Spectral Gradient Research Articles

Spectral Study of Measles Epidemics: The Dependence of Spectral Gradient on the Population Size of the Community

We have carried out spectral analysis of measles notifications in several communities in Denmark, UK and USA. The results confirm that each power spectral density (PSD) shows exponential characteristics, which are universally observed in the PSD for time series generated from nonlinear dynamical system. The exponential gradient increases with the population size. For almost all communities, many spectral lines observed in each PSD can be fully assigned to linear combinations of several fundamental periods, suggesting that the measles data are substantially noise-free. The optimum least squares fitting curve calculated using these fundamental periods essentially reproduces an underlying variation of the measles data, and an extension of the curve can be used to predict measles epidemics. For the communities with large population sizes, some PSD patterns obtained from segment time series analysis show a close resemblance to the PSD patterns at the initial stages of a period-doubling bifurcation process for the so-called susceptible/exposed/infectious/recovered (SEIR) model with seasonal forcing. The meaning of the relationship between the exponential gradient and the population size is discussed.

Observations of the Centaur 1999 UG5: Evidence of a Unique Outer Solar System Surface

ABSTRACTThe outer solar system body 1999 UG5 is a Centaur of medium brightness and slightly redder color when compared to other Centaurs. Similar to at least 1/5 of the known Centaurs, it is a Saturn‐crosser with a mean orbital distance between Saturn and Uranus. We present optical photometry data and near‐IR spectra obtained during 2000 September, November, and December. We find a rotation period of 13.41 ± 0.04 hr with an amplitude of 0.102 ± 0.005 mag and a phase curve with a Lumme‐Bowell G value of -0.13 ± 0.02. BVRI colors are reported, and they confirm the red spectral gradient observed previously. Our spectra reveal that this redward slope extends into near‐IR wavelengths and indicates possible localized differences in the surface composition.

ESO large program on physical studies of Transneptunian Objects and Centaurs: Visible photometry – First results

We present the first results of BVRI photometry of Transneptunian Objects (TNOs) and Centaurs obtained through the ESO Large Program on physical studies of these icy bodies in the outer solar system. In total 28 objects were observed of which 18 are new measurements. Combining our new BVRI photometry with the data summary published by Hainaut & Delsanti (2002) results in a database of 94 objects: 45 Cubewanos, 22 Plutinos, 13 scattered disk objects, 14 Centaurs. The reddening range seems to be similar among the four dynamical classes (− 5t o 55%/l00 nm) and only one outlier (1994 ES2) exists. The spectral gradient distribution of the Cubewanos peaks between 25 to 35%/l00 nm, while for the three other types the maximum seems to fall below 20%/l00 nm. A clustering of red Cubewanos with perihelia beyond ∼41 AU in low eccentricity and low inclination orbit suggests that these objects are less affected by the physical processes that potentially produce neutral colors, i.e. resurfacing by collision and by intrinsic activity. For Cubewanos and scattered disk objects, the range of reddening increases with decreasing perihelion distance and with increasing orbital excitation. A correlation of the spectral slope with inclination is present for Cubewanos and scattered disk objects, and is non-existent for the other dynamical types. It is unclear whether these trends (or their absence) are discriminative for the correctness of the resurfacing scenarios. If intrinsic activity is responsible for resurfacing, the start of the effect inside ∼41 AU from the Sun may be indicative for the driving agent, while in the collision scenario the survival of the red Cubewano cluster in the central region of the Kuiper-Belt argues for the existence of a population of bodies the surface of which is heavily radiation processed without impact resurfacing.

