ALBERT

Notes: Abstract Biological tree-like structures, such as mammalian tracheobronchial airways, are complicated branching systems. One problem in modeling such systems is the reassignment of the number of segments at a given generation in the model being constructed. A hypothesis is proposed which has successfully been used in modeling mammalian lung airways.

Notes: Abstract The chromosomal theory of inbreeding based on a gametic interaction system lead us to define a depression coefficientD. Comparison of random, sib and half-sib matings (with inbreeding coefficientF=0, 1/4 and 1/8) shows thatD depends on the structure of the starting population and on values of the model parameters. This result accounts for responses of lines whose depression does not depend directly on the inbreeding coefficient and which theories of inbreeding based on increasing homozygosity fail to explain.

Notes: Abstract An idealization of chemical combination is formulated as a model of computability, and it is shown that this model has universal computational power just in case assembly has at least two-dimensional space in which to occur. It is also shown that this model, under reinterpretation, corresponds to a cellular automaton in which growth occurs by differentiation only (i.e., the state into which any cell is born is thereadfter fixed). Hence this latter model of growth is also computationally universal.

Notes: Abstract Kinetics of biological light emission processes do not mean what they seem to mean, because measured light intensity is not proportional to reactant concentration but to reaction rate. Therefore, the differential equation for light decay is usually different from that of concentration decay, so that mass action interpretations cannot be applied directly to light intensity decay. An observed second order light decay for Chlorella at 6.5°C, implies Elovich solid state reaction kinetics, which agrees with other evidence for solid state processes in photosynthesis. An observed 1.5 order light decay for Cholorella at 28°C implies second order liquid or solid state reaction kinetics. First ordere light decay implies first order reaction kinetics.

Notes: Abstract Analysis based on the integration of differential inequalities is employed to derive upper and lower bounds on the total populationN(t) = ∫ R θ(x 1,x 2,t) dx 1 dx 2 of a biological species with an area-density distribution function θ=θ(x 1,x 2,t) (≥0) governed by a reaction-diffusion equation of the form ∂θ/∂t =D∇2θ +fθ −gθ n+1 whereD (〉0),n (〉0),f andg are constant parameters, θ=0 at all points on the boundary ∂R of an (arbitrary) two-dimensional regionR, and the initial distribution (θ(x 1,x 2, 0) is such thatN(0) is finite. Forg≥0 withR the entire two-dimensional Euclidean space, a lower bound onN(t) is obtained, showing in particular thatN(∞) is bounded below by a finite positive quantity forf≥0 andn〉1. An upper bound onN(t) is obtained for arbitrary bounded or unbounded)R withn=1,f andg negative, and ∫ R θ(x 1,x 2, 0)2 dx 1 dx 2 sufficiently small in magnitude, implying that the population goes to extinction with increasing values of the time,N(∞)=0. Forg≥0 andR of finite area, the analysis yields upper bounds onN(t), predicting eventual extinction of the population if eitherf≤0 or if the area ofR is less than a certain grouping of the parameters in cases for whichf is positive. These results are directly applicable to biological species with distributions satisfying the Fisher equation in two spatial dimensions and to species governed by certain specialized population models.

Notes: Abstract The equilibrium probability distribution of the process level is studied for a general class of reversible stochastic reactions. A calculationally convenient approximation for equilibrium probabilities is derived and its accuracy is investigated over a range of values of the equilibrium constant. A method of approximating the equilibrium means and variance is developed and illustrated forQ th-order processes.

Notes: Abstract Beside the concept of material inputs and outputs of components of the representation of biological systems given to us by Rosen, the concept of energy is incorporated. The interaction of material and energy is represented by a cartesian product; and separate material and energetical mappings are considered as the new representation of components. These developments generate aMα category, and it is shown thatMα is isomorphic to theM category of previous developments.

Notes: Abstract This paper discusses the solution of a generaln-compartment system with time dependent transition probabilities utilizing the technique described by Cardenas and Matis (1975) (hereafter abbreviated (CM)). In addition, the cumulant generating function is derived for a special class of reversiblen-compartment systems where the time-dependent intensity coefficients corresponding to the migration and death rates are some multiple of each other. The immigration rates can be any integrable function of time. The moments are also obtained and the solution to the two-compartment system is presented explicitly. The solution is illustrated with a linear and a periodic function which forms have been widely reported in the literature.

Notes: Abstract The relations (inflow) = (dose)/(area under indicator curve), and (volume of distribution) = (throughflow) × (mean transit time) are derived by a matrix method for a system of interconnected subsystems, within which spatial indicator activity gradients may exist, and for compartments, within which the indicator activity is spatially uniform. The inflow theorem, is different from the outflow theorem. Equivalent labeling of multi-input systems reduces them formally to single input systems. Foreign indicator flow-volume kinetics are more general than, and include as a special case, tracer flux-mass (metabolic) kinetics. Volume of distribution in the indicator steady state may be different from the equilibrium volume of distribution.

Notes: Abstract Perturbation methods are applied to a differential equation predator-prey model to find the approximate amplitudes and period of limit cycle solutions. In the model the feeding rate per unit predator per unit prey decreases as the prey become scare. The rigorous applicability of the perturbation technique depends on the assumptions that the limit cycle amplitude is relatively small and that near the equilibrium point the growth rate of each species is most sensitive to changes in the density of the other species. The second assumption is usually roughly satisfied in practice and examples are considered which suggest that the first assumption can be greatly relaxed.

Notes: Abstract Signal Detection Theory can be used to provide a mathematical model describing the choice of a predator trying to distinguish between a model and a Batesian mimic. The mathematical model yields a number of a deductions, in particular that it may or may not assist the mimic population if mimics more closely resemble their models. The assumptions underlying the analysis are discussed in some detail.

