Estimation of Hidden Markov Models parameters using differential evolution

Hidden Markov Models (HMMs) have been successfully applied to different modelling and classification problems from different areas over the recent years. An important step in using HMMs is the initialisation of the parameters of the model as the subsequent learning of HMM’s parameters will be dependent on these values. This initialisation should take into account the knowledge about the addressed problem and also optimisation techniques to estimate the best initial parameters given a cost function, and consequently, to estimate the best log-likelihood. This paper proposes the initialisation of Hidden Markov Models parameters using the optimisation algorithm Differential Evolution with the aim to obtain the best log-likelihood.

Exploration vs exploitation in differential evolution

Differential Evolution (DE) is a tool for efficient optimisation, and it belongs to the class of evolutionary algorithms, which include Evolution Strategies and Genetic Algorithms. DE algorithms work well when the population covers the entire search space, and they have shown to be effective on a large range of classical optimisation problems. However, an undesirable behaviour was detected when all the members of the population are in a basin of attraction of a local optimum (local minimum or local maximum), because in this situation the population cannot escape from it. This paper proposes a modification of the standard mechanisms in DE algorithm in order to change the exploration vs. exploitation balance to improve its behaviour.

Femtosecond pulse shaping using differential evolutionary algorithm and wavelet operators

Evolutionary meta-algorithms for pulse shaping of broadband femtosecond duration laser pulses are proposed. The genetic algorithm searching the evolutionary landscape for desired pulse shapes consists of a population of waveforms (genes), each made from two concatenated vectors, specifying phases and magnitudes, respectively, over a range of frequencies. Frequency domain operators such as mutation, two-point crossover average crossover, polynomial phase mutation, creep and three-point smoothing as well as a time-domain crossover are combined to produce fitter offsprings at each iteration step. The algorithm applies roulette wheel selection; elitists and linear fitness scaling to the gene population. A differential evolution (DE) operator that provides a source of directed mutation and new wavelet operators are proposed. Using properly tuned parameters for DE, the meta-algorithm is used to solve a waveform matching problem. Tuning allows either a greedy directed search near the best known solution or a robust search across the entire parameter space.

Search space pruning and global optimization of multiple gravity assist trajectories with deep space manoeuvres

This paper deals with the design of optimal multiple gravity assist trajectories with deep space manoeuvres. A pruning method which considers the sequential nature of the problem is presented. The method locates feasible vectors using local optimization and applies a clustering algorithm to find reduced bounding boxes which can be used in a subsequent optimization step. Since multiple local minima remain within the pruned search space, the use of a global optimization method, such as Differential Evolution, is suggested for finding solutions which are likely to be close to the global optimum. Two case studies are presented.

Towards the automatic reconstruction of dendritic trees using particle filters

The 3D reconstruction of a Golgi-stained dendritic tree from a serial stack of images captured with a transmitted light bright-field microscope is investigated. Modifications to the bootstrap filter are discussed such that the tree structure may be estimated recursively as a series of connected segments. The tracking performance of the bootstrap particle filter is compared against Differential Evolution, an evolutionary global optimisation method, both in terms of robustness and accuracy. It is found that the particle filtering approach is significantly more robust and accurate for the data considered.

Prospects for bio-molecular control using femtosecond transients parametrised in the wavelet domain [poster]

We discuss the parametrisation of am-plitude and phase genes corre-sponding to space encoded femto-second transients in the wavelet domain. Differential evolution is used to improve the speed of con-vergence of the genetic algorithm. We discuss prospects of bio-molecular control using such methodology.

Solving surface structures from normal incidence X-ray standing wave data

A program is provided to determine structural parameters of atoms in or adsorbed on surfaces by refinement of atomistic models towards experimentally determined data generated by the normal incidence X-ray standing wave (NIXSW) technique. The method employs a combination of Differential Evolution Genetic Algorithms and Steepest Descent Line Minimisations to provide a fast, reliable and user friendly tool for experimentalists to interpret complex multidimensional NIXSW data sets.

Single tap identification for fast BCI control

One of the major aims of BCI research is devoted to achieving faster and more efficient control of external devices. The identification of individual tap events in a motor imagery BCI is therefore a desirable goal. EEG is recorded from subjects performing and imagining finger taps with their left and right hands. A Differential Evolution based feature selection wrapper is used in order to identify optimal features in the spatial and frequency domains for tap identification. Channel-frequency band combinations are found which allow differentiation of tap vs. no-tap control conditions for executed and imagined taps. Left vs. right hand taps may also be differentiated with features found in this manner. A sliding time window is then used to accurately identify individual taps in the executed tap and imagined tap conditions. Highly statistically significant classification accuracies are achieved with time windows of 0.5 s and more allowing taps to be identified on a single trial basis.