A parsec-scale study of the 5/15-GHz spectral indices of the compact radio sources in M82

Observations of the starburst galaxy, M82, have been made with the Very Large Array (VLA) in its A configuration at 15 GHz and the Multi-Element Radio-Linked Interferometer Network (MERLIN) at 5 GHz, enabling a spectral analysis of the compact radio structure on a scale of <0.1 arcsec (1.6 pc). Crucial to these observations was the inclusion of the Pie Town Very Long Baseline Array (VLBA) antenna, which increased the resolution of the VLA observations by a factor of ∼2. A number of the weaker sources are shown to have thermal spectra and are identified as H II regions with emission measures ∼10 7 cm - 6 pc. Some of the sources appear to be optically thick at 5 GHz, implying even higher emission measures of ∼10 8 cm - 6 pc. The number of compact radio sources in M82 whose origin has been determined is now 46, of which 30 are supernova-related and the remaining 16 are HII regions. An additional 15 sources are noted, but have yet to be identified, meaning that the total number of compact sources in M82 is at least 61. Also, it is shown that the distribution of HII regions is correlated with the large-scale ionized gas distribution, but is different from the distribution of supernova remnants. In addition, the brightest HII region at (B1950) 09 h 51 m 42 s .21 + 69°54'59.2 shows a spectral index gradient across its resolved structure which we attribute to the source becoming optically thick towards its centre.

A passive microwave snow depth algorithm with a proxy for snow metamorphism

AbstractPassive microwave brightness temperatures of snowpacks depend not only on the snow depth, but also on the internal snowpack properties, particularly the grain size, which changes through the winter. Algorithms that assume a constant grain size can yield erroneous estimates of snow depth or water equivalent. For snowpacks that are subject to temperatures well below freezing, the bulk temperature gradient through the snowpack controls the metamorphosis of the snow grains. This study used National Weather Service (NWS) station measurements of snow depth and air temperature from the Northern US Great Plains to determine temporal and spatial variability of the snow depth and bulk snowpack temperature gradient. This region is well suited for this study because it consists primarily of open farmland or prairie, has little relief, is subject to very cold temperatures, and has more than 280 reporting stations. A geostatistical technique called Kriging was used to grid the randomly spaced snow depth measurements. The resulting snow depth maps were then compared with the passive microwave observations from the Special Sensor Microwave Imager (SSM/I). Two snow seasons were examined: 1988–89, a typical snow year, and 1996–97, a record year for snow that was responsible for extensive flooding in the Red River Basin. Inspection of the time series of snow depth and microwave spectral gradient (the difference between the 19 and 37 GHz bands) showed that while the snowpack was constant, the spectral gradient continued to increase. However, there was a strong correlation (0·6 &lt; R2 &lt; 0·9) between the spectral gradient and the cumulative bulk temperature gradient through the snowpack (TGI). Hence, TGI is an index of grain size metamorphism that has occurred within the snowpack. TGI time series from 21 representative sites across the region and the corresponding SSM/I observations were used to develop an algorithm for snow depth that requires daily air temperatures. Copyright © 2002 John Wiley &amp; Sons, Ltd.

VLT observations of comet 46P/Wirtanen

Comet 46P/Wirtanen, prime target of ESA's ROSETTA mission, was successfully observed at the Very Large Telescope Observatory in Chile: on 17 May 1999 with the Test Camera at the Cassegrain focus of the 8.2-m VLT Kueyen telescope and on 8 December 2001 with FORS1 at Unit Telescope 4 Yepun. May 1999: no coma was detected at heliocentric distance r = 4.98 AU. From the measured brightness in the Bessell R-filter, a mean nucleus radius of 555 ′ 40 m is derived (for a geometric albedo of 0.04 and a phase darkening of 0.04 mag/deg). The nucleus signal varies during the 2.7 h observing interval and a peak-to-peak amplitude of ∼0.38 mag is determined. The measured lightcurve is in agreement with a rotation period of 6-7.5 hours and a ratio of the main nucleus axes of at least 1.4. The non-detection of a coma allows one to put an approximate upper limit for Afp of <0.45 cm (suggesting a dust production rate of 0.05 kg/s). December 2001: a weak and condensed coma seems to be present in the seeing disk of the comet at 2.9 AU inbound, causing a higher brightness than expected from the previous size estimates of the nucleus. The colour of the comet appears very red (V - R spectral gradient ∼47%/100 nm). The Afp value of the comet was 6.5 ′ 2 cm (equivalent to a dust production rate of about 1 kg/s).