Notes: Abstract A new type of physical transition, denotedS→S *, has been detected in irradiated organic molecules (λ=546 nm) through their interaction with specific biological macromolecules. In a specific enzyme-substrate interaction, a clear enhancement of the reaction rate is observed, when the substrate is irradiated with sharply well defined times. These “efficient irradiation times” are always of the 5k sec type (k=1, 2, 3, …). They have been consistently revealed in a great number of specific biological interactions. The present note demonstrates an important property, i.e. that forevery irradiation time aS→S * transition is induced in organic molecules. It is shown that for any irradiation times different from the 5k sec type (k=1, 2, 3, …) states of theS * type may occur, but the biological macromolecules may “detect” only theS * states induced by irradiations of the 5k sec type.

Notes: Abstract A semi-empirical model applicable to the flow of blood and other particulate suspensions through narrow tubes has been developed. It envisages a central core of blood surrounded by a wall layer of reduced hematocrit. With the help of this model the wall layer thickness and extent of plug flow may be calculated using pressure drop, flow rate and hematocrit reduction data. It has been found from the available data in the literature that for a given sample of blood the extent of plug flow increases with decreasing tube diameter. Also for a flow through a given tube it increases with hematocrit. The wall layer thickness is found to decrease with increase in blood hematocrit. A comparison between the results of rigid particulate suspensions and blood reveals that the thicker wall layer and smaller plug flow radius in the case of blood may be attributed to the deformability of the erythrocytes.

Notes: Abstract Three dimensional laminar, viscid flow is developed for Newtonian fluids which provides absolute values for axial, radial and tangential velocity fields everywhere if the dimensions of the vessel are known and two simultaneous axial velocities e.g. on and off the central axis in the same plane, and the central axis axial velocity gradient are measured. In addition, normal and shear stresses are determinable. The equation set satisfies geometric and other known flow limiting conditions such as no slip at surfaces etc. and are amenable for inclusion in general, dynamic flow expressions. Alternatively they may be used alone for certain problems involving gradients and secondary flows. A range of illustrations are shown for a distorting vessel with elliptic cross-section and small axial taper (analogous to the pulmonary trunk during ejection).

Notes: Abstract A regulated left ventricular dynamics model is presented which involves interaction of the dynamics of the left ventricular and circulatory systems and their regulation by the central nervous system. On-line human parametric simulation (parameter estimation) and consequential prognostic implications (based on parametric values) are demonstrated. Model responses to simulated physiologic stresses help delineate tolerances of subjects. In order to have an estimate of the reliability of the model, the sensitivity of the model's responses to changes in the values of its intrinsic parameters is assessed. Also determined is the extent to which errors in measuring the pressure affect the calculated values of the model's simulation parameters and subsequently influence the values of other diagnostically useful variables (such as contractility, oxygen consumption rate, heart rate), when the model is used to determine the limiting physiological stress sustainable by the subject. A comparison of the model's composition with those of other similar cardio-circulatory models is included.

Notes: Abstract Then-stage harvesting strategy of Elizarov and Svirezhev is examined. As a result, some important new features appear. A discussion is presented on whether or not one should harvest a species at one time stage or wait until a later time. The paper is concerned with contributions which are primarily mathematical formulations and results for continuous, as well as discrete time, logistic growth of a single species being harvested. Age class structure is ignored.

Notes: Abstract In order to evaluate the effect of anatomic asymmetries on the gas concentration distribution in the pulmonary airways, a Monte Carlo simulation of combined bulk flow and molecular diffusion was carried out in a realistic distal airway model (Parkeret al., 1971). This airway model, composed of branches distal to the 0.5-ram diameter airways, contained an upper symmetric segment consisting of four generations of conducting airways and a lower asymmetric segment of alveolar ducts and sacs arranged in five transport paths of varying lengths. In accounting for the volume increases of these ducts and sacs occurring during normal respiration, uniform alveolar filling rates and a fixed length-to-diameter ratio of all airways were assumed. For a pulse injection of inert tracer gas, the simulation was employed to determine the longitudinal concentration profiles in the conducting airways. In the alveolated airways, not only were the longitudinal profiles determined along each path, but radial transport from the core to the periphery of the airways was considered. The results of the simulations indicate that geometric asymmetries alone contribute substantially to regional concentration variations in the distal airways. For example, when a gas bolus is injected at mid*inspiration, there are concentration differences as great as 40% between two points along different transport paths located equi-distant from the proximal end of the model. As viewed from the terminal end of the model (acinus), average concentration differences as large as 6-to-1 exist between the longest and shortest transport paths respectively for gas boli introduced near the end of inspiration. The results further indicate because of large radial diffusion rates, no significant concentration differences exist between the periphery a-ld the central core of alveolated airways. Simulation of the expired concentration profiles indicate that boll injected very late during inspiration exhibit a sloping tail, unlike the earlier injected boll whose tails are virtually horizontal. Through the use of superposition teehniqnes, it was found that these sloping tails correspond to an alveolar slope of 1.5 vol% between 750 and 1250 ml expired for a continuous washing of tracer. This result is in disagreement with other transport analyses which did not directly account for the effect of geometric asymmetries.

Notes: Abstract Assuming a spherical geometry for the left ventricle, passive elastic stiffness-stress relations have been obtained on the basis of linear elasticity theory and large deformation theory. Employing pressure-volume aata taken from rat hearts of various age groups, it is shown that young rat heart muscle (1 month) is stiffer than either adult (7 months) or old rat heart muscle (17 months). Although the qualitative results are similar for both elasticity theories, the large deformation theory gave results in closer agreement with those obtained from papillary muscle studies. These results imply that stiffness of muscleper se can be assessed from left ventricular pressure-volume data.

