Communications inspired linear discriminant analysis

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label. By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods, and comparisons are also made with a method in which Rényi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets. Copyright 2012 by the author(s)/owner(s).

Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

Development and Application of Covalent-Labeling Strategies for the Large-Scale Thermodynamic Analysis of Protein Folding and Ligand Binding

Thermodynamic stability measurements on proteins and protein-ligand complexes can offer insights not only into the fundamental properties of protein folding reactions and protein functions, but also into the development of protein-directed therapeutic agents to combat disease. Conventional calorimetric or spectroscopic approaches for measuring protein stability typically require large amounts of purified protein. This requirement has precluded their use in proteomic applications. Stability of Proteins from Rates of Oxidation (SPROX) is a recently developed mass spectrometry-based approach for proteome-wide thermodynamic stability analysis. Since the proteomic coverage of SPROX is fundamentally limited by the detection of methionine-containing peptides, the use of tryptophan-containing peptides was investigated in this dissertation. A new SPROX-like protocol was developed that measured protein folding free energies using the denaturant dependence of the rate at which globally protected tryptophan and methionine residues are modified with dimethyl (2-hydroxyl-5-nitrobenzyl) sulfonium bromide and hydrogen peroxide, respectively. This so-called Hybrid protocol was applied to proteins in yeast and MCF-7 cell lysates and achieved a ~50% increase in proteomic coverage compared to probing only methionine-containing peptides. Subsequently, the Hybrid protocol was successfully utilized to identify and quantify both known and novel protein-ligand interactions in cell lysates. The ligands under study included the well-known Hsp90 inhibitor geldanamycin and the less well-understood omeprazole sulfide that inhibits liver-stage malaria. In addition to protein-small molecule interactions, protein-protein interactions involving Puf6 were investigated using the SPROX technique in comparative thermodynamic analyses performed on wild-type and Puf6-deletion yeast strains. A total of 39 proteins were detected as Puf6 targets and 36 of these targets were previously unknown to interact with Puf6. Finally, to facilitate the SPROX/Hybrid data analysis process and minimize human errors, a Bayesian algorithm was developed for transition midpoint assignment. In summary, the work in this dissertation expanded the scope of SPROX and evaluated the use of SPROX/Hybrid protocols for characterizing protein-ligand interactions in complex biological mixtures.

Optimized approach to decision fusion of heterogeneous data for breast cancer diagnosis.

As more diagnostic testing options become available to physicians, it becomes more difficult to combine various types of medical information together in order to optimize the overall diagnosis. To improve diagnostic performance, here we introduce an approach to optimize a decision-fusion technique to combine heterogeneous information, such as from different modalities, feature categories, or institutions. For classifier comparison we used two performance metrics: The receiving operator characteristic (ROC) area under the curve [area under the ROC curve (AUC)] and the normalized partial area under the curve (pAUC). This study used four classifiers: Linear discriminant analysis (LDA), artificial neural network (ANN), and two variants of our decision-fusion technique, AUC-optimized (DF-A) and pAUC-optimized (DF-P) decision fusion. We applied each of these classifiers with 100-fold cross-validation to two heterogeneous breast cancer data sets: One of mass lesion features and a much more challenging one of microcalcification lesion features. For the calcification data set, DF-A outperformed the other classifiers in terms of AUC (p < 0.02) and achieved AUC=0.85 +/- 0.01. The DF-P surpassed the other classifiers in terms of pAUC (p < 0.01) and reached pAUC=0.38 +/- 0.02. For the mass data set, DF-A outperformed both the ANN and the LDA (p < 0.04) and achieved AUC=0.94 +/- 0.01. Although for this data set there were no statistically significant differences among the classifiers' pAUC values (pAUC=0.57 +/- 0.07 to 0.67 +/- 0.05, p > 0.10), the DF-P did significantly improve specificity versus the LDA at both 98% and 100% sensitivity (p < 0.04). In conclusion, decision fusion directly optimized clinically significant performance measures, such as AUC and pAUC, and sometimes outperformed two well-known machine-learning techniques when applied to two different breast cancer data sets.

