Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

Role of plasma in femtosecond laser pulse propagation

This paper describes physics of nonlinear ultra-short laser pulse propagation affected by plasma created by the pulse itself. Major applications are also discussed. Nonlinear propagation of the femtosecond laser pulses in gaseous and solid transparent dielectric media is a fundamental physical phenomenon in a wide range of important applications such as laser lidars, laser micro-machining (ablation) and microfabrication etc. These applications require very high intensity of the laser field, typically 1013–1015 TW/cm2. Such high intensity leads to significant ionisation and creation of electron-ion or electron-hole plasma. The presence of plasma results into significant multiphoton and plasma absorption and plasma defocusing. Consequently, the propagation effects appear extremely complex and result from competitive counteraction of the above listed effects and Kerr effect, diffraction and dispersion. The theoretical models used for consistent description of laser-plasma interaction during femtosecond laser pulse propagation are derived and discussed. It turns out that the strongly nonlinear effects such self-focusing followed by the pulse splitting are essential. These phenomena feature extremely complex dynamics of both the electromagnetic field and plasma density with different spatio-temporal structures evolving at the same time. Some numerical approaches capable to handle all these complications are also discussed. ©2006 American Institute of Physics

Modelling manufacturing planning and control systems:the application of object-oriented principles and discrete-event simulation

Manufacturing planning and control systems are fundamental to the successful operations of a manufacturing organisation. 10 order to improve their business performance, significant investment is made by companies into planning and control systems; however, not all companies realise the benefits sought Many companies continue to suffer from high levels of inventory, shortages, obsolete parts, poor resource utilisation and poor delivery performance. This thesis argues that the fit between the planning and control system and the manufacturing organisation is a crucial element of success. The design of appropriate control systems is, therefore, important. The different approaches to the design of manufacturing planning and control systems are investigated. It is concluded that there is no provision within these design methodologies to properly assess the impact of a proposed design on the manufacturing facility. Consequently, an understanding of how a new (or modified) planning and control system will perform in the context of the complete manufacturing system is unlikely to be gained until after the system has been implemented and is running. There are many modelling techniques available, however discrete-event simulation is unique in its ability to model the complex dynamics inherent in manufacturing systems, of which the planning and control system is an integral component. The existing application of simulation to manufacturing control system issues is limited: although operational issues are addressed, application to the more fundamental design of control systems is rarely, if at all, considered. The lack of a suitable simulation-based modelling tool does not help matters. The requirements of a simulation tool capable of modelling a host of different planning and control systems is presented. It is argued that only through the application of object-oriented principles can these extensive requirements be achieved. This thesis reports on the development of an extensible class library called WBS/Control, which is based on object-oriented principles and discrete-event simulation. The functionality, both current and future, offered by WBS/Control means that different planning and control systems can be modelled: not only the more standard implementations but also hybrid systems and new designs. The flexibility implicit in the development of WBS/Control supports its application to design and operational issues. WBS/Control wholly integrates with an existing manufacturing simulator to provide a more complete modelling environment.

Role of plasma in femtosecond laser pulse propagation

This paper describes physics of nonlinear ultra-short laser pulse propagation affected by plasma created by the pulse itself. Major applications are also discussed. Nonlinear propagation of the femtosecond laser pulses in gaseous and solid transparent dielectric media is a fundamental physical phenomenon in a wide range of important applications such as laser lidars, laser micro-machining (ablation) and microfabrication etc. These applications require very high intensity of the laser field, typically 1013–1015 TW/cm2. Such high intensity leads to significant ionisation and creation of electron-ion or electron-hole plasma. The presence of plasma results into significant multiphoton and plasma absorption and plasma defocusing. Consequently, the propagation effects appear extremely complex and result from competitive counteraction of the above listed effects and Kerr effect, diffraction and dispersion. The theoretical models used for consistent description of laser-plasma interaction during femtosecond laser pulse propagation are derived and discussed. It turns out that the strongly nonlinear effects such self-focusing followed by the pulse splitting are essential. These phenomena feature extremely complex dynamics of both the electromagnetic field and plasma density with different spatio-temporal structures evolving at the same time. Some numerical approaches capable to handle all these complications are also discussed. ©2006 American Institute of Physics