Notes: Abstract Deliberate evaluation of the quantum theory of nerve excitation is made by comparing it with Hill's theory in fitting the experimental data on threshold-frequency relation, optimum frequency (v0) for nerve excitation and strength-duration relation. Decrease of v0 and increase of all the time constants (Hill's λ andk, Wei'sT 2 and spike durationw) with decreasing temperature are interpreted on the basis of the dipole relaxation timeT 2 but inexplicable from Hill's theory or any other existing theory. The closeness ofk,T 2 andw values is explained. A variety of experimental results obtained by others is discussed. Finally, a comparison is made between the Hodgkin-Huxley equations and the quantum theory. Most of the facts (electrical and non-electrical) tend to support the thesis that nerve excitation is a macroscopic expression of quantum transitions of dipoles between energy states.

Notes: Abstract In the periodic Leslie model the asymptotic period of total population is a divisor of the asymptotic period of the population vector. Under reasonable circumstances these periods are identical.

Notes: Abstract A number of biological branching systems, such as the bronchial and pulmonary arterial trees, are being investigated in an ongoing study in order to define their physiological properties. The technique involves the description of branching trees by the use of hierarchical systems of ordering, especially those described by Horsfield and by Strahler. During this work some mathematical properties of branching trees were demonstrated and these are described in this paper.

Notes: Abstract Luteinizing hormone (LH) is secreted continuously from the anterior pituitary gland. The concentration in the blood of this gonadotropic hormone plays a regulatory role in the development of puberty in both sexes, in the induction of ovulation in females, and in the production of testosterone in males. The secretion of LH is in turn controlled by luteinizing hormone releasing hormone (LHRH) secreted by the hypothalamus. LH and LHRH are removed from the blood by degradation and excretion. This hormonal system is modelled by a system of ordinary differential equations based upon specific physiological and biochemical assumptions current among experimentalists in this field. The one exception is the assumption that LHRH may bind reversibly to a serum protein; an analysis of the data shows that this or a similar mechanism is a crucial specification. Data on the serum levels of LH and LHRH in two human subjects were fitted using the model. The data consist of the transients and subsequent decays created by a bolus intravenous injection of LHRH.

Notes: Abstract A thick-wall incompressible, elastic sphere was used as a model for the diastolic rat left ventricle. A model for myocardial nonhomogeneity was derived assuming that fiber (circumferential) stress was independent of position in the ventricular wall. The theoretical implications of the resulting constitutive relations together with the spherical model were analyzed in the context of large deformation elasticity theory. It was found that muscle stiffness at a given level of uniaxial stress increased monotonically from the endocardium to the epicardium. In addition, fiber stress was found to be essentially a linear function of transmural pressure above a pressure of 6 g/cm2. It was also shown theoretically that neglecting the nonhomogeneity of the myocardium resulted in a state of stress which differed significantly from that predicted by the nonhomogeneous model. For example, at a transmural pressure of 14 g/cm2, fiber stress in the nonhomogenous model was equal to 17 g/cm2 while fiber stress in the homogeneous model varied between 100 g/cm2 at the endocardial surface and 2 g/cm2 at the epicardial surface. The change in muscle stiffness with position which characterized the nonhomogeneous model also tended to linearize the highly curvilinear radial stress distribution predicted by the homogeneous model at a given transmural pressure.

Notes: Abstract The phenomenon of axonal transport has been well documented (Ochs, 971; Lasek, 1970; and Grafstein, 1967). In a previous paper, we showed how diffusion alone could not account for this process. In this report we show that convection or convection with diffusion can account for the observed build-up of material. By including a first-order catabolic sequestration term, we are able to offer an understanding of the several apparent rates of transport with the same underlying velocity and variable sequestration.

Notes: Abstract It is known that the Lotka-Volterra coupled nonlinear differential equations for a two-species prey-predator ecosystem possess a periodic solution, although its exact form is not yet obtained analytically. The conventional linearization approximation for solving these nonlinear equations leads to a harmonic oscillator whose frequency depends only on the intraspecific coefficients. We propose here a prescription for obtaining nonlinear correction to the linear frequency by using the Hamilton-Jacobi canonical formalism of classical mechanics. It is found that the first-order correction, which also involves interspecific parameters, exhibits the basic qualitative features of the nonlinearity.

Notes: Abstract Environmental safety testing typically requires procedures for extrapolating from the relatively high experimental to the very low use doses of potentially harmful substances. In the present paper, a stochastic mammillary compartmental model for environmental safety testing is proposed and extrapolation procedures based on its dose-response relationship are developed. The proposed model is a direct generalization of one of the basic safety models, the one-hit model, in that a harmful reaction is assumed to occur if at any time any of the peripheral compartments attains a specified threshold of particles. Consideration of a closed model yields an upper bound on the probability of attaining a certain threshold level, thus providing a conservative procedure for extrapolating to a low dose, while a lower bound obtained from a related open model provides a useful monitoring device as to the sharpness of the upper, bound. The extrapolation procedure is illustrated with simulated data and approximations for initial values are developed.

Notes: Abstract By using chromosome images as a framework, algorithms for finding most dissimilar images are presented and illustrated by examples. In terms of angles, a chromosome image consists of two exterior biangles and two interior biangles. Biangles are defined and classified into 180° biangles, 〉180° biangles and 〈180° biangles. The dissimilarity of biangles and its geometric interpretation together with various properties of biangles are also presented. The results may have useful applications in pattern recognition, scene analysis, information storage and retrieval, artificial intelligence and fuzzy set theory.

Notes: Abstract The Volterra equations which represent competitions between two species are utilized to examine the phenomenon of boundary formation between two species of plants. The set of stable stationary points for these equations is determined and is illustrated in a product space of parameters and dynamical variables. The stages of boundary appearance and succession are visualized by considering slow changes of the parameters as functions of time and space.

Notes: Abstract For certain environments, the Darwinian model allows unique prediction of a function that any surviving system adapted to such an environment has to perform. This is the case for those environments that determine a “survival functional” of position in space-time of known shape. Purely temporal survival functionals can be distinguished from spatial and mixed ones. In each case, there exists an optimum path in combined physical and (reduced) metabolic space. Dependent on the admissible error, approximate solutions of different complexity are sufficient. All solutions possess an afferent, a central, and an efferent part. Within this general frame, specific, “probably simplest”, solutions are proposed for adaptive chemotaxis, insect locomotion, lower vertebrates locomotion, higher vertebrates locomotion, chronobiological systems, and immune systems, respectively—or rather, for the underlying functionals.

