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.

Low rank subspace clustering (LRSC)

We consider the problem of fitting a union of subspaces to a collection of data points drawn from one or more subspaces and corrupted by noise and/or gross errors. We pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise and/or gross errors. By self-expressive we mean a dictionary whose atoms can be expressed as linear combinations of themselves with low-rank coefficients. In the case of noisy data, our key contribution is to show that this non-convex matrix decomposition problem can be solved in closed form from the SVD of the noisy data matrix. The solution involves a novel polynomial thresholding operator on the singular values of the data matrix, which requires minimal shrinkage. For one subspace, a particular case of our framework leads to classical PCA, which requires no shrinkage. For multiple subspaces, the low-rank coefficients obtained by our framework can be used to construct a data affinity matrix from which the clustering of the data according to the subspaces can be obtained by spectral clustering. In the case of data corrupted by gross errors, we solve the problem using an alternating minimization approach, which combines our polynomial thresholding operator with the more traditional shrinkage-thresholding operator. Experiments on motion segmentation and face clustering show that our framework performs on par with state-of-the-art techniques at a reduced computational cost.

Multivariate methods for correlated effects sizes

Current statistical methods for estimation of parametric effect sizes from a series of experiments are generally restricted to univariate comparisons of standardized mean differences between two treatments. Multivariate methods are presented for the case in which effect size is a vector of standardized multivariate mean differences and the number of treatment groups is two or more. The proposed methods employ a vector of independent sample means for each response variable that leads to a covariance structure which depends only on correlations among the $p$ responses on each subject. Using weighted least squares theory and the assumption that the observations are from normally distributed populations, multivariate hypotheses analogous to common hypotheses used for testing effect sizes were formulated and tested for treatment effects which are correlated through a common control group, through multiple response variables observed on each subject, or both conditions.^ The asymptotic multivariate distribution for correlated effect sizes is obtained by extending univariate methods for estimating effect sizes which are correlated through common control groups. The joint distribution of vectors of effect sizes (from $p$ responses on each subject) from one treatment and one control group and from several treatment groups sharing a common control group are derived. Methods are given for estimation of linear combinations of effect sizes when certain homogeneity conditions are met, and for estimation of vectors of effect sizes and confidence intervals from $p$ responses on each subject. Computational illustrations are provided using data from studies of effects of electric field exposure on small laboratory animals. ^

Impacto de la urbanización sobre las características hidroquímicas del acuífero libre : comparación estadística con el entorno rural, Coronel Moldes, Argentina

El objetivo consistió en evaluar el impacto que la actividad urbana ocasiona sobre la calidad del agua subterránea del área de Coronel Moldes. Se realizaron consideraciones geoquímicas en relación con el cálculo de línea de base hidroquímica, comparando con muestras extraídas del mismo acuífero en el entorno rural. Los indicadores de contaminación entre las distintas zonas rural y urbana (evaluados con la prueba t para muestras independientes y prueba no paramétrica de Mann- Whitney), indicaron que los valores de las componentes resultaban diferentes. Conductividad eléctrica, bicarbonatos, cloruros y nitratos mostraron en el área urbana valores medios superiores a aquellos del entorno rural que en general corresponden a los valores representativos del fondo natural regional de la calidad del agua subterránea. Se detectó en el área urbana un aumento en la dureza y Cl-/HCO3 - con importante contaminación microbiológica. Para evaluar el fondo regional se ajustaron los datos de los componentes iónicos analizados a las distribuciones teóricas (Normal, Laplace y f1). Se encontró que la distribución empírica presentaba un mejor acercamiento a f1 que a las otras dos, determinándose así como valor característico del fondo natural para cada ion, el estimador del parámetro de localización m* (combinación lineal entre la media y la mediana).

On the design of spherical gradient index lenses

Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.) design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the linearity of the integral transformation which allows us to derive new solutions from linear combinations of known lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the Abel integral equation with fixed limits, which is an ill-posed problem.

