Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.

Practical stability with respect to model mismatch of approximate discrete-time output feedback control

This paper establishes a practical stability result for discrete-time output feedback control involving mismatch between the exact system to be stabilised and the approximating system used to design the controller. The practical stability is in the sense of an asymptotic bound on the amount of error bias introduced by the model approximation, and is established using local consistency properties of the systems. Importantly, the practical stability established here does not require the approximating system to be of the same model type as the exact system. Examples are presented to illustrate the nature of our practical stability result.

A Raman spectroscopic study of the different vanadate-groups in solid-state compounds, model case : mineral phases vésigniéite, BaCu3(VO4)2(OH)2, and volborthite, Cu3V2O7(OH)2•2H2O

Raman spectroscopy has been used to study vanadates in the solid state. The molecular structure of the vanadate minerals vésigniéite [BaCu3(VO4)2(OH)2] and volborthite [Cu3V2O7(OH)2·2H2O] have been studied by Raman spectroscopy and infrared spectroscopy. The spectra are related to the structure of the two minerals. The Raman spectrum of vésigniéite is characterized by two intense bands at 821 and 856 cm−1 assigned to ν1 (VO4)3− symmetric stretching modes. A series of infrared bands at 755, 787 and 899 cm−1 are assigned to the ν3 (VO4)3− antisymmetric stretching vibrational mode. Raman bands at 307 and 332 cm−1 and at 466 and 511 cm−1 are assigned to the ν2 and ν4 (VO4)3− bending modes. The Raman spectrum of volborthite is characterized by the strong band at 888 cm−1, assigned to the ν1 (VO3) symmetric stretching vibrations. Raman bands at 858 and 749 cm−1 are assigned to the ν3 (VO3) antisymmetric stretching vibrations; those at 814 cm−1 to the ν3 (VOV) antisymmetric vibrations; that at 508 cm−1 to the ν1 (VOV) symmetric stretching vibration and those at 442 and 476 cm−1 and 347 and 308 cm−1 to the ν4 (VO3) and ν2 (VO3) bending vibrations, respectively. The spectra of vésigniéite and volborthite are similar, especially in the region of skeletal vibrations, even though their crystal structures differ.

Inhibition of p38 pathway leads to OA-like changes in a rat animal model

Objectives The p38 mitogen-activated protein kinase (MAPK) signal transduction pathway is involved in a variety of inflammatory responses, including cytokine generation, cell differentiation proliferation and apoptosis. Here, we examined the effects of systemic p38 MAPK inhibition on cartilage cells and osteoarthritis (OA) disease progression by both in vitro and in vivo approaches. Methods p38 kinase activity was evaluated in normal and OA cartilage cells by measuring the amount of phosphorylated protein. To examine the function of p38 signaling pathway in vitro, normal chondrocytes were isolated and differentiated in the presence or absence of p38 inhibitor; SB203580 and analysed for chondrogenic phenotype. Effect of systemic p38 MAPK inhibition in normal and OA (induced by menisectomy) rats were analysed by treating animals with vehicle alone (DMS0) or p38 inhibitor (SB203580). Damage to the femur and tibial plateau was evaluated by modified Mankin score, histology and immunohistochemistry. Results Our in vitro studies have revealed that a down-regulation of chondrogenic and increase of hypertrophic gene expression occurs in the normal chondrocytes, when p38 is neutralized by a pharmacological inhibitor. We further observed that the basal levels of p38 phosphorylation were decreased in OA chondrocytes compared with normal chondrocytes. These findings together indicate the importance of this pathway in the regulation of cartilage physiology and its relevance to OA pathogenesis. At in vivo level, systematic administration of a specific p38 MAPK inhibitor, SB203580, continuously for over a month led to a significant loss of proteoglycan; aggrecan and cartilage thickness. On the other hand, SB203580 treated normal rats showed a significant increase in TUNEL positive cells, cartilage hypertrophy markers such as Type 10 collagen, Runt-related transcription factor and Matrix metalloproteinase-13 and substantially induced OA like phenotypic changes in the normal rats. In addition, menisectomy induced OA rat models that were treated with p38 inhibitor showed aggravation of cartilage damage. Conclusions In summary, this study has provided evidence that the component of the p38 MAPK pathway is important to maintain the cartilage health and its inhibition can lead to severe cartilage degenerative changes. The observations in this study highlight the possibility of using activators of the p38 pathway as an alternative approach in the treatment of OA.

The impact of temperature on mortality in Tianjin, China : a case-crossover design with a distributed lag non-linear model

Background There has been increasing interest in assessing the impacts of temperature on mortality. However, few studies have used a case–crossover design to examine non-linear and distributed lag effects of temperature on mortality. Additionally, little evidence is available on the temperature-mortality relationship in China, or what temperature measure is the best predictor of mortality. Objectives To use a distributed lag non-linear model (DLNM) as a part of case–crossover design. To examine the non-linear and distributed lag effects of temperature on mortality in Tianjin, China. To explore which temperature measure is the best predictor of mortality; Methods: The DLNM was applied to a case¬−crossover design to assess the non-linear and delayed effects of temperatures (maximum, mean and minimum) on deaths (non-accidental, cardiopulmonary, cardiovascular and respiratory). Results A U-shaped relationship was consistently found between temperature and mortality. Cold effects (significantly increased mortality associated with low temperatures) were delayed by 3 days, and persisted for 10 days. Hot effects (significantly increased mortality associated with high temperatures) were acute and lasted for three days, and were followed by mortality displacement for non-accidental, cardiopulmonary, and cardiovascular deaths. Mean temperature was a better predictor of mortality (based on model fit) than maximum or minimum temperature. Conclusions In Tianjin, extreme cold and hot temperatures increased the risk of mortality. Results suggest that the effects of cold last longer than the effects of heat. It is possible to combine the case−crossover design with DLNMs. This allows the case−crossover design to flexibly estimate the non-linear and delayed effects of temperature (or air pollution) whilst controlling for season.