Decomposition of surface electromyographic signal using Hidden Markov Model

The detection of physiological signals from the motor system (electromyographic signals) is being utilized in the practice clinic to guide the therapist in a more precise and accurate diagnosis of motor disorders. In this context, the process of decomposition of EMG (electromyographic) signals that includes the identification and classification of MUAP (Motor Unit Action Potential) of a EMG signal, is very important to help the therapist in the evaluation of motor disorders. The EMG decomposition is a complex task due to EMG features depend on the electrode type (needle or surface), its placement related to the muscle, the contraction level and the health of the Neuromuscular System. To date, the majority of researches on EMG decomposition utilize EMG signals acquired by needle electrodes, due to their advantages in processing this type of signal. However, relatively few researches have been conducted using surface EMG signals. Thus, this article aims to contribute to the clinical practice by presenting a technique that permit the decomposition of surface EMG signal via the use of Hidden Markov Models. This process is supported by the use of differential evolution and spectral clustering techniques. The developed system presented coherent results in: (1) identification of the number of Motor Units actives in the EMG signal; (2) presentation of the morphological patterns of MUAPs in the EMG signal; (3) identification of the firing sequence of the Motor Units. The model proposed in this work is an advance in the research area of decomposition of surface EMG signals.

Changes in in vitro susceptibility of influenza A H3N2 viruses to a neuraminidase inhibitor drug during evolution in the human host

Objectives: Influenza A H3N2 viruses isolated recently have characteristic receptor binding properties that may decrease susceptibility to neuraminidase inhibitor drugs. A panel of clinical isolates and recombinant viruses generated by reverse genetics were characterized and tested for susceptibility to zanamivir. Methods: Plaque reduction assays and neuraminidase enzyme inhibition assays were used to assess susceptibility to zanamivir. Receptor binding properties of the viruses were characterized by differential agglutination of red blood cells (RBCs) from different species. Sequence analysis of the haemagglutinin (HA) and neuraminidase (NA) genes was carried out. Results: Characterization of a panel of H3N2 clinical isolates from 1968 to 2000 showed a gradual decrease in agglutination of chicken and guinea pig RBCs over time, although all isolates could agglutinate turkey RBCs equally. Sequence analysis of the HA and NA genes identified mutations in conserved residues of the HA1 receptor binding site, in particular Leu-226 --> Ile-226/Val-226, and modification of potential glycosylation site motifs. This may be indicative of changes in virus binding to sialic acid (SA) receptors in recent years. Although recent isolates had reduced susceptibility to zanamivir in MDCK cell based plaque reduction assays, no difference was found in an NA enzyme-inhibition assay. Assays with recombinant isogenic viruses showed that the recent HA, but not the NA, conferred reduced susceptibility to zanamivir. Conclusion: This study demonstrates that recent clinical isolates of influenza A H3N2 virus no longer agglutinate chicken RBCs, but despite significant receptor binding changes as a result of changes in HA, there was little variation in sensitivity of the NA to zanamivir.

Differential recognition of Staphylococcus aureus quorum-sensing signals depends on both extracellular loops 1 and 2 of the transmembrane sensor AgrC.

Virulence in Staphylococcus aureus is regulated via agr-dependent quorum sensing in which an autoinducing peptide (AIP) activates AgrC, a histidine protein kinase. AIPs are usually thiolactones containing seven to nine amino acid residues in which the thiol of the central cysteine is linked to the alpha-carboxyl of the C-terminal amino acid residue. The staphylococcal agr locus has diverged such that the AIPs of the four different S. aureus agr groups self-activate but cross-inhibit. Consequently, although the agr system is conserved among the staphylococci, it has undergone significant evolutionary divergence whereby to retain functionality, any changes in the AIP-encoding gene (agrD) that modifies AIP structure must be accompanied by corresponding changes in the AgrC receptor. Since AIP-1 and AIP-4 only differ by a single amino acid, we compared the transmembrane topology of AgrC1 and AgrC4 to identify amino acid residues involved in AIP recognition. As only two of the three predicted extracellular loops exhibited amino acid differences, site-specific mutagenesis was used to exchange the key AgrC1 and AgrC4 amino acid residues in each loop either singly or in combination. A novel lux-based agrP3 reporter gene fusion was constructed to evaluate the response of the mutated AgrC receptors. The data obtained revealed that while differential recognition of AIP-1 and AIP-4 depends primarily on three amino acid residues in loop 2, loop 1 is essential for receptor activation by the cognate AIP. Furthermore, a single mutation in the AgrC1 loop 2 resulted in conversion of (Ala5)AIP-1 from a potent antagonist to an activator, essentially resulting in the forced evolution of a new AIP group. Taken together, our data indicate that loop 2 constitutes the predicted hydrophobic pocket that binds the AIP thiolactone ring while the exocyclic amino acid tail interacts with loop 1 to facilitate receptor activation.