Decision boundary for discrete Bayesian network classifiers

Bayesian network classifiers are a powerful machine learning tool. In order to evaluate the expressive power of these models, we compute families of polynomials that sign-represent decision functions induced by Bayesian network classifiers. We prove that those families are linear combinations of products of Lagrange basis polynomials. In absence of V-structures in the predictor sub-graph, we are also able to prove that this family of polynomials does in- deed characterize the specific classifier considered. We then use this representation to bound the number of decision functions representable by Bayesian network classifiers with a given structure and we compare these bounds to the ones obtained using Vapnik-Chervonenkis dimension.

Decision boundary for discrete Bayesian network classifiers

Bayesian network classifiers are a powerful machine learning tool. In order to evaluate the expressive power of these models, we compute families of polynomials that sign-represent decision functions induced by Bayesian network classifiers. We prove that those families are linear combinations of products of Lagrange basis polynomials. In absence of V-structures in the predictor sub-graph, we are also able to prove that this family of polynomials does in- deed characterize the specific classifier considered. We then use this representation to bound the number of decision functions representable by Bayesian network classifiers with a given structure and we compare these bounds to the ones obtained using Vapnik-Chervonenkis dimension.

Decision boundary for discrete Bayesian network classifiers

Bayesian network classifiers are a powerful machine learning tool. In order to evaluate the expressive power of these models, we compute families of polynomials that sign-represent decision functions induced by Bayesian network classifiers. We prove that those families are linear combinations of products of Lagrange basis polynomials. In absence of V -structures in the predictor sub-graph, we are also able to prove that this family of polynomials does indeed characterize the specific classifier considered. We then use this representation to bound the number of decision functions representable by Bayesian network classifiers with a given structure.

Application of the homogenization techniques to the determination of the effective flexure constants of plate structural systems

A Mindlin plate with periodically distributed ribs patterns is analyzed by using homogenization techniques based on asymptotic expansion methods. The stiffness matrix of the homogenized plate is found to be dependent on the geometrical characteristics of the periodical cell, i.e. its skewness, plan shape, thickness variation etc. and on the plate material elastic constants. The computation of this plate stiffness matrix is carried out by averaging over the cell domain some solutions of different periodical boundary value problems. These boundary value problems are defined in variational form by linear first order differential operators on the cell domain and the boundary conditions of the variational equation correspond to a periodic structural problem. The elements of the stiffness matrix of homogenized plate are obtained by linear combinations of the averaged solution functions of the above mentioned boundary value problems. Finally, an illustrative example of application of this homogenization technique to hollowed plates and plate structures with ribs patterns regularly arranged over its area is shown. The possibility of using in the profesional practice the present procedure to the actual analysis of floors of typical buildings is also emphasized.

Mode Localization in a Nearly Cyclic Symmetric System

Thesis (Ph.D.)--University of Washington, 2016-06

Personality disorders and adult attachment dimensions in a mixed psychiatric sample: A multivariate study

The associations between personality disorders and adult attachment dimensions were assessed in a sample of 487 consecutively admitted psychiatric subjects. Canonical correlation analysis showed that two sets of moderately correlated canonical variates explained the correlations between personality disorders and adult attachment patterns. The first and second attachment variates closely resembled the avoidance and anxiety attachment dimensions, respectively. The first personality disorder variate was mainly characterized by avoidant, depressive, paranoid, and schizotypal personality disorders, whereas dependent, histrionic, and borderline personality disorders loaded on the second canonical variate. However, these linear combinations of personality disorders were different from those obtained from principal component analysis. The results extend previous studies linking personality disorders and attachment patterns and suggest the importance of focusing on specific constellations of symptoms associated with dimensions of insecurity.

