The method of least squares has been used in general for regression analysis. It is usually assumed that the errors are confined to the dependent variable, but in many cases both dependent and independent variables are typically measured with some stochastic errors. The statistical method of orthogonal regression has been used when both variables under investigation are subject to stochastic errors. Furthermore, the measurements sometimes may not be exact but have been censored. In this situation doing orthogonal regression with censored data directly between the two variables, it may yield an incorrect estimates of the relationship. In this work we discuss the estimation of orthogonal regression under censored data in one variable and then provide a method of estimation and two criteria on when the method is applicable. When the observations satisfy the criteria provided here, there will not be very large differences between the estimated orthogonal regression line and the theoretical orthogonal regression line.

It is becoming increasingly important to understand biological networks in order to understand complex diseases, identify novel, safer protein targets for therapies and design efficient drugs. 'Systems biology' has emerged as a discipline to uncover biological networks through genomic data. Computational methods for identifying these networks become immensely important and have been growing in number in parallel to increasing amount of genomic data under the discipline of 'Systems Biology'. In this thesis we introduced novel computational methods for identifying topological and dynamic properties of biological networks. Biological data is available in various forms. Experimental data on the interactions between biological components provides a connectivity map of the system as a network of interactions and time series or steady state experiments on concentrations or activity levels of biological constituents will give a dynamic picture of the web of these interactions. Biological data is scarce usually relative to the number of components in the networks and subject to high levels of noise. The data is available from various resources however it can have missing information and inconsistencies. Hence it is critical to design intelligent computational methods that can incorporate data from different resources while considering noise component. This thesis is organized as follows; Chapter 1 and 2 will introduce the basic concepts for biological network types. Chapter 2 will give a background on biochemical network identification data types and computational approaches for reverse engineering of these networks. Chapter 3 will introduce our novel constrained total least squares approach for recovering network topology and dynamics through noisy measurements. We proved our method to be superior over existing reverse engineering methods. Chapter 4 is an extension of chapter 3 where a Bayesian parameter estimation algorithm is presented that is capable of incorporating noisy time series and prior information for the connectivity of network. The quality of prior information is critical to be able to infer dynamics of the networks. The major drawback of prior connectivity data is the presence of false negatives, missing links. Hence, powerful link prediction methods are necessary to be able to identify missing links. At this junction a novel link prediction method is introduced in Chapter 5. This method is capable of predicting missing links in a connectivity data. An application of this method on protein-protein association data from a literature mining database will be demonstrated. In chapter 6 a further extension into link prediction applications will be given. An interesting application of these methods is the drug adverse effect prediction. Adverse effects are the major reason for the failure of drugs in pharmaceutical industry, therefore it is very important to identify potential toxicity risks in the early drug development process. Motivated by this chapter 6 introduces our computational framework that integrates drug-target, drug-side effect, pathway-target and mouse phenotype-mouse genes data to predict side effects. Chapter 7 will give the significant findings and overall achievements of the thesis. Subsequent steps will be suggested that can follow the work presented here to improve network prediction methods.

<p>This thesis consists of four independent papers concerningdifferent aspects of interior methods for optimization. Threeof the papers focus on theoretical aspects while the fourth oneconcerns some computational experiments.</p><p>The systems of equations solved within an interior methodapplied to a convex quadratic program can be viewed as weightedlinear least-squares problems. In the first paper, it is shownthat the sequence of solutions to such problems is uniformlybounded. Further, boundedness of the solution to weightedlinear least-squares problems for more general classes ofweight matrices than the one in the convex quadraticprogramming application are obtained as a byproduct.</p><p>In many linesearch interior methods for nonconvex nonlinearprogramming, the iterates can "falsely" converge to theboundary of the region defined by the inequality constraints insuch a way that the search directions do not converge to zero,but the step lengths do. In the sec ond paper, it is shown thatthe multiplier search directions then diverge. Furthermore, thedirection of divergence is characterized in terms of thegradients of the equality constraints along with theasymptotically active inequality constraints.</p><p>The third paper gives a modification of the analytic centerproblem for the set of optimal solutions in linear semidefiniteprogramming. Unlike the normal analytic center problem, thesolution of the modified problem is the limit point of thecentral path, without any strict complementarity assumption.For the strict complementarity case, the modified problem isshown to coincide with the normal analytic center problem,which is known to give a correct characterization of the limitpoint of the central path in that case.</p><p>The final paper describes of some computational experimentsconcerning possibilities of reusing previous information whensolving system of equations arising in interior methods forlinear programming.</p><p><b>Keywords:</b>Interior method, primal-dual interior method,linear programming, quadratic programming, nonlinearprogramming, semidefinite programming, weighted least-squaresproblems, central path.</p><p><b>Mathematics Subject Classification (2000):</b>Primary90C51, 90C22, 65F20, 90C26, 90C05; Secondary 65K05, 90C20,90C25, 90C30.</p>

