**Mathematical Colloquim
**

**PROGRAM**

ODELJENJE ZA MATEMATIKUMATEMATICKOG INSTITUTA SANU |
OPSTI MATEMATICKI SEMINAR
NA MATEMATICKOM FAKULTETU U BEOGRADU |

**
-- PROGRAM ZA SEPTEMBAR 2005 --
**

__Četvrtak, 01. septembar 2005. u 17h, sala 2, MI SANU:__

*
Prof. Yuri Kochetov, Sobolev Institute of Mathematics, Novosibirsk, Russia
*

THE 2D RECTANGULAR BIN PACKING PROBLEM WITH IMPURITIES

Abstract:
We consider the real-world two dimensional rectangular bin packing problem
originating in the steel industry. The bins are inhomogeneous sheets with
impurities. Each impure area is rectangle. For each bin we are given a set
of impurities, size, and location of each impurity into the bin. We need to
place the rectangular items into the minimal number of bins. The items have
the attribute whether they can be located in the area with impurities.
Overlaps of items are not allowed.

For solving this NP-hard problem we have developed a tailored Simulated
Annealing algorithm (SA) based on the directed root tree encoding scheme.
The scheme has linear decoding time if the maximal number of impurities per
bin is a constant. The initial solution is built by a greedy algorithm which
allows us to start SA with low temperature. Computational experiments show
that the algorithm produces feasible solutions with small deviations from
the lower bound within a few minutes.

__Petak, 02. septembar 2005. u 14h, sala 2, MI SANU:__

*
Dr. Zoran Obradović, Mathematical Institute SANU and Center for Information
Science and Technology, Temple University, Philadelphia, PA
*

INTEGRATION OF DETERMINISTIC AND STATISTICAL ALGORITHMS FOR RETRIEVAL AND
ANALYSIS OF GEOPHYSICAL PARAMETERS

Abstract:
Current methods for the retrieval of geophysical information from satellite
data are based on deterministic forward simulation algorithms. In this
approach, physical models predict what the instruments will observe under
possible atmospheric and reflective surface conditions. These predictions
are then compared to observations, and the condition corresponding to the
best prediction is assumed to hold. The drawbacks include high computational
cost and the manual enhancements to the postulated physical models. We
proposed a novel data mining based method for addressing these drawbacks by
complementing deterministic models with computationally cheaper statistical
algorithms that can exploit data of varying quality obtained from multiple
sources. Statistical retrieval involves learning classification or
regression mappings from observed attributes to
corresponding geophysical parameters.

Our case study is devoted to improving efficiency and accuracy of aerosol
optical thickness (AOT) retrievals by developing regression methods for
learning a mapping from observation attributes to the corresponding
parameters. We will first describe a statistical approach for exploiting
multiple sources of remote sensing data illustrated on faster and more
accurate AOT retrievals over the continental USA. Large test data is
obtained from MISR (Multi-angle Imaging SpectroRadiometer) and MODIS
(Moderate Resolution Imaging Spectrometer) instruments aboard Terra and Aqua
satellites. Next, we will present a fusion of models approach that improved
accuracy of MISR AOT retrievals over the continental USA by appropriately
weighting global and local statistical models. The fusion approach takes
advantage of learning from larger global data sets, but also exploits more
specific spatial properties at local sites.

Resulting discoveries provide a better understanding of the aerosol data
stream and allow developing more efficient and more accurate algorithms for
retrieving geophysical parameters from raw data. Developed techniques apply
to other Earth Observing System datasets (e.g. water and energy cycle;
carbon cycle; weather and climate; or chemistry-climate connection) and also
to other domains with complex spatio-temporal data properties.

Reported results are obtained in collaboration with A. Braverman (at
JPL/Caltech), B. Han, K. Peng, S. Vučetić, L. Yong and Q. Xu (all at Temple
University).

