TITLE

\n
Dose-volume requirements modeling for radiotherapy optimization

AB
STRACT

\nRadiation therapy is an important modality in cancer treatm
ent. To find a good treatment plan\, optimization models

\nand method
s are typically used\, while dose-volume requirements play an important ro
le in plan’s quality evaluation.

\nWe compare four different optimiza
tion approaches to incorporate the so-called dose-volume constraints into
the

\nfluence map optimization problem for intensity modulated radiot
herapy. Namely\, we investigate (1) conventional

\nemph{Mixed Integer
Programming} (MIP) approach\, (2) emph{Linear Programming} (LP) approach
to partial volume

\nconstraints\, (3) emph{Constrained Convex Moment}
(CCM) approach\, and (4) emph{Unconstrained Convex Moment

\nPenalty
} (UCMP) approach. The performance of the respective optimization models i
s assessed using anonymized data

\ncorresponding to eight previously
treated prostate cancer patients. Several benchmarks are compared\, with t
he goal

\nto evaluate the relative effectiveness of each method to qu
ickly generate a good initial plan\, with emphasis on

\nconformity to
DVH-type constraints\, suitable for further\, possibly manual\, improveme
nt.

BIO

\nDr. Zinchenko received his PhD from Cornell Univers
ity on 2005 under supervision of Prof. James Renegar.

\nFrom 2005 to
2008 he held a PDF position at the Advanced Optimization Lab at McMaster U
niversity\, working

\nwith Prof. Tamas Terlaky and Prof. Antone Deza\
, and spent portion of his fellowship with radiation oncology group

\nat the Princess Margaret Hospital in Toronto. Currently\, Yuriy is an As
sociate Professor of Mathematics & Stat at the

\nUniversity of Calgar
y.

\nDr. Zinchenko’s primary research interest lies in convex optimiz
ation\, and particularly\, the curvature of the central path for

\nin
terior-point methods\, and applications. Yuriy’s work on optimal radiother
apy design was recognized by 2008 MITACS

\nAward for Best Novel Use o
f Mathematics in Technology Transfer\, and in 2012-2015 he served as one o
f the PIs for

\nPIMS Collaborative Research Group grant on optimizati
on.

Smooth Action s of Compact Lie Groups on $S^2$ are Smoothly Equivalent to Linear Actions :

\n\n**Abstract:**\n

Mathematicians have been interested in group actions on spheres sin ce before the algebraic description of a group was defined. The rotational and reflective symmetries of the circle and of S^2 were naturally among t he first to be considered. When we restrict attention to a compact topolog ical group\, there is a classic theorem of Kerekjártó to the effect that f or S^2 \, these are essentially the only actions:

\nTheorem 1 (Kerek jártó\, [3]). Every continuous\, effective action of a compact topological group G on S^2 is topologically conjugate to a linear action (to the stan dard action of a subgroup of O(3) on S^2 as a subset of R^3 ).

\nThu s in the topological category\, in order to understand all effective actio ns of compact groups on S^2 \, it is enough to understand the subgroups G ≤ O(3) and their actions via matrix multiplication on S^2 ⊆ R^3 (so called linear actions).

\nThe goal of this paper is to extend this result to the smooth category. In other words\, we show that every smooth\, eff ective action of a compact Lie group\, on S^2 is smoothly conjugate (i.e. conjugate through a diffeomorphism) to a linear action.

\nThe main t heorem of the paper is helpful for studying the topology of the space of a ctions of compact Lie groups on S^2 and we present a corollary as an examp le of this. We also explicitly determine all compact subgroups of O(3) up to conjugacy within O(3)\, and use this information to construct explicit G-CW decompositions for preferred representatives of each of these conjug acy classes. The G-CW decompositions are useful in other areas for exampl e in the classification of G-equivariant vector bundles over S^2\, and in determining whether such bundles have algebraic models.

\n END:VEVENT BEGIN:VEVENT UID:b8nnnranhdcb6q7jttgpc3nask@google.com DTSTAMP:20170430T203816Z CATEGORIES;LANGUAGE=en-US:Colloquia and seminars CONTACT: DESCRIPTION: DTSTART;TZID=Pacific/Honolulu:20170505T130000 DTEND;TZID=Pacific/Honolulu:20170505T140000 SEQUENCE:0 SUMMARY:Logic Seminar: David Webb URL:http://math.hawaii.edu/wordpress/event/logic-seminar-david-webb/ END:VEVENT BEGIN:VEVENT UID:dld12o9684b945t7030605952s@google.com DTSTAMP:20170430T203816Z CATEGORIES;LANGUAGE=en-US:Colloquia and seminars CONTACT: DESCRIPTION:TBA DTSTART;TZID=Pacific/Honolulu:20170711T150000 DTEND;TZID=Pacific/Honolulu:20170711T160000 SEQUENCE:0 SUMMARY:PhD Defense – Ka Lun Wong @ TDA URL:http://math.hawaii.edu/wordpress/event/phd-defense-ka-lun-wong-tda/ X-ALT-DESC;FMTTYPE=text/html:\\n\\n\\nTBA

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