Approximating the longest path length of a stochastic DAG by a normal distribution in linear time

AbstractThis paper presents a linear time algorithm for approximating, in the sense below, the longest path length of a given directed acyclic graph (DAG), where each edge length is given as a normally distributed random variable. Let F(x) be the distribution function of the longest path length of the DAG. Our algorithm computes the mean and the variance of a normal distribution whose distribution function F˜(x) satisfies F˜(x)⩽F(x) as long as F(x)⩾a, given a constant a (1/2⩽a<1). In other words, it computes an upper bound 1−F˜(x) on the tail probability 1−F(x), provided x⩾F−1(a). To evaluate the accuracy of the approximation of F(x) by F˜(x), we first conduct two experiments using a standard benchmark set ITC'99 of logical circuits, since a typical application of the algorithm is the delay analysis of logical circuits. We also perform a worst case analysis to derive an upper bound on the difference F˜−1(a)−F−1(a)

High-speed atomic force microscopy for observing protein molecules in dynamic action

Directly observing protein molecules in dynamic action at high spatiotemporal resolution has long been a holy grail for biological science. To materialize this long quested dream, I have been developing high-speed atomic force microscopy (HS-AFM) since 1993. Tremendous strides were recently accomplished in its high-speed and low-invasive performances. Consequently, various dynamic molecular actions, including bipedal walking of myosin V and rotary propagation of structural changes in F1-ATPase, were successfully captured on video. The visualized dynamic images not only provided irrefutable evidence for speculated actions of the protein molecules but also brought new discoveries inaccessible with other approaches, thus giving great mechanistic insights into how the molecules function. HS-AFM is now transforming "static" structural biology into dynamic structural bioscience. © 2017 SPIE

Video imaging of biomolecular processes by high-speed AFM

金沢大学理工研究域数物科学系The imaging rate of conventional atomic force microscopy (AFM) is too low to capture the dynamic behavior of biomolecules. To overcome this problem, we have been developing various devices and techniques, including small cantilevers and high-speed scanners. The feedback bandwidth in the tapping-mode now exceeds 100 kHz and hence the maximum possible imaging rate reaches 25 frames per sec (fps). Importantly the tip-force exerting onto the sample is dramatically reduced. Thus, it is now possible to take video images of dynamically moving protein molecules in action without disturbing their function, including walking myosin V molecules along actin tracks

High-speed atomic force microscopy coming of age

High-speed atomic force microscopy (HS-AFM) is now materialized. It allows direct visualization of dynamic structural changes and dynamic processes of functioning biological molecules in physiological solutions, at high spatiotemporal resolution. Dynamic molecular events unselectively appear in detail in an AFM movie, facilitating our understanding of how biological molecules operate to function. This review describes a historical overview of technical development towards HS-AFM, summarizes elementary devices and techniques used in the current HS-AFM, and then highlights recent imaging studies. Finally, future challenges of HS-AFM studies are briefly discussed. © 2012 IOP Publishing Ltd

Techniques developed for high-speed AFM

This article describes fundamental devices and control techniques that have materialized high-speed atomic force microscopy (AFM) capable of recording dynamic processes of individual biomolecules on video at an imaging rate of 10-25 frames/s, without disturbing their biological functions. © 2011 Springer-Verlag Berlin Heidelberg

Molecular machines directly observed by high-speed atomic force microscopy

Molecular machines made of proteins are highly dynamic and carry out sophisticated biological functions. The direct and dynamic high-resolution visualization of molecular machines in action is considered to be the most straightforward approach to understanding how they function but this has long been infeasible until recently. High-speed atomic force microscopy has recently been realized, making such visualization possible. The captured images of myosin V, F1-ATPase, and bacteriorhodopsin have enabled their dynamic processes and structure dynamics to be revealed in great detail, giving unique and deep insights into their functional mechanisms. © 2013 Federation of European Biochemical Societies

High-speed Atomic Force Microscopy

High-speed atomic force microscopy (HS-AFM) has been developed as a nano-dynamics visualization technique. This microscopy permits direct observation of structure dynamics and dynamic processes of biological molecules in physiological solutions, at a subsecond to sub-100 ms temporal resolution and an ∼2 nm lateral and a 0.1 nm vertical resolution. Importantly, tip-sample interactions do not disturb the biomolecules\u27 functions. Various functioning proteins including myosin V walking on an actin filament and bacteriorhodopsin responding to light have been successfully visualized with HS-AFM. In the quest for understanding the functional mechanisms of proteins, inferences no longer have to be made from static snapshots of molecular structures and dynamic behavior of optical markers attached to proteins. High-resolution molecular movies obtained from HS-AFM observations reveal the details of molecules\u27 dynamic behavior in action, without the need for intricate analyses and interpretations. In this review, I first describe the fundamentals behind the achieved high imaging rate and low invasiveness to samples, and then highlight recent imaging studies. Finally, future studies are briefly described. © The Author 2013. Published by Oxford University Press [on behalf of The Japanese Society of Microscopy]. All rights reserved

Spin Drift in Highly Doped n-type Si

A quantitative estimation of spin drift velocity in highly doped n-type silicon (Si) at 8 K is presented in this letter. A local two-terminal Hanle measurement enables the detection of a modulation of spin signals from the Si as a function of an external electric field, and this modulation is analyzed by using a spin drift-diffusion equation and an analytical solution of the Hanle-type spin precession. The analyses reveal that the spin drift velocity is linearly proportional to the electric field. The contribution of the spin drift effect to the spin signals is crosschecked by introducing a modified nonlocal four-terminal method.Comment: 16 pages, 3 figure