Complex temporal patterns in molecular dynamics:a direct measure of the phase-space exploration by the trajectory at macroscopic time scales

Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the short-time correlations corresponding to the velocity autocorrelation decay times (â‰0.1â€ps), remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longer-time correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced. © 2008 The American Physical Society.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Analysis of carrier phase extraction methods in 112-Gbit/s NRZ-PDM-QPSK coherent transmission system

We present a comparative analysis on three carrier phase extraction approaches, including a one-tap normalized least mean square method, a block-average method, and a Viterbi-Viterbi method, in coherent transmission system considering equalization enhanced phase noise. © OSA 2012.

A design environment for deadlock-free concurrent software

Using current software engineering technology, the robustness required for safety critical software is not assurable. However, different approaches are possible which can help to assure software robustness to some extent. For achieving high reliability software, methods should be adopted which avoid introducing faults (fault avoidance); then testing should be carried out to identify any faults which persist (error removal). Finally, techniques should be used which allow any undetected faults to be tolerated (fault tolerance). The verification of correctness in system design specification and performance analysis of the model, are the basic issues in concurrent systems. In this context, modeling distributed concurrent software is one of the most important activities in the software life cycle, and communication analysis is a primary consideration to achieve reliability and safety. By and large fault avoidance requires human analysis which is error prone; by reducing human involvement in the tedious aspect of modelling and analysis of the software it is hoped that fewer faults will persist into its implementation in the real-time environment. The Occam language supports concurrent programming and is a language where interprocess interaction takes place by communications. This may lead to deadlock due to communication failure. Proper systematic methods must be adopted in the design of concurrent software for distributed computing systems if the communication structure is to be free of pathologies, such as deadlock. The objective of this thesis is to provide a design environment which ensures that processes are free from deadlock. A software tool was designed and used to facilitate the production of fault-tolerant software for distributed concurrent systems. Where Occam is used as a design language then state space methods, such as Petri-nets, can be used in analysis and simulation to determine the dynamic behaviour of the software, and to identify structures which may be prone to deadlock so that they may be eliminated from the design before the program is ever run. This design software tool consists of two parts. One takes an input program and translates it into a mathematical model (Petri-net), which is used for modeling and analysis of the concurrent software. The second part is the Petri-net simulator that takes the translated program as its input and starts simulation to generate the reachability tree. The tree identifies `deadlock potential' which the user can explore further. Finally, the software tool has been applied to a number of Occam programs. Two examples were taken to show how the tool works in the early design phase for fault prevention before the program is ever run.

Gaussian regression and optimal finite dimensional linear models

The problem of regression under Gaussian assumptions is treated generally. The relationship between Bayesian prediction, regularization and smoothing is elucidated. The ideal regression is the posterior mean and its computation scales as O(n³), where n is the sample size. We show that the optimal m-dimensional linear model under a given prior is spanned by the first m eigenfunctions of a covariance operator, which is a trace-class operator. This is an infinite dimensional analogue of principal component analysis. The importance of Hilbert space methods to practical statistics is also discussed.

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Transition from time-continuous systems to discrete mappings

Detailed transport studies in plasmas require the solution of the time evolution of many different initial positions of test particles in the phase space of the systems to be investigated. To reduce this amount of numerical work, one would like to replace the integration of the time-continues system with a mapping.

Advanced fibre gratings and their applications

This thesis describes a detailed study of advanced fibre grating devices using Bragg (FBG) and long-period (LPG) structures and their applications in optical communications and sensing. The major contributions presented in this thesis are summarised below. One of the most important contributions from the research work presented in this thesis is a systematic theoretical study of many distinguishing structures of fibre gratings. Starting from the Maxwell equations, the coupled-mode equations for both FBG and LPG were derived and the mode-overlap factor was analytically discussed. Computing simulation programmes utilising matrix transform method based on the models built upon the coupled-mode equations were developed, enabling simulations of spectral response in terms of reflectivity, bandwidth, sidelobes and dispersion of gratings of different structures including uniform and chirped, phase-shifted, Moiré, sampled Bragg gratings, phase-shifted and cascaded long-period gratings. Although the majority of these structures were modelled numerically, analytical expressions for some complex structures were developed with a clear physical picture. Several apodisation functions were proposed to improve sidelobe suppression, which guided effective production of practical devices for demanding applications. Fibre grating fabrication is the other major part involved in the Ph.D. programme. Both the holographic and scan-phase-mask methods were employed to fabricate Bragg and long-period gratings of standard and novel structures. Significant improvements were particularly made in the scan-phase-mask method to enable the arbitrarily tailoring of the spectral response of grating devices. Two specific techniques - slow-shifting and fast-dithering the phase-mask implemented by a computer controlled piezo - were developed to write high quality phase-shifted, sampled and apodised gratings. A large number of LabVIEW programmes were constructed to implement standard and novel fabrication techniques. In addition, some fundamental studies of grating growth in relating to the UV exposure and hydrogenation induced index were carried out. In particular, Type IIa gratings in non-hydrogenated B/Ge co-doped fibres and a re-generated grating in hydrogenated B/Ge fibre were investigated, showing a significant observation of thermal coefficient reduction. Optical sensing applications utilising fibre grating devices form the third major part of the research work presented in this thesis. Several experiments of novel sensing and sensing-demodulating were implemented. For the first time, an intensity and wavelength dual-coding interrogation technique was demonstrated showing significantly enhanced capacity of grating sensor multiplexing. Based on the mode-splitting measurement, instead of using conventional wavelength-shifting detection technique, successful demonstrations were also made for optical load and bend sensing of ultra-high sensitivity employing LPG structures. In addition, edge-filters and low-loss high-rejection bandpass filters of 50nm stop-band were fabricated for application in optical sensing and high-speed telecommunication systems

