Adaptation is not required to explain the long-term response of axons to molecular gradients

It has been suggested that growth cones navigating through the developing nervous system might display adaptation, so that their response to gradient signals is conserved over wide variations in ligand concentration. Recently however, a new chemotaxis assay that allows the effect of gradient parameters on axonal trajectories to be finely varied has revealed a decline in gradient sensitivity on either side of an optimal concentration. We show that this behavior can be quantitatively reproduced with a computational model of axonal chemotaxis that does not employ explicit adaptation. Two crucial components of this model required to reproduce the observed sensitivity are spatial and temporal averaging. These can be interpreted as corresponding, respectively, to the spatial spread of signaling effects downstream from receptor binding, and to the finite time over which these signaling effects decay. For spatial averaging, the model predicts that an effective range of roughly one-third of the extent of the growth cone is optimal for detecting small gradient signals. For temporal decay, a timescale of about 3 minutes is required for the model to reproduce the experimentally observed sensitivity.

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

Entangled-state cycles from conditional quantum evolution

A system of cascaded qubits interacting via the one-way exchange of photons is studied. While for general operating conditions the system evolves to a superposition of Bell states (a dark state) in the long-time limit, under a particular resonance condition no steady state is reached within a finite time. We analyze the conditional quantum evolution (quantum trajectories) to characterize the asymptotic behavior under this resonance condition. A distinct bimodality is observed: for perfect qubit coupling, the system either evolves to a maximally entangled Bell state without emitting photons (the dark state) or executes a sustained entangled-state cycle-random switching between a pair of Bell states while emitting a continuous photon stream; for imperfect coupling, two entangled-state cycles coexist, between which a random selection is made from one quantum trajectory to another.

Dark periods and revivals of entanglement in a two-qubit system

In a recent paper Yu and Eberly [Phys. Rev. Lett. 93, 140404 (2004)] have shown that two initially entangled and afterward not interacting qubits can become completely disentangled in a finite time. We study transient entanglement between two qubits coupled collectively to a multimode vacuum field, assuming that the two-qubit system is initially prepared in an entangled state produced by the two-photon coherences, and find the unusual feature that the irreversible spontaneous decay can lead to a revival of the entanglement that has already been destroyed. The results show that this feature is independent of the coherent dipole-dipole interaction between the atoms but it depends critically on whether or not collective damping is present.

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.

An object-oriented designed finite-difference time-domain simulator for electromagnetic analysis and design in MRI - application to high field analyses

This paper presents a finite-difference time-domain (FDTD) simulator for electromagnetic analysis and design applications in MRI. It is intended to be a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The pro-ram has been constructed in an object-oriented framework. The design procedure is detailed and the numerical solver has been verified against analytical solutions for simple cases and also applied to various field calculation problems. In particular, the simulator is demonstrated for inverse RF coil design, optimized source profile generation, and parallel imaging in high-frequency situations. The examples show new developments enabled by the simulator and demonstrate that the proposed FDTD framework can be used to analyze large-scale computational electromagnetic problems in modern MRI engineering. (C) 2004 Elsevier Inc. All rights reserved.

Practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer, and Cirac [Phys. Rev. Lett. 88, 237902 (2002)] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.

Adsorption of Lennard-Jones fluids in carbon slit pores of a finite length. A computer simulation study

The adsorption of simple Lennard-Jones fluids in a carbon slit pore of finite length was studied with Canonical Ensemble (NVT) and Gibbs Ensemble Monte Carlo Simulations (GEMC). The Canonical Ensemble was a collection of cubic simulation boxes in which a finite pore resides, while the Gibbs Ensemble was that of the pore space of the finite pore. Argon was used as a model for Lennard-Jones fluids, while the adsorbent was modelled as a finite carbon slit pore whose two walls were composed of three graphene layers with carbon atoms arranged in a hexagonal pattern. The Lennard-Jones (LJ) 12-6 potential model was used to compute the interaction energy between two fluid particles, and also between a fluid particle and a carbon atom. Argon adsorption isotherms were obtained at 87.3 K for pore widths of 1.0, 1.5 and 2.0 nm using both Canonical and Gibbs Ensembles. These results were compared with isotherms obtained with corresponding infinite pores using Grand Canonical Ensembles. The effects of the number of cycles necessary to reach equilibrium, the initial allocation of particles, the displacement step and the simulation box size were particularly investigated in the Monte Carlo simulation with Canonical Ensembles. Of these parameters, the displacement step had the most significant effect on the performance of the Monte Carlo simulation. The simulation box size was also important, especially at low pressures at which the size must be sufficiently large to have a statistically acceptable number of particles in the bulk phase. Finally, it was found that the Canonical Ensemble and the Gibbs Ensemble both yielded the same isotherm (within statistical error); however, the computation time for GEMC was shorter than that for canonical ensemble simulation. However, the latter method described the proper interface between the reservoir and the adsorbed phase (and hence the meniscus).