Notes: Abstract Mathematical models afford a procedure of unifying concepts and hypotheses by expressing quantitative relationships between observables. The model presented indicates the roles of both insulin and glucagon as regulators of blood glucose, albeit in different ranges of the blood glucose concentrations. Insulin secretion is induced during hyperglycemia, while glucagon secretion results during hypoglycemia. These are demonstrated by simulations of a mathematical model conformed to data from the oral glucose tolerance test and the insulin infusion test in normal control subjects and stable and unstable diabetic patients. The model studies suggest the parameters could prove of value in quantifying the diabetic condition by indicating the degree of instability.

Notes: Abstract A model for the dynamics of a single-species population whose birth rate depends on densities of previous generations is introduced. A difference equation formulation is proposed and the solutions classified for the various parameter values. Data from an experimental population of mice growing in limited space is cited and compared with the model predictions.

Notes: Abstract All soft tissues are modeled as either one-dimensionalstrings, two-dimensionalmembranes, or three-dimensionalsolids. Attention is restricted to tissues in which one of the principal stress components is large and positive in comparison with the other negligible components. Results indicate the following: (1) If a deformed string isconstrained to lie on a surface and is free of tangential pressure, the tension is carried by rays which are geodesics of the surface. If a string or membrane isfree to deform in space without normal pressure, the tension rays are straight lines. If a membrane deforms without tangential surface loads, the tension rays are always geodesics on the deformed surface. If a solid deforms without body forces, the tension rays are straight lines. (2) The stress in a string is a constant if the string is free of tangential pressure and has constant cross-sectional area. The stress in flat tension fields free of tangential surface loads decays inversely with distance along a tension ray from the edge of regression. The stress in a spherically symmetric tension field free of body forces decays inversely with the square of the distance from the center of the sphere. (3) Stress singularities can occur in soft tissues, such as at the corners of a closed rectangular hole in a flat membrane strip. (4) The tension rays in the torsion of soft annular membranes are more steeply inclined from the radial direction than the tension rays for hard metals equally displaced.

Notes: Conclusion For all these reasons, the rediscovery of the equivalence theorem, first stated by David Ricardo in 1817, must be rejected as an adequate basis for policy, just as Ricardo had denied its applicability to the real world. Correspondingly, the concern with the adverse consequences of unfunded social insurance wealth for the supply of national saving, capital intensity, and living standards remains well founded. p ]If, as a practical matter, public pension and social security programs will never be funded actuarially in the United States and most other postindustrial countries, then government-supervised substitution of private for public retirement plans is the only way to achieve at least partial funding. If such substitution follows the British model of allowing employers to contract out of the earnings-related part of the state scheme if equivalent pensions are provided by the company plan, payroll taxes and social security wealth decline so as to reduce their adverse impact on capital formation.

Notes: Summary: Social Policy in the Italian Economy Favourable social and economic conditions constitute the essential framework for a stable development of savings. Saving in the form of insurance becomes advantageous for the individual, and private insurance can thus extend its activity, when social attitudes and the economic situation favour the propensity to save. If conditions change, the State can take over the coverage of risks through social insurance. By means of this institutions, an anti-cyclical policy can be pursued: the amount of social security contributions, for instance, can be increased during the expansion of the cycle and the amounts thus accumulated can be used to grant benefits during the recession period, when contributions can be fixed at a lower percentage of wages. Another type of policy can be pursued by government authorities: that of adjusting social security contributions to industrial profits, thereby directing the subsequent effects on economic growth. Inflation cab cause instability in decisional policies taken by private insurance companies. A solution to the unbalanced increase of costs can be found in index-linking. Life policies of this kind, for instance, cab be closely related to investments in houses, to be bought by the insured themselves in price-linked instalments. After a reference to present developments regarding risk instability and to possibilities of new forms of insurance, this paper considers the competition resulting from the opening of the EEC insurance markets as an opportunity for the Italian market to strengthen its structures.

Notes: Abstract A number of apparently different lines of inquiry into fundamental biological processes point to the central role played by the notion of observation in the theory of biological systems. Not only do we use the results of our own observations to obtain the system descriptions which are the starting-points for an understanding of biological processes, but it is a basic postulate of physics that the interactions between biological systems themselves can be regarded as observations. On this basis, it is clear that we cannot properly understand biological interactions unless the observables we employ for system description are the same as those involved in the interactions we are describing. To do this requires a general theory of observables and system description, establishing the relationship between different modes of description. A sketch of such a theory is developed in the present paper, using only two postulates: (a) that all interactions are determined by the values of observables of a system evaluated on specific states, and (b) that real-valued observables suffice. As an application, a specific test is proposed whereby it can be determined whether the observables employed to describe interacting systems are sufficient to specify the observables involved in the interaction itself.

Notes: Abstract Differential equations are derived whose solution gives the cross-sectional shape of a flexible tube as a function of the transmural pressure. These equations are solved digitally to produce a series of closed curves, each curve representing the shape of a cross section for a particular set of conditions. These are then applied to the case of systemic arteries, pulmonary arteries, and large veins. The results predict that systemic arteries must always be circular, even when the internal and external pressures are equal. In veins, a small positive internal pressure causes them to become circular, regardless of their initial state, with negligible stretching. Further increases in internal pressure cause the area of the cross section to increase due only to stretching, the shape remaining essentially circular. With pulmonary arteries, known to be noncircular, changes in the cross-sectional area result from a combination of stretching and changes of shape.

