that is in accordance with the elemental abundances of Halley's dust found by Giotto mission.

Visible spectroscopy of the new ESO large programme on trans-Neptunian objects and Centaurs: final results

<i>Context. <i/>A second large programme (LP) for the physical studies of TNOs and Centaurs, started at ESO Cerro Paranal on October 2006 to obtain high-quality data, has recently been concluded. In this paper we present the spectra of these pristine bodies obtained in the visible range during the last two semesters (November 2007-November 2008) of the LP.<i>Aims. <i/> We investigate the spectral behaviour of the TNOs and Centaurs observed, and we analyse the spectral slopes distribution of the full data set coming from this LP and from the literature.<i>Methods. <i/>Spectroscopic observations in the visible range were carried out at the UT1 (Antu) telescope using the instrument FORS2. We computed the spectral slope for each observed object, and searched for possible weak absorption features. A statistical analysis was performed on a total sample of 73 TNOs and Centaurs to look for possible correlations between dynamical classes, orbital parameters, and spectral gradient. <i>Results. <i/>We obtained new spectra for 28 bodies (10 Centaurs, 6 classical, 5 resonant, 5 scattered disk, and 2 detached objects), 15 of which were observed for the first time. All the new presented spectra are featureless, including 2003 AZ84, for which a faint and broad absorption band possibly attributed to hydrated silicates on its surface has been reported. The data confirm a wide variety of spectral behaviours, with neutral-grey to very red gradients. An analysis of the spectral slopes available from this LP and in the literature for a total sample of 73 Centaurs and TNOs shows that there is a lack of very red objects in the classical population. We present the results of the statistical analysis of the spectral slope distribution versus orbital parameters. In particular, we confirm a strong anticorrelation between spectral slope and orbital inclination for the classical population. Nevertheless, we do not observe a change in the slope distribution at , the boundary between the dynamically hot and cold populations, but we find that objects with show no correlation between spectral slope and inclination, as has already been noticed on the colour-inclination relation for classical TNOs. A strong correlation is also found between the spectral slope and orbital eccentricity for resonant TNOs, with objects having higher spectral slope values with increasing eccentricity.

Tomographic inversion of the peak delay times to reveal random velocity fluctuations in the lithosphere: method and application to northeastern Japan

This study proposes a new approach to estimate a 3-D distribution of power spectral density function (PSDF) of random velocity inhomogeneities in the lithosphere and applies this method to northeastern Japan. Our approach analyses the peak delay times of high-frequency S wave for microearthquakes at plural frequency bands on the basis of the Markov approximation for the parabolic wave equation, where the peak delay time is measured as the time lag from the S-wave onset to the maximal amplitude arrival. This peak delay time is appropriate to quantify the accumulated scattering effects due to random inhomogeneities without significant effect of the intrinsic absorption. The target region is divided into many blocks, each of which is characterized by a von Kármán-type PSDF with two parameters. One of the two parameters characterizes the spectral decay and another one constrains the absolute values of the PSDF at wavelengths shorter than the correlation distance. The peak delay times are calculated with these parameters along the unperturbed ray path by means of a recursive formula that is based on the Markov approximation for the parabolic wave equation. According to this formula, the spatial variation of spectral decay can be identified only by the frequency dependence of the peak delay times. Considering this characteristic, we propose a two-step approach to achieve a stable estimation of both parameters. The first step constructs an initial model with an explicit constraint for the spatial variation of frequency dependence of the peak delay times. The second step improves the first-step result by minimizing the residual of the peak delay times at all frequency bands. In the synthetic test, this two-step approach successfully improves the estimation of both parameters. We apply this method for seismograms (2–4 Hz, 4–8 Hz, 8–16 Hz and 16–32 Hz) observed in northeastern Japan and reveal that strongly inhomogeneous regions are related to the Quaternary volcano distribution and seismicity. We investigate the PSDFs of random inhomogeneities P(m) for the case in which the correlation distance is 5 km, where m is the wavenumber. At the depth of 40–60 km beneath most of the Quaternary volcanoes, P(m) are estimated as 0.017m−3.5 km3∼0.035m−4.0 km3 at 0.5 < m < 50 km−1. A remarkable characteristic of these PSDFs is the weak spectral decay in the study area. This characteristic means that lateral variation of the PSDF becomes significant at large wavenumbers. On the other hand, a high seismicity area in the western Hidaka region in Hokkaido is characterized by a steep spectral gradient as P(m) = 0.023m−4.2∼ 0.050m−4.2 km3 at 0.5 < m < 50 km−1. The PSDF in this region is larger than in its neighbours, regardless of the wavenumbers. From the comparison with other geophysical observations, we speculate that these strong inhomogeneities are generated by liquid inclusions and/or fractured structures. These regions commonly indicate stronger inhomogeneities than those in their surrounding regions for large wavenumbers (m > 15 km−1), and our approach detects that they are described by different combinations of the two parameters. It implies that the parameters of random inhomogeneities estimated by our approach are useful to examine the earth medium in relation to seismotectonic conditions in the crust and uppermost mantle.

