Cycle symmetry, limit theorems, and fluctuation theorems for diffusion processes on the circle

Cyclic structure and dynamics are of great interest in both the fields of stochastic processes and nonequilibrium statistical physics. In this paper, we find a new symmetry of the Brownian motion named as the quasi-time-reversal invariance. It turns out that such an invariance of the Brownian motion is the key to prove the cycle symmetry for diffusion processes on the circle, which says that the distributions of the forming times of the forward and backward cycles, given that the corresponding cycle is formed earlier than the other, are exactly the same. With the aid of the cycle symmetry, we prove the strong law of large numbers, functional central limit theorem, and large deviation principle for the sample circulations and net circulations of diffusion processes on the circle. The cycle symmetry is further applied to obtain various types of fluctuation theorems for the sample circulations, net circulation, and entropy production rate.Comment: 28 page

Replication forks, chromatin loops and dormant replication origins

The plasticity of replication origin usage during mitosis is associated with longer-term changes to chromatin loop organization

A modified Brown algorithm for solving singular nonlinear systems with rank defects

AbstractA modified Brown algorithm for solving a class of singular nonlinear systems, F(x)=0, where x,F∈Rn, is presented. This method is constructed by combining the discreted Brown algorithm with the space transforming method. The second-order information of F(x) at a point is not required calculating, which is different from the tensor method and the Hoy's method. The Q-quadratic convergence of this algorithm and some numerical examples are given as well

Decentralized Non-Convex Learning with Linearly Coupled Constraints

Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns some local information and a local variable for jointly minimizing a cost function, but local variables are coupled by linear constraints. Most of the existing methods for such problems are only applicable for convex problems or problems with specific linear constraints. There still lacks a distributed algorithm for such problems with general linear constraints and under nonconvex setting. In this paper, to tackle this problem, we propose a new algorithm, called "proximal dual consensus" (PDC) algorithm, which combines a proximal technique and a dual consensus method. We build the theoretical convergence conditions and show that the proposed PDC algorithm can converge to an $\epsilon$-Karush-Kuhn-Tucker solution within $\mathcal{O}(1/\epsilon)$ iterations. For computation reduction, the PDC algorithm can choose to perform cheap gradient descent per iteration while preserving the same order of $\mathcal{O}(1/\epsilon)$ iteration complexity. Numerical results are presented to demonstrate the good performance of the proposed algorithms for solving a regression problem and a classification problem over a network where agents have only partial observations of data features

Fully integrated InGaAs/InP single-photon detector module with gigahertz sine wave gating

InGaAs/InP single-photon avalanche diodes (SPADs) working in the regime of GHz clock rates are crucial components for the high-speed quantum key distribution (QKD). We have developed for the first time a compact, stable and user-friendly tabletop InGaAs/InP single-photon detector system operating at a 1.25 GHz gate rate that fully integrates functions for controlling and optimizing SPAD performance. We characterize the key parameters of the detector system and test the long-term stability of the system for continuous operation of 75 hours. The detector system can substantially enhance QKD performance and our present work paves the way for practical high-speed QKD applications.Comment: 11 pages, 6 figures. Accepted for publication in Review of Scientific Instrument

Electrochemical probing of selective haemoglobin binding in hydrogel-based molecularly imprinted polymers

An electrochemical method has been developed for the probing of hydrogel-based molecularly imprinted polymers (HydroMIPs) on the surface of a glassy carbon electrode. HydroMIPs designed for bovine haemoglobin selectivity were electrochemically characterised and their rebinding properties were monitored using cyclic voltammetry. The electrochemical reduction of bovine oxyhaemoglobin (BHb) in solution was observed to occur at ?0.460 V vs (Ag/AgCl) in 150 mM phosphate buffer solution (PBS). When the protein was selectively bound to the MIP, the electrochemical reduction of oxyhaemoglobin could be observed at a similar peak potential of ?0.480 V vs (Ag/AgCl). When analysing the non-imprinted control polymer (NIP) interfaced at the electrode, which contained no protein, the peak reduction potential corresponded to that observed for dissolved oxygen in solution (?0.65 V vs (Ag/AgCl)). MIP and NIP (in the absence of protein) were interfaced at the electrode and protein allowed to diffuse through the polymers from the bulk solution end to the electrode. It was observed that whereas NIP exhibited a protein response within 10 min of protein exposure, up to 45 min of exposure time was required in the case of the MIP before a protein response could be obtained. Our results suggest that due to the selective nature of the MIP, BHb arrival at the electrode via diffusion is delayed by the MIP due to attractive selective interactions with exposed cavities, but not the NIP which is devoid of selective cavities