Multiple-spike waves in a one-dimensional integrate-and-fire neural network

This paper builds on the past study of single-spike waves in one-dimensional integrate-and-fire networks to provide a framework for the study of waves with arbitrary (finite or countably infinite) collections of spike times. Based on this framework, we prove an existence theorem for single-spike traveling waves, and we combine analysis and numerics to study two-spike traveling waves, periodic traveling waves, and general infinite spike trains. For a fixed wave speed, finite-spike waves, periodic waves, and other infinite-spike waves may all occur, and we discuss the relationships among them. We also relate the waves considered analytically to waves generated in numerical simulations by the transient application of localized excitation.Key words or phrases:Traveling waves, Integrate-and-fire network, Excitatory synaptic coupling     

Chemical excitation of Limulus photoreceptors. I. Phosphatase inhibitors induce discrete-wave production in the dark

Molybdate, tungstate, fluoride, vanadate, and GTP-gamma-S [guanosine-5'- 0-(3-thiotriphosphate)] were injected into Limulus ventral photoreceptors by ionophoresis from microelectrodes. All of these drugs induce discrete waves of depolarization similar in waveform to, but smaller in amplitude than, those normally elicited by dim light. As for light-evoked waves, the amplitude of drug-induced waves decreases with light adaptation. For the compounds examined so far (fluoride, vanadate, GTP-gamma-S), the drug-induced waves share a reversal potential with light-induced discrete waves at about +15 mV. The induction of discrete waves by fluoride, vanadate, and molybdate was found to be reversible, whereas the induction of waves by GTP-gamma-S was not. Unlike fluoride and vanadate, which induce waves when added to the bath, molybdate appears to be ineffective when applied extracellularly. Because of the similarity of the drug-induced waves to light-induced discrete waves, we conclude that the drug-induced waves arise from a process similar or perhaps identical to visual excitation of the photoreceptor. However, the smaller size of drug-induced waves suggests that they arise at a stage of phototransduction subsequent to the isomerization of rhodopsin. On the basis of the chemical properties and action of the drugs, we suggest that discrete waves may arise through the activation of a GTP-binding protein.     

Dichromatic Langmuir waves in degenerate quantum plasma

Langmuir waves in fully degenerate quantum plasma are considered. It is shown that, in the linear approximation, Langmuir waves are always dichromatic. The low-frequency component of the waves corresponds to classical Langmuir waves, while the high-frequency component, to free-electron quantum oscillations. The nonlinear problem on the profile of dichromatic Langmuir waves is solved. Solutions in the form of a superposition of waves and in the form of beatings of its components are obtained.     

Formation of planar and spiral Ca2+ waves in isolated cardiac myocytes.

A novel Nipkow-type confocal microscope was applied to image spontaneously propagating Ca2+ waves in isolated rat ventricular myocytes by means of fluo-3. The sarcolemma was imaged with di-8-ANEPPS and the nucleus with SYTO 11. Full frame images in different vertical sections were obtained at video frame rate by means of an intensified CCD camera. Three types of Ca2+ waves were identified: spherical waves, planar waves, and spiral waves. Both spherical waves and spiral waves could initiate a planar wave, and planar waves were not influenced by the presence of a nucleus. Spiral waves, however, were consistently found adjacent to a nucleus and displayed a slower propagation rate and slower rate of increase in Ca2+ concentration in the wave front than did spherical and planar waves. The planar waves were apparent throughout the vertical axis of the cell, whereas spiral waves appeared to have a vertical height of approximately 3 microm, less than the maximum thickness of the nucleus (5.0 +/- 0.3 microm). These results provide experimental confirmation of previous modeling studies which predicted an influence of the nucleus on spiral-type Ca2+ waves. When a spontaneous Ca2+ wave is small relative to the size of the nucleus, it appears that the Ca2+ buffering by the nucleus is sufficient to slow the rate of spontaneous propagation of the Ca2+ wave in close proximity to the nucleus. These findings thus support the idea that the nucleus can influence complex behavior of Ca2+ waves in isolated cardiac myocytes.     

