Jianzhong Su

Spontaneous and Evoked Glutamate Release Activates Two Populations of NMDA Receptors with Limited Overlap

In a synapse, spontaneous and action-potential-driven neurotransmitter release is assumed to activate the same set of postsynaptic receptors. Here, we tested this assumption using (+)-5-methyl-10,11-dihydro-5H-dibenzo [a,d] cyclohepten-5,10-imine maleate (MK-801), a well characterized use-dependent blocker of NMDA receptors. NMDA-receptor-mediated spontaneous miniature EPSCs (NMDA-mEPSCs) were substantially decreased by MK-801 within 2 min in a use-dependent manner. In contrast, MK-801 application at rest for 10 min did not significantly impair the subsequent NMDA-receptor-mediated evoked EPSCs (NMDA-eEPSCs). Brief stimulation in the presence of MK-801 significantly depressed evoked NMDA-eEPSCs but only mildly affected the spontaneous NMDA-mEPSCs detected on the same cell. Optical imaging of synaptic vesicle fusion showed that spontaneous and evoked release could occur at the same synapse albeit without correlation between their kinetics. In addition, modeling glutamate diffusion and NMDA receptor activation revealed that postsynaptic densities larger than ∼0.2 μm2 can accommodate two populations of NMDA receptors with nonoverlapping responsiveness. Collectively, these results support the premise that spontaneous and evoked neurotransmissions activate distinct sets of NMDA receptors and signal independently to the postsynaptic side.

ANALYSIS OF A CANARD MECHANISM BY WHICH EXCITATORY SYNAPTIC COUPLING CAN SYNCHRONIZE NEURONS AT LOW FIRING FREQUENCIES

A population of oscillatory Hodgkin--Huxley (HH) model neurons is shown numerically to exhibit a behavior in which the introduction of excitatory synaptic coupling synchronizes and dramatically slows firing. This effect contrasts with the standard theory that recurrent synaptic excitation promotes states of rapid, sustained activity, independent of intrinsic neuronal dynamics. The observed behavior is not due to simple depolarization block nor to standard elliptic bursting, although it is related to these phenomena. We analyze this effect using a reduced model for a single, self-coupled HH oscillator. The mechanism explained here involves an extreme form of delayed bifurcation in which the development of a vortex structure through interaction of fast and slow subsystems pins trajectories near a surface that consists of unstable equilibria of a certain reduced system, in a canard-like manner. Using this vortex structure, a new passage time calculation is used to approximate the interspike time interval. We...

Effects of noise on elliptic bursters

Elliptic bursting arises from fast–slow systems and involves recurrent alternation between active phases of large amplitude oscillations and silent phases of small amplitude oscillations. This paper is a geometric analysis of elliptic bursting with and without noise. We first prove the existence of elliptic bursting solutions for a class of fast–slow systems without noise by establishing an invariant region for the return map of the solutions. For noisy elliptic bursters, the bursting patterns depend on random variations associated with delayed bifurcations. We provide an exact formulation of the duration of delay and analyse its distribution. The duration of the delay, and consequently the durations of active and silent phases, is shown to be closely related to the logarithm of the amplitude of the noise. The treatment of noisy delayed bifurcation here is a general theory of delayed bifurcation valid for other systems involving delayed bifurcation as well and is a continuation of the rigorous Shishkova–Neishtadt theory on delayed bifurcation or delay of stability loss.

A globally convergent numerical method for an inverse elliptic problem of optical tomography

A new globally convergent numerical method is developed for an inverse problem for the elliptic equation with the unknown potential. The boundary data simulating measurements in optical tomography are generated by the running source. Global convergence analysis is presented along with numerical experiments.

Reconstruction method with data from a multiple-site continuous-wave source for three-dimensional optical tomography

A method is presented for reconstruction of the optical absorption coefficient from transmission near-infrared data with a cw source. As it is distinct from other available schemes such as optimization or Newtons iterative method, this method resolves the inverse problem by solving a boundary value problem for a Volterra-type integral-differential equation. It is demonstrated in numerical studies that this technique has a better than average stability with respect to the discrepancy between the initial guess and the actual unknown absorption coefficient. The method is particularly useful for reconstruction from a large data set obtained from a CCD camera. Several numerical reconstruction examples are presented.

A globally accelerated numerical method for optical tomography with continuous wave source

Abstract A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured as the data for the inverse problem. A rigorous convergence analysis shows that this method converges globally, provided that the so-called tail function is approximated well. This approximation is verified in numerical experiments, so as the global convergence. Applications to medical imaging, imaging of targets on battlefields and to electrical impedance tomography are discussed.

Numerical implementation of the convexification algorithm for an optical diffusion tomograph

A globally convergent (the so-called convexification) algorithm was previously developed for coefficient inverse problems (CIPs) with the time/frequency-dependent data. In this publication the convexification is extended to the case of a CIP for an elliptic equation with the data generated by the source running along a straight line. The data are incomplete, since they are given only at a part of the boundary. Applications to both electrical impedance and optical tomographies are feasible, which include, in particular, imaging of land mines and underground bunkers, as well as diffuse optical imaging of targets on battlefields through smogs and flames. However, our numerical setup is intended for medical applications to small animals. Numerical experiments in the 2D case are presented.

Three-Dimensional Modeling and Simulation of a Falling Electronic Device

This article focuses on a realistic mathematical model for multiple impacts of a rigid body to a viscoelastic ground and its comparison to theoretic results. The methodology is used to study impact on an electronic device. When an electronic device drops to the floor at an uneven level, the rapid successions of impact sequence are important for their shock response to internal structure of the devices. A three-dimensional, continuous contact, computational impact model has been developed to simulate a sequence of multiple impacts of a falling rigid body with the ground. The model simulates the impact procedure explicitly and thus is capable of providing detailed information regarding impact load, impact contact surface, and the status of the body during the impact. For the purposes of model verification, we demonstrate the numerical simulation of a falling rod problem, in which the numerical results are in good agreement with the analytic solutions based on discrete contact dynamics impact models. It is indicated by the numerical experiments that simultaneous impacts occurred to multiple locations of the body and that subsequent impacts might be larger than initial ones due to different angles of impact. The differential equation-based computational model is shown to be realistic and efficient in simulating impact sequence and laid a foundation for detailed finite element analysis of the interior impact response of an electronic device.

A direct method in Dacorogna-Moser's approach of grid generation problems

The deformation method of grid generation is further developed for general domains. By an initial mapping from the general domain to a sector of an annulus in Rn, the grid generation problem is solved explicitly. The resulting grid has prescribed cell sizes. The construction is valid for any dimension.

Modeling and simulation of multiple impacts of falling rigid bodies

When an electronic device drops at an inclination angle to the floor, the rapid successions of clattering sequence are important for their shock response to circuits, displays and disk drives. This article deals with both analytical and numerical analysis of multiple impacts. A three-dimensional computational dynamics code with a continuous contact impact model has been developed to simulate the multiple impacts of a falling rigid body with the ground. Results from the computational model as well as analytic analysis from a discrete contact impact model indicate that subsequent impacts might be larger than the initial impact in some situations. The differential equation based three-dimensional model is shown to be realistic in simulating a multiple-impact sequence and laid a foundation for detailed finite element analysis of the interior impact response of an electronic device.