A simple method of calculating eigenvalues and resonances in domains with infinite regular ends

A new approach is presented for the solution of spectral problems on infinite domains with regular ends, which avoids the need to solve boundary-value problems for many trial values of the spectral parameter. We present numerical results both for eigenvalues and for resonances, comparing with results reported by Aslanyan, Parnovski and Vassiliev.

Eigenvalues of a one-dimensional Dirac operator pencil

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of the coupling constant for which the kernel of the Dirac operator contains a square integrable function. In physics literature such a function is called a confined zero mode. Several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained. In particular, we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential. Surprisingly, it also depends on the arithmetic properties of certain quantities determined by the potential. We further observe that variable sign potentials may produce complex eigenvalues of the operator pencil. Some examples and numerical calculations illustrating these phenomena are presented.

The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.

Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

Spectroscopic analysis of terrestrial analogues for the interpretation of surface composition of rocky bodies in the solar system. Effects of mineral mixing and particle size. Applications to moon, mars and implications for mercury.

Among the Solar System’s bodies, Moon, Mercury and Mars are at present, or have been in the recent years, object of space missions aimed, among other topics, also at improving our knowledge about surface composition. Between the techniques to detect planet’s mineralogical composition, both from remote and close range platforms, visible and near-infrared reflectance (VNIR) spectroscopy is a powerful tool, because crystal field absorption bands are related to particular transitional metals in well-defined crystal structures, e.g., Fe2+ in M1 and M2 sites of olivine or pyroxene (Burns, 1993). Thanks to the improvements in the spectrometers onboard the recent missions, a more detailed interpretation of the planetary surfaces can now be delineated. However, quantitative interpretation of planetary surface mineralogy could not always be a simple task. In fact, several factors such as the mineral chemistry, the presence of different minerals that absorb in a narrow spectral range, the regolith with a variable particle size range, the space weathering, the atmosphere composition etc., act in unpredictable ways on the reflectance spectra on a planetary surface (Serventi et al., 2014). One method for the interpretation of reflectance spectra of unknown materials involves the study of a number of spectra acquired in the laboratory under different conditions, such as different mineral abundances or different particle sizes, in order to derive empirical trends. This is the methodology that has been followed in this PhD thesis: the single factors previously listed have been analyzed, creating, in the laboratory, a set of terrestrial analogues with well-defined composition and size. The aim of this work is to provide new tools and criteria to improve the knowledge of the composition of planetary surfaces. In particular, mixtures composed with different content and chemistry of plagioclase and mafic minerals have been spectroscopically analyzed at different particle sizes and with different mineral relative percentages. The reflectance spectra of each mixture have been analyzed both qualitatively (using the software ORIGIN®) and quantitatively applying the Modified Gaussian Model (MGM, Sunshine et al., 1990) algorithm. In particular, the spectral parameter variations of each absorption band have been evaluated versus the volumetric FeO% content in the PL phase and versus the PL modal abundance. This delineated calibration curves of composition vs. spectral parameters and allow implementation of spectral libraries. Furthermore, the trends derived from terrestrial analogues here analyzed and from analogues in the literature have been applied for the interpretation of hyperspectral images of both plagioclase-rich (Moon) and plagioclase-poor (Mars) bodies.

Retrievals of a size parameter for phytoplankton and spectral light absorption by colored detrital matter from water-leaving radiances at SeaWiFS channels in a continental shelf region off Brazil

Many efforts are currently oriented toward extracting more information from ocean color than the chlorophyll a concentration. Among biological parameters potentially accessible from space, estimates of phytoplankton cell size and light absorption by colored detrital matter (CDM) would lead to an indirect assessment of major components of the organic carbon pool in the ocean, which would benefit oceanic carbon budget models. We present here 2 procedures to retrieve simultaneously from ocean color measurements in a limited number of bands, magnitudes, and spectral shapes for both light absorption by CDM and phytoplankton, along with a size parameter for phytoplankton. The performance of the 2 procedures was evaluated using different data sets that correspond to increasing uncertainties: ( 1) measured absorption coefficients of phytoplankton, particulate detritus, and colored dissolved organic matter ( CDOM) and measured chlorophyll a concentrations and ( 2) SeaWiFS upwelling radiance measurements and chlorophyll a concentrations estimated from global algorithms. In situ data were acquired during 3 cruises, differing by their relative proportions in CDM and phytoplankton, over a continental shelf off Brazil. No local information was introduced in either procedure, to make them more generally applicable. Over the study area, the absorption coefficient of CDM at 443 nm was retrieved from SeaWiFS radiances with a relative root mean square error (RMSE) of 33%, and phytoplankton light absorption coefficients in SeaWiFS bands ( from 412 to 510 nm) were retrieved with RMSEs between 28% and 33%. These results are comparable to or better than those obtained by 3 published models. In addition, a size parameter of phytoplankton and the spectral slope of CDM absorption were retrieved with RMSEs of 17% and 22%, respectively. If these methods are applied at a regional scale, the performances could be substantially improved by locally tuning some empirical relationships.