Effective cell-centred time-domain Maxwell's equations numerical solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed. © 2004 Elsevier Inc. All rights reserved.

Analysis of cardiac ventricular wall motion based on a three-dimensional electromechanical biventricular model

This paper describes a biventricular model, which couples the electrical and mechanical properties of the heart, and computer simulations of ventricular wall motion and deformation by means of a biventricular model. In the constructed electromechanical model, the mechanical analysis was based on composite material theory and the finite-element method; the propagation of electrical excitation was simulated using an electrical heart model, and the resulting active forces were used to calculate ventricular wall motion. Regional deformation and Lagrangian strain tensors were calculated during the systole phase. Displacements, minimum principal strains and torsion angle were used to describe the motion of the two ventricles. The simulations showed that during the period of systole, (1) the right ventricular free wall moves towards the septum, and at the same time, the base and middle of the free wall move towards the apex, which reduces the volume of the right ventricle; the minimum principle strain (E3) is largest at the apex, then at the middle of the free wall and its direction is in the approximate direction of the epicardial muscle fibres; (2) the base and middle of the left ventricular free wall move towards the apex and the apex remains almost static; the torsion angle is largest at the apex; the minimum principle strain E3 is largest at the apex and its direction on the surface of the middle wall of the left ventricle is roughly in the fibre orientation. These results are in good accordance with results obtained from MR tagging images reported in the literature. This study suggests that such an electromechanical biventricular model has the potential to be used to assess the mechanical function of the two ventricles, and also could improve the accuracy ECG simulation when it is used in heart torso model-based body surface potential simulation studies.

Detecting finite bandwidth periodic signals in stationary noise using the signal coherence spectrum

All signals that appear to be periodic have some sort of variability from period to period regardless of how stable they appear to be in a data plot. A true sinusoidal time series is a deterministic function of time that never changes and thus has zero bandwidth around the sinusoid's frequency. A zero bandwidth is impossible in nature since all signals have some intrinsic variability over time. Deterministic sinusoids are used to model cycles as a mathematical convenience. Hinich [IEEE J. Oceanic Eng. 25 (2) (2000) 256-261] introduced a parametric statistical model, called the randomly modulated periodicity (RMP) that allows one to capture the intrinsic variability of a cycle. As with a deterministic periodic signal the RMP can have a number of harmonics. The likelihood ratio test for this model when the amplitudes and phases are known is given in [M.J. Hinich, Signal Processing 83 (2003) 1349-13521. A method for detecting a RMP whose amplitudes and phases are unknown random process plus a stationary noise process is addressed in this paper. The only assumption on the additive noise is that it has finite dependence and finite moments. Using simulations based on a simple RMP model we show a case where the new method can detect the signal when the signal is not detectable in a standard waterfall spectrograrn display. (c) 2005 Elsevier B.V. All rights reserved.

Motion analysis of right ventricular wall based on an electromechanical biventricular model

Based on our previously developed electrical heart model, an electromechanical biventricular model, which couples the electrical property and mechanical property of the heart, was constructed and the right ventricular wall motion and deformation was simulated using this model. The model was developed on the basis of composite material theory and finite element method. The excitation propagation was simulated by electrical heart model, and the resultant active forces were used to study the ventricular wall motion during systole. The simulation results show that: (1) The right ventricular free wall moves towards the septum, and at the same time, the base and middle of free wall move towards the apex, which reduce the volume of right ventricle; (2) The minimum principle strain (E3) is largest at the apex, then at the middle of free wall, and its direction is in the approximate direction of epicardial muscle fibers. These results are in good accordance with solutions obtained from MR tagging images. It suggests that such electromechanical biventricular model can be used to assess the mechanical function of two ventricles.