This paper is concerned with the numerical analysis of the autoconvolution equation $x*x=y$ restricted to the interval [0,1]. We present a discrete constrained least squares approach and prove its convergence in $L^p(0,1),1<p<\infinite$ , where the regularization is based on a prescribed bound for the total variation of admissible solutions. This approach includes the case of non-smooth solutions possessing jumps. Moreover, an adaption to the Sobolev space $H^1(0,1)$ and some remarks on monotone functions are added. The paper is completed by a numerical case study concerning the determination of non-monotone smooth and non-smooth functions x from the autoconvolution equation with noisy data y.

This paper deals with optimisation of food overloading at long distance flights. It is described how in case of two offered meals and two several passenger groups reserve meals are to distribute to both meals such that the probability that each passenger will get the meal of its choice is maximised. A statistical procedure is presented for estimation of needed demand probabilities.

This study evaluated a parent implemented in-situ pedestrian safety skills intervention for three individuals with autism. Specifically, this study examined the utility of using a behavioral skills training (BST) to help parents implement the most-to-least prompting procedures in training their children with autism pedestrian safety skills in community settings. A multiple baseline design across participants was used to assess parent implementation of in-situ pedestrian training as well as child participants' independently performed correct skills. Results indicated that parents implemented most-to-least prompting procedures with high levels of accuracy across streets during intervention and fading of BST. All child participants improved their safety skills significantly during intervention. For one child, the acquired skills maintained during follow- up. The percentages of their independent correct use of pedestrian safety skills were similar to those in baseline during generalization probes.

The construction of dams and hydro-power stations are some of the most common anthropogenic changes of watercourses and rivers. While being important to humans and society by providing electricity, these obstructions of watercourses can have severe consequences for the aquatic ecosystems. One consequence is that dams often hinder the important movement of migrating fish species between habitats. This can lead to decline and even extinction of important fish populations. To prevent these negative effects, a number of different fish passage systems, including nature-like fishways, have been developed. Nature-like fishways mimic natural streams in order to function as a natural corridor for a wide range of species. Planning and construction of a nature-like fishway is a complex task that often involves many different interests. In the present study a combination of multi-criteria decision analysis and least-cost path analysis is used for determining the best location for a nature-like fishway past Strömdalen dam in Gavleån, Sweden. An anisotropic least-cost path algorithm is applied on a friction-layer and a digital elevation model, and the least-cost path for a nature-like fishway is determined. The results show that the method is useful in areas of varying topography and steep slopes. However, because low slope is a very important factor when constructing a nature-like fishway, slope becomes the dominating factor in this analysis at the expense of e.g. distance to roads. Combining the methods with results from biological studies of fish behavior and detailed hydrological modelling would provide a very strong tool for the planning of nature-like fishways.

