Name：Risa Uechi
Title：Boston University, Center for Polymer Studies, Department of Physics
Institute: Bioinformatics Center (Akutsu Laboratory), Kyoto University Institute for Chemical
Research; Kyoto, Uji, Gokasho 611-0011, Japan
Partner institute: Random Matrix Theory and its application for complex phenomena
Duration: April 4, 2013 – July 1, 2013
Report:Overview
Owing to the support of ITP program, I had a chance to visit Boston University as a visiting
scholar during April 4th to July 1th, 2013. I stayed at the laboratory of H. Eugene Stanley, who isthe William Fairfield Warren Distinguished Professor, Professor of Physics, Professor of
Biomedical Engineering and Professor of Physiology (School of Medicine), Center for Polymer
studies, Department of Physics, Boston University. The office was located at 590 commonwealthavenue, which is close to Kenmore square. The
group of Gene Stanley is very large and there are a
lot of visiting students, visiting Professor at any
time from any country. Gene Stanley’s group havecontributed not only physiology and medicine
fields but many research fields such as statisticalphysics and neuroscience (Alzheimer's Disease),
econophysics, social science, social networks,percolation

theoryphenomena

inandwaterphasemolecule.

transition
They

also

collaborate actively with Albert-László Barabási
who is the Professor of Northeastern Universityand contributed complex phenomena using Powerlawmodel.

The

Gene

Stanley’sgroup

andAlbert-László Barabási group have joint seminar atNortheastern University twice in a month. During
the stay at BU, there were Ph. D. defense of Ph. D.
students in Gene Stanley’s group and every student
supported. Professor Shlomo Havlin, who is aProfessor in the Department of Physics at BarllanUniversity, discuss the topic of network systemwith graduate students. I mainly worked with Dr. Dror Kenett, who is the post doctor of Gene
Stanley’s group. We analyze the complex system such as social interaction, biological networks,stock market regulation using Random Matrix Theory and its correlation. I have learned a lot from

him and other faculties and they gave me useful comments for applying statistical method andconcepts for complex phenomena.
Research Project
1. Random Matrix Theory

Random Matrix Theory (RMT) is a statistical tool to evaluate eigenvalues that deviate from therange of the random ones assuming null hypothesis. RMT is developed in the field of nuclear
physics by Wigner, Dirac in order to explain the energy levels of complex quantum systems. Its
primary aim is to analyse large dimensional data sets. The RMT is widely applied not only inphysics but also image analysis, genomics, epidemiology and economics. If we get the empiricalcorrelation matrix C which is constructed from the time series data, which is constructed from thesmall changes of time, the correlation between i and j is described as follows

We can describe (2.1) as C = 1/TMMT , where M is a N × T rectangular matrix. If _ is the densityof eigenvalues of C, ρ is defined aswhere n is the number of eigenvalues of C less than _. If M is a T × N random matrix, has
self-similarity and known in the limit that n → ∞, T → ∞, and Q = T=n ≥ 1

The distribution is bounded by

2. Partial Correlation Metrics
Empirical correlation matrices are of great importance in data analysis in order to extract theunderlying information contained in experimental signals and time series. In addition to the direct
measure of correlation, various classes of statistical tools, such as principal component analysis,
singular value decomposition and factor analysis, strongly rely on the validity of the correlation
matrix in order to obtain the meaningful part of signal from experiments. Partial correlation is atool to assess how the correlation between two variables depends on the correlation of each of thevariable with a mediating variable. The partial correlation between variable i and j , using index m

as the mediating variable is defined as follow

where C(i; j) is the pairwise correlation between variable i and j, C(i;m) is the pairwise correlation
between stock i and the index m, and C(j;m) is the pairwise correlation between variable j and theindex. We examined the deviated number of eigenvalue. Deviations from the random matrix casemight then suggest the presence of true information. We found that the eigenvalue with partial
correlation contained more information than other correlation matrices using RMT.
OthersOther side of research activities, I visited some historical places in Boston. Boston has a lot of
historical places in which U.S. history has begun and famous author of American literature had
lived in Boston.

CONCORD MUSEUM (Concord)

THE HOUSE OF SEVEN GABLES (Salme)

With colleague at Japanese festival

With Dr. Kenett at office