Notes: Abstract Stochastic models of human reproduction are beginning to play significant roles in the evaluation of family planning programs. A class of stochastic processes called absorbing, agedependent, semi-Markov processes frequently arises in the construction of such models. The paper begins with a discussion of some technicalities regarding absorbing, age-dependent, semi-Markov processes. Then, an algorithm due to Littman, which makes possible the computerization of this class of stochastic processes, is presented. Briefly, Littman’s algorithm provides an efficient method for numerically solving systems of renewal type integral equations, provided the system does not contain a large number of equations. After setting down a concrete model for a large clinical trial of intrauterine devices conducted in Taiwan, the paper concludes with a discussion of a method for validating the model based on the data collected in the clinical trial.

Notes: Abstract Some theoretical requirements for the valid use of hemolytic plaque inhibition as a method for studying cellular selection and recognition in an immune response are reviewed. Aside from providing a rational basis for the use of this technique, the theory resolves a growing body of apparently conflicting results on the affinity regulation of IgM secreting cells and can also be used to deduce structural (in particular, morphological) features of the IgM molecule. The diverse predictions of the theory are examined in light of experimental results and find support in a wide data base. Additional specific experiments are proposed which can be used in conjunction with the theory to help clarify the relation between cellular proliferation and maturation.

Notes: Abstract A theory of the cell volume is presented with emphasis on the swelling effect of high concentrations of KCl and other chloride salts. In this theory a particular cell volume represents a state of balance between the tendency of the cell water to build deeper layers of polarized water and the restraining forces exerted by the salt linkages and H-bonds. Taking into account also the different structure-breaking effects of different salts, theoretical curves can be constructed which describe the complex multiple peak-plateau of swelling curve observed in frog muscle in response to increasing concentrations of different chloride salts.

Notes: Abstract Non-steady-state equations for kidney models are stated. General conservation relations for these equations are derived. Transient equations for the central core model of the renal medulla are developed. Solution of the equations by Laplace transform methods for time invariant volume flows is discussed. The general theory of solving models with time dependent flows by finite difference methods is developed.

Notes: Abstract The behavior of large systems of randomly-interacting variables is examined using an intentionally simplified model. The stable positive solutions are found to exhibit to a significant degree some well-known properties of ecological systems. This resemblance (including for example the predominance of “predator-prey” interactions) is all the more striking in view of the lack of biological “data” at the input end. The findings suggest it advisable to distinguish two kinds of properties in ecosystems. One kind would depend on specifically biological mechanisms; the other would characterize a wide class of persistent systems, and arise from the need for a dynamic balance between positive and negative feedback.

Notes: Abstract For the tumor model of Skipper and Zubrod, which has been analyzed previously for the theoretical FLM function and the effect of chemotherapy against tumors of known or assumed kinetic characteristics, the theoretical continuous labeling (CL) function is derived by considering an equivalent tumor (in terms of unlabeled cell populations) in which the density function of phase duration of cells inS-phasef 2(a 2)=δ(a 2−∞) and the loss functionL 2(t)=0. This mathematical concept of blocking is applied to the analysis of synchronization in tumor growth and blocking effects in cancer chemotherapy. These effects of chemical agents on the cell cycle progression are being incorporated into a previously written computer simulation program for cancer chemotherapy. Whereas, a program is written and used to simulate the CL functions for L1210 leukemia, and primary and metastatic Lewis lung carcinoma.

Notes: Abstract Global stability is established in a class of prey-predator models. This includes a prey-predator model in which the predator has Type 2 functional response and no intraspecific interactions. Two simple examples demonstrate that Kolmogoroff’s theorem does not apply to some members of this class of models.

Notes: Abstract The skeletal muscle is regarded as a periodically deformed plate. An equation of energy for the biological tissue in the system is used in the Lagrange variables. With the heat exchange through the above tissues to the exterior media and also with account of some relations between the physiological factors the approximate analytical solution for this equation is obtained and compared with the physiological data.

Notes: Abstract One of Bobisud's (1976) models for the evolution, of cannibalism is discussed. His analysis is criticised for not being based on the principle of individual selection. Assuming the operation of that principle, we show by simulating his model that cannibals may establish themselves in a noncannibal population. This will happen both in cases where Bobisud concluded cannibalism to be optimal and in cases where he concluded cannibalism not to be optimal.

Notes: Abstract The D'Arcy Thompson concept of biological transformations is developed in a form analogous to such physical concepts as the Law of Corresponding States in thermodynamics, and the Principles of Similitude found in engineering. We find that such concepts depend on a distinction between fundamental and derived quantities, in which the values assigned to the fundamental quantities set the natural scales for the derived ones. Among other things, we see that critical phenomena, such as phase transitions, arise as an immediate consequence of this distinction. In a biological context, we explore the implications of Thompson's hypothesis that closely related organisms are phenotypically similar, assuming that the organisms we see are the result of selection processes operating on phenotypes.

Notes: Abstract If information is coded in the combination of activities of many neurons operating in parallel, then information present in a network can be defined by the correlation of present network activity with the activity which had been elicited by a stimulus in the past; a high correlation indicates the presence of the previously encoded stimulus. Information is distributed in the network because coding is dependent upon the activities of all cells. A model based on Hartline-Ratliff lateral inhibition with a time delay shows that lateral inhibition can distribute information across a parallel network, reduce output noise, and also briefly store information. With no changes in model parameters, and the use of a correlation measure for recognition, the model can stimulate psychophysical results in eleven variations of the metacontrast masking paradigm.

Notes: Abstract A theory is derived to calculate the regional and total deposition of aerosol particles in the nasal passages during inhalation. The particle size studied range from 0.2 to 10.0 μm diameter. The deposition is calculated in five regions; (I) the region filled with nasal hair, (II) the nasal valve, (III) the expansion region, (IV) the turbinate region and (V) the posterior bend. Equations are derived to determine the deposition caused by direct impaction on the nasal hairs and bends of the passages. The calculations show the deposition due to direct impaction does not account for the amount or location of deposited particles measured in experiments. Secondary flows have been speculated to exist in the expansion region after the nasal valve and an equation is derived to estimate the deposition caused by the secondary flows. The calculated deposition, due to direct impaction and secondary flows, shows general agreement with the experiment as to the predicted amount and location of deposited particles.