Role of plasma in femtosecond laser pulse propagation

This paper describes physics of nonlinear ultra‐short laser pulse propagation affected by plasma created by the pulse itself. Major applications are also discussed. Nonlinear propagation of the femtosecond laser pulses in gaseous and solid transparent dielectric media is a fundamental physical phenomenon in a wide range of important applications such as laser lidars, laser micro‐machining (ablation) and microfabrication etc. These applications require very high intensity of the laser field, typically 1013–1015 TW/cm2. Such high intensity leads to significant ionisation and creation of electron‐ion or electron‐hole plasma. The presence of plasma results into significant multiphoton and plasma absorption and plasma defocusing. Consequently, the propagation effects appear extremely complex and result from competitive counteraction of the above listed effects and Kerr effect, diffraction and dispersion. The theoretical models used for consistent description of laser‐plasma interaction during femtosecond laser pulse propagation are derived and discussed. It turns out that the strongly nonlinear effects such self‐focusing followed by the pulse splitting are essential. These phenomena feature extremely complex dynamics of both the electromagnetic field and plasma density with different spatio‐temporal structures evolving at the same time. Some numerical approaches capable to handle all these complications are also discussed.

Analytical model for active metamaterials with quantum ingredients

We present an analytical model for describing complex dynamics of a hybrid system consisting of resonantly coupled classical resonator and quantum structures. Classical resonators in our model correspond to plasmonic metamaterials of various geometries, as well as other types of nano- and microstructure, the optical responses of which can be described classically. Quantum resonators are represented by atoms or molecules, or their aggregates (for example, quantum dots, carbon nanotubes, dye molecules, polymer or bio-molecules etc), which can be accurately modelled only with the use of the quantum mechanical approach. Our model is based on the set of equations that combines well established density matrix formalism appropriate for quantum systems, coupled with harmonic-oscillator equations ideal for modelling sub-wavelength plasmonic and optical resonators. As a particular example of application of our model, we show that the saturation nonlinearity of carbon nanotubes increases multifold in the resonantly enhanced near field of a metamaterial. In the framework of our model, we discuss the effect of inhomogeneity of the carbon-nanotube layer (bandgap value distribution) on the nonlinearity enhancement. © 2012 IOP Publishing Ltd.

On-off and multistate intermittencies in cascaded random distributed feedback fibre laser

