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https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events
Recent Events in en-usFri, 19 Apr 2024 05:46:57 PDT3600Mathematical Modeling of Lung Cancer Screening Studies
https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events/5
https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events/5Tue, 12 Feb 2019 12:05:00 PST
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 the lung cancer mortality benefit. The mortality benefit attributable to a program of CT screening is largely determined by the natural history of lung cancer progression. Tumor doubling times and the maximum tumor size at which a NSCLC would be curable by early detection (cure threshold) are key factors. In this talk, I will address novel statistical methodology used to estimate parameters governing a stochastic model of the natural history of lung cancer. We estimate the median tumor size at cure threshold among the most aggressive NSCLCs to be between 10-15 mm. We demonstrate consistency of our model with tumor size and stage data from distinct lung screening trials, namely, the Mayo Lung Project, the Mayo CT study and the NLST, in addition to data from SEER, the national cancer registry and highlight key differences between men and women. The majority of NSCLCs in the NLST were treated at tumor sizes greater than our median cure threshold estimates, consistent with the modest 20% mortality reduction attributable to CT screening observed in the NLST. These results highlight the strong need for novel classification technology that can better distinguish and treat the most aggressive NSCLCs when they are small (i.e. 5-15mm). This talk will also discuss the modelâ€™s consistency with the recently announced European NELSON lung screening trial results (October 2018). I will also discuss how novel DNA sequencing technologies may be incorporated into a lung screening regimen in order to improve outcomes.
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Deborah L. GoldwasserIrreducible sign patterns that require all distinct eigenvalues
https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events/4
https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events/4Fri, 01 Mar 2019 12:05:00 PST
A sign pattern (matrix) is a matrix whose entries are from the set {+, -, 0}. We say that a sign pattern A requires a certain matrix property P if every real matrix whose entries have signs agreeing with A has the property P. Some necessary or sufficient conditions for a square sign pattern to require all distinct eigenvalues are presented. Characterization of such sign pattern matrices is equivalent to determining when a certain real polynomial takes on only positive values whenever all of its variables are assigned arbitrary positive values. It is known that such sign patterns require a fixed number of real eigenvalues. The 3x3 irreducible sign patterns that require 3 distinct eigenvalues have been identified previously. We characterize the 4x4 irreducible sign patterns that require four distinct real eigenvalues and those that require four distinct nonreal eigenvalues. The 4x4 irreducible sign patterns that require two distinct real eigenvalues and two distinct nonreal eigenvalues are investigated. Joint work with: Yubin Gao, Victor Bailey, Frank Hall, Paul Kim.
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Zhongshan LiOn some generalizations of the numerical range and their properties
https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events/3
https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events/3Thu, 17 Jan 2019 12:05:00 PST
For a bounded linear operator A (or, in the finite dimensional setting, an n-by-n matrix A) its classical numerical range is defined as the mage of the unit sphere under the mapping f(x)=(Ax,x). The normalized numerical range results when in this definition (Ax,x) is replaced by (Ax,x)/||Ax||. We will discuss some general properties of this set, and in particular provide its complete description in the cases when A is normal or n=2.
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Ilya SpitkovskyModelling the Antibiotic Use in Intensive Care Units
https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events/2
https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events/2Tue, 27 Nov 2018 12:05:00 PST
Antimicrobial de-escalation refers to the treatment mechanism of switching from empiric antibiotics with good coverage to alternatives based on laboratory susceptibility test results, with the aims of reducing costs and avoiding unnecessary use of broad-spectrum antibiotics. Though widely practiced and recommended, the benefits and tradeoffs of this strategy have not been well understood. In this talk, we will first show our preliminary simulation results of a set of multi-strain-multi-drug models in an intensive care unit setting, to numerically compare de-escalation with the conventional strategy called antimicrobial continuation. Then we simplify the previous models to compare the long-term dynamical behaviors between de-escalation and continuation systems under a double-strain-double-drug scenario. Finally we extend our models to seek for optimal antibiotic use strategies under a triple-strain-triple-drug scenario. The major conclusion of this study shows that, suppose there are two identical intensive care units that separately adopt de-escalation and continuation as the major drug use strategy, then the one following de-escalation: (1) could maintain either higher or lower percentage of colonized patients in the two-strain transmission scenario; (2) is superior in preventing outbreaks of strains resistant to the empiric antibiotic.
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Xi HuoPerfect Zero-knowledge Proofs and Commutative Algebra
https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events/1
https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events/1Mon, 29 Oct 2018 12:05:00 PDT
In joint work with Rainer Steinwandt and Dominique Unruh, we look at how the notion of perfect zero-knowledge proof leads to an assumption about probabilistic Turing machines. We prove a theorem in commutative algebra which shows that this assumption is not valid.
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Lee Klingler