Notes: Abstract The paper reviews a series of models for circadian clocks and discusses their conclusions and predictions. Attention is focused on Pittendrigh's empirical model, two mathematical models by the author and Winfree's work.

Notes: Abstract From a model of facilitated ionic transport across axonal membranes proposed by McIlroy (1975), the equipotentials and electric field distributions in the vicinity of a potassium conducting pore and of a sodium conducting pore are computed and presented as two-dimensional mappings. The model is then extended to include the effect of impurity ions in the conducting pores viz. of potassium ions in a sodium pore and of sodium ions in a potassium pore. The ionic selectivities and permeabilities of the transported species are discussed in relation to the extended model. Bounds are deduced for the ionic selectivity coefficients for both the sodium and potassium current-carrying systems in squid giant axons and the electric-field distributions in the vicinities of the pores are computed for the extended model and compared with the impurity-free fields first calculated. Finally the permeability coefficients defined in terms of the extended model are shown to reconcile the results of attempts to measure permeability by means of radioactive tracer techniques, with the classical description of the resting nerve.

Notes: Abstract The partial differential equations describing transcapillary exchange and subsequent removal of solutis from an idealized liver sinusoid are amenable to solution by similarity analysis. The power and utility of this technique, which is not widely appreciated as a method for solving biological models, is illustrated here for a system whose Laplace transforms is difficult to invert.

Notes: Abstract The phenomenological theory for the chemotaxis and consumption of oxygen by motile aerobic bacteria is shown to yield a remarkably simple one-dimensional steady-state solution for a congregation of bacteria close to the surface of an oxygen-depleted aqueous medium.

Notes: Abstract In this paper biological compartmental models are considered which take into account the intrinsic randomness of the transport rate parameters and their possible variability in time. An identification procedure is presented for the estimation of the stochastic processes representing the transport rate parameters of a compartmental model from a noisy input-output experiment. The problem is formulated in terms of nonlinear filtering. A simple model is discussed for the case in which the transport rate parameters are independent of each other. The possibility of testing possible important features of the behavior of the transport rate parameters is also evidenced.

Notes: Abstract For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂ci/∂t=Di∇2ci+Qi(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c 1(x,t),...,c n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.

Notes: Abstract The results of an earlier effort to provide a geometrical analysis of Hutchinsonian niche space are extended. The concept of diversity of a species in niche space is introduced and the maximization of this diversity provides a rationale for a within-niche fitness distribution which is Gaussian. Niche expansion is seen as a consequence of diffusion in niche space, and an evolutionary version of the Volterra competition equations is proposed as a way to relate niche geometry with population dynamics. Applications to topics in community evolution, species packing and the statistical fitting of species abundance data are mentioned.

Notes: Abstract In this paper we use marginal probabilities to derive expressions for the means, variances and covariances ofm-compartment systems. We also present an efficient algorithm for the estimation of the parameters of the system using time series data when measurements are available fromk of them compartments. An application of the analysis and parameter estimation procedure for a model representing the results of a cancer treatment follow-up study is given.

Notes: Abstract The self-organizing properties of an ensemble of interconnected units are studied by linear stability analyses. Small perturbations of a uniform steady-state may result in bifurcations to other solutions that exhibit spatial or temporal order. We show that increasing the number of connections that a unit makes with its neighbors changes the nature of these solutions and tends to destroy spatiotemporal patterns. If an unconnected system is orginally stable, the formation of multiple interconnections can never induce temporal periodicity but may, under certain circumstances, allow the emergence of stationary spatial patterns. We have verified the predictions of the linear stability analysis on a model system and comment on the implications of these results for multicellular ensembles.

Notes: Abstract A performance criterion and weighting factors for the optimal cardiac assistance are investigated by applying Tellegen's network theorem and tolerance analysis on animal experimental data for left ventricular (LV) bypass on the failing heart. Two major factors with respect to cardiac assistance (total power delivered to the peripheral circulatory system, and changes in temporal pattern of ventricular contraction) are represented by two performance criteria,J 1 andJ 2 whereJ 1 relates to the sum of LV and pump power, andJ 2 relates to the “peakedness” factor of LV power. The total performance index (J) is determined as the weighted sum ofJ 1 andJ 2;J=w 1J1+w2J2. The weighting factors,w 1 andw 2, are computed as inverses of the tolerance in the performance contours with respect to improvement of stroke work per minute from pre- to post-bypass condition.

Notes: Abstract In treating the Volterra-Verhulst prey-predator system with time dependent coefficients, we ask how far this deterministic system represents or approximates the dynamics of the population evolving in a realistic environment which is stochastic in nature. We consider a stochastic system withsmall Gaussian noise type fluctuations. It is shown that the higher moments of the deviation of the deterministic system from the stochastic approach zero as the strength δ of the perturbation decays to zero. For any δ〉0 and allT〉0, ε〉0, the sample population paths that stay within ε distance from the deterministic path during [0,T] form a collection of positive probability. In comparing the stationary distributions of the two systems, we show that the weak limits of those of the stochastic system form a subset of those of the deterministic system. This is in analogy with a result of May connected with the stability of the two systems. Plant and rodent populations possess periodic parameters andexhibit periodic behaivor. We establish theoretically this periodicity under periodicity conditions on the coefficients and perturbing random forces. We also establish a central limit property for the prey-predator system.

