Biomedical subjects
Publications and source records attributed to Chin-Kun Hu.
We consider branching polymers on the planar square lattice with open boundary conditions and exactly calculate correlation functions of k polymer chains that connect two lattice sites with a large distance r apart for odd number of polymer chains k. We find that besides the standard power-law factor the leading term also has a logarithmic multiplier.
In the calculation of thermodynamic properties and three-dimensional structures of macromolecules, such as proteins, it is important to have an efficient algorithm for computing the solvent-accessible surface area of macromolecules. Here, we propose a new analytical method for this purpose. In the proposed algorithm we consider the transformation that maps the spherical circles formed by intersection of the atomic surfaces in three-dimensional space onto the circles on a two-dimensional plane, and the problem of computing the solvent-accessible surface area is reduced to the problem of computing the corresponding curve integrals on the plane. This allows to consider only the integrals along the circular trajectories on the plane. The algorithm is suitable for parallelization. Testings on many proteins as well as the comparison to the other analogous algorithms have shown that our method is accurate and efficient.
For percolation on (RL)xL two-dimensional rectangular domains with a width L and aspect ratio R, we propose that the existence probability of the percolating cluster E(p)(L,epsilon,R) as a function of L, R, and deviation from the critical point epsilon can be expressed as F(epsilonL(y(t))R(a)), where y(t) identical with1/nu is the thermal scaling power, a is a new exponent, and F is a scaling function. We use Monte Carlo simulation of bond percolation on square lattices to test our proposal and find that it is well satisfied with a=0.14(1) for R>2. We also propose superscaling for other critical quantities.
In a recent paper [Phys. Rev. E 69, 046121 (2004)]], we used the Suzuki-Trottere formalism to study a quasispecies biological evolution model in a parallel mutation-selection scheme with a single-peak fitness function and a point mutation. In the present paper, we extend such a study to evolution models with more general fitness functions or multiple mutations in the parallel mutation-selection scheme. We give some analytical equations to define the error thresholds for some general cases of mean-field-like or symmetric mutation schemes and fitness functions. We derive some equations for the dynamics in the case of a point mutation and polynomial fitness functions. We derive exact dynamics for two-point mutations, asymmetric mutations, and the four-value spin model with a single-peak fitness function. The same method is applied for the model with a royal road fitness function. We derive the steady-state distribution for the single-peak fitness function.
We propose a model of coupled random walks for stock-stock correlations. The walks in the model are coupled via a mechanism that the displacement (price change) of each walk (stock) is activated by the price gradients over some underlying network. We assume that the network has two underlying structures, describing the correlations among the stocks of the whole market and among those within individual groups, respectively, each with a coupling parameter controlling the degree of correlation. The model provides the interpretation of the features displayed in the distribution of the eigenvalues for the correlation matrix of real market on the level of time sequences. We verify that such modeling indeed gives good fitting for the market data of US stocks.
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.
Based on the connection between a quantum spin model and an asexual biological evolution model with a single-peak fitness function in parallel mutation-selection scheme, we solve exactly both static and dynamics of the evolution model. We find that relaxation in such a parallel scheme is faster than that in a connected scheme of Eigen model. Our method can also be extended to other fitness functions.
We map the Eigen model of biological evolution [Naturwissenschaften 58, 465 (1971)] into a quantum spin model with non-Hermitian Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen model to approach static energy landscape from various initial conditions. We also study a simple case of dynamic fitness function.
We consider the crossover behavior between special and ordinary surface transitions in three-dimensional semi-infinite Ising-like systems with random quenched bulk disorder. We calculate the surface crossover critical exponent Phi, the critical exponents of the layer alpha(1), and local specific heats alpha(11) by applying the field theoretic approach directly in three spatial dimensions (d=3) up to the two-loop approximation. The numerical estimates of the resulting two-loop series expansions for the surface critical exponents are computed by means of Padé and Padé-Borel resummation techniques. We find that Phi, alpha(1), alpha(11) obtained in the present paper are different from their counterparts of pure Ising systems. The obtained results support the idea that in a system with random quenched bulk disorder the plane boundary is characterized by a new set of critical exponents.
We use a discrete-time formulation of the asymmetric avalanche process (ASAP) [Phys. Rev. Lett. 87, 084301 (2001)]] of p particles on a finite ring of N sites to obtain an exact expression for the average avalanche size as a function of toppling probabilities and particle density rho=p/N. By mapping the model onto driven interface problems, we find that the ASAP incorporates the annealed Kardar-Parizi-Zhang and quenched tilted interface dynamics for rho rho(c), respectively, with rho(c) being the critical density for given toppling probabilities and N--> infinity. We analyze the crossover between two regimes and show which parameters are relevant near the transition point.