Rétractes Absolus de Voisinage Algébriques

2000 Mathematics Subject Classification: 54C55, 54H25, 55M20.

Microfluidics-based single-cell functional proteomics microchip for portraying protein signal transduction networks within the framework of physicochemical principles, with applications in fundamental and translational cancer research

Single-cell functional proteomics assays can connect genomic information to biological function through quantitative and multiplex protein measurements. Tools for single-cell proteomics have developed rapidly over the past 5 years and are providing unique opportunities. This thesis describes an emerging microfluidics-based toolkit for single cell functional proteomics, focusing on the development of the single cell barcode chips (SCBCs) with applications in fundamental and translational cancer research.

The microchip designed to simultaneously quantify a panel of secreted, cytoplasmic and membrane proteins from single cells will be discussed at the beginning, which is the prototype for subsequent proteomic microchips with more sophisticated design in preclinical cancer research or clinical applications. The SCBCs are a highly versatile and information rich tool for single-cell functional proteomics. They are based upon isolating individual cells, or defined number of cells, within microchambers, each of which is equipped with a large antibody microarray (the barcode), with between a few hundred to ten thousand microchambers included within a single microchip. Functional proteomics assays at single-cell resolution yield unique pieces of information that significantly shape the way of thinking on cancer research. An in-depth discussion about analysis and interpretation of the unique information such as functional protein fluctuations and protein-protein correlative interactions will follow.

The SCBC is a powerful tool to resolve the functional heterogeneity of cancer cells. It has the capacity to extract a comprehensive picture of the signal transduction network from single tumor cells and thus provides insight into the effect of targeted therapies on protein signaling networks. We will demonstrate this point through applying the SCBCs to investigate three isogenic cell lines of glioblastoma multiforme (GBM).

The cancer cell population is highly heterogeneous with high-amplitude fluctuation at the single cell level, which in turn grants the robustness of the entire population. The concept that a stable population existing in the presence of random fluctuations is reminiscent of many physical systems that are successfully understood using statistical physics. Thus, tools derived from that field can probably be applied to using fluctuations to determine the nature of signaling networks. In the second part of the thesis, we will focus on such a case to use thermodynamics-motivated principles to understand cancer cell hypoxia, where single cell proteomics assays coupled with a quantitative version of Le Chatelier's principle derived from statistical mechanics yield detailed and surprising predictions, which were found to be correct in both cell line and primary tumor model.

The third part of the thesis demonstrates the application of this technology in the preclinical cancer research to study the GBM cancer cell resistance to molecular targeted therapy. Physical approaches to anticipate therapy resistance and to identify effective therapy combinations will be discussed in detail. Our approach is based upon elucidating the signaling coordination within the phosphoprotein signaling pathways that are hyperactivated in human GBMs, and interrogating how that coordination responds to the perturbation of targeted inhibitor. Strongly coupled protein-protein interactions constitute most signaling cascades. A physical analogy of such a system is the strongly coupled atom-atom interactions in a crystal lattice. Similar to decomposing the atomic interactions into a series of independent normal vibrational modes, a simplified picture of signaling network coordination can also be achieved by diagonalizing protein-protein correlation or covariance matrices to decompose the pairwise correlative interactions into a set of distinct linear combinations of signaling proteins (i.e. independent signaling modes). By doing so, two independent signaling modes – one associated with mTOR signaling and a second associated with ERK/Src signaling have been resolved, which in turn allow us to anticipate resistance, and to design combination therapies that are effective, as well as identify those therapies and therapy combinations that will be ineffective. We validated our predictions in mouse tumor models and all predictions were borne out.

In the last part, some preliminary results about the clinical translation of single-cell proteomics chips will be presented. The successful demonstration of our work on human-derived xenografts provides the rationale to extend our current work into the clinic. It will enable us to interrogate GBM tumor samples in a way that could potentially yield a straightforward, rapid interpretation so that we can give therapeutic guidance to the attending physicians within a clinical relevant time scale. The technical challenges of the clinical translation will be presented and our solutions to address the challenges will be discussed as well. A clinical case study will then follow, where some preliminary data collected from a pediatric GBM patient bearing an EGFR amplified tumor will be presented to demonstrate the general protocol and the workflow of the proposed clinical studies.

A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.