ALBERT

Notes: Abstract Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.

Notes: Abstract The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.

Notes: Abstract Galerkin's finite element-Laplace transform technique (GAFELTTE) has been used to study transient temperature distribution in human skin and subcutaneous tissues. This study incorporates heat conduction, heat carried by perfusion of blood in the capillary beds and metabolic heat generation in the tissues. Different values of various quantities have been considered in all three parts, namely epidermis, dermis and subcutaneous tissues, depending on physiological considerations. The GAFELTTE provides interface temperatures for a wide range of the values of skin surface temperatures. These values have been used to obtain temperature profiles in the region considered. Steady-state temperature distribution has been deduced from the solution obtained by GAFELTTE and has been compared with the results obtained by using different methods.

Notes: Abstract Necessary and sufficient conditions are given for three equilibria to occur in a predatorprey model and conditions are given for two of these to be stable. The existence of two stable equilibria requires predator intraspecific competition for either space or food, and the lower the prey growth rate the stronger this predator self-regulation must be. A prey growth rate that is skewed to the right, the ability of a few predators to survive at low prey densities, and predators with high searching effectiveness, long handling times, and large maximum per capita rate of increase all make two stable equilibria more likely.

Notes: Abstract Drawing evidence from a variety of cardiovascular studies on the heart rate in homeothermic animals, the author establishes the following thesis. The servocontrol (i.e. the autonomic and reflex control) by the medulla oblongata of the heart (rate) is a negative feedback dynamic which is isomorphic (i.e. ‘diffeomorphic’) to the dyamic underlying the heat rate control in those animals (cf. Kuyk,Bull. math. Biol. 46, 81–102, 1984). In fact, unlike in the heat rate case, the qualitative evidence supporting this thesis can not be fully complemented by quantitative data stemming from experiments, because of a lack of pertinent experiments—which, indeed, should measuresimultaneously the heart rate state parameter and thefour control parameters at the input side of the medulla. The results of some of the existing experiments on animal preparations can nevertheless be adduced to recognize that this dynamic can be graphed by the five-dimensional butterfly catastrophe type. The theory leads to new ways of looking at experiments in the field and/or setting up such experiments in the future.

Notes: Abstract A model based upon minimization of surface energy is proposed as an explanation for compaction and internalization of cells during mammalian embryo development. The model is used to simulate and graphically display these phenomena on a computer.

Notes: Abstract This paper describes a growth model for binary topological trees. The model defines the branching probability of all segments in the tree. The branching probability of a segment is formulated as a function of two variables, one indicating its type (intermediate or terminal), the other representing its order, i.e. the topological distance to the root segment. The function is determined by two parameters, namely the ratio of branching probabilities of intermediate and terminal segments and the strength of the order dependency, implemented in an exponential form. Expressions are derived for the calculation of symmetry properties of the partitions and it is indicated which part of the parameter domain results in predominantly symmetrical trees.

Notes: Abstract The problem of cellular differentiation and consequent pattern generation during embryonic development has been mathematically investigated with the help of a reaction-diffusion model. It is by now a well-recognized fact that diffusion of micromolecules (through intercellular gap junctions), which is dependent on the spatial parameter (r), serve the purpose of ‘positional information’ for differentiation. Based on this principle the present model has been constructed by coupling the Goodwin-type equations for RNA and protein synthesis with the diffusion process. The homogeneous Goodwin system can exhibit stable periodic solution if the value of the cooperativity as measured by the Hill coefficient (ρ) is greater than 8, which is not biologically realistic. In the present work it has been observed that inclusion of a negative cross-diffusion can drive the system into local instability for any value of ρ and thus a time-periodic spatial solution is possible around the unstable local equilibrium, eventually leading to a definite pattern formation. Inclusion of a negative cross-diffusion thus makes the system biologically realistic. The cross-diffusion can also give rise to a stationary wave-like dissipative structure.

Notes: Abstract A nes software system is described for building simulation programs on micro- and minicomputers. Model equations are written as C subroutines, compiled and linked to the SCoP package to produce a menu-driven, interactive program. The system maintains a database of names, values, and units for all model parameters and variables. Run-time options include several methods for interactive parameter modification and both graphic and tabular outputs, with output values presented as they are calculated. Simulation output values can be compared with experimental data graphically and a companion program SCoPFit is provided for formal optimization of parameter values.

Notes: Abstract We consider the existence and global stability of aq-member equilibrium (1≤q≤n) in partially closed food-chains of lengthn having an abiotic component as resource. We observe that such existence demands bounds of resource supply rate and these bounds are weighted sums of interaction coefficients. Particular results of global sector-stability of partially feasible equilibria of simple food-chains obeying Lotka-Volterra dynamics are shown. Lastly the elasticity of such food-chains when a new species is introduced at the highest trophic level is investigated.