Notes: Abstract Adaptation of repetitively firing sensory neurons and nerve models is correlated with specific inhibitory feedback phenomena—an electrogenic sodium pump, and post synaptic self inhibition. The quality of the adaptive responses depends on the excitation properties of the neuron in the interspike interval, or the description of these properties by the underlying impulse encoder model. THis model dependence is demonstrated by comparisons of the behavior of two classes of models; the “leaky integrator models” which assume a passive neural membrane, and the “variable-γ models”, for which the neural state of excitation varies according to first order differential equations. The complexity inherent in the variable-γ models is effectively boiled down to mathematically simple relationships which are derived from studies of the neural- and model frequency responses to small amplitude sinusoidal stimuli. It is argued, and supported with examples, that these relationships hold for impulse frequency transients resulting from more general stimulus conditions. Expressions are then derived which permit feedback parameters to be determined from impulse frequency data. In this connection, recent studies of neural dynamics are brought to bear to resolve ambiguities in data interpretation.

Notes: Abstract A setQ(n) of noncongruent connected shapes, constructed from a fixed numbern of congruent regular hexagons laid edge to edge, is defined. Various measures of shape are applied toQ(n) and the results are numerically analyzed in the special casesn≦9. The concept of spatial entropy is introduced which affords a measure of the “complexity” of shape. Possible biological applications include the analysis of ecological cover,stigmergy or the complex nest-building activities of social insects and morphogenesis. Essentially any comparative study of shape, regardless of the specific application, might be carried out along the lines suggested in the paper.

Notes: Abstract This paper uses optimal control theory in conjunction with a Gompertzian type model for cellular growth to determine the optimal method of administering cycle non-specific chemotherapy or more generally the optimal durations of treatment and rest periods during chemotherapy. The performance critera employed to determine the relative merits of the therapy include not only the destruction of malignant cells, but also the sparing of a critical normal tissue. Since these criteria are at odds with one another, the solutions are found which satisfy the Pareto optimality conditions.

Notes: Abstract Oscillations governed by generalized Volterra-Gause-Witt equations to include retardation effects in population dynamics are considered. Models containing either small or significant time delay are discussed. The Krylov-Bogoliubov-Mitropolskii perturbation method and its extension for differential equations with retarded argument is used.

Notes: Abstract A general solution to the dynamical equation for the probability distribution associated withn interacting species is obtained by employing the author's generic canonical expression for the rate functions. Interacting species models with limit-cycle dynamics and no stable equilibrium points feature probability distributions that are asymptotic for large values oft to Dirac δ-distributions concentrated on the limit-cycles, as illustrated here for an analytically solvable two-species model. For ann-species Volterra model, a stationary or temporally-averaged probability distribution should generally be much more complicated than the specialized Poisson form studied by Kerner and others.

Notes: Abstract A set of coupled nonlinear differential equations, determining the concentration profiles and electric potentials valid for isothermal transport of ions and molecules across a diffusion barrier are formulated, using a correction to the limiting expression for chemical potential gradients and the molecular expression for frictional force. These differential equations are similar to Nernst-Planck equations and reduce to these under appropriate approximations. Solutions of these equations valid under specified conditions are presented. Expressions for permeability, concentration profiles of many ion systems are included.

Notes: Abstract The global flow equations of nonequilibrium thermodynamics for a single nonelectrolyte solute and water passing through a membrane are obtained by solving the local equations of motion. The method follows that developed for the general,n-solute case in the previous paper (Mikulecky, 1978). It is easily seen in this simple case that the passage from local interactions, formulated as position dependent frictional interactions in the equations of motion, to ghe global result involves a loss of any simple way of identifying particulars about local information. Two particular cases are analyzed in further detail: the case of no interaction within the pore and the case of constant interaction for both solute and solvent across the pore. In the former case, Onsager reciprocity survives in the global result if a self-consistent definition of the partial viscosity coefficients is used, while in the latter case, reciprocity is lost. Since, in many biologically interesting cases, the presence of interaction of the type considered here is likely to occur, the reciprocity condition should not automatically be assumed to hold.

Notes: Abstract This study is related to a model describing the behavior of barium-treatedAplysia neurons generating regular burst-plateau patterns. The model is represented by an autonomous dynamical system, defined inR 4 and depending on a small parameter. This paper is restricted to the qualitative study of three “reduced systems” deduced from the “complete system”. Part of the study is performed with the use of the qualitative theory of singular perturbations. The predicted behaviors are compared with experimental results.

Notes: Abstract Using linear stability analysis, the qualitative stability properties of open nonlinear chemical systems, in which reactions of any order may occur, will be studied. Systems will be classified in three fundamental classes: trees, cycles and loops, according to their knot graphs. The study of the Jacobian matrix for the kinetic equations of the system shows that the symmetrizability by a particular procedure (calledD-symmetrizability) is a sufficient condition for stability. It has been proved that tree-graphs always satisfy the above condition. For the cycle-graphs, theD-symmetrizability condition leads to a cyclic relation between forward and reverse steady state flows. The stability may be assured, even if the cyclic relation is not satisfied, providing that the “symmetry breaking” be lower than an upper bound; further alternative criteria for stability of cycles have been derived. All these results are independent of the number of diffusive exchanges with the environment.

Notes: Abstract The basis of an analytical description of the behaviour of large random nets of binary elements of the type first investigated in detail by S. A. Kauffman is presented. It is shown that information about the network dynamics can be deduced from quite general considerations of the properties of the state transition graph and matrix. An expression for the matrix elements of the state transition matrix in terms of the Boolean function specification of the net is derived. Using these ideas the distribution of limit cycle lengthsl for a completely random net is calculated and shown to bex 1/l, a result which agrees well with experimental data.

Notes: Abstract The state-transition matrix description of Kauffman binary networks described in the previous paper is further developed to obtain an analytical expression for the fraction of states involved in limit cycles as a function of the network size and connectivity. The result obtained for totally connected networks agrees with that derived from quite different considerations by other workers. For low connectivity networks the results are in qualitative agreement with the experimental data of Kauffman but there is a quantitative discrepancy which remains to be resolved.