Combining magnitude and shape features for hyperspectral classification

The spectral angle mapper (SAM) and maximum likelihood classification (MLC) are two traditional classifiers for hyperspectral classification. This paper presents two methods to combine magnitude and shape features, one for each classifier. As the magnitude and shape features are complementary, combining both features can improve the classification accuracy. First, magnitude features are represented by the spectral radiance vector, whereas shape features are represented by the spectral gradient vector. Then, in SAM, each feature vector generates a spectral angle for each class. The two generated angles are added together to obtain a single similarity, which is used for the final classification. Similarly, in MLC, after the dimensionality reduction using Fisher's linear discriminant (FLD), each feature vector in the new feature space generates a likelihood. The two generated likelihoods are multiplied to obtain a single value, which is adopted for the final classification. Experimental results on an Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data set demonstrate that the proposed methods outperform the methods with a single feature set.

Spectral gradient projection method for monotone nonlinear equations with convex constraints

A spectral gradient projection algorithm for monotone nonlinear equations with convex constraints is proposed. This new procedure is obtained by combining a modified spectral gradient method and a projection method. A relevant property of the presented method is that the computation of the iteration sequence does not require the solution of any subproblem. The algorithm is shown to be globally convergent under mild assumptions and it can be also applied to nonsmooth equations. Preliminary numerical tests show that the proposed method works quite well even for large scale problems.

Polarization properties of odd comet 17P/Holmes

We present results of polarimetric observations of comet 17P/Holmes that in 2007 surprised the observers by its outburst that resulted in dramatically increased brightness and unusual shape of the coma. Polarimetric properties of the comet also appeared to be very peculiar. Even though the comet showed negative polarization typical for the small phase angles, its absolute values were much lower than usually observed at these phase angles and the spectral gradient of the polarization was much more pronounced than usually observed for comets (although negative that is typical for other comets too). Both these results are different from the regular trends and indicate some specifics of the comet Holmes dust during the outburst. We discuss how such unusual polarimetric properties of the comet can be explained and show how a peculiar combination of aggregated and compact particles or a composition with a unique ratio of silicates to organics can explain the observational results.

The great wedge: Quantifying chromatic aberration in imaging spectroscopy systems and application to temperature measurements in the laser-heated diamond anvil cell

To aid in evaluating spatial and spectral imaging abilities of any imaging spectroradiometer system, we developed a spectral intensity gradient standard based on the behavior of a birefringent wedge imaged between cross polarizers. By comparing calculated with observed images of the wedge, a chromatic scrambling kernel was measured to generally estimate chromatic aberrations in any spectral imaging optical system. This technique provides a quantitative method to compare spectral imaging quality of different optical systems and also provides a quick test for severe misalignments in the optical path. Applying this method to the spectroradiometric measurement of temperature and temperature gradients in the laser-heated diamond cell, the observed scrambling kernel is used to infer original hotspot information from measured behavior, to provide a quantitative evaluation of the ability to measure a temperature gradient in any spectral system, and to yield an objective determination of precision of spectroradiometric temperature measurements. The birefringent wedge method and its application described in this paper are simple and inexpensive enough to be used on any spectroradiometric system.

