Different Shaker family alpha-subunit genes generate distinct voltage-dependent K+ currents when expressed in heterologous expression systems. Thus it generally is believed that diverse neuronal K+ current phenotypes arise, in part, from differences in Shaker family gene expression among neurons. It is difficult to evaluate the extent to which differential Shaker family gene expression contributes to endogenous K+ current diversity, because the specific Shaker family gene or genes responsible for a given K+ current are still unknown for nearly all adult neurons. In this paper we explore the role of differential Shaker family gene expression in creating transient K+ current (IA) diversity in the 14-neuron pyloric network of the spiny lobster, Panulirus interruptus. We used two-electrode voltage clamp to characterize the somatic IA in each of the six different cell types of the pyloric network. The size, voltage-dependent properties, and kinetic properties of the somatic IA vary significantly among pyloric neurons such that the somatic IA is unique in each pyloric cell type. Comparing these currents with the IAs obtained from oocytes injected with Panulirus shaker and shal cRNA (lobster Ishaker and lobster Ishal, respectively) reveals that the pyloric cell IAs more closely resemble lobster Ishal than lobster Ishaker. Using a novel, quantitative single-cell-reverse transcription-PCR method to count the number of shal transcripts in individual identified pyloric neurons, we found that the size of the somatic IA varies linearly with the number of endogenous shal transcripts. These data suggest that the shal gene contributes substantially to the peak somatic IA in all neurons of the pyloric network.

Necessary and sufficient conditions for impulsive controllability of linear dynamical systems are obtained, which provide a novel approach to problems that are basically defined by continuous dynamical systems, but on which only discrete-time actions are exercised. As an application, impulsive maneuvering of a spacecraft is discussed.

This paper discusses the mathematical analysis of a codimension two bifurcation determined by the coincidence of a subcritical Hopf bifurcation with a homoclinic orbit of the Hopf equilibrium. Our work is motivated by our previous analysis of a Hodgkin-Huxley neuron model which possesses a subcritical Hopf bifurcation [5]. In this model, the Hopf bifurcation has the additional feature that trajectories beginning near the unstable manifold of the equilibrium point return to pass through a small neighborhood of the equilibrium, that is, the Hopf bifurcation appears to be close to a homoclinic bifurcation as well. This model of the lateral pyloric (LP) cell of the lobster stomatogastric ganglion was analyzed for its ability to explain the phenomenon of spike-frequency adaptation [5], in which the time intervals between successive spikes grow longer until the cell eventually becomes quiescent. The presence of a subcritical Hopf bifurcation in this model was one identified mechanism for oscillatory trajectories to increase their period and finally collapse to a non-oscillatory solution. The analysis presented here explains the apparent proximity of homoclinic and Hopf bifurcations. We also develop an asymptotic theory for the scaling properties of the interspike intervals in a singularly perturbed system undergoing subcritical Hopf bifurcation that may be close to a codimension two subcritical Hopf-homclinic bifurcation.

Abstract-This paper presents a simple yet efficient dynamic programming (DP) shortest path algorithm for real-time collision-free robot path planning applicable to situations where targets and barriers are permitted to move. The algorithm works in real time and requires no prior knowledge of target or barrier movements. In the case that the barriers are stationary, this paper proves that this algorithm always results in the robot catching the target provided it moves at greater speed than the target, and the dynamic system update frequency is sufficiently large. Like most robot path planning approaches, the environment is represented by a topologically organized map. Each grid point on the map has only local connections to its neighboring grid points from which it receives information in real-time. The information stored at each point is a current estimate of the distance to the nearest target and the neighbor from which this distance was determined. Updating the distance estimate at each grid point is done using only information gathered from the point's neighbours, that is, each point can be considered an independent processor, and the order in which grid points are updated is not determined based on global knowledge of the current distances at each point or the previous history of each point. The robot path is determined in real-time completely from information at the robot's current grid-point location. The computational effort to update each point is minimal allowing for rapid propagation of the distance information outward along the grid from target locations. In the static situation, where both targets and barriers do not move, this algorithm is a DP solution to the shortest path problem, but is restricted by lack of global knowledge. In this case, this paper proves that the dynamic system converges in a small number of iterations to a state where the minimal distance to a target is recorded at each grid point and shows that this robot path-planning algorithm can be made to always choose an optimal path. The effectiveness of the algorithm is demonstrated through a number of simulations.

Abstract. The eigenvalue problem for a certain tridiagonal matrix with complex coefficients is considered. The eigenvalues and eigenvectors are shown to be expressible in terms of solutions of a certain scalar trigonometric equation. Explicit solutions of this equation are obtained for several special cases, and further analysis of this equation in several other cases provides information about the distribution of eigenvalues.

We consider whole-cell voltage-clamp data of isolated currents characterized by the Hodgkin-Huxley paradigm. We examine the errors associated with the typical parameter estimation method for these data and show them to be unsatisfactorally large especially if the time constants of activation and inactivation are not sufficiently separated. The size of these errors is due to the fact that the steady-state and kinetic properties of the current are estimated disjointly. We present an improved parameter estimation method that utilizes all of the information in the voltage-clamp conductance data to estimate steady-state and kinetic properties simultaneously and illustrate its success compared to the standard method using simulated data and data from P. interruptus shal channels expressed in oocytes.

Abstract-An efficient grid-based distance-propagating dynamic system is proposed for real-time robot path planning in dynamic environments which incorporates safety margins around obstacles using local penalty functions. The path through which the robot travels minimizes the sum of the current known distance to a target and the cumulative local penalty functions along the path. The algorithm is similar to D * but does not maintain a sorted queue of points to update. The resulting gain in computational speed is offset by the need to update all points in turn. Consequently, in situations where many obstacles and targets are moving at substantial distances from the current robot location, this algorithm is more efficient than D * . The properties of the algorithm are demonstrated through a number of simulations. A sufficient condition for capture of a target is provided.

Influenza A virus (IAV) in swine is a pathogen that causes a threat to the health as well as to the production of swine. Moreover, swine can spread this virus to other species including humans. The virus persists in different types of swine farms as evident in a number of studies. The core objectives of this study are (i) to analyze the dynamics of influenza infection of a farrow-to-finish swine farm, (ii) to explore the reinfection at the farm level, and finally (iii) to examine the effectiveness of two control strategies: vaccination and reduction of indirect contact. The analyses are conducted using a deterministic Susceptible-Exposed-Infectious-Recovered (SEIR) model. Simulation results show that the disease is maintained in gilts and piglets because of new susceptible pigs entering the population on a weekly basis. A sensitivity analysis shows that the results are not sensitive to variation in the parameters. The results of the reinfection simulation indicate that the virus persists in the entire farm. The control strategies studied in this work are not successful in eliminating the virus within the farm.