Classification and selection of biomarkers in genomic data using LASSO

High-throughput gene expression technologies such as microarrays have been utilized in a variety of scientific applications. Most of the work has been on assessing univariate associations between gene expression with clinical outcome (variable selection) or on developing classification procedures with gene expression data (supervised learning). We consider a hybrid variable selection/classification approach that is based on linear combinations of the gene expression profiles that maximize an accuracy measure summarized using the receiver operating characteristic curve. Under a specific probability model, this leads to consideration of linear discriminant functions. We incorporate an automated variable selection approach using LASSO. An equivalence between LASSO estimation with support vector machines allows for model fitting using standard software. We apply the proposed method to simulated data as well as data from a recently published prostate cancer study.

Efficiency of the Sieved-NPMLE in CAR-Missing Data Models

We consider nonparametric missing data models for which the censoring mechanism satisfies coarsening at random and which allow complete observations on the variable X of interest. W show that beyond some empirical process conditions the only essential condition for efficiency of an NPMLE of the distribution of X is that the regions associated with incomplete observations on X contain enough complete observations. This is heuristically explained by describing the EM-algorithm. We provide identifiably of the self-consistency equation and efficiency of the NPMLE in order to make this statement rigorous. The usual kind of differentiability conditions in the proof are avoided by using an identity which holds for the NPMLE of linear parameters in convex models. We provide a bivariate censoring application in which the condition and hence the NPMLE fails, but where other estimators, not based on the NPMLE principle, are highly inefficient. It is shown how to slightly reduce the data so that the conditions hold for the reduced data. The conditions are verified for the univariate censoring, double censored, and Ibragimov-Has'minski models.

Application and comparison of classification algorithms for recognition of Alzheimer's disease in electrical brain activity (EEG)

The early detection of subjects with probable Alzheimer's disease (AD) is crucial for effective appliance of treatment strategies. Here we explored the ability of a multitude of linear and non-linear classification algorithms to discriminate between the electroencephalograms (EEGs) of patients with varying degree of AD and their age-matched control subjects. Absolute and relative spectral power, distribution of spectral power, and measures of spatial synchronization were calculated from recordings of resting eyes-closed continuous EEGs of 45 healthy controls, 116 patients with mild AD and 81 patients with moderate AD, recruited in two different centers (Stockholm, New York). The applied classification algorithms were: principal component linear discriminant analysis (PC LDA), partial least squares LDA (PLS LDA), principal component logistic regression (PC LR), partial least squares logistic regression (PLS LR), bagging, random forest, support vector machines (SVM) and feed-forward neural network. Based on 10-fold cross-validation runs it could be demonstrated that even tough modern computer-intensive classification algorithms such as random forests, SVM and neural networks show a slight superiority, more classical classification algorithms performed nearly equally well. Using random forests classification a considerable sensitivity of up to 85% and a specificity of 78%, respectively for the test of even only mild AD patients has been reached, whereas for the comparison of moderate AD vs. controls, using SVM and neural networks, values of 89% and 88% for sensitivity and specificity were achieved. Such a remarkable performance proves the value of these classification algorithms for clinical diagnostics.

Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

Computational prediction of the influence of crosslink distribution on the thermo-mechanical properties of epoxies

Experimental studies on epoxies report that the microstructure consists of highly crosslinked localized regions connected with a dispersed phase of low crosslink density. The various thermo-mechanical properties of epoxies might be affected by the crosslink distribution. But as experiments cannot report the exact number of crosslinked covalent bonds present in the structure, molecular dynamics is thus being used in this work to determine the influence of crosslink distribution on thermo-mechanical properties. Molecular dynamics and molecular mechanics simulations are used to establish wellequilibrated molecular models of EPON 862-DETDA epoxy system with a range of crosslink densities and various crosslink distributions. Crosslink distributions are being varied by forming differently crosslinked localized clusters and then by forming different number of crosslinks interconnecting the clusters. Simulations are subsequently used to predict the volume shrinkage, thermal expansion coefficients, and elastic properties of each of the crosslinked systems. The results indicate that elastic properties increase with increasing levels of overall crosslink density and the thermal expansion coefficient decreases with overall crosslink density, both above and below the glass transition temperature. Elastic moduli and coefficients of linear thermal expansion values were found to be different for systems with same overall crosslink density but having different crosslink distributions, thus indicating an effect of the epoxy nanostructure on physical properties. The values of thermo-mechanical properties for all the crosslinked systems are within the range of values reported in literature.

