Convergence analysis of a discrete-time single-unit gradient ICA algorithm

We revisit the one-unit gradient ICA algorithm derived from the kurtosis function. By carefully studying properties of the stationary points of the discrete-time one-unit gradient ICA algorithm, with suitable condition on the learning rate, convergence can be proved. The condition on the learning rate helps alleviate the guesswork that accompanies the problem of choosing suitable learning rate in practical computation. These results may be useful to extract independent source signals on-line.

Neuromuscular-skeletal constraints on the acquisition of skill in a discrete torque production task

The organisation of the human neuromuscular-skeletal system allows an extremely wide variety of actions to be performed, often with great dexterity. Adaptations associated with skill acquisition occur at all levels of the neuromuscular-skeletal system although all neural adaptations are inevitably constrained by the organisation of the actuating apparatus (muscles and bones). We quantified the extent to which skill acquisition in an isometric task set is influenced by the mechanical properties of the muscles used to produce the required actions. Initial performance was greatly dependent upon the specific combination of torques required in each variant of the experimental task. Five consecutive days of practice improved the performance to a similar degree across eight actions despite differences in the torques required about the elbow and forearm. The proportional improvement in performance was also similar when the actions were performed at either 20 or 40% of participants' maximum voluntary torque capacity. The skill acquired during practice was successfully extrapolated to variants of the task requiring more torque than that required during practice. We conclude that while the extent to which skill can be acquired in isometric actions is independent of the specific combination of joint torques required for target acquisition, the nature of the kinetic adaptations leading to the performance improvement in isometric actions is influenced by the neural and mechanical properties of the actuating muscles.

Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Wideband beam and steering using a rectangular array of planar monopoles

This article presents the design of a wideband rectangular array of planar monopoles, which is able to steer its beam and nulls over a wide frequency band using real-valued weights. These weights can be realized in practice by amplifiers or attenuators leading to a low cost development of a wideband array antenna with beam and null steering capability. The weights are determined by applying an inverse discrete Fourier transform to an assumed radiation pattern. This wideband beam and null forming concept is verified by full electromagnetic simulations which take into account mutual coupling effects between the array elements.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

Full-field Fourier-domain optical coherence tomography

Full-field Fourier-domain optical coherence tomography (3F-OCT) is a full-field version of spectraldomain/swept-source optical coherence tomography. A set of two-dimensional Fourier holograms is recorded at discrete wavenumbers spanning the swept-source tuning range. The resultant three-dimensional data cube contains comprehensive information on the three-dimensional morphological layout of the sample that can be reconstructed in software via three-dimensional discrete Fourier-transform. This method of recording of the OCT signal confers signal-to-noise ratio improvement in comparison with "flying-spot" time-domain OCT. The spatial resolution of the 3F-OCT reconstructed image, however, is degraded due to the presence of a phase cross-term, whose origin and effects are addressed in this paper. We present theoretical and experimental study of imaging performance of 3F-OCT, with particular emphasis on elimination of the deleterious effects of the phase cross-term.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.