Non-ergodic transitions in many-body Langevin systems: a method of dynamical system reduction

We study a non-ergodic transition in a many-body Langevin system. We first derive an equation for the two-point time correlation function of density fluctuations, ignoring the contributions of the third- and fourth-order cumulants. For this equation, with the average density fixed, we find that there is a critical temperature at which the qualitative nature of the trajectories around the trivial solution changes. Using a method of dynamical system reduction around the critical temperature, we simplify the equation for the time correlation function into a two-dimensional ordinary differential equation. Analyzing this differential equation, we demonstrate that a non-ergodic transition occurs at some temperature slightly higher than the critical temperature.Comment: 8 pages, 1 figure; ver.3: Calculation errors have been fixe

Scale-free patterns at a saddle-node bifurcation in a stochastic system

We demonstrate that scale-free patterns are observed in a spatially extended stochastic system whose deterministic part undergoes a saddle-node bifurcation. Remarkably, the scale-free patterns appear only at a particular time in relaxation processes from a spatially homogeneous initial condition. We characterize the scale-free nature in terms of the spatial configuration of the exiting time from a marginal saddle where the pair annihilation of a saddle and a node occurs at the bifurcation point. Critical exponents associated with the scale-free patterns are determined by numerical experiments.Comment: 4 pages, 6 figure

Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation

A Langevin equation whose deterministic part undergoes a saddle-node bifurcation is investigated theoretically. It is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle-node bifurcation point in the weak-noise limit, while the final value of the deterministic solution changes discontinuously at the point. A systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method. In this formulation, the critical nature turns out to originate from the neutrality of exiting time from a saddle-point. The theoretical calculation explains results of numerical simulations.Comment: 18pages, 17figures.The version 2, in which minor errors have been fixed, will be published in Phys. Rev.

Dynamics of k-core percolation in a random graph

We study the edge deletion process of random graphs near a k-core percolation point. We find that the time-dependent number of edges in the process exhibits critically divergent fluctuations. We first show theoretically that the k-core percolation point is exactly given as the saddle-node bifurcation point in a dynamical system. We then determine all the exponents for the divergence based on a universal description of fluctuations near the saddle-node bifurcation.Comment: 16 pages, 4 figure

Singular perturbation near mode-coupling transition

We study the simplest mode-coupling equation which describes the time correlation function of the spherical p-spin glass model. We formulate a systematic perturbation theory near the mode-coupling transition point by introducing multiple time scales. In this formulation, the invariance with respect to the dilatation of time in a late stage yields an arbitrary constant in a leading order expression of the solution. The value of this constant is determined by a solvability condition associated with a linear singular equation for perturbative corrections in the late stage. The solution thus constructed provides exactly the alpha-relaxation time.Comment: 15 pages, 4 figure

Nationwide surveillance of bacterial respiratory pathogens conducted by the surveillance committee of Japanese Society of Chemotherapy, the Japanese Association for Infectious Diseases, and the Japanese Society for Clinical Microbiology in 2010: General view of the pathogens\u27 antibacterial susceptibility

The nationwide surveillance on antimicrobial susceptibility of bacterial respiratory pathogens from patients in Japan, was conducted by Japanese Society of Chemotherapy, Japanese Association for Infectious Diseases and Japanese Society for Clinical Microbiology in 2010.The isolates were collected from clinical specimens obtained from well-diagnosed adult patients with respiratory tract infections during the period from January and April 2010 by three societies. Antimicrobial susceptibility testing was conducted at the central reference laboratory according to the method recommended by Clinical and Laboratory Standard Institutes using maximum 45 antibacterial agents.Susceptibility testing was evaluable with 954 strains (206 Staphylococcus aureus, 189 Streptococcus pneumoniae, 4 Streptococcus pyogenes, 182 Haemophilus influenzae, 74 Moraxella catarrhalis, 139 Klebsiella pneumoniae and 160 Pseudomonas aeruginosa). Ratio of methicillin-resistant S.aureus was as high as 50.5%, and those of penicillin-intermediate and -resistant S.pneumoniae were 1.1% and 0.0%, respectively. Among H.influenzae, 17.6% of them were found to be β-lactamase-non-producing ampicillin (ABPC)-intermediately resistant, 33.5% to be β-lactamase-non-producing ABPC-resistant and 11.0% to be β-lactamase-producing ABPC-resistant strains. Extended spectrum β-lactamase-producing K.pneumoniae and multi-drug resistant P.aeruginosa with metallo β-lactamase were 2.9% and 0.6%, respectively.Continuous national surveillance of antimicrobial susceptibility of respiratory pathogens is crucial in order to monitor changing patterns of susceptibility and to be able to update treatment recommendations on a regular basis