Events
Department of Mathematics and Statistics
Texas Tech University
Arguably, all data can be stored as some sort of images: a picture is all it takes a car insurer to expedite the payment for a claim for a bumper scratch, satellite pictures of the Earth show that we are living indeed in a thin layer of air, medical images, first and second generation DNA sequence are initially stored as images, and digital cameras are at the fingertips of any smart phone owner. In each instance, certain information extracted from such images to be represented on a metric space, that often time has a smooth structure, or a structure of stratified space, thus opening the formidable doors to the realm of geometric and algebraic topological data analysis, for extracted from electronic images. A few simple examples of such methodology is presented here. This is joint work with Rob Paige (MST), Daniel Osborne, Mingfei Qiu, Ruite Guo, K. David Yao, David Lester, Yifang Deng, Shen Chen, Seunghee Choi and Hwiyoung Lee.Climate change requires a global perspective to understand the past and explore the future. The impacts of climate change, however, are experienced mainly at the local to regional level. A range of statistical techniques from simple to complex are commonly used to bridge the gap between the spatial scales at which climate is modeled on fundamental physical principles vs. the spatial and temporal scales at which impact assessments require climate projections. This step, often referred to as “downscaling” and bias correction, poses some significant challenges, but also has the potential to provide essential input to real-world decision-makers, from water managers to infrastructure engineers. In this presentation I will describe the methods and evaluation framework we have developed to generate and test these high-resolution climate projections, some of the ways that information has been used, and how I expect this field to continue to evolve in the future.
And I have a new co-authored book coming out with Cambridge University Press on this topic in November that people can refer to if they are interested in more information: here
The celebrated Riemann hypothesis can be reformulated as a simply-stated criterion concerning least-squares approximation. While carrying out computations related to this criterion, we have observed a curious phenomenon: for no apparent reason, at least the first billion entries of a certain infinite triangular matrix associated to the Riemann zeta function are all positive. In this talk, I shall explain the background leading to this observation, and make a conjecture. (Joint work with Hugues Bellemare et Yves Langlois.)Nearly 13.7 million (18.5%), or 1 in 5, children and adolescents were considered obese in the United States according to the Centers for Disease Control and Prevention (CDC). The progression of overweight and obesity among children and adolescents is complex, dynamic, and involves nonlinear interactions among many factors at the biological (genetics and physiology), behavioral, social, and environmental levels. In school environments, nutrition education and peer programs have key roles in shaping the health behaviors and health outcomes of young individuals. Many school-based policies have been implemented to improve diet and physical activity behaviors to address childhood obesity. However, variability in school policies and measurement errors in health research make program evaluation challenging. This session will give a high-level overview of applications of statistical and mathematical modeling methods to obesity and nutrition research in the context of health policy and interventions.
We consider a key-exchange protocol proposed based on a free nilpotent p-group. We found that by using an algorithm to solve a discrete logarithm problem with matrices over a finite field, we can then recover an integer through a series of multiplication in the group which mimics an intercepted private parameter.
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Capillary surfaces arise when mixing different fluids. In mathematics, they can be considered as critical points of a geometric functional under certain constraints. The stability index measures how far away one is from being a local minimizer. A critical point is stable if the index is zero. Naturally, constraints would play an influential role in applications as they decrease the degree of freedom available. In this talk, we discuss capillary hypersurfaces in a Euclidean ball and how to obtain sharp estimates for indices with respect to varying constraints. In particular, we show that, when fixing the enclosed volume and wetting area, the only stable ones are geodesic disks and spherical caps. At the heart of the proof is a functional analysis theorem which will be discussed in the Elasticity seminar preceding the Applied Math Seminar. This is a joint work with Detang Zhou.