Coinvasion-Coexistence Traveling Wave Solutions of an Integro-Difference Competition System

This paper is concerned with the traveling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion-coexistence process of two competitors with age structure. The existence of nontrivial traveling wave solutions is obtained by constructing generalized upper and lower solutions. The asymptotic and nonexistence of traveling wave solutions are proved by combining the theory of asymptotic spreading with the idea of contracting rectangle

Global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case

We consider the global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case; and obtain the dichotomy between scattering and finite time blow up.Comment: 24 pages. arXiv admin note: substantial text overlap with arXiv:1206.245

Global dynamics below the ground state energy for the Zakharov system in the 3D radial case

We consider the global dynamics below the ground state energy for the Zakharov system in the 3D radial case. We obtain dichotomy between the scattering and the growup.Comment: 28 page

Chemometrics and statistical analysis in raman spectroscopy-based biological investigations

As mentioned in the chapter 1, chemometrics has become an essential tool in Raman spectroscopy-based biological investigations and significantly enhanced the sensitivity of Raman spectroscopy-based detection. However, there are some open issues on applying chemometrics in Raman spectroscopy-based biological investigations. An automatic proce- dure is needed to optimize the parameters of the mathematical baseline correction. Spectral reconstruction algorithm is required to recover a fluorescence-free Raman spectrum from the two Raman spectra measured with different excitation wavelengths for the shifted-excitation Raman difference spectroscopy (SERDS) technique. Guidelines are necessary for reliable model optimization and rigorous model evaluation to ensure high accuracy and robustness in Raman spectroscopy-based biological detection. Computational methods are required to enable a trained model to successfully predict new data that is significantly different from the training data due to inter-replicate variations. These tasks were tackled in this thesis. The related investigations were related to three main topics: baseline correction, statistical modeling, and model transfer.Wie im Kapitel 1 erwähnt, ist die Chemometrie zu einem essentiellen Werkzeug für biolo- gische Untersuchungen mittels der Raman-Spektroskopie geworden und hat die Sensitivität der Raman-spektroskopischen Detektion erheblich verbessert. Es gibt jedoch einige offene Fragen, welche die Anwendung der Chemometrie in Raman-spektroskopischen Untersuchun- gen biologischer Proben betreffen. Zum Beispiel wird eine automatische Prozedur benötigt, um die Parameter einer mathematischen Basislinienkorrektur zu optimieren. Ein SERDS- Rekonstruktionsalgorithmus ist erforderlich, um ein Fluoreszenz-freies Raman-Spektrum aus den zwei Raman-Spektren zu extrahieren, welche bei der Shifted-excitation-Raman-Differenz- Spektroskopie (SERDS) gemessen werden. Des Weiteren sind Richtlinien erforderlich, welche eine zuverlässige Modelloptimierung und eine rigorose Modellevaluation erlauben. Durch diese Richtlinien wird eine hohe Genauigkeit und Robustheit der Raman-spektroskopischen Detektion biologischer Proben gewährleistet. Computergestützte Methoden sind nötig, um mit einem trainierten Modell erfolgreich neue Daten, die sich aufgrund von Inter-Replikat- Variationen signifikant von den Trainingsdaten unterscheiden, vorherzusagen. Diese vier Probleme sind Beispiele für offene Fragen in der Chemometrie und diese vier Probleme wur- den in dieser Arbeit behandelt. Die damit verbundenen Untersuchungen bezogen sich auf drei Hauptthemen: die Basislinienkorrektur, die statistische Modellierung und der Modell- transfer

Modified PCA and PLS: Towards a better classification in Raman spectroscopy–based biological applications

Raman spectra of biological samples often exhibit variations originating from changes of spectrometers, measurement conditions, and cultivation conditions. Such unwanted variations make a classification extremely challenging, especially if they are more significant compared with the differences between groups to be separated. A classifier is prone to such unwanted variations (ie, intragroup variations) and can fail to learn the patterns that can help separate different groups (ie, intergroup differences). This often leads to a poor generalization performance and a degraded transferability of the trained model. A natural solution is to separate the intragroup variations from the intergroup differences and build the classifier based on merely the latter information, for example, by a well-designed feature extraction. This forms the idea of this contribution. Herein, we modified two commonly applied feature extraction approaches, principal component analysis (PCA) and partial least squares (PLS), in order to extract merely the features representing the intergroup differences. Both of the methods were verified with two Raman spectral datasets measured from bacterial cultures and colon tissues of mice, respectively. In comparison to ordinary PCA and PLS, the modified PCA was able to improve the prediction on the testing data that bears significant difference to the training data, while the modified PLS could help avoid overfitting and lead to a more stable classification. © 2019 The Authors. Journal of Chemometrics published by John Wiley & Sons Lt

Deep learning a boon for biophotonics

This review covers original articles using deep learning in the biophotonic field published in the last years. In these years deep learning, which is a subset of machine learning mostly based on artificial neural network geometries, was applied to a number of biophotonic tasks and has achieved state-of-the-art performances. Therefore, deep learning in the biophotonic field is rapidly growing and it will be utilized in the next years to obtain real-time biophotonic decision-making systems and to analyze biophotonic data in general. In this contribution, we discuss the possibilities of deep learning in the biophotonic field including image classification, segmentation, registration, pseudostaining and resolution enhancement. Additionally, we discuss the potential use of deep learning for spectroscopic data including spectral data preprocessing and spectral classification. We conclude this review by addressing the potential applications and challenges of using deep learning for biophotonic data. © 2020 The Authors. Journal of Biophotonics published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinhei

