Stabilization of metastable dynamical rotating waves in a ring of unidirectionally coupled sigmoidal neurons due to shortcuts.

Effects of shortcut connection on metastable dynamical rotating waves in a ring of sigmoidal neurons with unidirectional excitatory coupling are considered. A kinematical equation describing the propagation of wave fronts is derived with a sign function for the output function of neurons. Unstable rotating waves can be stabilized in the presence of an inhibitory shortcut.

Effects of self-coupling and asymmetric output on metastable dynamical transient firing patterns in arrays of neurons with bidirectional inhibitory coupling.

Metastable dynamical transient patterns in arrays of bidirectionally coupled neurons with self-coupling and asymmetric output were studied. First, an array of asymmetric sigmoidal neurons with symmetric inhibitory bidirectional coupling and self-coupling was considered and the bifurcations of its steady solutions were shown. Metastable dynamical transient spatially nonuniform states existed in the presence of a pair of spatially symmetric stable solutions as well as unstable spatially nonuniform solutions in a restricted range of the output gain of a neuron.

Effects of asymmetric coupling and self-coupling on metastable dynamical transient rotating waves in a ring of sigmoidal neurons.

Transient rotating waves in a ring of sigmoidal neurons with asymmetric bidirectional coupling and self-coupling were studied. When a pair of stable steady states and an unstable traveling wave coexisted, rotating waves propagating in a ring were generated in transients. The pinning (propagation failure) of the traveling wave occurred in the presence of asymmetric coupling and self-coupling, and its conditions were obtained.

Metastable dynamical patterns and their stabilization in arrays of bidirectionally coupled sigmoidal neurons.

Transient patterns in a bistable ring of bidirectionally coupled sigmoidal neurons were studied. When the system had a pair of spatially uniform steady solutions, the instability of unstable spatially nonuniform steady solutions decreased exponentially with the number of neurons because of the symmetry of the system. As a result, transient spatially nonuniform patterns showed dynamical metastability: Their duration increased exponentially with the number of neurons and the duration of randomly generated patterns obeyed a power-law distribution.

Transient chaotic rotating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol oscillators near a codimension-two bifurcation point.

Propagating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol (BVP) oscillators were studied. The parameter values of the BVP oscillators were near a codimension-two bifurcation point around which oscillatory, monostable, and bistable states coexist. Bifurcations of periodic, quasiperiodic, and chaotic rotating waves were found in a ring of three oscillators.

Exponential transient propagating oscillations in a ring of spiking neurons with unidirectional slow inhibitory synaptic coupling.

Transient oscillations in a ring of spiking neuron models unidirectionally coupled with slow inhibitory synapses are studied. There are stable spatially fixed steady firing-resting states and unstable symmetric propagating firing-resting states. In transients, firing-resting patterns rotate in the direction of coupling (propagating oscillations), the duration of which increases exponentially with the number of neurons (exponential transients).

Noise-sustained propagation of unstable pulses due to exponential interaction between pulse fronts in bistable systems with flows.

We study effects of noise on pulse propagation in two bistable systems with flows: a chain of unidirectionally coupled neurons and a reaction-diffusion-convection equation with cubic nonlinearity. Pulse propagation in the systems is described by a common kinematical equation, which has exponential interaction between adjacent pulse fronts. The propagation length of pulses is then dealt with as a first passage time problem on it.

Effects of noise and variations on the duration of transient oscillations in unidirectionally coupled bistable ring networks.

We study effects of spatiotemporal noise and spatial variations on long-lasting transient oscillations in ring networks of unidirectionally coupled bistable elements (neurons), the duration of which increases exponentially with the number of neurons. On the one hand, spatiotemporal noise tends to sustain the transient oscillations. The duration of the oscillations occurring from fixed initial conditions changes nonmonotonically with noise strength and takes the maximum value at intermediate noise strength.

Duration of transient fronts in a bistable reaction-diffusion equation in a one-dimensional bounded domain.

The duration of transient fronts in a bistable reaction-diffusion equation in a bounded domain is considered. The speed of the front decreases exponentially with the length of the domain, and the duration increases exponentially with the domain length. The duration of the fronts generated from random initial conditions is distributed in a power-law form up to a cutoff time.

Widespread vertebral and epidural venous plexus metastasis of prostatic carcinoma presenting wedge-shaped radial lesions in the spinal cord.

The present case is the first autopsy case of prostatic carcinoma presenting widespread spinal epidural venous plexus tumor cell emboli with wedge-shaped spinal cord lesions. There has been no previous report of prostatic carcinoma showing tumor cell emboli in the spinal and cranial base epidural venous plexus, in spite of the fact that the incidence of vertebral metastasis in prostatic carcinoma is high, and that presence of continuity from pelvic organs to venous plexus around vertebrae, up to foramen magnum, has been reported. The present case shows that the possibility of spinal cord injury, not by direct compression, but by venous circulatory disturbance as a result of tumor cell emboli to veins, should be taken into consideration on medical treatment of prostatic carcinoma.