Availability of Spectral Gradient Acoustic Reflectometry

Background and Objectives Spectral gradient acoustic reflectometry (SGAR) determines the probability of middle ear fluid by measuring the response of the tympanic membrane to a sound. To assess the sensitivity and specificity of SGAR for the diagnosis of otitis media with effusion (OME) in the Korean population, we compared accurate diagnostic rates of OME obtained from SGAR and tympanometry. Pneumatic otoscope was used for diagnostic standard of OME. Subjects and Method SGAR and tympanometry were performed on 488 ears from May 27th, 2008 to July 30th, 2008. Exclusion criteria were the presence of tympanic membrane perforation, and/or pressure equalization tubes, noncompliance, otorrhea, external auditory canal stenosis and signs of acute inflammation such as fever or otalgia. In all cases, pneumatic otoscopic examination was conducted and diagnostic accurate rates of OME were calculated in SGAR and tympanogram. Results Using spectral gradients of 3 or higher as breakpoints for indicating OME, in the case of pediatrics under 2 years old, with the sensitivity of 58.3%, specificity of 94.7%, positive predictive value (PPV) of 77.8% and negative predictive value (NPV) of 87.8%. In the case of the pediatrics between 2 and 12 years old, it showed the sensitivity of 67.2%, specificity of 90.3%, PPV of 74.5% and NPV of 86.8%. In the case of the pediatrics over 12 years old, they showed sensitivity of 87.3%, specificity of 88.8%, PPV of 67.6% and NPV of 96.3%. Conclusion SGAR has the higher tendency of specificity and NPV, and will be a useful screeningtest with good portability and economical efficiency.

Coherent anti-Stokes Raman scattering spectral interferometry with large spectral phase gradient induced by highly dispersive optical elements

In a conventional coherent anti-Stokes Raman scattering (CARS) microscope system, we generate a local oscillator CARS field and a sample CARS field successively along a single-beam path. A large gradient of relative spectral phase between the two fields is naturally induced by highly dispersive microscope elements. The resulting spectral interferogram is a form of fast varying sinusoidal fringes modulated by the amplitude and phase of the sample CARS field. With the help of the Hilbert transform on the heterodyne part of the interferogram, both real and imaginary quadratures of the sample CARS spectrum are extracted with an improved signal-to-noise ratio.

Difference in skylight intensity is a new celestial cue for sandhopper orientation (Amphipoda, Talitridae)

We investigated the use of the skylight intensity gradient as a new celestial compass cue in sandhoppers (Talitrus saltator). Experiments were conducted at different latitudes (temperate and equatorial) with different zenithal distances of the sun under a translucent (opaline) Plexiglas dome. We also used a blue filter placed on the translucent dome to remove the spectral sky gradient, and a screen for the sun to remove the skylight intensity gradient. Therefore, in our experimental conditions, the spectral gradient and skylight polarization were impossible to use as directional information. Sandhoppers used the difference in skylight intensity in their directional choice when zenithal distance was greater than 10°. Therefore, the anisotropic radiance distribution (i.e. the difference in skylight intensity between the hemidome containing the sun and the opposite one) is a real celestial factor in animal spatial orientation. However, it is probably more imprecise than the solar orientation and could not be used by all animals.

Is cortical distribution of spectral power a stable individual characteristic?

General understanding in EEG research is that cortical distribution of spectral power varies as a function of time, frequency, state, and experimental condition. There are findings, however, which show that individual-specific patterns of cortical spectral power distribution could be amazingly stable, at least in some experimental conditions. In this study two different experimental datasets were used to analyze stability and variability of individual pattern of cortical spectral power distribution across time, experimental conditions, and frequency bands. First experiment consisted of presentation of pictures of emotional facial expressions. Second experiment was an auditory stop-signal task. In both experiments a number of psychometric measures were obtained from each participant. It has been shown that in spite of high short-term variability, individual-specific patterns of cortical spectral power distribution are remarkably stable across frequency bands, long periods of time, and experimental conditions. These patterns are related to state and trait participant's characteristics. The antero-posterior spectral power gradient emerged as the most prominent feature associated with important personality dimensions. Relatively higher oscillatory activity in the frontal cortical region relates to female gender and Behavioral Inhibition tendencies. Relatively higher activity at posterior sites is associated with Extraversion. Significant differences in event-related spectral perturbations upon presentation of emotionally loaded stimuli were found between high and low antero-posterior gradient participants. These data show that cortical distribution of oscillatory activity may be seen as a relatively stable individual characteristic. Enhanced or diminished oscillatory activity of some cortical regions, such as the prefrontal cortex, may play an important role in organization of human behavior.

