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K R Berger

Publications and source records attributed to K R Berger.

12 recordsLinked to original sources
PubMed1991

Angular homeostasis. VIII. Pursuit of a slowly moving target in a plane: relevance to lateralization in cardiovascular ontogeny.

We explore the pursuit in a plane of a target moving at constant slow speed in a straight line. Two models of the pursuit are given. In the continuous case, the pursuer is moving at constant speed and is subject to proportionate angular homeostasis with correction constant b. In the discrete version movement occurs at a constant speed in a sequence of straight line segments of constant length (called the step size, s) the end of the segments being called the vertices. The pattern considered is not the absolute position of the pursuer, but its distance and orientation relative to the target. Both the transients and the asymptotic orbit are addressed. A key quantity is r, the speed of the target expressed as a fraction of that of the pursuer. If the speed of the pursuer is defined as unity, r is also the ratio of the speeds. There exists a critical speed fraction, R(b,s), a function of b and s, that defines what the term slow designates. R(b,s), which has to be found numerically, has the following property. For r less than R(b,s), the asymptotic path is a simple closed curve. In the discrete case the vertices converge to a simple closed curve. The larger r, the more the path (or in the discrete analogue its set of vertices) departs from a circle, and the more eccentric the target is with respect to it. Interest centers on two issues. First we address the transient patterns of the path, notably whether or not the sense of any particular path (clockwise or counterclockwise) is the same throughout, or changes at some stage.(ABSTRACT TRUNCATED AT 250 WORDS)

Dextrocardia↗
PubMed1991

Angular homeostasis VII: non-monotonic correction systems.

We extend our model of angular homeostasis to correction functions that have a single maximum at a discrepant angle less than pi radians. We find that there are stable, and asymptotically stable, solutions that in general consist of self-intersecting curves. We investigate conditions for these curves to be periodic, and describe their symmetries. One typical pattern of such a closed curve involves a finite number of loops, each having a reflection axis of symmetry, with the complete curve having a cyclic rotation group. These bear a close resemblance to patterns found in lobulated biological structures (such as the petals of a flower or the primitive fetal hand). We further discuss implications for morphogenesis.

Animals↗
PubMed1990

Angular homeostasis: VI. Threshold processes with bivariate liabilities.

The general structure of the threshold model of multifactorial determination is discussed. It is supposed that in place of a single liability (in Falconer's sense) there are two separate liabilities; and whether or not the pathological trait is present depends on a non-additive interaction between the liabilities, so that the region has curved boundaries. The genetics of ontogeny of a process involving spatial orientation (e.g., cardiac ontogeny) is used as a substantive illustration. Genetic analysis of the trait (as contrasted with the liabilities) yields results that on the one hand may seem quite counterintuitive, yet on the other hand they correspond to the kind of bizarre patterns encountered in quasi-empirical genetic counseling for cleft palate or neural tube defect. The impact of refinement of phenotype made possible by non-invasive methods is sketched. This model can be generalized to any number of liabilities, independent or not.

Embryonic and Fetal Development↗
PubMed1989

Angular homeostasis: III. The formalism of discrete orbits in ontogeny.

The formal properties of orbits in a plane are explored by elementary topology. The notions developed from first principles include: convex and polygonal orbits; convexity; orientation, winding number and interior; convex and star-shaped regions. It is shown that an orbit that is convex with respect to each of its interior points bounds a convex region. Also, an orbit that is convex with respect to a fixed point bounds a star-shaped region. Biological considerations that directed interest to these patterns are indicated, and the implications of the prospect of higher orders of star-shapedness mentioned.

Cell Communication↗
PubMed1989

Angular homeostasis: IV. Polygonal orbits.

Some properties are discussed of regular polygons that may result from angular homeostatic processes in stable orbit. To characterize these "homeostatic polygons" we need to discuss the winding number, the sidedness (integer, fractional and irrational), multiplicity, envelopes, and density. A regular (i.e., equilateral, equiangular) polygon may be closed in one revolution about its unique center, in multiple revolutions, or not at all. A homeostatic polygon can be generated only if all vertices are included in a single polygon, which occurs if and only if the number of vertices and the number of revolutions required to complete the polygon are relatively prime. For the homeostatic polygon to have a finite number of sides (without repeating itself) the angle subtended by any two successive vertices at the center must be a rational multiple of 2 pi. Biological implications of these properties are illustrated.

Cell Communication↗
PubMed1988

Angular homeostasis II: Pursuit of a moving target in a plane and some implications for cardiac teratology.

A model of cardiac ontogenesis is analyzed. It is cast in terms of the geometry of the pursuit of a linearly moving target by the growth of a chain of cells in the same plane, the pursuer, which at each step adjusts its direction of growth towards the current position of the target. The endpoint is the fusion between them, which can occur in 2 modes: either by the leading cell of the pursuer catching up with the target (pursuer-mediated fusion, or PMF) or by the target running into the preformed side of the pursuer (target-mediated fusion, or TMF). The causal specifications are the step size, the speed of the pursuer, the speed of the target, the restoration constant, and the initial direction of the pursuer; the outcome variables are the number of steps to fusion and the mode of fusion. The pattern of behavior is complicated, being more-or-less regular over large tracts of values, interspersed with abrupt, threshold-like changes that may generate a dichotomous pattern of inheritance despite a continuous gradation of genetic or other causes. The temporary abolition of the correction process (a change introduced to simulate the pattern of the effect of a teratogen) may delay fusion and suggest how a septum may fail to fuse, the ductus arteriosus to close, or an endocardial cushion to form. But the model also predicts that under certain plausible conditions, the "teratogen" would speed up fusion and hence perhaps offset a genetic predisposition to a congenital defect.