Associations between FSH concentrations and major and minor follicular waves in pregnant mares

Follicular waves were detected in 19 pregnant mares (Days 11 to 40) by a significant increase followed by a significant decrease in diameters of follicles after removing large (>/=25 mm) follicles from the data sets. The waves were defined as major (largest follicle, >/=35 mm; n=18) or minor (largest follicle, <35 mm; n=17). Six mares (32%) had 2 successive major waves beginning on mean Days 15.2 and 26.8; 6 had a solitary major wave beginning on Days 11 to 20; and 6 had only minor waves occurring at irregular intervals. The mean interval between minor waves (7.8 days) was less (P<0.05) than for major waves (11.7 days). Mean divergence in diameters of the largest and second largest follicles of a wave began 4 days after the detected emergence of consecutive major waves, and was taken as the beginning of the expression of dominance by the largest follicle. The interval from emergence to divergence was several days longer (P<0.05) for solitary major waves than for consecutive waves. Dominance was not detected for the minor waves, using mean diameters of the 2 largest follicles, but was apparent on inspection of individual wave profiles in 5 of 17 (29%) minor waves. Minor waves, compared with major waves, had larger diameter of follicles on the day of wave emergence (15.0 versus 12.1 mm), and significantly greater variation in the day of attainment of maximal diameter of largest follicle and small follicles. A mean increase in FSH was temporally associated with the emergence of both major and minor waves. In mares with minor waves, concentrations of FSH were higher, on average, over Days 11 to 40, which seemed consistent with the origin of follicular waves from larger follicles in the basal populations. The lower overall FSH levels in mares with major waves seemed at least partly due to depression of FSH levels beginning at the time of divergence between the 2 largest follicles.     

Two Cortical Circuits Control Propagating Waves in Visual Cortex

Visual stimuli produce waves of activity that propagate across the visual cortex of fresh water turtles. This study used a large-scale model of the cortex to examine the roles of specific types of cortical neurons in controlling the formation, speed and duration of these waves. The waves were divided into three components: initial depolarizations, primary propagating waves and secondary waves. The maximal conductances of each receptor type postsynaptic to each population of neurons in the model was systematically varied and the speed of primary waves, durations of primary waves and total wave durations were measured. The analyses indicate that wave formation and speed are controlled principally by feedforward excitation and inhibition, while wave duration is controlled principally by recurrent excitation and feedback inhibition.     

Similarities and differences in the propagation of slow waves and peristaltic waves

The relationship between slow waves and peristaltic reflexes has not been well analyzed. In this study, we have recorded the electrical activity of slow waves together with that generated by spontaneous peristaltic contractions at 240 extracellular sites simultaneously. Recordings were made from five isolated tubular and six sheet segments of feline duodenum superfused in vitro. In all preparations, slow waves propagated as broad wave fronts along the longitudinal axis of the preparation in either the aborad or the orad direction. Electrical potentials recorded during peristalsis (peristaltic waves) also propagated as broad wave fronts in either directions. Peristaltic waves often spontaneously stopped conducting (46%), in contrast to slow waves that never did. Peristaltic waves propagated at a lower velocity than the slow waves (0.98 +/- 0.25 and 1.29 +/- 0.28 cm/s, respectively; P < 0.001; n = 24) and in a direction independent of the preceding slow wave direction (64% in the same direction, 46% in the opposite direction). In conclusion, slow waves and peristaltic waves in the isolated feline duodenum seem to constitute two separate electrical events that may drive two different mechanisms of contraction in the small intestine.     

Slow nonlinear waves in magnetic flux tubes

A theory of weakly nonlinear slow waves in magnetic flux tubes is developed in the ideal MHD approximation. Fairly simple approximate dispersion relations are derived that are valid for waves of arbitrary wavelength. These dispersion relations make it possible to obtain a number of new model evolutionary equations for body and surface slow waves in magnetic flux tubes. It is established that there are two families of exact analytic solutions to the equations for weakly nonlinear slow waves. It is found that both the body and surface solitary waves can be in the form of either contractions or bulges running along the tube. A model Korteweg-de Vries-Burgers equation is derived and generalized to waves of arbitrary wavelength. It is shown that exact analytic solutions to these equations correspond to shock waves and hydraulic jumps (or bores) with nonoscillating fronts.     