Physical and dynamical characterization of (5201) Ferraz-Mello, a possible extinct Jupiter family comet

Context. The subject of asteroids in cometary orbits (ACOs) has been of growing interest lately. These objects have the orbital characteristics typical of comets, but are asteroidal in appearance, i.e., show no signs of a coma at any part of their orbits. At least a fraction of these objects are thought to be comets that have either exhausted all their volatile content or developed a refractory crust that prevents sublimation. In particular, the asteroid (5201) Ferraz-Mello has, since its discovery, been suspected to be an extinct Jupiter family comet due to the peculiar nature of its orbit. Aims. The aim of this work is to put constraints on the possible origin of (5201) Ferraz-Mello by means of spectroscopic characterization and a study of the dynamics of this asteroid Methods. We used the SOAR Optical Imager (SOI) to obtain observations of (5201) Ferraz-Mello using four SDSS filters. These observations were compared to asteroids listed in the Sloan Moving objects catalog and also to photometry of cometary nuclei, Centaurs, and TNOs. The orbital evolution of (5201) Ferraz-Mello and of a sample of asteroids and comets that are close to that object in the a − e plane were simulated using a pure N-body code for 4 000 years forward and 4 000 years backward in time. Results. The reflectance spectrum obtained from its colors in the SDSS system is unusual, with a steep spectral gradient that is comparable to TNOs and Centaurs, but with an increase in the reflectance in the g band that is not common in those populations. A similar behavior is seen in cometary nuclei that were observed in the presence of a faint dust coma. The dynamical results confirm the very chaotic evolution found previously and its dynamical similarity to the chaotic evolution of some comets. The asteroid is situated in the very stochastic layer at the border of the 2/1 resonance, and it has a very short Lyapunov time (30–40) years. Together, the spectral characteristcs and the dynamical evolution suggest that (5201) Ferraz-Mello is a dormant or extinct comet.

A scaled nonlinear conjugate gradient algorithm for unconstrained optimization

The best spectral conjugate gradient algorithm by (Birgin, E. and Martínez, J.M., 2001, A spectral conjugate gradient method for unconstrained optimization. Applied Mathematics and Optimization, 43, 117–128). which is mainly a scaled variant of (Perry, J.M., 1977, A class of Conjugate gradient algorithms with a two step varaiable metric memory, Discussion Paper 269, Center for Mathematical Studies in Economics and Management Science, Northwestern University), is modified in such a way as to overcome the lack of positive definiteness of the matrix defining the search direction. This modification is based on the quasi-Newton BFGS updating formula. The computational scheme is embedded into the restart philosophy of Beale–Powell. The parameter scaling the gradient is selected as spectral gradient or in an anticipative way by means of a formula using the function values in two successive points. In very mild conditions it is shown that, for strongly convex functions, the algorithm is global convergent. Computational results and performance profiles for a set consisting of 700 unconstrained optimization problems show that this new scaled nonlinear conjugate gradient algorithm substantially outperforms known conjugate gradient methods including: the spectral conjugate gradient SCG by Birgin and Martínez, the scaled Fletcher and Reeves, the Polak and Ribière algorithms and the CONMIN by (Shanno, D.F. and Phua, K.H., 1976, Algorithm 500, Minimization of unconstrained multivariate functions. ACM Transactions on Mathematical Software, 2, 87–94).

Hybrid spectral gradient method for the unconstrained minimization problem

We present a hybrid algorithm that combines a genetic algorithm with the Barzilai---Borwein gradient method. Under specific assumptions the new method guarantees the convergence to a stationary point of a continuously differentiable function, from any arbitrary initial point. Our preliminary numerical results indicate that the new methodology finds efficiently and frequently the global minimum, in comparison with the globalized Barzilai---Borwein method and the genetic algorithm of the Toolbox of Genetic Algorithms of MatLab.

