Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators

Subject of investigation in this paper is a one-dimensional Schrödinger equation, where the potential is a sum of a periodic function and a perturbation decaying at . It is well known that the essential spectrum consists of spectral bands, and that there may or may not be additional eigenvalues below the lowest band or in the gaps between the bands. While enclosures for gap eigenvalues can comparatively easily be obtained from numerical approximations, e.g. by D. Weinstein's bounds, there seems to be no method available so far which is able to exclude eigenvalues in spectral gaps, i.e. which identifies subregions (of a gap) which contain no eigenvalues. Here, we propose such a method. It makes heavy use of computer assistance; nevertheless, the results are completely rigorous in the strict mathematical sense, because all computational errors are taken into account.

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Causal Probabilistic Network and Power Spectral Estimation Used in Sleep Stage Classification

Methods of Information in Medicine ◽

10.1055/s-0038-1636853 ◽

1997 ◽

Vol 36 (04/05) ◽

pp. 41-46

Author(s):

A. Kjaer ◽

W. Jensen ◽

T. Dyrby ◽

L. Andreasen ◽

J. Andersen ◽

...

Keyword(s):

Sleep Stage ◽

Spectral Estimation ◽

Interrater Agreement ◽

Probabilistic Networks ◽

Probabilistic Network ◽

Spectral Bands ◽

Power Spectral ◽

Stage Classification ◽

Sleep Stage Classification ◽

The Brain

Abstract.A new method for sleep-stage classification using a causal probabilistic network as automatic classifier has been implemented and validated. The system uses features from the primary sleep signals from the brain (EEG) and the eyes (AOG) as input. From the EEG, features are derived containing spectral information which is used to classify power in the classical spectral bands, sleep spindles and K-complexes. From AOG, information on rapid eye movements is derived. Features are extracted every 2 seconds. The CPN-based sleep classifier was implemented using the HUGIN system, an application tool to handle causal probabilistic networks. The results obtained using different training approaches show agreements ranging from 68.7 to 70.7% between the system and the two experts when a pooled agreement is computed over the six subjects. As a comparison, the interrater agreement between the two experts was found to be 71.4%, measured also over the six subjects.

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Selection of Spectral Bands for Recognizing Plant Species by Reflection Characteristics in the Optical Region

Telecommunications and Radio Engineering ◽

10.1615/telecomradeng.v52.i10.220 ◽

1998 ◽

Vol 52 (10) ◽

pp. 83-86

Author(s):

D. M. Piza ◽

S. V. Morshchavka

Keyword(s):

Plant Species ◽

Spectral Bands ◽

Optical Region ◽

Reflection Characteristics ◽

Selection Of

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Optics and photonics. Spectral bands

10.3403/30112984u ◽

2015 ◽

Keyword(s):

Spectral Bands

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Triatomic molecules

10.1093/oso/9780198788980.003.0004 ◽

2018 ◽

Author(s):

John H. D. Eland ◽

Raimund Feifel

Keyword(s):

Degrees Of Freedom ◽

Normal Modes ◽

Electronic States ◽

Triatomic Molecules ◽

Doubly Charged Ions ◽

Spectral Bands ◽

Valence Electrons ◽

Doubly Charged ◽

Charged Ions ◽

Double Ionisation

Double ionisation of the triatomic molecules presented in this chapter shows an added degree of complexity. Besides potentially having many more electrons, they have three vibrational degrees of freedom (three normal modes) instead of the single one in a diatomic molecule. For asymmetric and bent triatomic molecules multiple modes can be excited, so the spectral bands may be congested in all forms of electronic spectra, including double ionisation. Double photoionisation spectra of H2O, H2S, HCN, CO2, N2O, OCS, CS2, BrCN, ICN, HgCl2, NO2, and SO2 are presented with analysis to identify the electronic states of the doubly charged ions. The order of the molecules in this chapter is set first by the number of valence electrons, then by the molecular weight.

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Growth Stages Classification of Potato Crop Based on Analysis of Spectral Response and Variables Optimization

Sensors ◽

10.3390/s20143995 ◽

2020 ◽

Vol 20 (14) ◽

pp. 3995 ◽

Cited By ~ 3

Author(s):

Ning Liu ◽

Ruomei Zhao ◽

Lang Qiao ◽

Yao Zhang ◽

Minzan Li ◽

...

