Shearlets and Optimally Sparse Approximations

Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field.Comment: in "Shearlets: Multiscale Analysis for Multivariate Data", Birkh\"auser-Springe

Adjusting a cancer mortality-prediction model for disease status-related eligibility criteria

<p>Abstract</p> <p>Background</p> <p>Volunteering participants in disease studies tend to be healthier than the general population partially due to specific enrollment criteria. Using modeling to accurately predict outcomes of cohort studies enrolling volunteers requires adjusting for the bias introduced in this way. Here we propose a new method to account for the effect of a specific form of healthy volunteer bias resulting from imposing disease status-related eligibility criteria, on disease-specific mortality, by explicitly modeling the length of the time interval between the moment when the subject becomes ineligible for the study, and the outcome.</p> <p>Methods</p> <p>Using survival time data from 1190 newly diagnosed lung cancer patients at MD Anderson Cancer Center, we model the time from clinical lung cancer diagnosis to death using an exponential distribution to approximate the length of this interval for a study where lung cancer death serves as the outcome. Incorporating this interval into our previously developed lung cancer risk model, we adjust for the effect of disease status-related eligibility criteria in predicting the number of lung cancer deaths in the control arm of CARET. The effect of the adjustment using the MD Anderson-derived approximation is compared to that based on SEER data.</p> <p>Results</p> <p>Using the adjustment developed in conjunction with our existing lung cancer model, we are able to accurately predict the number of lung cancer deaths observed in the control arm of CARET.</p> <p>Conclusions</p> <p>The resulting adjustment was accurate in predicting the lower rates of disease observed in the early years while still maintaining reasonable prediction ability in the later years of the trial. This method could be used to adjust for, or predict the duration and relative effect of any possible biases related to disease-specific eligibility criteria in modeling studies of volunteer-based cohorts.</p

A Mean-Value Laplacian For Finsler Spaces

Part I of this thesis defines a Laplacian A for a Finsler space; we obtain A by requiring that ( A f) ( x) for a function f measures the infinitesimal average of f around x. This A is a linear, elliptic, 2nd-order differential operator. Furthermore, Af can be written in a divergence form, like the Riemannian Laplacian, but with respect to a canonical osculating Riemannian metric and Busemann&apos;s intrinsic volume form. We interpret divergence form as the result of minimizing a certain energy functional on Finsler space, and further use this approach to define harmonic forms, and harmonic mappings between Finsler manifolds. As a byprod-uct of the Laplacian, in Part I1 we derive a simple volume-form inequality which characterizes Riemannian manifolds, and define a scalar invariant V ( x) for Finsler spaces. We show that, on a Berwald space, the met-ric&apos;s first derivatives vanish in normal co-ordinates, and use that result t

Effects of a comprehensive cardiac rehabilitation program on quality of life and exercise tolerance in women: A retrospective analysis

BACKGROUND: Currently, there are a lack of investigations that have examined the effect of participating in a comprehensive cardiac rehabilitation program on quality of life and physiological measures in women of different ages. The purpose of this investigation was to examine the effect of participating in a comprehensive cardiac rehabilitation program on quality of life, exercise tolerance, blood pressure and lipids in women between 33 and 82 years of age. METHODS: The 126 women participated in a 14-week cardiac rehabilitation program that consisted of 7 weeks of formal supervised exercise training and 7 weeks of unsupervised exercise and lifestyle modification. Physiologic and quality of life outcome measures obtained at the outset and after 14 weeks included: 1) exercise treadmill time; 2) resting and peak systolic and diastolic blood pressure; 3) total cholesterol, low-density lipoprotein cholesterol, high density lipoprotein cholesterol and Triglycerides; 4) Cardiac Quality of Life Index questionnaire. RESULTS: Significant improvements were found in the following quality of life measures after participating in the cardiac rehabilitation program: physical well being, psychosocial, worry, nutrition and symptoms. No significant differences were seen for any QOL variable between the different age groups. Significant improvements were seen in exercise tolerance (+21%) and high density lipoprotein (+5%). CONCLUSION: Cardiac rehabilitation may play an important role in improving quality of life, exercise tolerance and high density lipoprotein cholesterol levels in younger and older women with underlying cardiovascular disease

Consensus on circulatory shock and hemodynamic monitoring. Task force of the European Society of Intensive Care Medicine.

OBJECTIVE: Circulatory shock is a life-threatening syndrome resulting in multiorgan failure and a high mortality rate. The aim of this consensus is to provide support to the bedside clinician regarding the diagnosis, management and monitoring of shock. METHODS: The European Society of Intensive Care Medicine invited 12 experts to form a Task Force to update a previous consensus (Antonelli et al.: Intensive Care Med 33:575-590, 2007). The same five questions addressed in the earlier consensus were used as the outline for the literature search and review, with the aim of the Task Force to produce statements based on the available literature and evidence. These questions were: (1) What are the epidemiologic and pathophysiologic features of shock in the intensive care unit ? (2) Should we monitor preload and fluid responsiveness in shock ? (3) How and when should we monitor stroke volume or cardiac output in shock ? (4) What markers of the regional and microcirculation can be monitored, and how can cellular function be assessed in shock ? (5) What is the evidence for using hemodynamic monitoring to direct therapy in shock ? Four types of statements were used: definition, recommendation, best practice and statement of fact. RESULTS: Forty-four statements were made. The main new statements include: (1) statements on individualizing blood pressure targets; (2) statements on the assessment and prediction of fluid responsiveness; (3) statements on the use of echocardiography and hemodynamic monitoring. CONCLUSIONS: This consensus provides 44 statements that can be used at the bedside to diagnose, treat and monitor patients with shock

Observation of the decay \psip\rar\kstark

Using 14 million $\psi(2S)$ events collected with the BESII detector, branching fractions of \psip\rar\kstarkpm and \kstarknn are determined to be: \calB(\psip\rar\kstarkpm)=(2.9^{+1.3}_{-1.7}\pm0.4)\times 10^{-5} and \calB(\psip\rar\kstarknn)=(13.3^{+2.4}_{-2.7}\pm1.9)\times 10^{-5}. The results confirm the violation of the "12%" rule for these two decay channels with higher precision. A large isospin violation between the charged and neutral modes is observed.Comment: 5 pages, 3 figure

Vasopressors and Inotropes in the Treatment of Human Septic Shock: Effect on Innate Immunity?

Catecholamines have been suggested to modulate innate immune responses in experimental settings. The significance hereof in the treatment of human septic shock is unknown. We therefore sought if and how vasopressor/inotropic doses relate to pro-inflammatory mediators during treatment of septic shock. We prospectively studied 20 consecutive septic shock patients. For 3 days after admission, hemodynamic variables, lactate and plasma levels of interleukins (IL)-6 and 8, tumor necrosis factor (TNF)-α, and elastase-α1-antitrypsin were measured six hourly. Doses of vasoactive drugs were recorded. Of the 20 patients, nine died in the intensive care unit. Dobutamine doses were positively associated and related to TNF-α plasma levels, independently of disease severity, hemodynamics, and outcome, in multivariable models. Dopamine doses were positively associated with IL-6, and norepinephrine was inversely associated with IL-8 and TNF-α levels. Our observations suggest that catecholamines used in the treatment of human septic shock differ in their potential modulation of the innate immune response to sepsis in vivo. Dobutamine treatment may contribute to circulating TNF-α and dopamine to IL-6, independently of activated neutrophils. Conversely, norepinephrine may lack pro-inflammatory actions