We report results from all-atom Monte Carlo simulations of the 36-residue villin headpiece subdomain HP-36. Protein-solvent interactions are approximated by an implicit solvent model. The parallel tempering is used to overcome the problem of slow convergence in low-temperature protein simulations. Our results show that this technique allows one to sample native-like structures of small proteins and points out the need for improved energy functions.
One important step in the renormalization-group (RG) approach to a lattice sandpile model is the exact enumeration of all possible toppling processes of sandpile dynamics inside a cell for RG transformations. Here we propose a computer algorithm to carry out such exact enumeration for cells of planar lattices in the RG approach to the Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett. 59, 381 (1987)] and consider both the reduced-high RG equations proposed by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. 72, 1690 (1994)], and the real-height RG equations proposed by Ivashkevich [Phys. Rev. Lett. 76, 3368 (1996)]. Using this algorithm, we are able to carry out RG transformations more quickly with large cell size, e.g., 3x3 cell for the square (SQ) lattice in PVZ RG equations, which is the largest cell size at the present, and find some mistakes in a previous paper [Phys. Rev. E 51, 1711 (1995)]. For SQ and plane triangular (PT) lattices, we obtain the only attractive fixed point for each lattice and calculate the avalanche exponent tau and the dynamical exponent z. Our results suggest that the increase of the cell size in the PVZ RG transformation does not lead to more accurate results. The implication of such result is discussed.
We use a three-dimensional massive field theory up to the two-loop approximation to study the critical behavior of semi-infinite quenched random Ising-like systems at the special surface transition. Besides, we extend up to the next-to leading order, the previous first-order results of the sqrt[epsilon] expansion obtained by Ohno and Okabe [Phys. Rev. B 46, 5917 (1992)]. The numerical estimates for surface critical exponents in both cases are computed by means of the Padé analysis. Moreover, in the case of the massive field theory we perform Padé-Borel resummation of the resulting two-loop series expansions for surface critical exponents. The most reliable estimates for critical exponents of semi-infinite systems with quenched bulk randomness at the special surface transition, which we can obtain in the frames of the present approximation scheme, are eta(//)=-0.238, Delta(1)=1.098, eta( perpendicular )=-0.104, beta(1)=0.258, gamma(11)=0.839, gamma(1)=1.426, delta(1)=6.521, and delta(11)=4.249. These values are different from critical exponents for pure semi-infinite Ising-like systems and show that in a system with quenched bulk randomness the plane boundary is characterized by a new set of critical exponents at the special surface transition.
Finite-size scaling, finite-size corrections, and boundary effects for critical systems have attracted much attention in recent years. Here we derive exact finite-size corrections for the free energy F and the specific heat C of the critical ferromagnetic Ising model on the Mu x 2 Nu square lattice with Brascamp-Kunz (BK) boundary conditions [J. Math. Phys. 15, 66 (1974)] and compare such results with those under toroidal boundary conditions. When the ratio xi/2=(Mu+1)/2 Nu is smaller than 1 the behaviors of finite-size corrections for C are quite different for BK and toroidal boundary conditions; when ln(xi/2) is larger than 3, finite-size corrections for C in two boundary conditions approach the same values. In the limit Nu-->infinity we obtain the expansion of the free energy for infinitely long strip with BK boundary conditions. Our results are consistent with the conformal field theory prediction for the mixed boundary conditions by Cardy [Nucl. Phys. B 275, 200 (1986)] although the definitions of boundary conditions in two cases are different in one side of the long strip.
Using the random-cluster representation of the q-state Potts models we consider the pooling of data from cluster-update Monte Carlo simulations for different thermal couplings K and number of states per spin q. Proper combination of histograms allows for the evaluation of thermal averages in a broad range of K and q values, including noninteger values of q. Due to restrictions in the sampling process correct normalization of the combined histogram data is nontrivial. We discuss the different possibilities and analyze their respective ranges of applicability.
Let f, U, and C represent, respectively, the free energy, the internal energy, and the specific heat of the critical Ising model on the MxN square lattice with periodic boundary conditions, and f(infinity) represents f for fixed M/N and N-->infinity. We find that f, U, and C can be written as N(f-f(infinity))= summation operator(infinity)(i=1)f(2i-1)/N(2i-1), U=-square root of [2]+ summation operator(infinity)(i=1)u(2i-1)/N(2i-1), and C=8 ln N/pi+ summation operator(infinity)(i=0)c(i)/N(i), i.e., Nf and U are odd functions of N(-1). We also find that u(2i-1)/c(2i-1)=1/square root of [2] and u(2i)/c(2i)=0 for 1 < or = i <infinity and obtain closed form expressions for f, U, and C up to orders 1/N(5), 1/N(5), and 1/N(3), respectively, which implies an analytic equation for c(5).