Date :

 1 July (Thursday) 2004

Place :

 The First Meeting Room, 5F, Institute of Physics, Academia Sinica (Taipei)

10:00-10:50

Theory of Resistor Networks

Professor F. Y. Wu (Department of Physics, Northeastern University)

11:10-12:00

Exact finite-size corrections for the dimer model

Dr. N. Sh. Izmailian (Institute of Physics, Academia Sinica)

Lunch Break

Transfer matrices for the Potts model partition function on lattice strips

Dr. Shu-Chiuan Chang (National Center for Theoretical Sciences at Taipei)

15:00-15:30

Correlated random walks for stock-stock correlations

Dr. Wen-Jong Ma (Institute of Physics, Academia Sinica)

Quantifying complexity of biological signals: From DNA to heartbeat

Professor Chung-Kang Peng (Harvard Medical School)

Unzipping of DNA with correlated base sequence

Dr. Zh. S. Gevorkian (Institute of Physics, Academia Sinica)

Scalable Peer-to-Peer Networked Virtual Environment

Mr. Shun-Yun Hu (Dept. of Computer Science and Information Engineering, Tamkang University)

      Abstracts:  (ordered by speakers' last names)

 Dr. Shu-Chiuan Chang (National Center for Theoretical Sciences at Taipei)

Transfer matrices for the Potts model partition function on lattice strips

     We present transfer matrices for the q-state Potts model partition functions Z(G,q,v) for arbitrary q and temperature variable v on the square, triangular, and honeycomb lattice strips of arbitrarily great length. The method is reviewed for free and cylindrical strips first, then generalized to cyclic and Mobius strips. Dimensions of the transfer matrices are determined for arbitrary width. The corresponding results are given for the partition functions of the zero-temperature Potts antiferromagnet.

 Dr. Zh. S. Gevorkian (Institute of Physics, Academia Sinica)

Unzipping of DNA with correlated base sequence

     We consider force-induced unzipping transition for a heterogeneous DNA model with a correlated base sequence. Both finite-range and long-range correlated situations are considered. It is shown that finite-range correlations increase stability of DNA with respect to the external unzipping force. Due to long-range correlations the number of unzipped base pairs displays two widely different scenarios depending on the details of the base sequence: either there is no unzipping phase transition at all, or the transition is realized via a sequence of jumps with magnitude comparable to the size of the system. Both scenarios are different from the behavior of the average number of unzipped base pairs (non-self-averaging). The results can be relevant for explaining the biological purpose of correlated structures in DNA.

 Mr. Shun-Yun Hu (Department of Computer Science and Information Engineering, Tamkang University)

Scalable Peer-to-Peer Networked Virtual Environment

    We propose a fully-distributed peer-to-peer architecture to solve the scalability problem of Networked Virtual Environment in a simple and efficient manner. Our method exploits locality of user interest inherent to such systems and is based on the mathematical construct Voronoi diagram. Scalable, responsive, fault-tolerant NVE can thus be constructed and deployed in an affordable way.

 Dr. N. Sh. Izmailian (Institute of Physics, Academia Sinica)

Exact finite-size corrections for the dimer model

     We study the finite-size scaling properties of the dimers under different boundary conditions. We derive the exact asymptotic expansion of the logarithm of the partition function. In the case of infinitely long strip of finite odd width N we have found that critical properties of the dimer model crucially depends on the boundary conditions. In particular for free boundary conditions we get a conformal theory with central charge c=-2. In the case of periodic boundary conditions we get a conformal theory with central charge c=-1/2. And for twisted boundary conditions we get a conformal theory with central charge c=1 as in the case of the dimer model on an infinitely long strip of finite even width N.

 Dr. Wen-Jong Ma (Institute of Physics, Academia Sinica)

Correlated random walks for stock-stock correlations

     We present recent progress in studying   the model called coupled random walks, which was proposed to describe the cross correlation in financial fluctuations [1]. In the model, the price change (displacement) of each stock (walk) is driven by the price gradient between the stock and the stocks in the whole market, with a parameter controlling the degree of such correlation. The fluctuations in the dominant collective mode diverge in approaching to the fully correlated situation, in the infinite size limit. We show that such divergence is in fact described by a power law in contorl parameter with an exponent of value 2, for a class of systems of corrrelated random walks.
[1] W.-J. Ma, C.-K. Hu and R. E. Amritkar, Phys. Rev. E 69, in press (2004).

 Professor Chung-Kang Peng (Harvard Medical School)

Quantifying complexity of biological signals: From DNA to heartbeat

Theory of Resistor Networks

    The resistance between arbitrary two nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulas for two-point resistances are deduced for regular lattices in one, two, and three dimensions under various boundary conditions including that of a Moebius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyze finite-size corrections and evaluate resistances in two and higher dimensions.