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Full-Text Articles in Physical Sciences and Mathematics
How Good Are Standard Copulas Anyway?, Dragan Radulovic
How Good Are Standard Copulas Anyway?, Dragan Radulovic
Mathematics Colloquium Series
First, we will raise a question: How good are standard copulas in capturing the dependency structure? To this end we will offer a series of simulated/numerical examples demonstrating that, more often than not, standard model copulas do not capture the underlying dependency structure. We believe that copula models, unlike other statistical tools, are too readily accepted by practitioners. Rigorous, goodness-of-fit tests are commonly replaced by off-hand statements like: “it works well”. To this end, the second part of the talk offers a theoretical result, an umbrella type theorem tailored for creating numerous Goodness of Fit tests for copulas.
Algebraic Frames And Ultrafilters, Papiya Bhattacharjee
Algebraic Frames And Ultrafilters, Papiya Bhattacharjee
Mathematics Colloquium Series
A frame, also known as pointfree topology, is a complete lattice that satisfies a strong distributive property, known as the 'frame law.' Originally, the study of frames began as studying topological spaces without points, hence the name pointfree topology. Due to this connection, different topological concepts can be generalized to frames, for example, compactness. In the first part of the talk, I will explain the basic notions of frames and their connection with topology. It turns out that we can find frame structure in other categories than topological spaces. For example, given a commutative ring R with identity, the lattice …
How Mathematics Can Help Winning The War Against Cancer?, Peng Feng
How Mathematics Can Help Winning The War Against Cancer?, Peng Feng
Mathematics Colloquium Series
In this talk, I will present a few mathematical models that aims to understand how our immune system interact with cancer cells. In particular, we focus on a model that studies the role or regulatory T cells. Recent advance in the field of regulatory T cell reveals that it plays a vital role during immunotherapy. For example, a higher ratio between regulatory T cells and effector T cells within tumor tissue is associated with worse prognoses in many cancers, including ovarian cancer (Leffers et al., 2009), lung cancer (Tao et al., 2012), glioblastoma (Sayour et al., 2015). On the other …
Using Slow-Fast Dynamical Systems To Understand Regime Shifts In Ecology, Ting-Hao Hsu
Using Slow-Fast Dynamical Systems To Understand Regime Shifts In Ecology, Ting-Hao Hsu
Mathematics Colloquium Series
In ecology, regime shifts are continual rapid change between different long-lasting dynamics. For instance, rapid evolutionary changes have been observed in a wide variety of organisms, both in predators and in prey. Another example is disease outbreak, where a system exhibits qualitative changes after long periods of apparent quiescence. Using the theory of slow-fast dynamics, for systems of differential equations with sufficiently large separation of time scales we derive conditions under which regime shifts occur. This is joint work with Shigui Ruan and Gail Wolkowicz.
Mathematical Modeling Of Lung Cancer Screening Studies, Deborah L. Goldwasser
Mathematical Modeling Of Lung Cancer Screening Studies, Deborah L. Goldwasser
Mathematics Colloquium Series
Lung cancer has the second highest cancer incidence, second only to prostate cancer in men and breast cancer in women. Furthermore, more cancer deaths are attributable to lung cancer than any other cancer for both genders. There is a high public health need for effective secondary prevention in the form of early detection and early treatment, complementary to smoking cessation efforts. The U.S. National Lung Screening Trial (NLST) demonstrated that non-small cell lung cancer (NSCLC) mortality can be reduced by 20% through a program of annual CT screening in high-risk individuals. However, CT screening regimens and adherence vary, potentially impacting …