Springer Science and Business Media LLC

This paper considers a class of set-theoretical entities, calledn-rank Linnaean structures, which are intended as abstract models of the taxonomic classificatory systems of biology. In the first part, devoted to formalism, finite Linnaean structures are discussed in complete generality; but, in addition, eight distinct subclasses are noted and some of the properties of their elements are explored. In the second part, concerned with applications, it is shown that taxonomic systems may be recast in the form of finite Linnaean structures, and an effort is made to show that some undesirable features of earlier models are avoided without artificiality and without abandoning extensional mathematics.

The effect of one judgment upon the next judgment in a discrimination situation is considered to be the result of two types of perseveration. One arises from the judgment itself. The other results from a persistence, from one trial to the next, of a transient bias. It is shown that the resulting perseveration can then be a function of the difficulty of the first of the pair of choices. Expressions are derived from which the extent of each effect can be measured from observed proportions of responses.

The probability distribution of the process level is derived for a general class of irreversible reaction systems. A method of approximating the mean and variance of the process level is developed and shown to be more accurate for small irreversible systems than other approximations used in the stochastic approach to kinetics.

Some organisms maintain a battery of defensive strategies against their exploiters (predators, parasites or parasitoids), while others fail to employ a defence that seems obvious. In this paper, we shall investigate the circumstances under which defence strategies might be expected to evolve. Brood parasites and their hosts provide our main motivation, and we shall discuss why the reed warbler Acrocephalus scirpaceus has evolved an egg-rejection but not a chick-rejection strategy as a defence against the common (Eurasian) cuckoo Cuculus canorus, while the superb fairy-wren Malurus cyaneus has evolved a chick-rejection but not an egg-rejection strategy as a defence against Horsfield's bronze-cuckoo Chrysococcyx basalis. We suggest that the answers lie in strategy-blocking, where one strategy (the blocking strategy) prevents the appearance of another (the blocked strategy) that would be adaptive in its absence. This may be common in exploiter–victim systems.

We formulate a mathematical model of functional partial differential equations for oncolytic virotherapy which incorporates virus diffusivity, tumor cell diffusion, and the viral lytic cycle based on a basic oncolytic virus dynamics model. We conduct a detailed analysis for the dynamics of the model and carry out numerical simulations to demonstrate our analytic results. Particularly, we establish the positive invariant domain for the $$\omega $$ limit set of the system and show that the model has three spatially homogenous equilibriums solutions. We prove that the spatially uniform virus-free steady state is globally asymptotically stable for any viral lytic period delay and diffusion coefficients of tumor cells and viruses when the viral burst size is smaller than a critical value. We obtain the conditions, for example the ratio of virus diffusion coefficient to that of tumor cells is greater than a value and the viral lytic cycle, is greater than a critical value, under which the spatially uniform positive steady state is locally asymptotically stable. We also obtain conditions under which the system undergoes Hopf bifurcations, and stable periodic solutions occur. We point out medical implications of our results which are difficult to obtain from models without combining diffusive properties of viruses and tumor cells with viral lytic cycles.

We describe a new model for laser-induced retinal damage. Our treatment is prompted by the failure of the traditional approach to accurately describe the image size dependence of laser-induced retinal injuries and by a recently reported study which demonstrated that laser injuries to the retina might not appear for up to 48 h post exposure. We propose that at threshold a short-duration, laser-induced, temperature rise melts the membrane of the melanosomes found in the pigmented retinal epithelial cells. This results in the generation of free radicals which initiate a slow chain reaction. If more than a critical number of radicals are generated then cell death may occur at a time much later than the return of the retina to body temperature. We show that the equations consequent upon this mechanism result in a good fit to the recent image size data although more detailed experimental data for rate constants of elementary reactions is still required. This paper contributes to the current understanding of damage mechanisms in the retina and may facilitate the development of new treatments to mitigate laser injuries to the eye. The work will also help minimize the need for further animal experimentation to set laser eye safety standards.

A Lie-topology of human behavior has been generated in terms of a group of continuous transformations in multidimensional reactivity-adaptability coordinates, connections between the conscious and unconscious surfaces being made through a finite number of interpretive parameters. Neuroses and personality disorders are mathematically classified in terms of pure rotation groups, while reactive depressions and reactive manias fall into the category of dilation groups. The distortions, exaggerations and multiply-fragmented behaviors characteristic of psychoses are explained and classified by combined rotation-dilation Lie groups that can include both real and imaginary parameters. Neurobiophysical implications of the Lie topology are mentioned in relation to abnormal reaction formations and behavioral complexes that may be environmental or organic in origin.

A model of left ventricle is described which takes into account the physiologic variations of thickness, a function of time and distance prior to and during ejection, by assuming that the prolate spheroids are confocal at a given instant. The hyperbolic segment of arc between innermost and outermost spheroids, confocal with the latter, defines a so-called functional thickness, for which a derivation is given. Results show that this model operates in a range of eccentricity wherein thickness change per unit internal volume change are greatest.