Effects of Viscosity and Constraints on the Dispersion and Dissipation of Waves in Large Blood Vessels: I. Theoretical Analysis

The propagation of sounds and pulse waves within the cardiovascular system is subject to strong dissipative mechanisms. To investigate the effects of blood viscosity on dissipation as well as dispersion of small waves in arteries and veins, a parametric study has been carried out. A linearized analysis of axisymmetric waves in a cylindrical membrane that contains a viscous fluid indicates that there are two families of waves: a family of slow waves and one of fast waves. The faster waves are shown to be more sensitive to variations in the elastic properties of the medium surrounding the blood vessels and at high values of the frequency parameter α defined by α = √ρωR²₀/μ the blood viscosity attenuates them more strongly over a length than the slow waves. At low values of α, the effects of viscosity on attenuation are reversed; that is, the family of slow waves is much more attenuated than the family of fast waves. For the slow waves the radial displacement component generally exceeds the axial component except at very low frequencies. Conversely the axial displacements are much larger than the radial displacement for the faster waves. The presence of external constraints, however, can modify these results. In the case of the slow waves the phase angle between pressure and radial wall displacement is virtually negligible in the presence of mild external constraints, while the phase angles between pressure and fluid mass flow are at most 45°. The corresponding phase angles for the fast waves exhibit much larger variations with changes in the elastic properties of the surrounding medium.     

Excitation of inertial Alfvén waves via modulational interaction with lower hybrid waves

The concept of modulational instability, which results from the coupling of waves modes of very different time and space scales, was introduced to plasma physics through an elegant paper by Vedenov and Rudakov in 1964 [1]. Our paper is devoted to the theory of modulational instability resulting from the interaction of lower hybrid waves and slow density perturbations associated with inertial Alfvén waves. The nonlinear set of equations describing the modulational coupling of these two types of waves is constructed. The lower hybrid wave trajectories are analyzed within predefined density structures and it is shown that these waves can be trapped in the vicinity of the density extremum. The density modulations, originally being associated with inertial Alfvén waves, deepen due to the trapping of lower hybrid waves; this leads to modulational instability. A dispersion relation describing the modulational instability is constructed and analyzed. The threshold intensity of the lower hybrid waves for the onset of instability is obtained and it is shown that instability can serve as an efficient mechanism for the excitation of inertial Alfvén waves in the auroral ionosphere.     

Follicle and systemic hormone interrelationships during spontaneous and ablation-induced ovulatory waves in mares

The characteristics of ovulatory follicular waves were studied for spontaneous waves and waves induced during the next estrous cycle by ovarian follicle ablations and administration of PGF2alpha 10 days after ovulation in 21 mares. In the induced group, both the days of the FSH surge and day of deviation were more synchronized, LH concentrations were greater before and after deviation, estradiol concentrations were greater after deviation, and the ovulatory follicle grew at a faster rate (3.4+/-0.2 compared with 2.7+/-0.1 mm/day). The frequency of two dominant follicles/wave was not different between induced waves (7 of 21) and spontaneous waves (9 of 21), but both dominant follicles ovulated more frequently in induced waves (6 of 7 waves compared with 0 of 9).     