Heart Defects, Congenital↗
PubMed1988

Angular homeostasis. V: Some issues in genetics, ontogeny, and evolution.

We discuss a provisional model that deals with aspects of normal control of the direction in which cells grow; hence, the organization of structure. The interacting issues of genetics, ontogeny, and phylogeny in relationship to normal development and its defects are addressed. Our main goal is to define a model with a small and sufficient set of conditions that would make it possible to undertake statistically efficient genetic studies of certain congenital defects. But to do so in plausible and heuristic terms, one must address two classical questions: 1) How is the genome translated (or sometimes mistranslated) into a phenotype that is clinically conspicuous and that can be the object of genetic selection, and hence of evolution? 2) Granted that evolution of species occurs in small, rare steps, what is the path that calls for the smallest number of mutations through which ontogenesis could have developed, the intermediate stages being conserved because of actual phenotypic advantage?

Cell Division↗
PubMed1987

The dynamics of angular homeostasis: I. General principles.

A general model is proposed casting aspects of ontogeny in quantitative terms amenable to genetic analysis. Its primordial construct is a chain of cells (termed a "pursuer") growing under the influence of a signal towards a fixed structure termed a "target." There is provision for graduated correction of the direction of growth of the pursuer. The determinants of scale include the size of the cells and the distance from the target. The minimum number of parameters is two: the initial angle of growth; and the force of the correction of errors of direction. Both are potentially of genetic interest. The impact of variation in these factors on the path of growth is studied. These findings are readily translated into biological terms, notably in congenital defects of the heart. Besides the primordial purposes, there are other objectives to the process. Some membranes require free edges, or large curvatures, or circular arrays. These secondary qualities require that the cells never reach the target. The target then becomes simply a construction point: that is, while remaining a center of attraction, it is no longer a true goal. If, because of undercorrection, the cell line misses the target at the first pass, it assumes a permanent orbit about it. The orbit rapidly comes to lie on a circle, with a radius independent of the initial angle of growth but related to the cell size and the restoration constant. From this property, several kinds of structures other than a simple bridge may result, especially when a series of lines of growth together form a tissue: a cusp, a free-floating membrane, or a circular membrane to fill a gap.

Growth↗
PubMed1987

The bingo model. IV. The statistics of survivorship in the bingo-gamma model.

The survivorship (time to death or failure) of a bingo-gamma (BG) model is defined as the minimum among the waiting times for completion among k independent gamma processes. The ith process is of order ni, with a mean rate for the occurrence of hits of ai. In this paper we address the case where, for all competing processes, the order and the rate at which hits occur are the same but both they and k are unknown. We denote by k the multiplicity, by n the order or the number of hits to failure, and by a the transition parameter. The joint maximum likelihood estimator (MLE) of the three parameters of this BG process is developed. An algorithm for calculating it has been devised and a computer program in BASIC has been written. The properties of the MLE have been explored systematically, mainly by Monte Carlo simulation. The distributions, means, variances, covariances, and correlation coefficients of the three parameters are explored for samples of size 25 and samples of size 100. Also, the simple average of the observed survival times (which gives a method of moments estimator of the mean survival) is compared with the MLE of the mean survival; the two estimators seem to be unbiased and about equally efficient.

Humans↗
PubMed1987

The bingo model of survivorship. V. The problems of conformation to the empirical evidence.

We discuss the statistical and biological problems of adapting the theoretical bingo model to the analysis of empirical data. A distinction is made between an idealized pathogenetic model, which aims to represent the disease in as much authentic detail as the present state of knowledge allows and in components that have literal interpretation, and an empirical model, which deals with those effects of the pathogenetic model that one may hope to observe clinically. We review a variety of empirical models distinguishable by the amount of data available on intermediate degrees of damage short of total destruction. The relationship of damage to time is explored, and we consider the criteria and usefulness of linearization of this relationship where the diachronic ("longitudinal") data are few and extend over a comparatively short time. Every time a patient is examined, the degree of cumulative damage is assessed in each of the body systems of interest. Thus the examination will furnish a set of measurements, which is obtained on each of several examinations, taken over a period that for preference is long relative to the survival of the system. Specific disorders discussed include dentition and enlargement of the aorta with age in the Marfan syndrome.

Aorta↗
PubMed1979

Clinical importance of directional statistics for electrocardiographic differentiation of smoking habits.

Statistical methods for the analysis of directional data are of relatively recent origin and have not been generally applied in clinical investigations where they are appropriate. This study compares spherical means and standard deviations for directional polarcardiographic variables with the linear means and standard deviations of the same variables for a typical industrial cohort of male white collar workers. Normal subjects were classified by smoking status and by independent clinical evidence of the presence of CHD, and both directional and linear statistics are applied to compare the PCG variables in these groups. Directional statistics more accurately define the spherical means and variances of heart vectors and thereby permit more reliable differentiation of directions, or angles to aid diagnosis.

Adult↗