Notes: Abstract Persistence-extinction in simple food chains modelled by Lotka-Volterra dynamics is governed by a single parameter which depends upon the interspecific interaction coefficients, the intraspecific interaction coefficients, and the length of the food chain. In persistent systems with nonzero carrying capacity, two new features predominate. Trophic level influence factors relate persistence on different trophic levels and determine, in conjunction with the persistence parameter, the magnitude of persistence. Equilibrium component ordering, which results in persistent systems, mandates once again that systems need to be studied on the complete ecosystem level; static field measurements reflect species location in the food chain, the total length of the food chain and assume characteristics according to these factors.

Notes: Abstract The study of systems exhibiting a band-pass function is completed for systems whose parameters are time-dependent. In the case of periodic parametric excitations, it is demonstrated that some systems can get into “resonance” for a particular frequency. By studying this problem, a new and probably fruitful approach of some rhythmic behaviours can be made.

Notes: Abstract Analytical techniques are developed which permit objective control of asiist device driving systems. In addition to being objective, the techniques described in this paper are optimal in the sense of minimizing a performance index which consists of a term involving left ventricular power and a term involving deviations of aorta hemodynamic parameters from normal values. Comparisons are included of off-line computations and measurements on dogs with experimentally induced myocardial infarctions undergoing intraaortic balloon pumping.

Notes: Abstract A mathematical model simulating a cell growing in a culture medium is obtained. Using this model, various behavioral patterns of the cell are obtained under different types of disturbances, in particular when (i) a Mg2+ deficiency experiment and, (ii) a split-dose ionizing radiation experiment are carried out, (iii) when disturbances on the rate constants of the biochemical reactions taking place in the nucleus of the cell are applied, and (iv) when the cell's interior components are perturbed. The cell model results obtained agree well with experimental results for the Mg2+ and split dose experiments, and explain the mechanism of the split dose radiation experiment without the need to introduce additional axioms (e.g. healing processes) into the dynamics of the cell. Conditions are obtained which cause the cell to behave in a rapidly growing ‘tumor-like’ mode; it is shown that once the cell moves into this ‘tumor-like’ mode, its behavior is irreversible, i.e. if a disturbance of opposite type is then applied to the ‘tumor’ cell, the cell will not revert back to its original normal behavior.

Notes: Abstract Solution of the equation that describes simulatenous liquid flow and diffusion in a spherical model of the vitreous body of the eye shows that a small dissolved specie can move both anteriorly and posteriorly from a source behind the lens even though there is a slow liquid movement almost entirely in the posterior direction. This results explains why tracer studies using large particles (dyes or colloids) show only a posterior flow, whereas studies using sodium ion show anterior movement as well.

Notes: Abstract The equations relating hybridized RNA to free RNA, in the case of simple hybridization, or to ratio of labelled and unlabelled RNA in competitive hybridization, are derived. Analysis of the equations shows how hybridization data may be used to infer properties of the distribution of components in an RNA mixture, or the relation between two distributions in competitive hybridization. A critical examination of the assumptions underlying the equations indicates that some of then may be violated in certain cases, or have no current support, evidential or theoretical. The consequences of such qualifications for the interpretation of hybridization data are indicated.

Notes: Abstract A method, based on symmetry, is suggested for determining the information content of systems. A comparison has been made between the information for symmetry, topology, and chemical composition. The new information measure increases when the asymmetry of the molecules and the number of atoms in the latter increases. It can distinguish between different molecular conformations, and give a linear correlation with the absolute entropy for homologous series of chemical compounds.

Notes: Abstract The micromorphic theory of Eringen is applied to study the tube flow of blood. The blood is considered to be a deformable suspension, with constitutive relations of the form of those of simple microfluids. By means of energy consideration, a relation is established between the local concentration parameter and the measure of rotationality involving both macro-and micromotions. The tube flow problem is then solved with some analyses on viscosity coefficients and boundary conditions. The results obtained indicate an integrated explanation of various important physical phenomena associated with blood flow, such as the tube size dependence of the apparent viscosity and the non-uniform concentration distribution over a tube cross section.

Notes: Abstract By observing that the n-tuple of rate functionsQ(c) is orthogonal to the c-space gradients of each of the (n - 1) constants of the motion Φ v (c), a generic canonical expression for the rate functions is given in terms of the exterior product of the gradients of the (n - 1) Φ v 's. For models withQ so prescribed from the outset, an analytical general solution is obtainable directly for the system of autonomous ordinary differential equations dc/dt =Q(c). Thus, the generic canonical expression for the rate functions can be utilized to construct analytically solvable models for interacting biological species, as ilIus~rated by examples here.

Notes: Abstract The steady state spatial patterns arising in nonlinear reaction-diffusion systems beyond an instability point of the thermodynamic branch are studied on a simple model network. A detailed comparison between the analytical solutions of the kinetic equations, obtained by bifurcation theory, and the results of computer simulations is presented for different boundary conditions. The characteristics of the dissipative structures are discussed and it is shown that the observed behavior depends strongly on both the boundary and initial conditions. The theoretical expressions are limited to the neighborhood of the marginal stability point. Computer simulations allow not only the verification of their predictions but also the investigation of the behavior of the system for larger deviations from the instability point. It is shown that new features such as multiplicity of solutions and secondary bifurcations can appear in this region.

Notes: Abstract A model for the extraocular plant of the human visual eye tracking mechanisms is discussed. Its sensitivity to variation of controller signal nervous activity is studied in order to determine the type of activity that yields realistic simulations characteristic of typical saccadic eye movements.

Notes: Abstract Mathematical models of predator-prey systems in which the prey species has a three-stage life cycle are studied. Certain stages of the prey life history are allowed to use younger stages as food. It is shown that sufficiently restricted cannibalism can result in an increase in the numbers of adult prey on a sustained basis when cannibalism decreases the vulnerability of a stage subject to predation or increases overall productivity.