超短波促进烧伤肉芽创面植皮片愈合的临床观察

目的:观察超短波对烧伤肉芽创面受皮区皮片成活的影响。方法:32例自身对照邮票皮移植及40例整张刃厚皮移植术后根据是否给予超短波治疗分别分为两组,治疗组术后接受无热量超短波治疗,对照组术后未接受超短波治疗,观察创面完全愈合时间和愈合创面水泡出现情况进行疗效判定。结果:根据两组患者创面愈合时间进行比较,治疗组明显低于对照组(P<0.01);而在创面水泡出现程度比较中,实验组水泡发生率和严重程度均明显低于对照组(P<0.05)。结论:超短波治疗能明显促进烧伤肉芽创面植皮片的成活,加速烧伤创面的愈合。     

Light-Evoked and Spontaneous Discrete Waves in the Ventral Nerve Photoreceptor of Limulus

Discrete waves, recorded from the ventral nerve photoreceptor, occur in the light and in the dark. Spontaneous waves, on the average, are smaller than light-evoked waves. This suggests that not all spontaneous waves can arise from spontaneous changes in the visual pigment molecule identical to changes induced by photon absorption. Spontaneous and light-evoked waves are statistically independent of each other. This is shown by determination of frequency of response as a function of pulse energy for short pulses and determination of the distribution of intervals between waves evoked by steady lights. The available data can be explained by two models. In the first each photon produces a time-dependent excitation that goes to zero the instant the wave occurs so that the number of effective absorptions from a short light pulse equals the number of waves produced by the light pulse. In the second the excitation produced by photon absorption is unaffected by the occurrence of the waves so that the number of waves produced from a short light pulse may be different from the number of effective absorptions. Present results do not allow a choice between the two models.     

Calcium waves

Waves through living systems are best characterized by their speeds at 20 degrees C. These speeds vary from those of calcium action potentials to those of ultraslow ones which move at 1-10 and/or 10-20 nm s(-1). All such waves are known or inferred to be calcium waves. The two classes of calcium waves which include ones with important morphogenetic effects are slow waves that move at 0.2-2 microm s(-1) and ultraslow ones. Both may be propagated by cycles in which the entry of calcium through the plasma membrane induces subsurface contraction. This contraction opens nearby stretch-sensitive calcium channels. Calcium entry through these channels propagates the calcium wave. Many slow waves are seen as waves of indentation. Some are considered to act via cellular peristalsis; for example, those which seem to drive the germ plasm to the vegetal pole of the Xenopus egg. Other good examples of morphogenetic slow waves are ones through fertilizing maize eggs, through developing barnacle eggs and through axolotl embryos during neural induction. Good examples of ultraslow morphogenetic waves are ones during inversion in developing Volvox embryos and across developing Drosophila eye discs. Morphogenetic waves may be best pursued by imaging their calcium with aequorins.     

Stretch-activated calcium channels relay fast calcium waves propagated by calcium-induced calcium influx

For nearly 30 years, fast calcium waves have been attributed to a regenerative process propagated by CICR (calcium-induced calcium release) from the endoplasmic reticulum. Here, I propose a model containing a new subclass of fast calcium waves which is propagated by CICI (calcium-induced calcium influx) through the plasma membrane. They are called fast CICI waves. These move at the order of 100 to 1000 microm/s (at 20 degrees C), rather than the order of 3 to 30 microm/s found for CICR. Moreover, in this proposed subclass, the calcium influx which drives calcium waves is relayed by stretch-activated calcium channels. This model is based upon reports from approx. 60 various systems. In seven of these reports, calcium waves were imaged, and, in five of these, evidence was presented that these waves were regenerated by CICI. Much of this model involves waves that move along functioning flagella and cilia. In these systems, waves of local calcium influx are thought to cause waves of local contraction by inducing the sliding of dynein or of kinesin past tubulin microtubules. Other cells which are reported to exhibit waves, which move at speeds in the fast CICI range, include ones from a dozen protozoa, three polychaete worms, three molluscs, a bryozoan, two sea urchins, one arthropod, four insects, Amphioxus, frogs, two fish and a vascular plant (Equisetum), together with numerous healthy, as well as cancerous, mammalian cells, including ones from human. In two of these systems, very gentle local mechanical stimulation is reported to initiate waves. In these non-flagellar systems, the calcium influxes are thought to speed the sliding of actinomyosin filaments past each other. Finally, I propose that this mechanochemical model could be tested by seeing if gentle mechanical stimulation induces waves in more of these systems and, more importantly, by imaging the predicted calcium waves in more of them.     