RF-sputter fabrication of magnetic garnet thin films and simulation modeling for 1-D magnetic photonic crystal waveguide devices

One dimensional magnetic photonic crystals (1D-MPC) are promising structures for integrated optical isolator applications. Rare earth substituted garnet thin films with proper Faraday rotation are required to fabricate planar 1D-MPCs. In this thesis, flat-top response 1D-MPC was proposed and spectral responses and Faraday rotation were modeled. Bismuth substituted iron garnet films were fabricated by RF magnetron sputtering and structures, compositions, birefringence and magnetooptical properties were studied. Double layer structures for single mode propagation were also fabricated by sputtering for the first time. Multilayer stacks with multiple defects (phase shift) composed of Ce-YIG and GGG quarter-wave plates were simulated by the transfer matrix method. The transmission and Faraday rotation characteristics were theoretically studied. It is found that flat-top response, with 100% transmission and near 45o rotation is achievable by adjusting the inter-defect spacing, for film structures as thin as 30 to 35 μm. This is better than 3-fold reduction in length compared to the best Ce-YIG films for comparable rotations, thus allows a considerable reduction in size in manufactured optical isolators. Transmission bands as wide as 7nm were predicted, which is considerable improvement over 2 defects structure. Effect of repetition number and ratio factor on transmission and Faraday rotation ripple factors for the case of 3 and 4 defects structure has been discussed. Diffraction across the structure corresponds to a longer optical path length. Thus the use of guided optics is required to minimize the insertion losses in integrated devices. This part is discussed in chapter 2 in this thesis. Bismuth substituted iron garnet thin films were prepared by RF magnetron sputtering. We investigated or measured the deposition parameters optimization, crystallinity, surface morphologies, composition, magnetic and magnetooptical properties. A very high crystalline quality garnet film with smooth surface has been heteroepitaxially grown on (111) GGG substrate for films less than 1μm. Dual layer structures with two distinct XRD peaks (within a single sputtered film) start to develop when films exceed this thickness. The development of dual layer structure was explained by compositional gradient across film thickness, rather than strain gradient proposed by other authors. Lower DC self bias or higher substrate temperature is found to help to delay the appearance of the 2nd layer. The deposited films show in-plane magnetization, which is advantageous for waveguide devices application. Propagation losses of fabricated waveguides can be decreased by annealing in an oxygen atmosphere from 25dB/cm to 10dB/cm. The Faraday rotation at λ=1.55μm were also measured for the waveguides. FR is small (10° for a 3mm long waveguide), due to the presence of linear birefringence. This part is covered in chapter 4. We also investigated the elimination of linear birefringence by thickness tuning method for our sputtered films. We examined the compressively and tensilely strained films and analyze the photoelastic response of the sputter deposited garnet films. It has been found that the net birefringence can be eliminated under planar compressive strain conditions by sputtering. Bi-layer GGG on garnet thin film yields a reduced birefringence. Temperature control during the sputter deposition of GGG cover layer is critical and strongly influences the magnetization and birefringence level in the waveguide. High temperature deposition lowers the magnetization and increases the linear birefringence in the garnet films. Double layer single mode structures fabricated by sputtering were also studied. The double layer, which shows an in-plane magnetization, has an increased RMS roughness upon upper layer deposition. The single mode characteristic was confirmed by prism coupler measurement. This part is discussed in chapter 5.

Development of an In Situ Measurement Device for Obtaining Material Thermal Properties

This thesis presents a methodology for measuring thermal properties in situ, with a special focus on obtaining properties of layered stack-ups commonly used in armored vehicle components. The technique involves attaching a thermal source to the surface of a component, measuring the heat flux transferred between the source and the component, and measuring the surface temperature response. The material properties of the component can subsequently be determined from measurement of the transient heat flux and temperature response at the surface alone. Experiments involving multilayered specimens show that the surface temperature response to a sinusoidal heat flux forcing function is also sinusoidal. A frequency domain analysis shows that sinusoidal thermal excitation produces a gain and phase shift behavior typical of linear systems. Additionally, this analysis shows that the material properties of sub-surface layers affect the frequency response function at the surface of a particular stack-up. The methodology involves coupling a thermal simulation tool with an optimization algorithm to determine the material properties from temperature and heat flux measurement data. Use of a sinusoidal forcing function not only provides a mechanism to perform the frequency domain analysis described above, but sinusoids also have the practical benefit of reducing the need for instrumentation of the backside of the component. Heat losses can be minimized by alternately injecting and extracting heat on the front surface, as long as sufficiently high frequencies are used.

Linear and Piecewise Functions

This morning Dr. Battle will review basic concepts of linear functions and piecewise functions and how they can be used as models for real-world applications. She will also introduce techniques for using a spreadsheet to analyze data.

