Colegas,
o Departamento de Estatistica da USP e da UFMG estao recebendo
nesta semana e na seguinte o pesquisador e professor Elvan Ceyhan da
da Koc University, Turquia. O professor Elvan fez seu mestrado e doutorado
ndo departamento de bioestatistica da John Hopkins University e
trabalhou por alguns
anos nos EUA como professor. Recentemente ele decidiu voltar para seu
pais de origem (Parentesis: a Koc University e' uma universidade
privada localizada em
Istambul e e' um espanto de boa qualidade. Eu fui ate' le' e fiquei
quase chocado com
o que vi: as aulas sao todas em ingles, todos os professores tem
doutorado e tem de fazer
pesquisa para ter os contratos renovados, os alunos (e professores se
quiserem) residem
no campus em moradias excelentes, o campus e' coalhado de obras de arte, etc.
A universidade forma a elite turca. Os ricos de la' sao ricos de
3000 anos...).
Ele vai fazer um seminario no IME_USP na quinta-feira, dia 24/09
(maiores informacoes
com o professor Fabio Machado, fmachado@ime.usp.br) e na UFMG na
sexta-feira, dia 25/09.
O seminario da UFMG sera' na sala 2076, no ICEx (Instututo de Ciencias
Exatas), campus
Pampulha, as 13:30.
O resumo do seminario segue abaixo.
Inte'
Renato Assuncao
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Random Proximity Catch Digraphs: Theory and Applications
Elvan Ceyhan,
Department of Mathematics
Koç University, 34450 Sar?yer, Istanbul, Turkey
Abstract
Relative neighborhood graphs (RNGs) were introduced in 1980. Since
then, various graph theo-retic methods have been developed and RNGs have
grown into a more general family of graphs called proximity graphs. The
proposed method used only one class of points at a time and was applied
in non-random pattern classification. In 2001, a data-random directed
graph called class cover catch digraph (CCCD) is introduced. CCCDs were
defined based on two or more classes and have applications in
statistical pattern classification. I have introduced Proximity Catch
Di-graphs (PCDs) in with during my doctoral study in 2003 and used
them in for il-lustrative purposes. These PCDs are closely related to
but are more general than CCCDs. The reason for introducing PCDs was to
remove the shortcomings of CCCDs. In particular, a direct extension of
CCCDs to with lacked mathematical tractability of the distribution
of the domination number, moments of relative density of PCDs, and
geometry invariance for uniform data. In this talk I will investigate
two major aspects of the PCDs: the distribution of the domina-tion
number and the relative density of the PCDs. Our PCDs have the advantage
of making trac-table the mathematics in multiple dimensions, thereby
enhancing the applicability of the method-ology to statistical
hypothesis testing (of e.g. spatial point patterns) and pattern
classification. The PCDs are constructed in terms of the relative
positions of members of one class with respect to each other and the
Delaunay tessellation of the other class or classes. I will also
describe the families of PCDs introduced, investigate their
probabilistic and graph theoretical properties, pro-vide sample
application areas, and will state the open research topics in this
area.