A range of physical and engineering systems exhibit an irregular complex dynamics featuring alternation of quiet and burst time intervals called the intermittency. The intermittent dynamics most popular in laser science is the on-off intermittency [1]. The on-off intermittency can be understood as a conversion of the noise in a system close to an instability threshold into effective time-dependent fluctuations which result in the alternation of stable and unstable periods. The on-off intermittency has been recently demonstrated in semiconductor, Erbium doped and Raman lasers [2-5]. Recently demonstrated random distributed feedback (random DFB) fiber laser has an irregular dynamics near the generation threshold [6,7]. Here we show the intermittency in the cascaded random DFB fiber laser. We study intensity fluctuations in a random DFB fiber laser based on nitrogen doped fiber. The laser generates first and second Stokes components 1120 nm and 1180 nm respectively under an appropriate pumping. We study the intermittency in the radiation of the second Stokes wave. The typical time trace near the generation threshold of the second Stokes wave (Pth) is shown at Fig. 1a. From the number of long enough time-traces we calculate statistical distribution between major spikes in time dynamics, Fig. 1b. To eliminate contribution of high frequency components of spikes we use a low pass filter along with the reference value of the output power. Experimental data is fitted by power law, ~(P-Pth)y, where is a mean time between pikes. There are two different intermittency regimes. Just above Pth, the mean time is approximated by the -3/2 power law. The -3/2 power law is typical to the on-off intermittency with hopping between two states (first and second Stokes waves in our case) [7]. At higher power, the mean time is approximated by -4 power law, that indicates a change in intermittency type to multistate. Multistable dynamics is observed in erbium-doped fiber lasers [8]. The origin of multiples states in our system could be probably connected with polarization hopping or other reasons and should be further investigated. We have presented a first experimental statistical characterisation of the on-off and multistate intermittencies that occur in the generation of the second Stokes wave in nitrogen doped random DFB fiber laser. References [1] H. Fujisaka and T. Yamada, “A New Intermittency in Coupled Dynamical Systems,” Prog. Theor. Phys. 74, 918 (1985). [2] S. Osborne, A. Amann, D. Bitauld, and S. O’Brien, “On-off intermittency in an optically injected semiconductor laser,” Phys. Rev. E 85, 056204 (2012). [3] S. Sergeyev, K. O'Mahoney, S. Popov, and A. T. Friberg, “Coherence and anticoherence resonance in high-concentration erbium-doped fiber laser,” Opt. Lett. 35, 3736 (2010). [4] A.E. El-Taher, S.V. Sergeyev, E.G. Turitsyna, P. Harper, and S. K. Turitsyn, “Intermittent Self-Pulsing in a Fiber Raman Laser”, In proc. Conf. Nonlin. Photon., paper ID 1367139, Colorado Springs, USA, 2012 [5] S.K. Turitsyn, S.A. Babin, A.E. El-Taher, P. Harper, D.V. Churkin, S.I. Kablukov, J.D. Ania-Castañón, V. Karalekas, and E.V. Podivilov, “Random distributed feedback fibre laser”, Nat. Photon..4, 231 (2010). [6] I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, "Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm," Opt. Express 19, 18486 (2011). [7] W. Feller, An introduction to probability theory and its applications, Vol. 1, 3rd ed. (Wiley, New-York, 1968). [8] G. Huerta-Cuellar, A.N. Pisarchik, and Y.O. Barmenkov, “Experimental characterization of hopping dynamics in a multistable fiber laser,” Phys. Rev. E 78, 035202(R) (2008).

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.

T-cell epitope prediction and immune complex simulation using molecular dynamics:state of the art and persisting challenges

Atomistic Molecular Dynamics provides powerful and flexible tools for the prediction and analysis of molecular and macromolecular systems. Specifically, it provides a means by which we can measure theoretically that which cannot be measured experimentally: the dynamic time-evolution of complex systems comprising atoms and molecules. It is particularly suitable for the simulation and analysis of the otherwise inaccessible details of MHC-peptide interaction and, on a larger scale, the simulation of the immune synapse. Progress has been relatively tentative yet the emergence of truly high-performance computing and the development of coarse-grained simulation now offers us the hope of accurately predicting thermodynamic parameters and of simulating not merely a handful of proteins but larger, longer simulations comprising thousands of protein molecules and the cellular scale structures they form. We exemplify this within the context of immunoinformatics.

Toward an atomistic understanding of the immune synapse:large-scale molecular dynamics simulation of a membrane-embedded TCR-pMHC-CD4 complex

T-cell activation requires interaction of T-cell receptors (TCR) with peptide epitopes bound by major histocompatibility complex (MHC) proteins. This interaction occurs at a special cell-cell junction known as the immune or immunological synapse. Fluorescence microscopy has shown that the interplay among one agonist peptide-MHC (pMHC), one TCR and one CD4 provides the minimum complexity needed to trigger transient calcium signalling. We describe a computational approach to the study of the immune synapse. Using molecular dynamics simulation, we report here on a study of the smallest viable model, a TCR-pMHC-CD4 complex in a membrane environment. The computed structural and thermodynamic properties are in fair agreement with experiment. A number of biomolecules participate in the formation of the immunological synapse. Multi-scale molecular dynamics simulations may be the best opportunity we have to reach a full understanding of this remarkable supra-macromolecular event at a cell-cell junction.