A case study of HF radar spectral width in the post midnight magnetic local time sector and its relationship to the polar cap boundary

Abstract. The aim of this paper is to advance the current understanding of the spectral width parameter observed by coherent high frequency (HF) radars. In particular, we address the relationship of a frequently observed gradient, between low ( &lt; 200 m/s) and high ( &gt; 200 m/s) spectral width, to magnetospheric boundaries. Previous work has linked this gradient in the spectral width, in the nightside sector of magnetic local time, to the Polar Cap Boundary (PCB), and also to the boundary between the Central Plasma Sheet (CPS) and the Plasma Sheet Boundary Layer (PSBL). The present case study investigates the former by comparison with the 630.0 nm optical emission. No suitable data were available to test the second of the two hypotheses. It is found that during the interval in question the spectral width gradient is within the region of the 630.0 nm optical emission. A comparison of coherent and incoherent scatter radar data is also conducted, which indicates that values of high spectral width are typically collocated with elevated F-region electron temperatures. We conclude that the high spectral width region in the interval under study is associated with particle precipitation and also that the spectral width gradient is not a reliable method for locating the PCB.Key words. Ionosphere (auroral ionosphere; ionospheric irregularities)

Northern Great Plains 1996/97 seasonal evolution of snowpack parameters from satellite passive-microwave measurements

AbstractFor the American northern Great Plains region, the 1996/97 snow season had snow accumulations much greater than normal, which combined with rapid warming to produce extensive flooding in the Red River of the North river basin. Passive-microwave observations from the Special Sensor Microwave/Imager (SSM/I) are used to follow the evolution of the snowpack during the snow season and to map the extent of standing water or very saturated soils during spring 1997. SSM/I-derived snow-depth algorithms that assume a fixed snow grain-size constantly underestimated the snow depth by a factor of 2 in the region where extensive flooding occurred. An estimate of the thermal gradient through the snowpack is used to model the growth of the snow grain-size and to compute more accurately the evolution of the snow depth over the region. As is commonly observed, when the melt season begins, liquid water in the snowpack causes the SSM/I spectral gradient to drop to zero. In this case, the spectral gradient fell to unusually negative values, which were indicative of large areas of open water, and not wet snow or soil.

Preconditioned spectral gradient method

The spectral gradient method is a nonmonotone gradient method for large-scale unconstrained minimization. We strengthen the algorithm by modifications which globalize the method and present strategies to apply preconditioning techniques. The modified algorithm replaces a condition of uniform positive definitness of the preconditioning matrices, with mild conditions on the search directions. The result is a robust algorithm which is effective on very large problems. Encouraging numerical experiments are presented for a variety of standard test problems, for solving nonlinear Poisson-type equations, an also for finding molecular conformations by distance geometry.

CN, NH$_{\mathsf 2}$, and dust in the atmosphere of comet C/1999 J3 (LINEAR)

Comet C/1999 J3 (LINEAR) was observed with 2 m telescope of the Pik Terskol Observatory on September 19, 1999. Narrow-band CCD images of the CN, NH2 , and dust atmospheres were recorded with the Two-Channel focal reducer of the Max-Plank-Institute for Aeronomy. The distributions of the CN and NH2 molecules in the comet atmosphere were fitted with a Monte Carlo model. For the CN atmosphere the best agreement between observed and calculated surface profiles was reached with the CN photodissociation lifetime s and with the parent photodissociation lifetime s. This result indicates that HCN is the main source of the CN radicals in the atmosphere of comet C/1999 J3 (LINEAR). Regarding the NH2 radicals, there is no doubt that NH3 is the dominant source of this species in the comet atmosphere. The lifetimes s for NH2 and s for its parent are close to theoretical calculations. The gas-production rates of CN, mol s-1 , and NH2 , mol s-1 have also been determined. The appearance of the comet and the obtained data show that the comet is a gaseous one. The values are 21.6 cm for the blue spectral window and 23.4 cm for the red one. The normalized spectral gradient of the cometary dust is low, 4.0% per 1000 A. The ratio log((/Q (CN)) = -24.25 indicates a very low dust to gas ratio as well.

