Measuring complexity through average symmetry

This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different) complexity to either deterministic or random homogeneous densities and higher complexity to the intermediate cases. This new measure is easily computable, breaks the coarse graining paradigm and can be straightforwardly generalized, including to continuous cases and general networks. By applying this measure to a series of objects, it is shown that it can be consistently used for both small scale structures with exact symmetry breaking and large scale patterns, for which, differently from similar measures, it consistently discriminates between repetitive patterns, random configurations and self-similar structures

The role of pinning and instability in a class of non-equilibrium growth models

We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following standard coarse graining procedures, it is shown that in the large time, long distance limit, the continuum model predicts a curvature independent KPZ phase, thereby suppressing all explicit effects of curvature and local pinning in the system, in the "perturbative" limit. A direct numerical integration of this growth equation, in 1+1 dimensions, supports this observation below a critical parametric range, above which generic instabilities, in the form of isolated pillared structures lead to deviations from standard scaling behaviour. Possibilities of controlling this instability by introducing statistically "irrelevant" (in the sense of renormalisation groups) higher ordered nonlinearities have also been discussed.

Integration of the Manakov-PMD Equation with Precomputed M(w) Matrices for PMD Simulation

A novel direct integration technique of the Manakov-PMD equation for the simulation of polarisation mode dispersion (PMD) in optical communication systems is demonstrated and shown to be numerically as efficient as the commonly used coarse-step method. The main advantage of using a direct integration of the Manakov-PMD equation over the coarse-step method is a higher accuracy of the PMD model. The new algorithm uses precomputed M(w) matrices to increase the computational speed compared to a full integration without loss of accuracy. The simulation results for the probability distribution function (PDF) of the differential group delay (DGD) and the autocorrelation function (ACF) of the polarisation dispersion vector for varying numbers of precomputed M(w) matrices are compared to analytical models and results from the coarse-step method. It is shown that the coarse-step method achieves a significantly inferior reproduction of the statistical properties of PMD in optical fibres compared to a direct integration of the Manakov-PMD equation.

Polarisation mode dispersion correlations with the coarse-step method

Having a fixed differential-group delay (DGD) term b′ in the coarse-step method results in a repetitive pattern in the autocorrelation function (ACF). We solve this problem by inserting a varying DGD term at each integration step. Furthermore we compute the range of values needed for b′ and simulate the phenomenon of polarisation mode dispersion for different statistical distributions of b′. We examine systematically the modified coarse-step method compared to the analytical model, through our simulation results. © 2006 Elsevier B.V. All rights reserved.

Numerical implementation of the coarse step method with a varying differential group delay

The effect of having a fixed differential group delay term in the coarse step method results in a periodic pattern in the inserting a varying DGD term at each integration step, according to a Gaussian distribution. Simulation results are given to illustrate the phenomenon and provide some evidence about its statistical nature.

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.

Modelling and simulation strategies for the electric systems of large passenger aircraft

The simulation of a power system such as the More Electric Aircraft is a complex problem. There are conflicting requirements of the simulation, for example in order to reduce simulation run-times, power ratings that need to be established over long periods of the flight can be calculated using a fairly coarse model, whereas power quality is established over relatively short periods with a detailed model. An important issue is to establish the requirements of the simulation work at an early stage. This paper describes the modelling and simulation strategy adopted for the UK TIMES project, which is looking into the optimisation of the More Electric Aircraft from a system level. Essentially four main requirements of the simulation work have been identified, resulting in four different types of simulation. Each of the simulations is described along with preliminary models and results.

Numerical implementation of the coarse step method with a varying differential group delay

The effect of having a fixed differential-group delay term in the coarse-step method results in a periodic pattern in the autocorrelation function. We solve this problem by inserting a varying DGD term at each integration step, according to a Gaussian distribution. Simulation results are given to illustrate the phenomenon and provide some evidence, about its statistical nature.