Mapping of heavy metal pollution in stream sediments using combined geochemistry, field spectroscopy, and hyperspectral remote sensing: A case study of the Rodalquilar mining area, SE Spain

The aim of this study is to derive parameters from spectral variations associated with heavy metals in soil and to explore the possibility of extending the use of these parameters to hyperspectral images and to map the distribution of areas affected by heavy metals on HyMAP data. Variations in the spectral absorption features of lattice OH and oxygen on the mineral surface due to the combination of different heavy metals were linked to actual concentrations of heavy metals. The ratio of 610 to 500 nm ( R 610,500 nm) in the visible and near-infrared (VNIR) range, absorption area at 2200 nm (Area 2200 nm), and asymmetry of the absorption feature at 2200 nm (Asym 2200 nm) showed significant correlations with concentrations of Pb, Zn, and As, respectively. The resulting spectral gradient maps showed similar spatial patterns to geochemical gradient maps. The ground-derived spectral parameters showed a reliable quantitative relationship with heavy metal levels based on multiple linear regression. To examine the feasibility to applying these parameters to a HyMAP image, image-derived spectral parameters were compared with ground-derived parameters in terms of R 2, one-way ANOVA, and spatial patterns in the gradient map. The R 1344,778 nm and Area 2200 nm parameters showed a weak relationship between the two datasets ( R 2 > 0.5), and populations of spectral parameter values, Depth 500 nm, R 1344,778 nm, and Area 2200 nm derived from the image pixels were comparable with those of ground-derived spectral parameters along a section of the stream channel. The pixels classified in the rule image of Depth 500 nm, R 1344,778 nm, and Area 2200 nm derived from a HyMAP image showed similar spatial patterns to the gradient maps of ground-derived spectral parameters. The results indicate the potential applicability of the parameters derived from spectral absorption features in screening and mapping the distribution of heavy metals. Correcting for differences in spectral and spatial resolution between ground and image spectra should be considered for quantitative mapping and the retrieval of heavy metal concentrations from HyMAP images.

Recursive formula for the peak delay time with travel distance in von Kármán type non-uniform random media on the basis of the Markov approximation

SUMMARY Direct waves of microearthquakes in the high-frequency range (>1 Hz) strongly reflect the random inhomogeneities near their ray paths. This study conducts numerical simulations of envelope broadening of impulsively radiated wavelet assuming spatially non-uniform distri- bution of random inhomogeneities. We assume plural von Karman type power spectral density functions (PSDF) for random inhomogeneity to clarify how the non-uniformly distributed ran- dom media affect the frequency dependence of envelope broadening. We employ the stochastic ray path method based on the Markov approximation for the mutual coherence function. This method is appropriate to simulate multiple forward scattering during the wave propagation. We mainly examine the travel distance and frequency dependence of the peak delay time in relation to the parameters characterizing the PSDFs. The peak delay time, which is defined as the time lag from the direct-wave onset to the maximum amplitude arrival of its envelope, is the best parameter reflecting the accumulated scattering effect in random media and is quite insensitive to the intrinsic attenuation. According to the numerical simulations in various non-uniform random media, we find some remarkable features in travel distance and frequency dependence, which cannot be found in uniform random media. For example, the frequency dependence in uniform random media is uniquely determined by the spectral gradient of PSDF for arbitrary travel distance; however, that in non-uniform media gradually changes as travel distance in- creases if the waves have experienced a change of spectral gradient in PSDF. Considering the results of our simulation, we propose a simple recursive formula to calculate the peak delay time in non-uniform random media. This recursive formula can predict the simulation results appropriately and relate the peak delay times to two parameters quantifying the von Karman type PSDF in short wavelengths. It will become a mathematical base for the inversion of peak delay times of bandpass filtered traces to estimate the spatial distribution of random inhomogeneity spectra.

The spectral gradient method for unconstrained optimal control problems

Optimal control problems and their discretized form can be viewed as optimization problems. Kelley and Sachs have already solved the discretized problem by using quasi-Newton methods. In this contribution, the problem is solved by a low-cost algorithm, the spectral gradient method, which is suitable for large-scale problems. The convergence behaviour of the method to finite-dimensional approximation is analysed. Numerical examples are given and the reported results show the good performance of the algorithm when it is applied to large optimal control problems.