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https://nsuworks.nova.edu/mathematics_colloquium/ay_2018-2019/events
Recent Events in en-usTue, 12 Feb 2019 13:53:14 PST3600Irreducible 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