Source-sink Pairs Research Articles

Periglomerular cell action on mitral cells in olfactory bulb shown by current source density analysis

The sign of action of periglomerular (PG) cells on the apical dendrites of mitral cells in olfactory bulb glomeruli was investigated by constructing current source density (CSD) profiles from potentials evoked by primary olfactory nerve (PON) and lateral olfactory tract (LOT) stimulation. Evoked potentials were recorded and averaged from anesthetized rabbit simultaneously with a1 × 16 array of electrodes positioned perpendicular to the bulbar surface. A one-dimensional CSD analysis with depth was made in the center of PON- and LOT-evoked potential activity. CSD was plotted vs depth for specific times during the average evoked potential (AEP): at the surface peaks of the first surface-negative wave (N1), the first surface-positive wave (P1), and the second surface-negative wave (N2). N1, P1 and N2 corresponded to excitation, dis-excitation (equivalent to inhibition), and dis-inhibition (re-excitation) of the granule cell population through mitral cell basal dendrites. The granule cells generated both PON and LOT oscillatory AEPs. When N1 and P1 profiles or P1 and N2 profiles were combined, the source and sink due to granule cell activity were minimized and another source-sink pair was revealed on PON but not LOT stimulation. PON-evoked N1 + P1 or P1 + N2 profiles showed a secondary souce-sink pair not present with LOT stimulation. The sink was located in the glomerular layer (GL) and outer plexiform layer (EPL) and the source in the inner EPL. It was concluded that long-lasting excitation of the mitral cells was taking place at the GL and GL/EPL border. This excitation was ascribed to concomitant PG cell activity, possibly in combination with prolonged monosynaptic PON excitation of the apical dendrites. The results support the occurrence of direct excitatory action of PG cells onto mitral cells.

On the solution of problems of filtration with a limit gradient

The plane stable filtration of an incompressible liquid with a limit gradient is considered /1/. A special non-linear filtration law is introduced, for which the basic system of equations obtained by transformation of the hodograph /2/ has a general solution which enables the theory of functions of a complex variable to be effectively employed. As a special case the proposed law contains the law considered in /3/. Solutions of the problems of the motion produced by a source in a narrow zone, and the motion from a source-sink pair are presented.

A membrane-carrier mechanism for generating new sources and sinks within gradient-controlled tissues—Its application to regeneration in Oncopeltus

A model is presented that can, in principle, generate new sources and sinks within an existing gradient in the concentration of a morphogen. The novel and crucial feature of the model is that morphogens are transported between cells by membrane-based carrier molecules and not by diffusion. A further aspect of the model is the presence of a second substance within each cell whose concentration is uniform over the tissue; this molecule binds to but is not transported by the carrier and is therefore a competitive inhibitor of the morphogen. The concentration of free inhibitor in a cell determines its fate: if at any time it exceeds some threshold, that cell becomes a morphogen source; if it falls below a second threshold, the cell becomes a sink; in between them, the cell shows no special properties. Provided that differences in morphogen concentration between adjacent cells are not too great, the mechanism is indistinguishable from a normal, diffusion gradient. Examination of the kinetics of the system over a one-dimensional line of cells, however, shows that any stable morphogen difference leads to a carrier imbalance and to a change in the degree of inhibitor binding. If this difference is sufficiently great and if there is morphogen homostasis in each cell, then the free inhibitor concentration in the high morphogen cell may exceed the higher threshold causing it to become a source while the low morphogen cell becomes a sink. A numerical example of the mechanism is given and the results calculated for two-dimensional cellular arrays on either side of a morphogen discontinuity. The predictions match the observations of Wright & Lawrence (1981 a, b) on Oncopeltus. These authors showed that, if pieces of epidermis from sufficiently different positions were grafted together in vivo, an ectopic boundary would form with regions of reversed polarity on either side of the join. The ability of the model to explain the regeneration and axial graft observations on hydra is also discussed and some experiments that might test the model are put forward. It is suggested that the significance of the membrane-carrier mechanism in vivo is twofold: first, to interpret the basic segmentation mechanism in embryogenesis by turning its morphogen discontinuities into source-sink pairs and so generating actual boundaries; second, to act as a homeostatic mechanism in later development, thus ensuring the maintenance of boundaries.

Transient internal waves produced by a moving body in a tank of density-stratified fluid

The internal waves produced by a moving body are generally longer in the direction of motion than the corresponding surface waves. This difference is accentuated when the density variation is slight and the body velocity is large in which case a very long towing tank may be required for the simulation of a steady-state condition. The following theoretical study of transient waves is intended as a step in relating test conditions and requisite towing-tank sizes.A source–sink pair travelling for a finite time is used to represent the restricted motion of a body in a tank. The approximate length and volume of the body are fixed, but its precise shape (somewhat irregular and slightly time dependent) is assumed to be of secondary importance and is not calculated here. The density-stratified fluid is assumed to have a constant Brunt–Väisälä frequency.A solution in the form of a triple sum over the tank eigenfunctions applies quite generally for the internal wave system (neglecting surface waves and the potential-flow-type solution near the body). Examples covering the large-scale structure of the flow field have been solved for two values of an approximate similarity parameter. The value of the similarity parameter indicates how closely steady-state conditions are approached. The first (larger) value chosen produces a well-defined quasi-steady state near the body with transient fluctuations of the order of ± 10%. The second (smaller) value gives a poorly defined quasisteady state with fluctuations of the order of ±50%. More elaborate studies varying the tank length, width and depth could be made by programming the calculations.The effect of a collapsing wake has not been considered here, but might possibly be treated by similar methods.

Pathfinding through a communication network

A technique is proposed by which all paths of exactly q branches interconnecting a given source-sink node pair can be obtained. Using the proposed technique, paths of increasing length can be found sequentially. The method is based on a symbolic noncommutative multiplication among the entries of an Nmatrix which is a modified version of the vertex adjacency matrix.

A per letter converse to the channel coding theorem

By relating the average probability of error to the distortion measure of a source-sink pair, we prove a converse to the channel coding theorem. This converse lower-bounds the probability of error per source letter. It differs from the more familiar "weak" and "strong" converses which bound the probability of error of an entire message. The result is applicable to all stationary sources, all channels, and all block lengths. Lower-bounding the rate distortion function of the source-sink pair with which the channel is to be used reduces the new result to a lower bound on the achievable probability of error per source letter expressed in terms of the source entropy, alphabet size, and maximum achievable average mutual information on the channel. This latter result had been proved previously only for a memoryless channel operating with an independent letter source.

Comparison of surface potentials due to several singularity representations of the human heart

In electrocardiography the electrical potentials due to the heart actions can be analyzed by assuming the human body to be a conductor of homogeneous medium and the heart to be a combination of singularities within it. For a spherical conductor the “interior sphere theorem” of G. Ludford, J. Martinek, and G. Yeh (Proc. Cambridge Phil. Soc.,51, 389–93, 1955) renders potential expressions due to any singularity. For a conductor of prolate spheroidal shape the potential expressions due to a source-sink pair and a general dipole have been given by J. R. Wait (Jour. App. Physics,24, 496–97, 1953) and the authors (paper at the Conference on the Electrophysiology of the Heart, Feb. 16–17, 1956, in New York, to appear in theAnn. N. Y. Acad. Sciences) respectively. (A theorem which applies to any singularity inside a prolate or oblate spheroid will be published by the authors soon). This paper presents numerical and graphical results of potentials on the surfaces of a prolate spheroid and a sphere due to source-sink pairs and dipoles of several locations and directions and compares the various representations. A discussion on the judicious choice of heart models concludes the paper.