Comparability of Raman Spectroscopic Configurations: A LargeScale Cross-Laboratory Study

The variable configuration of Raman spectroscopic platforms is one ofthe major obstacles in establishing Raman spectroscopy as a valuable physicochemicalmethod within real-world scenarios such as clinical diagnostics. For such real worldapplications like diagnostic classification, the models should ideally be usable to predictdata from different setups. Whether it is done by training a rugged model with data frommany setups or by a primary-replica strategy where models are developed on a‘primary’setup and the test data are generated on‘replicate’setups, this is only possible if the Raman spectra from different setups are consistent, reproducible, and comparable.However, Raman spectra can be highly sensitive to the measurement conditions, and they change from setup to setup even if thesame samples are measured. Although increasingly recognized as an issue, the dependence of the Raman spectra on the instrumentalconfiguration is far from being fully understood and great effort is needed to address the resulting spectral variations and to correctfor them. To make the severity of the situation clear, we present a round robin experiment investigating the comparability of 35Raman spectroscopic devices with different configurations in 15 institutes within seven European countries from the COST(European Cooperation in Science and Technology) action Raman4clinics. The experiment was developed in a fashion that allowsvarious instrumental configurations ranging from highly confocal setups tofibre-optic based systems with different excitationwavelengths. We illustrate the spectral variations caused by the instrumental configurations from the perspectives of peak shifts,intensity variations, peak widths, and noise levels. We conclude this contribution with recommendations that may help to improvethe inter-laboratory studie

Comparison of conventional and shifted excitation Raman difference spectroscopy for bacterial identification

Raman spectroscopy is an emerging tool for fast bacterial identification. However, Raman spectroscopy is depending on suitable preprocessing of the spectra, thereby background removal is a decisive step for conventional Raman spectroscopy. The background has to be estimated, which is challenging especially for high fluorescence backgrounds. Shifted excitation Raman difference spectroscopy (SERDS) eliminates the background through the experimental procedure and holds as promising approach for highly fluorescent samples. Bacterial Raman spectra might be especially complex because these spectra consist of a multitude of overlapping Raman bands from a large multiplicity of biomolecules and only subtitle differences between the species Raman spectra enable the bacterial identification. Here, we investigate the benefits of SERDS compared with conventional Raman spectroscopy specific for the study and identification of bacteria. The comparison utilizes spectra sets of four bacterial species measured with conventional Raman spectroscopy and SERDS and covers three processing approaches for SERDS spectra, for example, the reconstruction with a non‐negative least square algorithm

FLIM data analysis based on Laguerre polynomial decomposition and machine-learning

Significance: The potential of fluorescence lifetime imaging microscopy (FLIM) is recently being recognized, especially in biological studies. However, FLIM does not directly measure the lifetimes, rather it records the fluorescence decay traces. The lifetimes and/or abundances have to be estimated from these traces during the phase of data processing. To precisely estimate these parameters is challenging and requires a well-designed computer program. Conventionally employed methods, which are based on curve fitting, are computationally expensive and limited in performance especially for highly noisy FLIM data. The graphical analysis, while free of fit, requires calibration samples for a quantitative analysis. Aim: We propose to extract the lifetimes and abundances directly from the decay traces through machine learning (ML). Approach: The ML-based approach was verified with simulated testing data in which the lifetimes and abundances were known exactly. Thereafter, we compared its performance with the commercial software SPCImage based on datasets measured from biological samples on a time-correlated single photon counting system. We reconstructed the decay traces using the lifetime and abundance values estimated by ML and SPCImage methods and utilized the root-mean-squared-error (RMSE) as marker. Results: The RMSE, which represents the difference between the reconstructed and measured decay traces, was observed to be lower for ML than for SPCImage. In addition, we could demonstrate with a three-component analysis the high potential and flexibility of the ML method to deal with more than two lifetime components

Fiber-based SORS-SERDS system and chemometrics for the diagnostics and therapy monitoring of psoriasis inflammatory disease in vivo

Psoriasis is considered a widespread dermatological disease that can strongly affect the quality of life. Currently, the treatment is continued until the skin surface appears clinically healed. However, lesions appearing normal may contain modifications in deeper layers. To terminate the treatment too early can highly increase the risk of relapses. Therefore, techniques are needed for a better knowledge of the treatment process, especially to detect the lesion modifications in deeper layers. In this study, we developed a fiber-based SORS-SERDS system in combination with machine learning algorithms to non-invasively determine the treatment efficiency of psoriasis. The system was designed to acquire Raman spectra from three different depths into the skin, which provide rich information about the skin modifications in deeper layers. This way, it is expected to prevent the occurrence of relapses in case of a too short treatment. The method was verified with a study of 24 patients upon their two visits: the data is acquired at the beginning of a standard treatment (visit 1) and four months afterwards (visit 2). A mean sensitivity of ≥85% was achieved to distinguish psoriasis from normal skin at visit 1. At visit 2, where the patients were healed according to the clinical appearance, the mean sensitivity was ≈65%