__Petak, 2. septembar 2005. u 16h, sala 2, MI SANU:__

*
Pierre Hansen, GERAD and HEC, University of Montreal, Canada
*

DISCRIMINANT ANALYSIS AND MATHEMATICAL PROGRAMMING

Abstract: The linear discriminant analysis problem, as expressed by
Mangasarian, consists in finding a hyperplane which separates points of two
given sets (good and bad ones) while minimizing the sum of distances, in
Lp-Norm, of misclassified points to the hyperplane. We give a VNS heuristic
valid for all p greater than or equal to 1, an improved exact algorithm for
the case p=1 and new exact algorithms for the cases p=2 and p=infinity. We
also discuss the choice of p, and the close objective of minimizing the
number of misclassified points (sometimes called the L0-norm). (Joint work
with Simon Blanchard, Gilles Caporossi and Alexandro Karam).

__Četvrtak, 01. septembar 2005. u 12h, sala 61, ETF:__

*
Dr. Zoran Obradović, Mathematical Institute SANU and Center for Information
Science and Technology, Temple University, Philadelphia, PA
*

MICROARRAY FUNCTIONAL EXPRESSION PROFILES ANALYSIS TOOLBOX

Abstract:
Microarray technology allows measuring expression level of thousands genes
at once. Such data can in principle be used to identify genes that
differentiate various groups of subjects. However, reducing uncertainty when
analyzing such a high dimensional sample collected over a small number of
subjects requires developing novel statistical techniques and also
exploiting prior domain knowledge. In this talk we will present our novel
software tool aimed at functional characterization of gene expression
profiles. The tool consisting of profiles ranking and clustering modules is
used to explore a hypothesis that genes with same or similar function are
likely to have similar expression profiles. When analyzing 1,051 Gene
Ontology (GO) terms represented by at least two genes in microarray data set
of Plasmodium Falciparum (a parasite that causes malaria) Intraerythrocytic
Developmental Cycle, we found that gene expression profiles in 550 of them
are significantly (P<0.05) correlated. We represented each of the 550
significant GO terms with the functional expression profile defined as
average expression profile of all genes annotated with a given GO term.
Using Kmeans clustering, we clustered 199 profiles corresponding to GO
molecular functions into 4 groups. This was repeated on 228 profiles
corresponding to GO biological process. We quantified the clustering quality
by introducing a measure of GO term similarity defined as the minimal
distance between two GO terms in GO direct acyclic graph. The results based
on this measure showed that the obtained clustering is biologically relevant
which supports our hypothesis that genes with similar functions have similar
expressions. Consistent findings were obtained when applying this fairly
simple tool for microarray data analysis of Caccharomyces Cerevisiae, Mus
Musculus and Home Sapiens cell cycle.

Results were obtained through a collaboration with Hongbo Xie, Slobodan
Vučetić, Hao Sun and Pooja Hedge.

About speaker: Zoran Obradović is Director at the Center for Information
Science and Technology, Associate Director at the Center for Quantitative
Biology and Biomedical Mathematics and a Professor of Computer and
Information Sciences at Temple University. His research interests focus on
developing data mining and statistical learning technology for an efficient
knowledge discovery at large databases. Funded by NSF, NIH, DOE and industry
he contributed to about 160 refereed articles on these and related topics
and to several academic and commercial software systems. For more details
see www.ist.temple.edu/~zoran.

Rukovodioci Odeljenja za matematiku Matematickog instituta SANU i Opsteg matematickog seminara na Matematickom fakultetu u Beogradu, Stevan Pilipovic i Sinisa Vrecica predlazu zajednicki program rada naucnih sastanaka.

Predavanja ce se odrzavati na Matematickom Institutu (sala 2), petkom sa pocetkom u 14 casova. Odeljenje za matematiku je opsti seminar sa najduzom tradicijom u Institutu.

Svakog meseca, jedno predavanje ce biti odrzano na Matematickom Fakultetu u terminu koji ce biti posebno odredjen.

Molimo sve zainteresovane ucesnike u radu naucnih sastanaka da posebno obrate paznju na vreme odrzavanja svakog sastanka. Na Matematickom fakultetu su moguce izmene termina.

Obavestenje o programu naucnih sastanaka ce biti objavljeno na oglasnim tablama MI (Beograd), MF (Beograd), PMF (Novi Sad), PMF (Nis) i PMF (Kragujevac).

Odeljenje za matematiku Matematickog instituta SANU

Stevan Pilipovic

Opsti matematicki seminar na Matematickom fakultetu u Beogradu,

Sinisa Vrecica

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