Component Neural Systems for the Creation of Emotional Memories during Free Viewing of a Complex, Real-World Event.

To investigate the neural systems that contribute to the formation of complex, self-relevant emotional memories, dedicated fans of rival college basketball teams watched a competitive game while undergoing functional magnetic resonance imaging (fMRI). During a subsequent recognition memory task, participants were shown video clips depicting plays of the game, stemming either from previously-viewed game segments (targets) or from non-viewed portions of the same game (foils). After an old-new judgment, participants provided emotional valence and intensity ratings of the clips. A data driven approach was first used to decompose the fMRI signal acquired during free viewing of the game into spatially independent components. Correlations were then calculated between the identified components and post-scanning emotion ratings for successfully encoded targets. Two components were correlated with intensity ratings, including temporal lobe regions implicated in memory and emotional functions, such as the hippocampus and amygdala, as well as a midline fronto-cingulo-parietal network implicated in social cognition and self-relevant processing. These data were supported by a general linear model analysis, which revealed additional valence effects in fronto-striatal-insular regions when plays were divided into positive and negative events according to the fan's perspective. Overall, these findings contribute to our understanding of how emotional factors impact distributed neural systems to successfully encode dynamic, personally-relevant event sequences.

Does commitment to rehabilitation influence clinical outcome of total hip resurfacing arthroplasty?

BACKGROUND: The purpose of this study was to evaluate whether compliance and rehabilitative efforts were predictors of early clinical outcome of total hip resurfacing arthroplasty. METHODS: A cross-sectional survey was utilized to collect information from 147 resurfacing patients, who were operated on by a single surgeon, regarding their level of commitment to rehabilitation following surgery. Patients were followed for a mean of 52 months (range, 24 to 90 months). Clinical outcomes and functional capabilities were assessed utilizing the Harris hip objective rating system, the SF-12 Health Survey, and an eleven-point satisfaction score. A linear regression analysis was used to determine whether there was any correlation between the rehabilitation commitment scores and any of the outcome measures, and a multivariate regression model was used to control for potentially confounding factors. RESULTS: Overall, an increased level of commitment to rehabilitation was positively correlated with each of the following outcome measures: SF-12 Mental Component Score, SF-12 Physical Component Score, Harris Hip score, and satisfaction scores. These correlations remained statistically significant in the multivariate regression model. CONCLUSIONS: Patients who were more committed to their therapy after hip resurfacing returned to higher levels of functionality and were more satisfied following their surgery.

Are component positioning and prosthesis size associated with hip resurfacing failure?

BACKGROUND: Recent studies suggest that there is a learning curve for metal-on-metal hip resurfacing. The purpose of this study was to assess whether implant positioning changed with surgeon experience and whether positioning and component sizing were associated with implant longevity. METHODS: We evaluated the first 361 consecutive hip resurfacings performed by a single surgeon, which had a mean follow-up of 59 months (range, 28 to 87 months). Pre and post-operative radiographs were assessed to determine the inclination of the acetabular component, as well as the sagittal and coronal femoral stem-neck angles. Changes in the precision of component placement were determined by assessing changes in the standard deviation of each measurement using variance ratio and linear regression analysis. Additionally, the cup and stem-shaft angles as well as component sizes were compared between the 31 hips that failed over the follow-up period and the surviving components to assess for any differences that might have been associated with an increased risk for failure. RESULTS: Surgeon experience was correlated with improved precision of the antero-posterior and lateral positioning of the femoral component. However, femoral and acetabular radiographic implant positioning angles were not different between the surviving hips and failures. The failures had smaller mean femoral component diameters as compared to the non-failure group (44 versus 47 millimeters). CONCLUSIONS: These results suggest that there may be differences in implant positioning in early versus late learning curve procedures, but that in the absence of recognized risk factors such as intra-operative notching of the femoral neck and cup inclination in excess of 50 degrees, component positioning does not appear to be associated with failure. Nevertheless, surgeons should exercise caution in operating patients with small femoral necks, especially when they are early in the learning curve.