First-Passage Time Distribution and Non-Markovian Diffusion Dynamics of Protein Folding

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described in terms of an order parameter given by the fraction of native conformations. The non-Markovian diffusion dynamics is analyzed in detail and an expression for the mean first-passage time (MFPT) from non-native unfolded states to native folded state is obtained. It was found that the MFPT has a V-shaped dependence on the temperature. We also find that the MFPT is shortened as one increases the gap between the energy of the native and average non-native folded states relative to the fluctuations of the energy landscape. The second- and higher-order moments are studied to infer the first-passage time (FPT) distribution. At high temperature, the distribution becomes close to a Poisson distribution, while at low temperatures the distribution becomes a L\'evy-like distribution with power-law tails, indicating a non-self-averaging intermittent behavior of folding dynamics. We note the likely relevance of this result to single-molecule dynamics experiments, where a power law (L\'evy) distribution of the relaxation time of the underlined protein energy landscape is observed.Comment: 26 pages, 10 figure

Differentially Private Data Releasing for Smooth Queries with Synthetic Database Output

We consider accurately answering smooth queries while preserving differential privacy. A query is said to be $K$-smooth if it is specified by a function defined on $[-1,1]^d$ whose partial derivatives up to order $K$ are all bounded. We develop an $\epsilon$-differentially private mechanism for the class of $K$-smooth queries. The major advantage of the algorithm is that it outputs a synthetic database. In real applications, a synthetic database output is appealing. Our mechanism achieves an accuracy of $O (n^{-\frac{K}{2d+K}}/\epsilon )$, and runs in polynomial time. We also generalize the mechanism to preserve $(\epsilon, \delta)$-differential privacy with slightly improved accuracy. Extensive experiments on benchmark datasets demonstrate that the mechanisms have good accuracy and are efficient

Universal R-matrix Of The Super Yangian Double DY(gl(1|1))

Based on Drinfeld realization of super Yangian Double DY(gl(1|1)), its pairing relations and universal R-matrix are given. By taking evaluation representation of universal R-matrix, another realization $L^{\pm}(u)$ of DY(gl(1|1)) is obtained. These two realizations of DY(gl(1|1)) are related by the supersymmetric extension of Ding-Frenkel map.Comment: 6 pages, latex, no figure

Diffusion Dynamics, Moments, and Distribution of First Passage Time on the Protein-Folding Energy Landscape, with Applications to Single Molecules

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We obtain information for the first passage-time (FPT) distribution and its moments. The results show a dynamic transition temperature below which the FPT distribution develops a power-law tail, a signature of the intermittency phenomena of the folding dynamics. We also discuss the possible application of the results to single-molecule dynamics experiments

An almost globally convergent observer for visual SLAM without persistent excitation

In this paper we propose a novel observer to solve the problem of visual simultaneous localization and mapping (SLAM), only using the information from a single monocular camera and an inertial measurement unit (IMU). The system state evolves on the manifold $SE(3)\times \mathbb{R}^{3n}$, on which we design dynamic extensions carefully in order to generate an invariant foliation, such that the problem is reformulated into online \emph{constant parameter} identification. Then, following the recently introduced parameter estimation-based observer (PEBO) and the dynamic regressor extension and mixing (DREM) procedure, we provide a new simple solution. A notable merit is that the proposed observer guarantees almost global asymptotic stability requiring neither persistency of excitation nor uniform complete observability, which, however, are widely adopted in most existing works with guaranteed stability