A New System of Parallel Isolated Nonthermal Filaments near the Galactic Center: Evidence for a Local Magnetic Field Gradient

We report the discovery of a system of isolated nonthermal filaments approximately 0.5 deg. northwest (75 pc in projection) of Sgr A. Unlike other isolated nonthermal filaments which show subfilamentation, braiding of subfilaments, and flaring at their ends, these filaments are simple linear structures and more closely resemble the parallel bundled filaments in the Galactic center radio arc. However, the most unusual feature of these filaments is that the 20/90 cm spectral index uniformly decreases as a function of length, in contrast to all other nonthermal filaments in the Galactic center. This spectral gradient may not be due to simple particle aging but could be explained by a curved electron energy spectrum embedded in a diverging magnetic field. If so, the scale of the magnetic gradient is not consistent with a large scale magnetic field centered on Sgr A* suggesting that this filament system is tracing a local magnetic field.

Algorithm 813

Fortran 77 software implementing the SPG method is introduced. SPG is a nonmonotone projected gradient algorithm for solving large-scale convex-constrained optimization problems. It combines the classical projected gradient method with the spectral gradient choice of steplength and a nonmonotone line-search strategy. The user provides objective function and gradient values, and projections onto the feasible set. Some recent numerical tests are reported on very large location problems, indicating that SPG is substantially more efficient than existing general-purpose software on problems for which projections can be computed efficiently.

VERTICAL LEAF SPECTRAL VARIATION AS AN INDICATOR OF NITROGEN NUTRITION STATUS IN RICE PLANTS

A field experiment was conducted to study the response of individual leaf spectral reflectance to five levels of nitrogen fertilizer treatments in rice (Oriza sativa L.) plants. Sampling was combined through a rice canopy at upper, medium and low levels for biomass, nitrogen and water content measurements with spectral signals from the leaves. The vertical gradients of leaf biomass, nitrogen and water contents were associated with the nitrogen availability during tillering, panicle formation, initial heading and heading. Rice plants treated with the lowest rate of N could be characterized with the lowest value of gradient in leaf biomass and leaf water content and the highest value of gradient in leaf N concentration. A spectral gradient of single reflectance (R), ratio (RVI) and normalized difference (ND) of two individual reflectances was defined as this yielded a better relationship between the spectral data and leaf nitrogen concentration. The results suggested the spectral gradients may be used as an improved diagnostic tool for nitrogen status.

Soil freeze/thaw cycles over snow‐free land detected by passive microwave remote sensing

The timing, duration, and areal extent of the near‐surface soil freeze/thaw status were investigated using passive microwave satellite remote sensing data for the 1997/98 winter over the contiguous United States. A frozen soil algorithm was validated using soil temperature data at 0 cm and 5 cm depths from more than 20 sites over the study area. Results indicated that a negative spectral gradient and a cut‐off 37‐GHz vertical polarized brightness temperature of 258.2K can be used to determine near‐surface soil freeze/thaw status with confidence. The microwave freeze/thaw boundary generally agreed with −5.0°C isotherm of air temperature although frozen soils occurred sporadically between 0°C and −5.0°C isotherms. The maximum frozen soil area over snow‐free land surface was about 3.75 × 106 km² or about 37% of the total study area during the 1997/98 winter. The near‐surface soils often froze before snow covered the land surface, but soil freeze/thaw status under snow cover cannot be detected using this microwave technique. The onset of soil freeze mainly occurred in October and November, while the last days of soil freeze occurred in March and April, resulting in the duration of soil freezing varying from five to seven months over the majority of the study areas. The number of days of surface soil freezing varied from several days to longer than five months.

A Spectral Conjugate Gradient Method for Unconstrained Optimization

A family of scaled conjugate gradient algorithms for large-scale unconstrained minimization is defined. The Perry, the Polak—Ribiere and the Fletcher—Reeves formulae are compared using a spectral scaling derived from Raydan's spectral gradient optimization method. The best combination of formula, scaling and initial choice of step-length is compared against well known algorithms using a classical set of problems. An additional comparison involving an ill-conditioned estimation problem in Optics is presented.