The dynamics of a genetic algorithm under stabilizing selection

A formalism recently introduced by Prugel-Bennett and Shapiro uses the methods of statistical mechanics to model the dynamics of genetic algorithms. To be of more general interest than the test cases they consider. In this paper, the technique is applied to the subset sum problem, which is a combinatorial optimization problem with a strongly non-linear energy (fitness) function and many local minima under single spin flip dynamics. It is a problem which exhibits an interesting dynamics, reminiscent of stabilizing selection in population biology. The dynamics are solved under certain simplifying assumptions and are reduced to a set of difference equations for a small number of relevant quantities. The quantities used are the population's cumulants, which describe its shape, and the mean correlation within the population, which measures the microscopic similarity of population members. Including the mean correlation allows a better description of the population than the cumulants alone would provide and represents a new and important extension of the technique. The formalism includes finite population effects and describes problems of realistic size. The theory is shown to agree closely to simulations of a real genetic algorithm and the mean best energy is accurately predicted.

The dynamics of power and resistance in police interview discourse

This is a study of police interviewing using an integrated approach, drawing on CA, CDA and pragmatics. The study focuses on the balance of power and control, finding that in particular the institutional status of the participants, the discursive roles assigned to them by the context, and their relative knowledge, are significant factors affecting the dynamics of the discourse. Four discursive features are identified as particularly significant, and a detailed analysis of the complex interplay of these features shows that power and control are constantly under negotiation, and are always open to challenge and resistance. Further it is shown that discursive dominance is not necessarily advantageous to participants, due to the specific goals and purposes of the police interview context. A wider consideration of the context illustrates the contribution that linguistics can make to the use of police interview data as evidence in the UK criminal justice system.

Structure, dynamics, and energetics of siRNA-cationic vector complexation:a molecular dynamics study

The design and synthesis of safe and efficient nonviral vectors for gene delivery has attracted significant attention in recent years. Previous experiments have revealed that the charge density of a polycation (the carrier) plays a crucial role in complexation and the release of the gene from the complex in the cytosol. In this work, we adopt an atomistic molecular dynamics simulation approach to study the complexation of short strand duplex RNA with six cationic carrier systems of varying charge and surface topology. The simulations reveal detailed molecular-level pictures of the structures and dynamics of the RNA-polycation complexes. Estimates for the binding free energy indicate that electrostatic contributions are dominant followed by van der Waals interactions. The binding free energy between the 8(+)polymers and the RNA is found to be larger than that of the 4(+)polymers, in general agreement with previously published data. Because reliable binding free energies provide an effective index of the ability of the polycationic carrier to bind the nucleic acid and also carry implications for the process of gene release within the cytosol, these novel simulations have the potential to provide us with a much better understanding of key mechanistic aspects of gene-polycation complexation and thereby advance the rational design of nonviral gene delivery systems.

Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity.

Structure and dynamics of multiple cationic vectors-siRNA complexation by all-atomic molecular dynamics simulations

Understanding the molecular mechanism of gene condensation is a key component to rationalizing gene delivery phenomena, including functional properties such as the stability of the gene-vector complex and the intracellular release of the gene. In this work, we adopt an atomistic molecular dynamics simulation approach to study the complexation of short strand duplex RNA with four cationic carrier systems of varying charge and surface topology at different charge ratios. At lower charge ratios, polymers bind quite effectively to siRNA, while at high charge ratios, the complexes are saturated and there are free polymers that are unable to associate with RNA. We also observed reduced fluctuations in RNA structures when complexed with multiple polymers in solution as compared to both free siRNA in water and the single polymer complexes. These novel simulations provide a much better understanding of key mechanistic aspects of gene-polycation complexation and thereby advance progress toward rational design of nonviral gene delivery systems.