Sabine Van Huffel

The total least squares problem : computational aspects and analysis

Incandescent source of visible radiations comprises a refractory support member having a thin, refractory material layer thereover, with both the support and the thin layer adapted to be heated to high temperatures. The material comprising the thin layer is highly absorptive for visible radiations and thus is a correspondingly good emitter for such visible radiations, and the material comprising the thin layer is highly transmissive for infrared radiations and a correspondingly poor emitter for such infrared radiations. Minute optical discontinuities in the thin layer act to scatter infrared radiations and the infrared radiations which are generated in the support member are scattered back to the support member in order to contribute to the heating of same. Visible radiations, in contrast, are absorbed and emitted by the thin layer so that this layer is a very selective radiator. In this manner, infrared radiations generated in the support member are selectively scattered to contribute to the heating of the support member and thus the generation of more visible radiations which the thin layer emits.

Overview of total least-squares methods

We review the development and extensions of the classical total least-squares method and describe algorithms for its generalization to weighted and structured approximation problems. In the generic case, the classical total least-squares problem has a unique solution, which is given in analytic form in terms of the singular value decomposition of the data matrix. The weighted and structured total least-squares problems have no such analytic solution and are currently solved numerically by local optimization methods. We explain how special structure of the weight matrix and the data matrix can be exploited for efficient cost function and first derivative computation. This allows to obtain computationally efficient solution methods. The total least-squares family of methods has a wide range of applications in system theory, signal processing, and computer algebra. We describe the applications for deconvolution, linear prediction, and errors-in-variables system identification.

Antenatal maternal anxiety is related to HPA-axis dysregulation and self-reported depressive symptoms in adolescence: a prospective study on the fetal origins of depressed mood.

Depressive symptomatology can proceed from altered hypothalamic-pituitary-adrenocortex (HPA)-axis function. Some authors stress the role that early life stress (ELS) may play in the pathophysiology of depressive symptoms. However, the involvement of the HPA-axis in linking prenatal ELS with depressive symptoms has not been tested in a prospective-longitudinal study extending until after puberty in humans. Therefore, we examined whether antenatal maternal anxiety is associated with disturbances in HPA-axis regulation and whether the HPA-axis dysregulation mediates the association between antenatal maternal anxiety and depressive symptoms in post-pubertal adolescents. As part of a prospective-longitudinal study, we investigated maternal anxiety at 12–22, 23–32, and 32–40 weeks of pregnancy (wp) with the State Trait Anxiety Inventory (STAI). In the 14–15-year-old offspring (n=58) HPA-axis function was measured through establishing a saliva cortisol day-time profile. Depressive symptoms were measured with the Childrens Depression symptoms Inventory (CDI). Results of regression analyses showed that antenatal exposure to maternal anxiety at 12–22 wp was in both sexes associated with a high, flattened cortisol day-time profile (P=0.0463) which, in female adolescents only, was associated with depressive symptoms (P=0.0077). All effects remained after controlling for maternal smoking, birth weight, obstetrical optimality, maternal postnatal anxiety and puberty phase. Our prospective study demonstrates, for the first time, the involvement of the HPA-axis in the link between antenatal maternal anxiety/prenatal ELS and depressive symptoms for post-pubertal female adolescents.

Logistic Regression Model to Distinguish Between the Benign and Malignant Adnexal Mass Before Surgery: A Multicenter Study by the International Ovarian Tumor Analysis Group

PURPOSE To collect data for the development of a more universally useful logistic regression model to distinguish between a malignant and benign adnexal tumor before surgery. PATIENTS AND METHODS Patients had at least one persistent mass. More than 50 clinical and sonographic end points were defined and recorded for analysis. The outcome measure was the histologic classification of excised tissues as malignant or benign. RESULTS Data from 1,066 patients recruited from nine European centers were included in the analysis; 800 patients (75%) had benign tumors and 266 (25%) had malignant tumors. The most useful independent prognostic variables for the logistic regression model were as follows: (1) personal history of ovarian cancer, (2) hormonal therapy, (3) age, (4) maximum diameter of lesion, (5) pain, (6) ascites, (7) blood flow within a solid papillary projection, (8) presence of an entirely solid tumor, (9) maximal diameter of solid component, (10) irregular internal cyst walls, (11) acoustic shadows, and (12) a color score of intratumoral blood flow. The model containing all 12 variables (M1) gave an area under the receiver operating characteristic curve of 0.95 for the development data set (n = 754 patients). The corresponding value for the test data set (n = 312 patients) was 0.94; and a probability cutoff value of .10 gave a sensitivity of 93% and a specificity of 76%. CONCLUSION Because the model was constructed from multicenter data, it is more likely to be generally applicable. The effectiveness of the model will be tested prospectively at different centers.

Review on solving the forward problem in EEG source analysis

BackgroundThe aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.MethodsWhile other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field.ResultsIt starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poissons differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poissons equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poissons equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method.ConclusionSolving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.

SLICOT—A Subroutine Library in Systems and Control Theory

This chapter describes the subroutine library SLICOT that provides Fortran 77 implementations of numerical algorithms for computations in systems and control theory. Around a nucleus of basic numerical linear algebra subroutines, this library builds methods for the design and analysis of linear control systems. A brief history of the library is given together with a description of the current version of the library and the ongoing activities to complete and improve the library in several aspects.

Analysis and properties of the generalized total least squares problem AX≈B when some or all columns in A are subject to error

The Total Least Squares (TLS) method has been devised as a more global fitting technique than the ordinary least squares technique for solving overdetermined sets of linear equations

Triple-negative breast cancer: Present challenges and new perspectives

AX \approx B

Simple ultrasound rules to distinguish between benign and malignant adnexal masses before surgery: prospective validation by IOTA group

when errors occur in all data. This method, introduced into numerical analysis by Golub and Van Loan, is strongly based on the Singular Value Decomposition (SVD). If the errors in the measurements A and B are uncorrelated with zero mean and equal variance, TLS is able to compute a strongly consistent estimate of the true solution of the corresponding unperturbed set

A tutorial on support vector machine-based methods for classification problems in chemometrics

A_0 X = B_0