Can we observe collective neuronal activity from macroscopic aggregate signals?

The fundamental problem faced by noninvasive neuroimaging techniques such as EEG/MEG1 is to elucidate functionally important aspects of the microscopic neuronal network dynamics from macroscopic aggregate measurements. Due to the mixing of the activities of large neuronal populations in the observed macroscopic aggregate, recovering the underlying network that generates the signal in the absence of any additional information represents a considerable challenge. Recent MEG studies have shown that macroscopic measurements contain sufficient information to allow the differentiation between patterns of activity, which are likely to represent different stimulus-specific collective modes in the underlying network (Hadjipapas, A., Adjamian, P., Swettenham, J.B., Holliday, I.E., Barnes, G.R., 2007. Stimuli of varying spatial scale induce gamma activity with distinct temporal characteristics in human visual cortex. NeuroImage 35, 518–530). The next question arising in this context is whether aspects of collective network activity can be recovered from a macroscopic aggregate signal. We propose that this issue is most appropriately addressed if MEG/EEG signals are to be viewed as macroscopic aggregates arising from networks of coupled systems as opposed to aggregates across a mass of largely independent neural systems. We show that collective modes arising in a network of simulated coupled systems can be indeed recovered from the macroscopic aggregate. Moreover, we show that nonlinear state space methods yield a good approximation of the number of effective degrees of freedom in the network. Importantly, information about hidden variables, which do not directly contribute to the aggregate signal, can also be recovered. Finally, this theoretical framework can be applied to experimental MEG/EEG data in the future, enabling the inference of state dependent changes in the degree of local synchrony in the underlying network.

Quantifying the complexity of chaos in multibasin multidimensional dynamics of molecular systems

The simulated classical dynamics of a small molecule exhibiting self-organizing behavior via a fast transition between two states is analyzed by calculation of the statistical complexity of the system. It is shown that the complexity of molecular descriptors such as atom coordinates and dihedral angles have different values before and after the transition. This provides a new tool to identify metastable states during molecular self-organization. The highly concerted collective motion of the molecule is revealed. Low-dimensional subspaces dynamics is found sensitive to the processes in the whole, high-dimensional phase space of the system. © 2004 Wiley Periodicals, Inc.

Dynamic complexity of chaotic transitions in high-dimensional classical dynamics:Leu-Enkephalin folding

Leu-Enkephalin in explicit water is simulated using classical molecular dynamics. A ß-turn transition is investigated by calculating the topological complexity (in the "computational mechanics" framework [J. P. Crutchfield and K. Young, Phys. Rev. Lett., 63, 105 (1989)]) of the dynamics of both the peptide and the neighbouring water molecules. The complexity of the atomic trajectories of the (relatively short) simulations used in this study reflect the degree of phase space mixing in the system. It is demonstrated that the dynamic complexity of the hydrogen atoms of the peptide and almost all of the hydrogens of the neighbouring waters exhibit a minimum precisely at the moment of the ß-turn transition. This indicates the appearance of simplified periodic patterns in the atomic motion, which could correspond to high-dimensional tori in the phase space. It is hypothesized that this behaviour is the manifestation of the effect described in the approach to molecular transitions by Komatsuzaki and Berry [T. Komatsuzaki and R.S. Berry, Adv. Chem. Phys., 123, 79 (2002)], where a "quasi-regular" dynamics at the transition is suggested. Therefore, for the first time, the less chaotic character of the folding transition in a realistic molecular system is demonstrated. © Springer-Verlag Berlin Heidelberg 2006.

Design verification and validation in product lifecycle

The verification and validation of engineering designs are of primary importance as they directly influence production performance and ultimately define product functionality and customer perception. Research in aspects of verification and validation is widely spread ranging from tools employed during the digital design phase, to methods deployed for prototype verification and validation. This paper reviews the standard definitions of verification and validation in the context of engineering design and progresses to provide a coherent analysis and classification of these activities from preliminary design, to design in the digital domain and the physical verification and validation of products and processes. The scope of the paper includes aspects of system design and demonstrates how complex products are validated in the context of their lifecycle. Industrial requirements are highlighted and research trends and priorities identified. © 2010 CIRP.