The evolution of the sun’s open magnetic flux: II. full solar cycle simulations

In this paper the origin and evolution of the Sun’s open magnetic flux is considered by conducting magnetic flux transport simulations over many solar cycles. The simulations include the effects of differential rotation, meridional flow and supergranular diffusion on the radial magnetic field at the surface of the Sun as new magnetic bipoles emerge and are transported poleward. In each cycle the emergence of roughly 2100 bipoles is considered. The net open flux produced by the surface distribution is calculated by constructing potential coronal fields with a source surface from the surface distribution at regular intervals. In the simulations the net open magnetic flux closely follows the total dipole component at the source surface and evolves independently from the surface flux. The behaviour of the open flux is highly dependent on meridional flow and many observed features are reproduced by the model. However, when meridional flow is present at observed values the maximum value of the open flux occurs at cycle minimum when the polar caps it helps produce are the strongest. This is inconsistent with observations by Lockwood, Stamper and Wild (1999) and Wang, Sheeley, and Lean (2000) who find the open flux peaking 1–2 years after cycle maximum. Only in unrealistic simulations where meridional flow is much smaller than diffusion does a maximum in open flux consistent with observations occur. It is therefore deduced that there is no realistic parameter range of the flux transport variables that can produce the correct magnitude variation in open flux under the present approximations. As a result the present standard model does not contain the correct physics to describe the evolution of the Sun’s open magnetic flux over an entire solar cycle. Future possible improvements in modeling are suggested.

The evolution of the Sun's open magnetic flux: I. a single bipole

In this paper the origin and evolution of the Sun’s open magnetic flux are considered for single magnetic bipoles as they are transported across the Sun. The effects of magnetic flux transport on the radial field at the surface of the Sun are modeled numerically by developing earlier work by Wang, Sheeley, and Lean (2000). The paper considers how the initial tilt of the bipole axis (α) and its latitude of emergence affect the variation and magnitude of the surface and open magnetic flux. The amount of open magnetic flux is estimated by constructing potential coronal fields. It is found that the open flux may evolve independently from the surface field for certain ranges of the tilt angle. For a given tilt angle, the lower the latitude of emergence, the higher the magnitude of the surface and open flux at the end of the simulation. In addition, three types of behavior are found for the open flux depending on the initial tilt angle of the bipole axis. When the tilt is such that α ≥ 2◦ the open flux is independent of the surface flux and initially increases before decaying away. In contrast, for tilt angles in the range −16◦ < α < 2◦ the open flux follows the surface flux and continually decays. Finally, for α ≤ −16◦ the open flux first decays and then increases in magnitude towards a second maximum before decaying away. This behavior of the open flux can be explained in terms of two competing effects produced by differential rotation. Firstly, differential rotation may increase or decrease the open flux by rotating the centers of each polarity of the bipole at different rates when the axis has tilt. Secondly, it decreases the open flux by increasing the length of the polarity inversion line where flux cancellation occurs. The results suggest that, in order to reproduce a realistic model of the Sun’s open magnetic flux over a solar cycle, it is important to have accurate input data on the latitude of emergence of bipoles along with the variation of their tilt angles as the cycle progresses.

Evolution PDEs and augmented eigenfunctions. half line.

The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the unified transform introduced by Fokas in the 90's. On the other hand, it is known that many initial-boundary value problems can be solved via a classical transform pair, constructed via the spectral analysis of the associated spatial operator. For example, the Dirichlet problem for the heat equation can be solved by applying the Fourier sine transform pair. However, for many other initial-boundary value problems there is no suitable transform pair in the classical literature. Here we pose and answer two related questions: Given any well-posed initial-boundary value problem, does there exist a (non-classical) transform pair suitable for solving that problem? If so, can this transform pair be constructed via the spectral analysis of a differential operator? The answer to both of these questions is positive and given in terms of augmented eigenfunctions, a novel class of spectral functionals. These are eigenfunctions of a suitable differential operator in a certain generalised sense, they provide an effective spectral representation of the operator, and are associated with a transform pair suitable to solve the given initial-boundary value problem.