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This paper introduced an analytical solution and improved one-factor Gaussian copula models to the pricing of tranches of a Collateralized debt obligations (CDO) portfolio. Prices of CDO tranches are calculated and compared using the analytical model and different one-factor Gaussian copula models including a two-category heterogeneous model and a completely heterogeneous model that uses individual rate parameter and correlation coefficient for each reference entity in a CDO portfolio. When correlation among reference entities is low, the price calculated from the analytical model matches very well with the one-factor Gaussian copula models. However, as the correlation among reference entities increases, prices calculated using both the analytical solution and the homogeneous or two-category one-factor Gaussian copula models significantly deviate from the completely heterogeneous one-factor Gaussian copula model. This result verifies our belief that uniform parameters cannot completely capture all the heterogeneities in a CDO portfolio. Completely heterogeneous one-factor Gaussian copula model using individual rate parameters and correlation coefficients for each reference entities provides more reliable and accurate prices for structured securities.

Native fluorescence spectra are acquired from fresh normal and cancerous human prostate tissues. The fluorescence data are analyzed using an unsupervised machine learning algorithm such as non-negative matrix factorization. The nonnegative spectral components are retrieved and attributed to the native fluorophores such as collagen, reduced nicotinamide adenine dinucleotide (NADH), and flavin adenine dinucleotide (FAD) in tissue. The retrieved scores of the components are used to estimate the relative concentrations of the native fluorophores such as NADH and FAD and the redox ratio. A supervised machine learning algorithm such as support vector machine (SVM) is used to classify normal and cancerous tissue samples based on either the relative concentrations of NADH and FAD or the redox ratio alone. Various statistical measures such as sensitivity, specificity, and accuracy, along with the area under receiver operating characteristic (ROC) curve are used to show the classification performance. A cross validation method such as leave-one-out is used to further evaluate the predictive performance of the SVM classifier to avoid bias due to overfitting, and the accuracy was found to be 93.3%.

Native fluorescence spectra are acquired from fresh normal and cancerous human prostate tissues. The fluorescence data are analyzed using a multivariate analysis algorithm such as non-negative matrix factorization. The nonnegative spectral components are retrieved and attributed to the native fluorophores such as collagen, reduced nicotinamide adenine dinucleotide (NADH), and flavin adenine dinucleotide (FAD) in tissue. The retrieved weights of the components, e.g. NADH and FAD are used to estimate the relative concentrations of the native fluorophores and the redox ratio. A machine learning algorithm such as support vector machine (SVM) is used for classification to distinguish normal and cancerous tissue samples based on either the relative concentrations of NADH and FAD or the redox ratio alone. The classification performance is shown based on statistical measures such as sensitivity, specificity, and accuracy, along with the area under receiver operating characteristic (ROC) curve. A cross validation method such as leave-one-out is used to evaluate the predictive performance of the SVM classifier to avoid bias due to overfitting.

Food spoilage is mainly caused by microorganisms, such as bacteria. In this study, we measure the autofluorescence in meat samples longitudinally over a week in an attempt to develop a method to rapidly detect meat spoilage using fluorescence spectroscopy. Meat food is a biological tissue, which contains intrinsic fluorophores, such as tryptophan, collagen, nicotinamide adenine dinucleotide (NADH) and flavin adenine dinucleotide (FAD) etc. As meat spoils, it undergoes various morphological and chemical changes. The concentrations of the native fluorophores present in a sample may change. In particular, the changes in NADH and FAD are associated with microbial metabolism, which is the most important process of the bacteria in food spoilage. Such changes may be revealed by fluorescence spectroscopy and used to indicate the status of meat spoilage. Therefore, such native fluorophores may be unique, reliable and nonsubjective indicators for detection of spoiled meat. The results of the study show that the relative concentrations of all above fluorophores change as the meat samples kept in room temperature (~19° C) spoil. The changes become more rapidly after about two days. For the meat samples kept in a freezer (~-12° C), the changes are much less or even unnoticeable over a-week-long storage.

Food spoilage is mainly caused by microorganisms, such as bacteria. In this study, we measure the autofluorescence in meat samples longitudinally over a week in an attempt to develop a method to rapidly detect meat spoilage using fluorescence spectroscopy. Meat food is a biological tissue, which contains intrinsic fluorophores, such as tryptophan, collagen, nicotinamide adenine dinucleotide (NADH) and flavin adenine dinucleotide (FAD) etc. As meat spoils, it undergoes various morphological and chemical changes. The concentrations of the native fluorophores present in a sample may change. In particular, the changes in NADH and FAD are associated with microbial metabolism, which is the most important process of the bacteria in food spoilage. Such changes may be revealed by fluorescence spectroscopy and used to indicate the status of meat spoilage. Therefore, such native fluorophores may be unique, reliable and non-subjective indicators for detection of spoiled meat. The results of the study show that the relative concentrations of all above fluorophores change as the meat samples kept in room temperature (~19°C) spoil. The changes become more rapidly after about two days. For the meat samples kept in a freezer (~ -12°C), the changes are much less or even unnoticeable over a-week-long storage.

Worldwide breast cancer incidence has increased by more than twenty percent in the past decade. It is also known that in that time, mortality due to the affliction has increased by fourteen percent. Using optical-based diagnostic techniques, such as Raman spectroscopy, has been explored in order to increase diagnostic accuracy in a more objective way along with significantly decreasing diagnostic wait-times. In this study, Raman spectroscopy with 532-nm excitation was used in order to incite resonance effects to enhance Stokes Raman scattering from unique biomolecular vibrational modes. Seventy-two Raman spectra (41 cancerous, 31 normal) were collected from nine breast tissue samples by performing a ten-spectra average using a 500-ms acquisition time at each acquisition location. The raw spectral data was subsequently prepared for analysis with background correction and normalization. The spectral data in the Raman Shift range of 750- 2000 cm-1 was used for analysis since the detector has highest sensitivity around in this range. The matrix decomposition technique nonnegative matrix factorization (NMF) was then performed on this processed data. The resulting leave-oneout cross-validation using two selective feature components resulted in sensitivity, specificity and accuracy of 92.6%, 100% and 96.0% respectively. The performance of NMF was also compared to that using principal component analysis (PCA), and NMF was shown be to be superior to PCA in this study. This study shows that coupling the resonance Raman spectroscopy technique with subsequent NMF decomposition method shows potential for high characterization accuracy in breast cancer detection.