VERTICAL LEAF SPECTRAL VARIATION AS AN INDICATOR OF NITROGEN NUTRITION STATUS IN RICE PLANTS

A field experiment was conducted to study the response of individual leaf spectral reflectance to five levels of nitrogen fertilizer treatments in rice\%(Oriza sativa L.)\% plants. Sampling was combined through a rice canopy at upper, medium and low levels for biomass, nitrogen and water content measurements with spectral signals from the leaves. The vertical gradients of leaf biomass ,nitrogen and water contents were associated with the nitrogen availability during tillering, panicle formation, initial heading and heading. Rice plants treated with the lowest rate of N could be characterized with the lowest value of gradient in leaf biomass and leaf water content and the highest value of gradient in leaf N concentration. A spectral gradient of single reflectance(R),ratio(RVI) and normalized difference(ND) of two individual reflectances was defined as this yielded a better relationship between the spectral data and leaf nitrogen concentration. The results suggested the spectral gradients may be used as an improved diagnostic tool for nitrogen status.

A fast and global two point low storage optimization technique for tracing rays in 2D and 3D isotropic media

We present the problem of tracing rays in 2D and 3D heterogeneous isotropic media as a set of optimization problems. Each optimization problem is obtained by applying Fermat's principle to an approximation of the travel time equation from a fixed source to a fixed receiver. We assume a piecewise linear ray path that simplifies the computations of the problem, in the same way Mao and Stuart suggested in a very recent paper. Here, instead, the reflector geometry and the velocity function are computed by using nonuniformly biharmonic splines. On the other hand, to solve the optimization problem we use the Global Spectral Gradient method. This recent developed optimization scheme is a low storage optimization technique that requires very few floating point operations. It only requires the gradient of the travel time function, and it is global because it converges independently of the initial guess, that is, it does not require a close initial ray path. These three properties of the optimization method and the assumption of piecewise linear rays make this ray tracing scheme a very fast, global and effective method when estimating velocities via tomography. Moreover, in a homogeneous stratified or dipped media, any solution of the optimization problem is the best solution, i.e., it is the global minimum, no matter what numerical approach is used. We present some numerical results that show the computational advantages and the performance of this ray tracing in homogeneous and heterogeneous media.

New hierarchy of integrable system bi-Hamiltonian structure and constrained flows

We have considered the hierarchy of integrable systems associated with the unstable nonlinear Schrodinger equation. The spectral gradient approach and the trace identity are used to derive the bi-Hamiltonian structure of the system. The bi-Hamiltonian property and the square eigenfunctions determined via the spectral gradient approach are then used to construct constrained flows, which is also proved to be derivable from a rational Lax operator. This new Lax operator of the constrained flows is seen to generate the classical r-matrix. Lastly it is also explicitly demonstrated that the different integrals of motion of the constrained flows Poisson commute.

Nonmonotone Spectral Projected Gradient Methods on Convex Sets

Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo--Lampariello--Lucidi nonmonotone line search. In particular, the nonmonotone strategy is combined with the spectral gradient choice of steplength to accelerate the convergence process. In addition to the classical projected gradient nonlinear path, the feasible spectral projected gradient is used as a search direction to avoid additional trial projections during the one-dimensional search process. Convergence properties and extensive numerical results are presented.

Low Cost Optimization Techniques for Solving the Nonlinear Seismic Reflection Tomography Problem

The nonlinear seismic reflection tomography problem consists on minimizing the function g(p) = ∥T − f(p)∥22, where p is a vector containing the velocity model parameters and depth position of the reflectors, T contains the travel time of the rays, and f(p) is a highly nonlinear function that depends on the velocity of the subsurfaces. This problem has been solved using the Gauss-Newton method, and reconstruction techniques. These methods require either too many storage locations or too many iterations to converge. We present a different approach. We apply recently developed low storage minimization techniques directly on the function g(p). In particular, we use the recent global version of the spectral gradient method, and recent implementations of the conjugate gradient method. We present encouraging preliminary numerical results that indicate that our new approach clearly outperforms the classical techniques in CPU time and accuracy of the approximate solutions.