Recent advances in travel demand modeling have concentrated on adding behavioral realism by focusing on an individual’s activity participation. And, to account for trip-chaining, tour-based methods are largely replacing trip-based methods. Alongside these advances and innovations in dynamic traffic assignment (DTA) techniques, however, time-of-day (TOD) modeling remains an Achilles’ heel. As congestion worsens and operators turn to variable road pricing, sensors are added to networks, cell phones are GPS-enabled, and DTA techniques become practical, accurate time-of-day forecasts become critical. In addition, most models highlight tradeoffs between travel time and cost, while neglecting variations in travel time. Research into stated and revealed choices suggests that travel time variability can be highly consequential. This dissertation introduces a method for imputing travel time variability information as a continuous function of time-of-day, while utilizing an existing method for imputing average travel times (by TOD). The methods employ ordinary least squares (OLS) regression techniques, and rely on reported travel time information from survey data (typically available to researchers), as well as travel time and distance estimates by origin-destination (OD) pair for free-flow and peak-period conditions from network data. This dissertation also develops two models of activity timing that recognize the imputed average travel times and travel time variability. Both models are based in random utility theory and both recognize potential correlations across time-of-day alternatives. In addition, both models are estimated in a Bayesian framework using Gibbs sampling and Metropolis-Hastings (MH) algorithms, and model estimation relies on San Francisco Bay Area data collected in 2000. The first model is the continuous cross-nested logit (CCNL) and represents tour outbound departure time choice in a continuous context (rather than discretizing time) over an entire day. The model is formulated as a generalization of the discrete cross-nested logit (CNL) for continuous choice and represents the first random utility maximization model to incorporate the ability to capture correlations across alternatives in a continuous choice context. The model is then compared to the continuous logit, which represents a generalization of the multinomial logit (MNL) for continuous choice. Empirical results suggest that the CCNL out-performs the continuous logit in terms of predictive accuracy and reasonableness of predictions for three tolling policy simulations. Moreover, while this dissertation focuses on time-of-day modeling, the CCNL could be used in a number of other continuous choice contexts (e.g., location/destination, vehicle usage, trip durations, and profit-maximizing production). The second model is a bivariate multinomial probit (BVMNP) model. While the model relies on discretization of time (into 30-minute intervals), it captures both key dimensions of a tour’s timing (rather than just one, as in this dissertation’s application of the CCNL model), which is important for tour- and activity-based models of travel demand. The BVMNP’s ability to capture correlations across scheduling alternatives is something no existing two-dimensional choice models of tour timing can claim. Both models represent substantial contributions for continuous choice modeling in transportation, business, biology, and various other fields. In addition, the empirical results of the models evaluated here enhance our understanding of individuals’ time-of-day decisions. For instance, average travel time and its variance are estimated to have a negative effect on workers’ utilities, as expected, but are not found to be that practically relevant here, probably because most workers are rather constrained in their activity scheduling and/or work hours. However, correlations are found to be rather strong in both models, particularly for home-to-work journeys, suggesting that if models fail to accommodate such correlations, biased application results may emerge. / text

The purpose of this study was to determine if there was a functional relation between a peer-delivered modified system of least prompts procedure (SLP) and an increase in level and trend of performance on finding the area of polygons or finding the volume of cylinders, spheres, and cones, and could the peer tutor reliably implement the modified SLP procedure with middle school students with mild to severe disabilities. A multiple probe days across participants design was used. Results from this study show that there was a functional relation across students in which students were able to make progress on academic math skills when taught by a peer tutor using the modified SLP procedure. The peer tutor was able to reliably implement the procedure to multiple students. Limitations and implications for practice are discussed.

Ein zusammengesetzter Index ist eine aggregierte Variable, die aus individuellen Indikatoren und Gewichten besteht, wobei die Gewichte die relative Wichtigkeit jedes Indikators darstellen. Zusammengesetzte Indizes werden oft benutzt um latente Phänomene zu schreiben oder komplexe Informationen zu einer geringen Anzahl an Variablen zusammenzufassen. Es ist von großer Bedeutung richtige Gewichte für die Variablen, die einen zusammengesetzten Index bilden, zu wählen. Hauptkomponentenanalyse (PCA) ist ein populärer Ansatz um Gewichte abzuleiten, aber es ist ungeeignet, wenn informative Variationen nur kleine Varianzen der Variablen in einem zusammengesetzten Index haben. Deshalb schlägt diese Studie vor, Partial Least Squares (PLS) anzuwenden, welches die Beziehung zwischen Zielvariablen and den Variablen in einem zusammengesetzten Index ausnutzt. Unsere Simulationsstudie zeigt, dass PLS so gut wie PCA funktioniert oder erheblich es übertrifft. Zusätzlich sind in der Praxis die Variablen in einem zusammengesetzten Index häufig nicht-metrisch. Solche Variablen benötigen spezielle Verfahren, um PCA oder PLS anzuwenden. Diese Studie untersucht mehrere PCA und PLS Algorithmen für nicht-metrische Variablen in der vorliegenden Literatur und vergleicht sie durch umfangreiche Simulationsstudien, um Empfehlungen für die Praxis abzugeben. Dummy coding zeigt häufig zufriedenstellende Leistung im Vergleich zu komplizierteren Methoden. Als unsere Anwendungen betrachten wir Vermögen, Globalisierung, Geschlechtergleichheit und Korruption, indem PCA- und PLS-basierte zusammengesetzte Indizes angewendet werden. PLS erzeugt für die jeweiligen Zielvariablen massgeschnittene zusammengesetzte Indizes, die häufig bessere Leistung als PCA zeigten. Ein Vergleich zwischen PCA und PLS Gewichten und Koeffizienten zeigt, welche Variablen für die jeweiligen Zielvariablen besonders relevant sind.