The F-Signature of Toric Varieties.

In this thesis, we express the $F$-signature of the coordinate ring of an affine toric variety as the volume of a polytope, generalizing a formula of Watanabe and Yoshida. We introduce the notion of the $F$-signature function for divisors on a normal projective variety and show that this function is piecewise rational on the big cone of a projective toric variety.PHDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/93995/1/vonkorff_1.pd

The science of clinical practice: disease diagnosis or patient prognosis? Evidence about "what is likely to happen" should shape clinical practice.

BACKGROUND: Diagnosis is the traditional basis for decision-making in clinical practice. Evidence is often lacking about future benefits and harms of these decisions for patients diagnosed with and without disease. We propose that a model of clinical practice focused on patient prognosis and predicting the likelihood of future outcomes may be more useful. DISCUSSION: Disease diagnosis can provide crucial information for clinical decisions that influence outcome in serious acute illness. However, the central role of diagnosis in clinical practice is challenged by evidence that it does not always benefit patients and that factors other than disease are important in determining patient outcome. The concept of disease as a dichotomous 'yes' or 'no' is challenged by the frequent use of diagnostic indicators with continuous distributions, such as blood sugar, which are better understood as contributing information about the probability of a patient's future outcome. Moreover, many illnesses, such as chronic fatigue, cannot usefully be labelled from a disease-diagnosis perspective. In such cases, a prognostic model provides an alternative framework for clinical practice that extends beyond disease and diagnosis and incorporates a wide range of information to predict future patient outcomes and to guide decisions to improve them. Such information embraces non-disease factors and genetic and other biomarkers which influence outcome. SUMMARY: Patient prognosis can provide the framework for modern clinical practice to integrate information from the expanding biological, social, and clinical database for more effective and efficient care

Report of the NIH Task Force on Research Standards for Chronic Low Back Pain

Despite rapidly increasing intervention, functional disability due to chronic low back pain (cLBP) has increased in recent decades. We often cannot identify mechanisms to explain the major negative impact cLBP has on patients’ lives. Such cLBP is often termed non-specific, and may be due to multiple biologic and behavioral etiologies. Researchers use varied inclusion criteria, definitions, baseline assessments, and outcome measures, which impede comparisons and consensus. The NIH Pain Consortium therefore charged a Research Task Force (RTF) to draft standards for research on cLBP. The resulting multidisciplinary panel recommended using 2 questions to define cLBP; classifying cLBP by its impact (defined by pain intensity, pain interference, and physical function); use of a minimal data set to describe research participants (drawing heavily on the PROMIS methodology); reporting “responder analyses” in addition to mean outcome scores; and suggestions for future research and dissemination. The Pain Consortium has approved the recommendations, which investigators should incorporate into NIH grant proposals. The RTF believes these recommendations will advance the field, help to resolve controversies, and facilitate future research addressing the genomic, neurologic, and other mechanistic substrates of chronic low back pain. We expect the RTF recommendations will become a dynamic document, and undergo continual improvement.Perspective: A Task Force was convened by the NIH Pain Consortium, with the goal of developing research standards for chronic low back pain. The results included recommendations for definitions, a minimal dataset, reporting outcomes, and future research. Greater consistency in reporting should facilitate comparisons among studies and the development of phenotypes

Outcome measures for low back pain research: A proposal for standardized use

Study Design. An international group of back pain researchers considered recommendations for standardized measures in clinical outcomes research in patients with back pain. Objectives. To promote more standardization of outcome measurement in clinical trials and other types of outcomes research, including recta-analyses, cost-effectiveness analyses, and multicenter studies. Summary of Background Data. Better standardization of outcome measurement would facilitate comparison of results among studies, and more complete reporting of relevant outcomes. Because back pain is rarely fatal or completely cured, outcome assessment is complex and involves multiple dimensions. These include symptoms, function, general well-being, work disability, and satisfaction, with care. Methods. The panel considered several factors in recommending a standard battery of outcome measures. These included reliability, validity, responsiveness, and practicality of the measures. In addition, compatibility with widely used and promoted batteries such as the American Academy of Orthopaedic Surgeons Lumbar Cluster were considered to minimize the need for changes when these instruments are used. Results. First, a six-item set was proposed, which is sufficiently brief that it could be used in routine care settings for quality improvement and for research purposes. An expanded outcome set, which would provide more precise measurement for research purposes, includes measures of severity and frequency of symptoms, either the Roland or the Oswestry Disability Scale, either the SF-12 or the EuroQol measure of general health status, a question about satisfaction with symptoms, three types of 'disability days,' and an optional single item on overall satisfaction with medical care. Conclusion. Standardized measurement of outcomes would facilitate scientific advances in clinical care. A short, 6-item questionnaire and a somewhat expanded, more precise battery of questionnaires can be recommended. Although many considerations sup port such recommendations, more data on responsiveness and the minimally important change n scores are needed for most of the instruments

A localized view on molecular dissociation via electron-ion partial covariance

Inner-shell photoelectron spectroscopy provides an element-specific probe of molecular structure, as core-electron binding energies are sensitive to the chemical environment. Short-wavelength femtosecond light sources, such as Free-Electron Lasers (FELs), even enable time-resolved site-specific investigations of molecular photochemistry. Here, we study the ultraviolet photodissociation of chiral (R/S)-1-iodo-2-methylbutane, probed by XUV pulses from the Free-electron LASer in Hamburg (FLASH) through the ultrafast evolution of the iodine 4d binding energy. Methodologically, we introduce electron-ion partial covariance imaging as a technique to isolate otherwise elusive features in a two-dimensional photoelectron spectrum arising from different photofragmentation pathways. The experimental and theoretical results for the time-resolved electron spectra of the 4d$_{3/2}$ and 4d$_{5/2}$ atomic and molecular levels that are disentangled by this method provide a key step towards studying structural and chemical changes from a specific spectator site. We thus pave the way for approaching femto-stereochemistry with FELs