Effect of disodium monofluorophosphate, calcium and vitamin D supplementation on bone mineral density in patients chronically treated with glucocorticosteroids: a prospective, randomized, double-blind study

To study the effect of fluoride on bone mineral density (BMD) in patients treated chronically with glucocorticosteroids, 15 subjects (renal grafted, n = 12; skin disease, n = 1; broncho pulmonary disorder, n = 1; Crohn's disease, n = 1) were prospectively studied in a double-blinded manner and randomly allocated either to group 1 (n = 8) receiving 13.2 mg/day fluoride given as disodium monofluorophosphate (MFP) supplemented with calcium (1,000 mg/day) and 25-hydroxyvitamin D (calcifediol) (50 micrograms/day), or to group 2 (n = 7) receiving Cas+ calcifediol alone. An additional group of 14 renal transplant patients treated chronically with glucocorticosteroids but exempt of specific therapeutic intervention for bone disease was set up as historical controls. BMD was measured by dual-energy X-ray absorptiometry (DXA, Hologic QDR 1000) performed at months 0, 6 and 12 for groups 1 and 2 (lumbar spine, total upper femur, diaphysis and epiphysis of distal tibia), or 11-31 months apart with calculation of linear yearly changes for the historical cohort. Lumbar BMD tended to rise in groups 1 and 2, and to fall in group 3, the change reaching statistical significance (p < 0.05) in group 1, thus leading to a significant difference between groups 1 and 3 (p < 0.05). At upper femur, tibial diaphysis and tibial epiphysis, no significant change in BMD occurred in any of the groups. In conclusion, lumbar BMD rises more after a mild dosis of fluoride given as MFP and combined to calcium and calcifediol than on Ca+ calcifediol alone, without changes in BMD at the upper femur or distal tibia.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Analysis of Pressure Head-Flow Loops of Pulsatile Rotodynamic Blood Pumps

The clinical importance of pulsatility is a recurring topic of debate in mechanical circulatory support. Lack of pulsatility has been identified as a possible factor responsible for adverse events and has also demonstrated a role in myocardial perfusion and cardiac recovery. A commonly used method for restoring pulsatility with rotodynamic blood pumps (RBPs) is to modulate the speed profile, synchronized to the cardiac cycle. This introduces additional parameters that influence the (un)loading of the heart, including the timing (phase shift) between the native cardiac cycle and the pump pulses, and the amplitude of speed modulation. In this study, the impact of these parameters upon the heart-RBP interaction was examined in terms of the pressure head-flow (HQ) diagram. The measurements were conducted using a rotodynamic Deltastream DP2 pump in a validated hybrid mock circulation with baroreflex function. The pump was operated with a sinusoidal speed profile, synchronized to the native cardiac cycle. The simulated ventriculo-aortic cannulation showed that the level of (un)loading and the shape of the HQ loops strongly depend on the phase shift. The HQ loops displayed characteristic shapes depending on the phase shift. Increased contribution of native contraction (increased ventricular stroke work [WS ]) resulted in a broadening of the loops. It was found that the previously described linear relationship between WS and the area of the HQ loop for constant pump speeds becomes a family of linear relationships, whose slope depends on the phase shift.

Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.

A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.

Empirical Analysis of Credit Risk Regime Switching and Temporal Conditional Default Correlation in Credit Default Swap Valuation: The Market liquidity effect

In this paper, we extend the debate concerning Credit Default Swap valuation to include time varying correlation and co-variances. Traditional multi-variate techniques treat the correlations between covariates as constant over time; however, this view is not supported by the data. Secondly, since financial data does not follow a normal distribution because of its heavy tails, modeling the data using a Generalized Linear model (GLM) incorporating copulas emerge as a more robust technique over traditional approaches. This paper also includes an empirical analysis of the regime switching dynamics of credit risk in the presence of liquidity by following the general practice of assuming that credit and market risk follow a Markov process. The study was based on Credit Default Swap data obtained from Bloomberg that spanned the period January 1st 2004 to August 08th 2006. The empirical examination of the regime switching tendencies provided quantitative support to the anecdotal view that liquidity decreases as credit quality deteriorates. The analysis also examined the joint probability distribution of the credit risk determinants across credit quality through the use of a copula function which disaggregates the behavior embedded in the marginal gamma distributions, so as to isolate the level of dependence which is captured in the copula function. The results suggest that the time varying joint correlation matrix performed far superior as compared to the constant correlation matrix; the centerpiece of linear regression models.

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^