Retrievals of a size parameter for phytoplankton and spectral light absorption by colored detrital matter from water-leaving radiances at SeaWiFS channels in a continental shelf region off Brazil

Many efforts are currently oriented toward extracting more information from ocean color than the chlorophyll a concentration. Among biological parameters potentially accessible from space, estimates of phytoplankton cell size and light absorption by colored detrital matter (CDM) would lead to an indirect assessment of major components of the organic carbon pool in the ocean, which would benefit oceanic carbon budget models. We present here 2 procedures to retrieve simultaneously from ocean color measurements in a limited number of bands, magnitudes, and spectral shapes for both light absorption by CDM and phytoplankton, along with a size parameter for phytoplankton. The performance of the 2 procedures was evaluated using different data sets that correspond to increasing uncertainties: ( 1) measured absorption coefficients of phytoplankton, particulate detritus, and colored dissolved organic matter ( CDOM) and measured chlorophyll a concentrations and ( 2) SeaWiFS upwelling radiance measurements and chlorophyll a concentrations estimated from global algorithms. In situ data were acquired during 3 cruises, differing by their relative proportions in CDM and phytoplankton, over a continental shelf off Brazil. No local information was introduced in either procedure, to make them more generally applicable. Over the study area, the absorption coefficient of CDM at 443 nm was retrieved from SeaWiFS radiances with a relative root mean square error (RMSE) of 33%, and phytoplankton light absorption coefficients in SeaWiFS bands ( from 412 to 510 nm) were retrieved with RMSEs between 28% and 33%. These results are comparable to or better than those obtained by 3 published models. In addition, a size parameter of phytoplankton and the spectral slope of CDM absorption were retrieved with RMSEs of 17% and 22%, respectively. If these methods are applied at a regional scale, the performances could be substantially improved by locally tuning some empirical relationships.

Sensitivity and specificity of machine learning classifiers for glaucoma diagnosis using Spectral Domain OCT and standard automated perimetry

PURPOSE: To evaluate the sensitivity and specificity of machine learning classifiers (MLCs) for glaucoma diagnosis using Spectral Domain OCT (SD-OCT) and standard automated perimetry (SAP). METHODS: Observational cross-sectional study. Sixty two glaucoma patients and 48 healthy individuals were included. All patients underwent a complete ophthalmologic examination, achromatic standard automated perimetry (SAP) and retinal nerve fiber layer (RNFL) imaging with SD-OCT (Cirrus HD-OCT; Carl Zeiss Meditec Inc., Dublin, California). Receiver operating characteristic (ROC) curves were obtained for all SD-OCT parameters and global indices of SAP. Subsequently, the following MLCs were tested using parameters from the SD-OCT and SAP: Bagging (BAG), Naive-Bayes (NB), Multilayer Perceptron (MLP), Radial Basis Function (RBF), Random Forest (RAN), Ensemble Selection (ENS), Classification Tree (CTREE), Ada Boost M1(ADA),Support Vector Machine Linear (SVML) and Support Vector Machine Gaussian (SVMG). Areas under the receiver operating characteristic curves (aROC) obtained for isolated SAP and OCT parameters were compared with MLCs using OCT+SAP data. RESULTS: Combining OCT and SAP data, MLCs' aROCs varied from 0.777(CTREE) to 0.946 (RAN).The best OCT+SAP aROC obtained with RAN (0.946) was significantly larger the best single OCT parameter (p<0.05), but was not significantly different from the aROC obtained with the best single SAP parameter (p=0.19). CONCLUSION: Machine learning classifiers trained on OCT and SAP data can successfully discriminate between healthy and glaucomatous eyes. The combination of OCT and SAP measurements improved the diagnostic accuracy compared with OCT data alone.

Spectral properties of chaotic signals with applications in communications

This paper investigates the characteristics of the Power Spectral Density (PSD) of chaotic signals generated by skew tent maps. The influence of the Lyapunov exponent on the autocorrelation sequence and on the PSD is evaluated via computational simulations. We conclude that the essential bandwidth of these signals is strongly related to this exponent and they can be low-pass or high-pass depending on the family`s parameter. This way, the PSD of a chaotic signal is a function of the generating map although this is not a one-to-one relationship. (C) 2009 Elsevier Ltd. All rights reserved.

