Chihiro Nakajima

Phase of neural excitation relative to basilar membrane motion in the organ of Corti: Theoretical considerations

Although the auditory transduction process is dependent on neural excitation of the auditory nerve in relation to motion of the basilar membrane (BM) in the organ of Corti (OC), specifics of this process are unclear. In this study, therefore, an attempt was made to estimate the phase of the neural excitation relative to the BM motion using a finite-element model of the OC at the basal turn of the gerbil, including the fluid-structure interaction with the lymph fluid. It was found that neural excitation occurs when the BM exhibits a maximum velocity toward the scala vestibuli at 10 Hz and shows a phase delay relative to the BM motion with increasing frequency up to 800 Hz. It then shows a phase advance until the frequency reaches 2 kHz. From 2 kHz, neural excitation again shows a phase delay with increasing frequency. From 800 Hz up to 2 kHz, the phase advances because the dominant force exerted on the hair bundle shifts from a velocity-dependent Couette flow-induced force to a displacement-dependent force induced by the pressure difference. The phase delay that occurs from 2 kHz is caused by the resonance process of the hair bundle of the IHC.

Localization and size distribution of a polymer knot confined in a channel

We have examined the behaviors of a knotted linear polymer in narrow channels using Langevin dynamics simulation to investigate the knot localization property in one-dimensional (1D) geometry. We have found that the knot is strongly localized in such a geometry. By observing the distribution function of the size of the localized knot, we found the scaling behavior of the fluctuation around the most probable size with the radius of confinement. Based on the analysis of the probability distribution of the knot size, we show that the strong localization behavior and the fluctuation around the most probable size can be encompassed by a simple argument based on virtual tubes composed of parallel strands and the overlap among them.

Miscibility phase diagram of ring-polymer blends: A topological effect.

The miscibility of polymer blends, a classical problem in polymer science, may be altered, if one or both of the component do not have chain ends. Based on the idea of topological volume, we propose a mean-field theory to clarify how the topological constraints in ring polymers affect the phase behavior of the blends. While the large enhancement of the miscibility is expected for ring-linear polymer blends, the opposite trend toward demixing, albeit comparatively weak, is predicted for ring-ring polymer blends. Scaling formulas for the shift of critical point for both cases are derived. We discuss the valid range of the present theory, and the crossover to the linear polymer blends behaviors, which is expected for short chains. These analyses put forward a view that the topological constraints could be represented as an effective excluded-volume effects, in which the topological length plays a role of the screening factor.

Statistical Mechanical Formulation and Simulation of Prime Factorization of Integers

We propose a new formulation of the problem of prime factorization of integers. With replica exchange Monte Carlo simulation, the behavior which is seemed to indicate exponential computational hardness is observed. But this formulation is expected to give a new insight into the computational complexity of this problem from a statistical mechanical point of view.

Statistical Mechanical Models of Integer Factorization Problem

We formulate the integer factorization problem via a formulation of the searching problem for the ground state of a statistical mechanical Hamiltonian. The first passage time required to find a correct divisor of a composite number signifies the exponential computational hard- ness. Analysis of the density of states of two macroscopic quantities, i.e. the energy and the Hamming distance from the correct solutions, leads to the conclusion that the ground state (the correct solution) is completely isolated from the other low energy states, with the distance being proportional to the system size. In addition, the profile of the microcanonical entropy of the model has two peculiar features which are each related to two dramatic changes in the energy region sampled via Monte Carlo simulation or simulated annealing. Hence, we find a peculiar first-order phase transition in our model.

Computing a Knot Invariant as a Constraint Satisfaction Problem

We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides an algorithm to find the solution. The method also allows one to get some deeper insight into the structural complexity of knots, which is expected to be related with the landscape structure of constraint satisfaction problem.