Learning poly-synaptic paths with traveling waves

Traveling waves are commonly observed across the brain. While previous studies have suggested the role of traveling waves in learning, the mechanism remains unclear. We adopted a computational approach to investigate the effect of traveling waves on synaptic plasticity. Our results indicate that traveling waves facilitate the learning of poly-synaptic network paths when combined with a reward-dependent local synaptic plasticity rule. We also demonstrate that traveling waves expedite finding the shortest paths and learning nonlinear input/output mapping, such as exclusive or (XOR) function.     

Theory of slow waves in transversely nonuniform plasma waveguides

A general method is developed for a numerical analysis of the frequency spectra of internal, internal-surface, and surface slow waves in a waveguide with transverse plasma density variations. For waveguides with a piecewise constant plasma filling, the spectra of slow waves are thoroughly examined in the limits of an infinitely weak and an infinitely strong external magnetic field. For a smooth plasma density profile, the frequency spectrum of long-wavelength surface waves remains unchanged, but a slow damping rate appears that is caused by the conversion of the surface waves into internal plasma waves at the plasma resonance point. As for short-wavelength internal waves, they are strongly damped by this effect. It is pointed out that, for annular plasma geometry, which is of interest from the experimental point of view, the spectrum of the surface waves depends weakly on the magnetic field strength in the waveguide.     

Shock Wave Application to Cell Cultures

Shock waves nowadays are well known for their regenerative effects. Basic research findings showed that shock waves do cause a biological stimulus to target cells or tissue without any subsequent damage. Therefore, in vitro experiments are of increasing interest. Various methods of applying shock waves onto cell cultures have been described. In general, all existing models focus on how to best apply shock waves onto cells.However, this question remains: What happens to the waves after passing the cell culture? The difference of the acoustic impedance of the cell culture medium and the ambient air is that high, that more than 99% of shock waves get reflected! We therefore developed a model that mainly consists of a Plexiglas built container that allows the waves to propagate in water after passing the cell culture. This avoids cavitation effects as well as reflection of the waves that would otherwise disturb upcoming ones. With this model we are able to mimic in vivo conditions and thereby gain more and more knowledge about how the physical stimulus of shock waves gets translated into a biological cell signal (“mechanotransduction").     

Dissipative surface waves in plasma

Debatable aspects of the theory of nonpotential surface waves propagating along the boundary of a dissipative medium with frequency dispersion are discussed. On the basis of the known theoretical results and theoretical analysis carried out in this work, a theory of surface waves that is valid for any dissipation of the perturbation energy in the medium is developed. It is shown that, if dissipation is sufficiently strong, there can be surface waves the physical nature and dispersion law of which differ radically from those of ordinary surface waves. The damping rate of such waves is low even at large dissipation in the medium, and their group and phase velocities exceed the speed of light. In particular, surface waves on the interface between vacuum and cold collisional electron plasma are considered. The existence of such surface waves for different media of laboratory and natural origin is discussed.     

Wave Propagation through a Viscous Fluid Contained in a Tethered, Initially Stressed, Orthotropic Elastic Tube

To give a realistic representation of the pulse propagation in arteries a theoretical analysis of the wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube is considered. The tube is assumed to be orthotropic and its longitudinal motion is constrained by a uniformly distributed additional mass, a dashpot and a spring. The fluid is assumed to be Newtonian. The analysis is restricted to propagation of small amplitude harmonic waves whose wavelength is large compared to the radius of the vessel. Elimination of arbitrary constants from the general solutions of the equations of motion of the fluid and the wall gives a frequency equation to determine the velocity of propagation. Two roots of this equation give the velocity of propagation of two distinct outgoing waves. One of the waves propagates slower than the other. The propagation properties of s lower waves are very slightly affected by the degree of anisotropy of the wall. The velocity of propagation of faster waves decreases as the ratio of the longitudinal modulus of elasticity to the circumferential modulus decreases; transmission of these waves is very little affected. The influence of the tethering on the propagation velocity of slower waves is negligibly small; transmission of these waves is seriously affected. In tethered tubes faster waves are completely attenuated.