Finding transition pathways using the string method with swarms of trajectories

An approach to find transition pathways in complex systems is presented. The method, which is related to the string method in collective variables of Maragliano et al. (J. Chem. Phys. 2006, 125, 024106), is conceptually simple and straightforward to implement. It consists of refining a putative transition path in the multidimensional space supported by a set of collective variables using the average dynamic drift of those variables. This drift is estimated on-the-fly via swarms of short unbiased trajectories started at different points along the path. Successive iterations of this algorithm, which can be naturally distributed over many computer nodes with negligible interprocessor communication, refine an initial trial path toward the most probable transition path (MPTP) between two stable basins. The method is first tested by determining the pathway for the C7eq to C7ax transition in an all-atom model of the alanine dipeptide in vacuum, which has been studied previously with the string method in collective variables. A transition path is found with a committor distribution peaked at 1/2 near the free energy maximum, in accord with previous results. Last, the method is applied to the allosteric conformational change in the nitrogen regulatory protein C (NtrC), represented here with a two-state elastic network model. Even though more than 550 collective variables are used to describe the conformational change, the path converges rapidly. Again, the committor distribution is found to be peaked around 1/2 near the free energy maximum between the two stable states, confirming that a genuine transition state has been localized in this complex multidimensional system.     

A new approach to liquid penetrant inspection: radiolabeled QDots

Penetrant technique is a sensitive non-destructive testing (NDT) method for detecting and locating the presence of cracks in sample surface. Today, NDT is used in a wide range of industries including aerospace, biotechnology, defence, marine, oil–gas and energy plants. This work focuses on potential use of radiolabeled ZnS coated CdTe quantum dots (QDots) as a penetrant for liquid penetrant testing. The synthesized QDots as a precursor were tested for surface defects detection in welded joints. The experimental results show the highest activities were found in defects on the sample surface. These finding are consistent with the sample NDT inspection test report.     

A mathematical model for personalized advertisement in virtual reality environments

We consider a personalized advertisement assignment problem faced by the manager of a virtual reality environment. In this online environment, users log in/out, and they spend time in different virtual locations while they are online. Every time a user visits a new virtual location, the site manager can show the ad of an advertiser. At the end of a fixed time horizon, the manager collects revenues from all of the advertisers, and the total revenue depends on the number of ads of different advertisers she displays to different users. In this setup, the objective of the manager is to find an optimal dynamic ad display policy in order to maximize her expected revenue. In the current paper, we formulate this problem as a continuous time stochastic optimization problem in which the actions of users are represented with two-state Markov processes and the manager makes display decisions at the transition times of these processes. To our best knowledge, no formal stochastic model and rigorous analysis has been given for this practical problem. Such a model and its analysis are the major contributions of this paper along with an optimal solution.     

Stability of high‐mass molecular libraries: the role of the oligoporphyrin core

Molecular beam techniques are a key to many experiments in physical chemistry and quantum optics. In particular, advanced matter‐wave experiments with high‐mass molecules profit from the availability of slow, neutral and mass‐selected molecular beams that are sufficiently stable to remain intact during laser heating and photoionization mass spectrometry. We present experiments on the photostability with molecular libraries of tailored oligoporphyrins with masses up to 25 000 Da. We compare two fluoroalkylsulfanyl‐functionalized libraries based on two different molecular cores that offer the same number of anchor points for functionalization but differ in their geometry and electronic properties. A pentaporphyrin core stabilizes a library of chemically well‐defined molecules with more than 1600 atoms. They can be neutrally desorbed with velocities as low as 20 m/s and efficiently analyzed in photoionization mass spectrometry. Copyright © 2015 John Wiley & Sons, Ltd.     

On the solution of the Abel equation of the second kind by the shifted Chebyshev polynomials

This paper presents a new approximate method of Abel differential equation. By using the shifted Chebyshev expansion of the unknown function, Abel differential equation is approximately transformed to a system of nonlinear equations for the unknown coefficients. A desired solution can be determined by solving the resulting nonlinear system. This method gives a simple and closed form of approximate solution of Abel differential equation. The solution is calculated in the form of a series with easily computable components. The numerical results show the effectiveness of the method for this type of equation. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.     

Rational Chebyshev collocation method for solving higher‐order linear ordinary differential equations

A collocation method to find an approximate solution of higher‐order linear ordinary differential equation with variable coefficients under the mixed conditions is proposed. This method is based on the rational Chebyshev (RC) Tau method and Taylor‐Chebyshev collocation methods. The solution is obtained in terms of RC functions. Also, illustrative examples are included to demonstrate the validity and applicability of the technique, and performed on the computer using a program written in maple9. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1130–1142, 2011     

Functionalized Ag nanoparticles with tunable optical properties for selective protein analysis

We present a preparation procedure for small sized biocompatibly coated Ag nanoparticles with tunable surface plasmon resonances. The conditions were optimised with respect to the resonance Raman signal enhancement of heme proteins and to the preservation of the native protein structure.     

Simulating electron spin resonance spectra of macromolecules labeled with two dipolar-coupled nitroxide spin labels from trajectories

An efficient method for simulating continuous-wave electron spin resonance spectra (ESR) of molecules labeled with two dipolar-coupled nitroxides from trajectories of the molecular motion is presented. Two approximate treatments of the dipolar spin evolution, resulting in significantly shorter simulation times, are examined in order to determine their range of applicability. The approach is illustrated in the context of a double-helical B-DNA. ESR spectra for DNA undergoing anisotropic global diffusion and internal stretching dynamics are calculated for three different labeling geometries with the spin labels bracketing, respectively, three, two and one base pairs. While multifrequency spectra of all three labeling schemes are very sensitive to DNA tumbling, the last one is found to be most informative about the local DNA dynamics.