TITLE

\nDose-volume requirements modeling for radiother
apy optimization

ABSTRACT

\nRadiation therapy is an important
modality in cancer treatment. To find a good treatment plan\, optimizati
on models

\nand methods are typically used\, while dose-volume requir
ements play an important role in plan’s quality evaluation.

\nWe comp
are four different optimization approaches to incorporate the so-called do
se-volume constraints into the

\nfluence map optimization problem for
intensity modulated radiotherapy. Namely\, we investigate (1) conventiona
l

\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 C
onvex Moment

\nPenalty} (UCMP) approach. The performance of the respe
ctive optimization models is assessed using anonymized data

\ncorresp
onding to eight previously treated prostate cancer patients. Several bench
marks are compared\, with the goal

\nto evaluate the relative effecti
veness of each method to quickly generate a good initial plan\, with empha
sis on

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

BIO

\nDr. Zinchenko received h
is PhD from Cornell University on 2005 under supervision of Prof. James Re
negar.

\nFrom 2005 to 2008 he held a PDF position at the Advanced Opt
imization Lab at McMaster University\, working

\nwith Prof. Tamas Ter
laky and Prof. Antone Deza\, and spent portion of his fellowship with radi
ation oncology group

\nat the Princess Margaret Hospital in Toronto.
Currently\, Yuriy is an Associate Professor of Mathematics & Stat at the**\nUniversity of Calgary.\nDr. Zinchenko’s primary research inter
est lies in convex optimization\, and particularly\, the curvature of the
central path for\ninterior-point methods\, and applications. Yuriy’s
work on optimal radiotherapy design was recognized by 2008 MITACS\n
Award for Best Novel Use of Mathematics in Technology Transfer\, and in 20
12-2015 he served as one of the PIs for\nPIMS Collaborative Research
Group grant on optimization.**

Smooth Actions of Compact Lie Groups on $S^2$ are Smoothly E quivalent to Linear Actions:

\n\n< strong>Abstract:

\nMathematicians have been interested in g roup actions on spheres since before the algebraic description of a group was defined. The rotational and reflective symmetries of the circle and of S^2 were naturally among the first to be considered. When we restrict att ention to a compact topological group\, there is a classic theorem of Kere kjártó to the effect that for S^2 \, these are essentially the only action s:

\nTheorem 1 (Kerekjártó\, [3]). Every continuous\, effective acti on of a compact topological group G on S^2 is topologically conjugate to a linear action (to the standard action of a subgroup of O(3) on S^2 as a s ubset of R^3 ).

\nThus in the topological category\, in order to und erstand all effective actions of compact groups on S^2 \, it is enough to understand the subgroups G ≤ O(3) and their actions via matrix multiplicat ion on S^2 ⊆ R^3 (so called linear actions).

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

\nThe main theorem of the paper is helpful for studying the topology of the space of actions of compact Lie groups on S^2 and we pres ent a corollary as an example of this. We also explicitly determine all c ompact subgroups of O(3) up to conjugacy within O(3)\, and use this inform ation to construct explicit G-CW decompositions for preferred representati ves of each of these conjugacy classes. The G-CW decompositions are usefu l in other areas for example in the classification of G-equivariant vector bundles over S^2\, and in determining whether such bundles have algebraic models.

DTSTART;TZID=Pacific/Honolulu:20170504T093000 DTEND;TZID=Pacific/Honolulu:20170504T103000 LOCATION:Keller Hall\,Room 401\, Honolulu\, HI\, United States SEQUENCE:0 SUMMARY:MA defense: Sean Sanford URL:http://math.hawaii.edu/wordpress/event/ma-defense-sean-sanford/ END:VEVENT BEGIN:VEVENT UID:b8nnnranhdcb6q7jttgpc3nask@google.com DTSTAMP:20170430T051733Z 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:20170430T051733Z 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/ END:VEVENT END:VCALENDAR