Keyword(s):

Growth Stage ◽

Spectral Response ◽

Classification Model ◽

Growth Stages ◽

Potato Field ◽

Spectral Bands ◽

Svm Model ◽

Selection Algorithms ◽

Potato Crops

Potato is the world’s fourth-largest food crop, following rice, wheat, and maize. Unlike other crops, it is a typical root crop with a special growth cycle pattern and underground tubers, which makes it harder to track the progress of potatoes and to provide automated crop management. The classification of growth stages has great significance for right time management in the potato field. This paper aims to study how to classify the growth stage of potato crops accurately on the basis of spectroscopy technology. To develop a classification model that monitors the growth stage of potato crops, the field experiments were conducted at the tillering stage (S1), tuber formation stage (S2), tuber bulking stage (S3), and tuber maturation stage (S4), respectively. After spectral data pre-processing, the dynamic changes in chlorophyll content and spectral response during growth were analyzed. A classification model was then established using the support vector machine (SVM) algorithm based on spectral bands and the wavelet coefficients obtained from the continuous wavelet transform (CWT) of reflectance spectra. The spectral variables, which include sensitive spectral bands and feature wavelet coefficients, were optimized using three selection algorithms to improve the classification performance of the model. The selection algorithms include correlation analysis (CA), the successive projection algorithm (SPA), and the random frog (RF) algorithm. The model results were used to compare the performance of various methods. The CWT-SPA-SVM model exhibited excellent performance. The classification accuracies on the training set (Atrain) and the test set (Atest) were respectively 100% and 97.37%, demonstrating the good classification capability of the model. The difference between the Atrain and accuracy of cross-validation (Acv) was 1%, which showed that the model has good stability. Therefore, the CWT-SPA-SVM model can be used to classify the growth stages of potato crops accurately. This study provides an important support method for the classification of growth stages in the potato field.

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Development of the Statistical Model for Monitoring Salinization in the Mekong Delta of Vietnam Using Remote Sensing Data and In-Situ Measurements

Proceedings ◽

10.3390/iecg_2018-05362 ◽

2018 ◽

Vol 2 (10) ◽

pp. 565

Author(s):

Nguyen Nguyen Vu ◽

Le Van Trung ◽

Tran Thi Van

Keyword(s):

Statistical Model ◽

Mekong Delta ◽

Remote Sensing Data ◽

Principal Component ◽

Measured Data ◽

In Situ Measurements ◽

Landsat 8 ◽

Spectral Bands ◽

Component Band

This article presents the methodology for developing a statistical model for monitoring salinity intrusion in the Mekong Delta based on the integration of satellite imagery and in-situ measurements. We used Landsat-8 Operational Land Imager and Thermal Infrared Sensor (Landsat- 8 OLI and TIRS) satellite data to establish the relationship between the planetary reflectance and the ground measured data in the dry season during 2014. The three spectral bands (blue, green, red) and the principal component band were used to obtain the most suitable models. The selected model showed a good correlation with the exponential function of the principal component band and the ground measured data (R2 > 0.8). Simulation of the salinity distribution along the river shows the intrusion of a 4 g/L salt boundary from the estuary to the inner field of more than 50 km. The developed model will be an active contribution, providing managers with adaptation and response solutions suitable for intrusion in the estuary as well as the inner field of the Mekong Delta.

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Understanding Vine Hyperspectral Signature through Different Irrigation Plans: A First Step to Monitor Vineyard Water Status

Remote Sensing ◽

10.3390/rs13030536 ◽

2021 ◽

Vol 13 (3) ◽

pp. 536

Author(s):

Eve Laroche-Pinel ◽

Mohanad Albughdadi ◽

Sylvie Duthoit ◽

Véronique Chéret ◽

Jacques Rousseau ◽

...