Spectral characteristics of atrial electrograms in sinus rhythm correlates with sites of ganglionated plexuses in patients with paroxysmal atrial fibrillation

Aims To verify whether spectral components of atrial electrograms (AE) during sinus rhythm (SR) correlate with cardiac ganglionated plexus (GP) sites. Methods and results Thirteen patients undergoing atrial fibrillation (AF) ablation were prospectively enrolled. Prior to radio frequency application, endocardial AE were recorded with a sequential point-by-point approach. Electrical stimuli were delivered at 20 Hz, amplitude 100 V, and pulse width of 4 ms. A vagal response was defined as a high-frequency stimulation (HFS) evoked atrioventricular block or a prolongation of RR interval. Spectral analysis was performed on single AE during SR, sampling rate of 1000 Hz, Hanning window. Overall, 1488 SR electrograms were analysed from 186 different left atrium sites, 129 of them corresponding to negative vagal response sites, and 57 to positive response sites. The electrogram duration and the number of deflections were similar in positive and negative response sites. Spectral power density of sites with vagal response was lower between 26 and 83 Hz and higher between 107 and 200 Hz compared with negative response sites. The area between 120 and 170 Hz normalized to the total spectrum area was tested as a diagnostic parameter. Receiver operating characteristic curve analysis demonstrated that an area120-170/area(total) value >0.14 identified vagal sites with 70.9% sensitivity and 72.1% specificity. Conclusion Spectral analysis of AE during SR in sites that correspond to the anatomical location of the GP is feasible and may be a simpler method of mapping the cardiac autonomic nervous system, compared with the HFS technique.

Comparison of Different Spectral Domain Optical Coherence Tomography Scanning Areas for Glaucoma Diagnosis

Purpose: To evaluate retinal nerve fiber layer (RNFL), optic nerve head (ONH), and macular thickness measurements for glaucoma detection using the RTVue spectral domain optical coherence tomograph. Design: Diagnostic, case-control study. Participants: One hundred forty eyes of 106 glaucoma patients and 74 eyes of 40 healthy subjects from the Diagnostic Innovations in Glaucoma Study (DIGS). Methods: All patients underwent ocular imaging with the commercially available RTVue. Optic nerve head, RNFL thickness, and macular thickness scans were obtained during the same visit. Receiver operating characteristic (ROC) curves and sensitivities at fixed specificities (80% and 95%) were calculated for each parameter. Main Outcome Measures: Areas under the ROC curves (AUC) and sensitivities at fixed specificities of 80% and 95%. Results: The AUC for the RNFL parameter with best performance, inferior quadrant thickness, was significantly higher than that of the best-performing ONH parameter, inferior rim area (0.884 vs 0.812, respectively; P = 0.04). There was no difference between ROC curve areas of the best RNFL thickness parameters and the best inner macular thickness measurement, ganglion cell complex root mean square (ROC curve area = 0.870). Conclusions: The RTVue RNFL and inner retinal macular thickness measurements had good ability to detect eyes with glaucomatous visual field loss and performed significantly better than ONH parameters.

Effect of Disease Severity on the Performance of Cirrus Spectral-Domain OCT for Glaucoma Diagnosis

PURPOSE. To evaluate the effect of disease severity on the diagnostic accuracy of the Cirrus Optical Coherence Tomograph (Cirrus HD-OCT; Carl Zeiss Meditec, Inc., Dublin, CA) for glaucoma detection. METHODS. One hundred thirty-five glaucomatous eyes of 99 patients and 79 normal eyes of 47 control subjects were recruited from the longitudinal Diagnostic Innovations in Glaucoma Study (DIGS). The severity of the disease was graded based on the visual field index (VFI) from standard automated perimetry. Imaging of the retinal nerve fiber layer (RNFL) was obtained using the optic disc cube protocol available on the Cirrus HD-OCT. Pooled receiver operating characteristic (ROC) curves were initially obtained for each parameter of the Cirrus HD-OCT. The effect of disease severity on diagnostic performance was evaluated by fitting an ROC regression model, with VFI used as a covariate, and calculating the area under the ROC curve (AUCs) for different levels of disease severity. RESULTS. The largest pooled AUCs were for average thickness (0.892), inferior quadrant thickness (0.881), and superior quadrant thickness (0.874). Disease severity had a significant influence on the detection of glaucoma. For the average RNFL thickness parameter, AUCs were 0.962, 0.932, 0.886, and 0.822 for VFIs of 70%, 80%, 90%, and 100%, respectively. CONCLUSIONS. Disease severity had a significant effect on the diagnostic performance of the Cirrus HD-OCT and thus should be considered when interpreting results from this device and when considering the potential applications of this instrument for diagnosing glaucoma in the various clinical settings. (Invest Ophthalmol Vis Sci. 2010;51:4104-4109) DOI:10.1167/iovs.094716