Derivation of the space horopter.

The horopter--the locus of those points in space that would stimulate corresponding points on the retinae of the two eyes--has been previously considered to be a plane curve lying in the horizontal plane. The two-dimensional character of this curve arises as a consequence of limiting all considerations to two dimensions only. However, by considering the retina as a two-dimensional surface in 3-space, geometric analysis reveals the horopter to be a non-planar curve: a twisted cubic curve in space. The classical horopter experiments can then be seen to be plotting self-corresponding lines rather than self-corresponding points, and these lines are found to be the chords of this cubic curve. The equations determining the horopter curve in parametric form have been found expressing each point of the curve as a function of the coordinates of the point of fixation.     

Properties of the space horopter.

For general points of fixation the space horopter has been found to be a twisted cubic curve, which, when fixation is in the median plane, degenerates into a conic curve inclined to the plane of fixation. The inclination of the plane of this conic is found to be a function of the angles of torsion of the two eyes. If these angles are zero and fixation is horizontal the space horopter reduces to the Vieth-Müller circle. Previous experimental techniques for plotting the horopter curve do not in fact determine the locus in space of those points that will stimulate corresponding points in the two retinae: they are, locate the position of certain chords of the space horopter. The Hering-Hillebrand deviation coefficient is found theoretically to be a linear function of the fixation distance. This had been shown experimentally by previous workers, but without any satisfactory explanation.     

A note on the reafference principle

Two alternative circuits to realize the reafference principle are considered and quantitatively analyzed. Both are combinations of a conventional control loop with negative feedback and linear transfer functions, as well as of an efference copy branch. The feedback control loop compensates for passive movements of the body or of its parts, and generates active movements, whenever the set point differs from zero. The efference copy branch should eliminate sensory messages to higher brain centres during active body movements and, thus, mediate perceptual stability. In one of the combinations, discussed also briefly by Mittelstaedt (1971), the efference copy branch interacts with and thus modifies the properties of the feedback loop. The performance of this circuit is very sensitive to variations of the system parameters and, therefore, requires precise adjustment. When the transfer function of the efference copy branch exactly matches that of the feedback loop and its gain amounts to 1, this circuit performs as a control loop with an integrator in the negative feedback branch: there is no steady state control error. However, for certain parameter combination the circuit becomes unstable. In the alternative circuit proposed here, the efference copy branch does not interfere with the feedback loop. It is robust against parameter variations. The transient properties of both circuits are described under simplified assumptions regarding the linear transfer functions in the different branches.     

A note on the cybernetics of segregation

The results of a preceding paper (Progress in Biocybernetics,2, Elsevier, 1965) are generalized to express the intensity of anti-Negro feelings, and of the segregation index as functions of the percentage of Negroes in the population. Previous results are applied to effects of migration of Negroes from regions of strong racial prejudice to regions of lesser racial prejudice.     

A note on the measurement of redundancy

Plant Ecology - The present paper points out a simpler method for computing the redundancy coefficient proposed by Orlóci (1975) using the inverse of the variance-covariance matrix. It is...     

A note on the diffusion drag forces

A formal derivation of the expression for the diffusion drag force is given. The expression involves the coefficient of diffusion of the solute through the solvent and the coefficient of diffusion which the solute would posses if it diffused through itself in the form of a gas, in the absence of the solvent.     

A note on the cybernetics of segregation

The results of a preceding paper (Progress in Biocybernetics,2, Elsevier, 1965) are generalized to express the intensity of anti-Negro feelings, and of the segregation index as functions of the percentage of Negroes in the population. Previous results are applied to effects of migration of Negroes from regions of strong racial prejudice to regions of lesser racial prejudice.     

A note on the geometrization of biology

In connection with a recently proposed topological model of an organism (Bull. Math. Biophysics,18, 31–56, 1956), it is pointed out that the dependence of some properties of the studied topological spaces on the type of space in which they are imbedded reflects some aspects of the dependence of the organism on its environment.     

A note on regression to the mean

Sex‐related Cognitive Differences: By Julia A. Sherman. Charles C Thomas, Springfield, Illinois, 1978. 262 pp. Cloth, $16.25; paper, $12.25.

Kinometrics: Determinants of So‐cioeconomic Success Within and Between Families. Edited by Paul Taubman. North‐Holland Publishing Company, Amsterdam, 1977. $28.25

Nutrition and Human Reproduction: Edited by W. Henry Mosley. Plenum Publishing Corporation, New York, 1978. 526 pp. $42.50.

Manual of the International Statistical Classification of Diseases, Injuries, and Causes of Death, Volume 1: World Health Organization, 1977. 777 pp. $12.00 (hardbound). (Also to be published in French, Spanish, and Russian.)

Women in Jamaica: Patterns of Reproduction and Family: By George W. Roberts and Sonja A. Sinclair. KTO Press, New York, 1978. $16.00.     

A note on the fetal-infant mortality problem

This paper considers the age pattern of mortality between conception and first birthday. It highlights the various problems that still limit our understanding of the ways in which the age components of mortality are associated, especially during the perinatal period. A mathematical function is fitted which captures the interaction between six mortality components for a typical high mortality society, one in which the infant mortality rate is 150 per thousand live births. This experiment helps to clarify the need to link infant with fetal mortality, to conduct further research on the level of risk in each component, and to consider the cumulative early-age mortality profile in its entirety.     

A note on the Olduvai clavicular fragment

Certain features of the Olduvai clavicular fragment have been examined in the light of data already existing on the form of the clavicle in primates. Although similar to that of modern man, the fragment exhibits features which suggest that its function may have differed somewhat from that of the clavicle in man. The new information correlates well with that obtained from the fragmentary Sterkfontein scapula.