Keyword(s):

Near Infrared ◽

Water Status ◽

Vegetation Indices ◽

Remote Sensing Data ◽

Short Wave ◽

Spatial And Temporal Scales ◽

Spectral Bands ◽

Main Challenge ◽

Spectral Scale ◽

Grape Varieties

The main challenge encountered by Mediterranean winegrowers is water management. Indeed, with climate change, drought events are becoming more intense each year, dragging the yield down. Moreover, the quality of the vineyards is affected and the level of alcohol increases. Remote sensing data are a potential solution to measure water status in vineyards. However, important questions are still open such as which spectral, spatial, and temporal scales are adapted to achieve the latter. This study aims at using hyperspectral measurements to investigate the spectral scale adapted to measure their water status. The final objective is to find out whether it would be possible to monitor the vine water status with the spectral bands available in multispectral satellites such as Sentinel-2. Four Mediterranean vine plots with three grape varieties and different water status management systems are considered for the analysis. Results show the main significant domains related to vine water status (Short Wave Infrared, Near Infrared, and Red-Edge) and the best vegetation indices that combine these domains. These results give some promising perspectives to monitor vine water status.

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Forensic analysis of beverage stains using hyperspectral imaging

Scientific Reports ◽

10.1038/s41598-021-85737-x ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Binu Melit Devassy ◽

Sony George

Keyword(s):

Hyperspectral Imaging ◽

Crime Scene ◽

Forensic Analysis ◽

Classification Model ◽

Support Vector ◽

Additional Information ◽

Non Invasive ◽

Spectral Bands ◽

Data Dimensionality Reduction ◽

Gradient Based

AbstractDocumentation and analysis of crime scene evidences are of great importance in any forensic investigation. In this paper, we present the potential of hyperspectral imaging (HSI) to detect and analyze the beverage stains on a paper towel. To detect the presence and predict the age of the commonly used drinks in a crime scene, we leveraged the additional information present in the HSI data. We used 12 different beverages and four types of paper hand towel to create the sample stains in the current study. A support vector machine (SVM) is used to achieve the classification, and a convolutional auto-encoder is used to achieve HSI data dimensionality reduction, which helps in easy perception, process, and visualization of the data. The SVM classification model was re-established for a lighter and quicker classification model on the basis of the reduced dimension. We employed volume-gradient-based band selection for the identification of relevant spectral bands in the HSI data. Spectral data recorded at different time intervals up to 72 h is analyzed to trace the spectral changes. The results show the efficacy of the HSI techniques for rapid, non-contact, and non-invasive analysis of beverage stains.

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Hyperspectral Imaging for Bloodstain Identification

Sensors ◽

10.3390/s21093045 ◽

2021 ◽

Vol 21 (9) ◽

pp. 3045

Author(s):

Maheen Zulfiqar ◽

Muhammad Ahmad ◽

Ahmed Sohaib ◽

Manuel Mazzara ◽

Salvatore Distefano

Keyword(s):

Hyperspectral Imaging ◽

Dna Analysis ◽

Forensic Sciences ◽

Blood Protein ◽

Chemical Methods ◽

Acrylic Paint ◽

Spectral Bands ◽

Nail Polish ◽

Spatial Dimensions ◽

Non Destructive

Blood is key evidence to reconstruct crime scenes in forensic sciences. Blood identification can help to confirm a suspect, and for that reason, several chemical methods are used to reconstruct the crime scene however, these methods can affect subsequent DNA analysis. Therefore, this study presents a non-destructive method for bloodstain identification using Hyperspectral Imaging (HSI, 397–1000 nm range). The proposed method is based on the visualization of heme-components bands in the 500–700 nm spectral range. For experimental and validation purposes, a total of 225 blood (different donors) and non-blood (protein-based ketchup, rust acrylic paint, red acrylic paint, brown acrylic paint, red nail polish, rust nail polish, fake blood, and red ink) samples (HSI cubes, each cube is of size 1000 × 512 × 224, in which 1000 × 512 are the spatial dimensions and 224 spectral bands) were deposited on three substrates (white cotton fabric, white tile, and PVC wall sheet). The samples are imaged for up to three days to include aging. Savitzky Golay filtering has been used to highlight the subtle bands of all samples, particularly the aged ones. Based on the derivative spectrum, important spectral bands were selected to train five different classifiers (SVM, ANN, KNN, Random Forest, and Decision Tree). The comparative analysis reveals that the proposed method outperformed several state-of-the-art methods.

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