Quantitative recurrence statistics and convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems

For non-uniformly hyperbolic dynamical systems we consider the time series of maxima along typical orbits. Using ideas based upon quantitative recurrence time statistics we prove convergence of the maxima (under suitable normalization) to an extreme value distribution, and obtain estimates on the rate of convergence. We show that our results are applicable to a range of examples, and include new results for Lorenz maps, certain partially hyperbolic systems, and non-uniformly expanding systems with sub-exponential decay of correlations. For applications where analytic results are not readily available we show how to estimate the rate of convergence to an extreme value distribution based upon numerical information of the quantitative recurrence statistics. We envisage that such information will lead to more efficient statistical parameter estimation schemes based upon the block-maxima method.Comment: This article is a revision of the previous article titled: "On the convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems." Relative to this older version, the revised article includes new and up to date results and developments (based upon recent advances in the field

IUPUI Imaging Research Initiative: Research Center for Quantitative Renal Imaging

poster abstractMission: The overall mission of the Research Center for Quantitative Renal Imaging is to provide a focused research environment and resource for the development, implementation, and dissemination of innovative, quantitative imaging methods designed to assess the status of and mechanisms associated with acute and chronic kidney disease and evaluate efficacy of therapeutic interventions. Currently, there is no comprehensive research center within the United States that is solely dedicated to the development of quantitative imaging methods specifically designed to diagnose kidney disease, monitor its progression, and evaluate efficacy of therapeutic interventions. The Research Center for Quantitative Renal Imaging represents a very unique resource within the nephrology and medical imaging communities that is distinctly associated with IUPUI and the IU School of Medicine. Nature of the Center: Our plan is to build upon the individually successful research programs and infrastructure that currently exist within our institution and weave these individual components into a new, unified, and unique Research Center focused on developing novel and innovative methods for quantitative imaging of the kidney. Goals: The Research Center for Quantitative Renal Imaging will achieve its mission by: • Identifying, developing, and implementing innovative imaging methods that provide quantitative imaging biomarkers for assessing and inter-relating renal structure, function, hemodynamics and underlying tissue microenvironmental factors contributing to kidney disease. • Establishing an environment that facilitates and encourages interdisciplinary collaborations among investigators, helps advance the research careers of junior faculty, and offers research support to investigators focused on developing and utilizing innovative quantitative imaging methods in support of kidney disease research. • Providing a resource to inform the greater research and healthcare communities of advances in quantitative renal imaging and its potential for enhanced patient management and care. • Offering an imaging research resource to pharmaceutical companies and medical device manufacturers engaged in product development associated with the diagnosis and treatment of kidney disease

IUPUI Imaging Research Initiative

poster abstractImaging has become an essential research tool in a majority of scientific disciplines. The IUPUI Imaging Research Initiative (IRI) has been established to bring together researcher investigators who develop innovative imaging technologies with those who utilize imaging tools to advance their research with the primary objective of building a large scale imaging research infrastructure at IUPUI. An Imaging Research Council has been created to establish priorities for the IRI and help guide the development of an IUPUI research imaging infrastructure and sustainable research funding base. The goals of the IUPUI Imaging Research Initiative include: • To encourage and coordinate collaboration among IUPUI researchers from different disciplines • To provide advice and guidance in the realization of highly competitive large grant proposals that will support and grow the IUPUI imaging efforts into major nationally and internationally recognized programs • To develop a strategic plan that will enable IUPUI to become nationally and internationally known as the place for innovative imaging research and its applications • To determine strategic areas of strength and growth • To determine available and needed resources • To determine strategic external partnership

On "Sexual contacts and epidemic thresholds," models and inference for Sexual partnership distributions

Recent work has focused attention on statistical inference for the population distribution of the number of sexual partners based on survey data. The characteristics of these distributions are of interest as components of mathematical models for the transmission dynamics of sexually-transmitted diseases (STDs). Such information can be used both to calibrate theoretical models, to make predictions for real populations, and as a tool for guiding public health policy. Our previous work on this subject has developed likelihood-based statistical methods for inference that allow for low-dimensional, semi-parametric models. Inference has been based on several proposed stochastic process models for the formation of sexual partnership networks. We have also developed model selection criteria to choose between competing models, and assessed the fit of different models to three populations: Uganda, Sweden, and the USA. Throughout this work, we have emphasized the correct assessment of the uncertainty of the estimates based on the data analyzed. We have also widened the question of interest to the limitations of inferences from such data, and the utility of degree-based epidemiological models more generally. In this paper we address further statistical issues that are important in this area, and a number of confusions that have arisen in interpreting our work. In particular, we consider the use of cumulative lifetime partner distributions, heaping and other issues raised by Liljeros et al. in a recent working paper.Comment: 22 pages, 5 figures in linked working pape