Regularization of descriptor systems

Implicit dynamic-algebraic equations, known in control theory as descriptor systems, arise naturally in many applications. Such systems may not be regular (often referred to as singular). In that case the equations may not have unique solutions for consistent initial conditions and arbitrary inputs and the system may not be controllable or observable. Many control systems can be regularized by proportional and/or derivative feedback.We present an overview of mathematical theory and numerical techniques for regularizing descriptor systems using feedback controls. The aim is to provide stable numerical techniques for analyzing and constructing regular control and state estimation systems and for ensuring that these systems are robust. State and output feedback designs for regularizing linear time-invariant systems are described, including methods for disturbance decoupling and mixed output problems. Extensions of these techniques to time-varying linear and nonlinear systems are discussed in the final section.

Clinical predictors of response to cognitive-behavioural therapy in pediatric anxiety disorders: the Genes for Treatment (GXT) Study

Objective The Genes for Treatment study is an international, multisite collaboration exploring the role of genetic, demographic, and clinical predictors in response to cognitive-behavioral therapy (CBT) in pediatric anxiety disorders. The current article, the first from the study, examined demographic and clinical predictors of response to CBT. We hypothesized that the child’s gender, type of anxiety disorder, initial severity and comorbidity, and parents’ psychopathology would significantly predict outcome. Method A sample of 1,519 children 5 to 18 years of age with a primary anxiety diagnosis received CBT across 11 sites. Outcome was defined as response (change in diagnostic severity) and remission (absence of the primary diagnosis) at each time point (posttreatment, 3-, 6-, and/or 12-month follow-up) and analyzed using linear and logistic mixed models. Separate analyses were conducted using data from posttreatment and follow-up assessments to explore the relative importance of predictors at these time points. Results Individuals with social anxiety disorder (SoAD) had significantly poorer outcomes (poorer response and lower rates of remission) than those with generalized anxiety disorder (GAD). Although individuals with specific phobia (SP) also had poorer outcomes than those with GAD at posttreatment, these differences were not maintained at follow-up. Both comorbid mood and externalizing disorders significantly predicted poorer outcomes at posttreatment and follow-up, whereas self-reported parental psychopathology had little effect on posttreatment outcomes but significantly predicted response (although not remission) at follow-up. Conclusion SoAD, nonanxiety comorbidity, and parental psychopathology were associated with poorer outcomes after CBT. The results highlight the need for enhanced treatments for children at risk for poorer outcomes.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

A new calibrated sunspot group series since 1749: statistics of active day fractions

Although the sunspot-number series have existed since the mid-19th century, they are still the subject of intense debate, with the largest uncertainty being related to the "calibration" of the visual acuity of individual observers in the past. Daisy-chain regression methods are applied to inter-calibrate the observers which may lead to significant bias and error accumulation. Here we present a novel method to calibrate the visual acuity of the key observers to the reference data set of Royal Greenwich Observatory sunspot groups for the period 1900-1976, using the statistics of the active-day fraction. For each observer we independently evaluate their observational thresholds [S_S] defined such that the observer is assumed to miss all of the groups with an area smaller than S_S and report all the groups larger than S_S. Next, using a Monte-Carlo method we construct, from the reference data set, a correction matrix for each observer. The correction matrices are significantly non-linear and cannot be approximated by a linear regression or proportionality. We emphasize that corrections based on a linear proportionality between annually averaged data lead to serious biases and distortions of the data. The correction matrices are applied to the original sunspot group records for each day, and finally the composite corrected series is produced for the period since 1748. The corrected series displays secular minima around 1800 (Dalton minimum) and 1900 (Gleissberg minimum), as well as the Modern grand maximum of activity in the second half of the 20th century. The uniqueness of the grand maximum is confirmed for the last 250 years. It is shown that the adoption of a linear relationship between the data of Wolf and Wolfer results in grossly inflated group numbers in the 18th and 19th centuries in some reconstructions.

Socioeconomic correlates of global mammalian conservation status

The main causes of biodiversity decline are related to human use of resources, which is ultimately triggered by the socioeconomic decisions made by individuals and nations. Characterizing the socioeconomic attributes of areas in which biodiversity is most threatened can help us identify decisions and conditions that promote the presence or absence of threats and potentially suggest more sustainable strategies. In this study we explored how diverse indicators of social and economic development correlate with the conservation status of terrestrial mammals within countries explicitly exploring hypothesized linear and quadratic relationships. First, comparing countries with and without threatened mammals we found that those without threatened species are a disparate group formed by European countries and Small Island Developing States (SIDS) with little in common besides their slow population growth and a past of human impacts. Second, focusing on countries with threatened mammals we found that those with a more threatened mammalian biota have mainly rural populations, are predominantly exporters of goods and services, receive low to intermediate economic benefits from international tourism, and have medium to high human life expectancy. Overall, these results provide a comprehensive characterization of the socioeconomic profiles linked to mammalian conservation status of the world's nations, highlighting the importance of transborder impacts reflected by the international flux of goods, services and people. Further studies would be necessary to unravel the actual mechanisms and threats that link these socioeconomic profiles and indicators with mammalian conservation. Nevertheless, this study presents a broad and complete characterization that offers testable hypotheses regarding how socioeconomic development associates with biodiversity.

Taste components of Sherry wines

Sherry wine has characteristic taste and aroma, different from other wine-based alcoholic beverages. This paper reports a study of the non-volatile, low-molecular weight compounds found in sherry and related alcoholic beverages that may contribute to taste. Compounds analysed included free amino acids, organic acids, sugars and small peptides (linear and cyclic). A series of seven diketopiperazines (cyclic dipeptides) namely, cyclo(Leu-Leu), cyclo(Pro-Leu), cyclo(Pro-Ile), cyclo(Pro-Met), cyclo( Pro-Val), cyclo(Pro-Pro) and cyclo(Val-Ala) were identified for the first time in sherry. Although traces were found in some other alcoholic beverages, levels were low compared with sherry. The base wine used in the sherry production had only traces of diketopiperazines, indicating that the casking stage of sherry production might be responsible for their formation.