Notes: Abstract Criteria are established for three classes of models of single-species dynamics with a single discrete delay to have a globally asymptotically stable positive equilibrium independent of the length of delay.

Notes: Abstract The main concern of this paper is with survival or extinction of predators in models of predator-prey systems exhibiting group defence of the prey. It is shown that if there is no mutual interference among predators, enrichment could result in their extinction. However, if there is mutual interference, the predator population survives (at least deterministically).

Notes: Abstract In this paper a general class of semi-Markov compartmental systems is studied. Two models for different input processes are analysed. Attention has been paid to the recurrence times associated with each compartment and to the distribution of the number of particles in each compartment. As an example, a three-compartment system is discussed to study the movement between three health states of patients with chronic diseases.

Notes: Abstract A strategy is presented for searching the gene and protein sequence data banks which combines the use of two previously described algorthms. The implementation of this strategy is thoroughly evaluated with respect to sensitivity, specificity and speed. The establishment of standard benchmarks for comparing programs that rearch the sequence data banks for homology is proposed.

Notes: Abstract During functional linkage, ligand receptors are coupled to other receptors and to the cell's metabolic-transport apparatus. The linkage guides the cellular processing of matter, energy and information. Previous conceptions of functional linkage have used the ideas of classical physics appropriate to macroscopic objects. This study presents an initial quantum mechanical model of functional linkage in the case of ligands moving through lipid bilayers and hydrophilic transmembrane channels (‘pores’) of molecular dimensions. On the basis of permeability data, energy surfaces consisting of piecewise-constant potential regions are used to model the lipid bilayers and transmembrane channels. The centre-of-mass wavefunction for a ligand on such energy surfaces is analysed and the permeability coefficients calculated from the wavefunction's transmission characteristics. It is found that quasi-bound states in the several ligand-binding regions of a bilayer or pore system can functionally link to facilitate the passage of the molecule across the permeability barrier. Appearance of the linkage is a sensitive function of the ligand's energy. If the centre-of-mass energies are distributed as in a thermalized fluid, the flux via the quantum functional linkage can equal or exceed that of a classical flux for proton transport through rigid pores in which the intrasite barriers are relatively high (0.25–1 eV) and narrow (0.1–1 Å). The functional linkage plays a less important role in bilayer (rather than pore) energy surfaces and at higher molecular weights. If the ligand-receptor interaction is accompanied by energy transfer to or from ligands, the flux via the quantum functional linkage can equal or exceed the classically expected flux at all relevant ligand molecular weights. These findings are discussed in relation to earlier work and the limitations of the model emphasized.

Notes: Abstract A new measure of subalignment similarity is introduced. Specifically, similaritys(l,c) is defined as the logarithm to the basep of the probability of findingc or fewer mismatches in a subalignment of lengthl, wherep is the probability of a match. Previous algorithms can not use this measure to find locally optimal subalignments because, unlike Needleman-Wunsch and Sellers similarities, this measure is nonlinear. A new pattern recognition algorithm is described for finding all locally optimal subalignments of two nucleotide sequences. The DD algorithm can uses(l, c) or any other reasonable similarity function to assess the relative interest of subalignments. The DD algorithm searches only the diagonal graph, which lacks insertions and deletions. This search strategy greatly decreases the computation time and does not require an arbitrary choice of gap cost. The paths of the resulting DD graph usually draw attention to likely locations for insertions and deletions. A heuristic formula is derived for estimating significance levels fors(l, c) in the context of the lengths of the two aligned sequences. The DD algorithm has been used to find interesting subalignments between the nucleotide sequences for human and murine interleukin 2.

Notes: Abstract Nonlinear similarity functions are often better than linear functions at distinguishing interesting subalignments from those due to chance. Nonlinear similarity functions useful for comparing biological sequences are developed. Several new algorithms are presented for finding locally optimal subalignments of two sequences. Unlike previous algorithms, they may use any reasonable similarity function as a selection criterion. Among these algorithms are VV-1, which finds all and only the locally optimal subalignments of two sequences, and CC-1, which finds all and only the weakly locally optimal subalignments of two sequences. The VV-1 algorithm is slow and interesting only for theoretical reasons. In contrast, the CC-1 algorithm has average time complexityO(MN) when used to find only very good subalignments.

Notes: Abstract A resource-based competition model of two consumer species and one resource species is formulated in the form of a Lotka-Volterra system. The competition involves both exploitation and interference. By a method of asymptotic estimates, sufficient conditions are derived for the three species system to converge ast→∞ to an equilibrium point with all three species present; a generalization of the result forn≥2 and single resource species is indicated. The strong form of equilibrium perisistence of the three species consumer-resource system is achieved by the ability of each of the consumer species to exploit the resource and interfere with others in such a way which will avoid exclusion by the other.

Notes: Abstract The parameter domain for which the quasi-steady state assumption is valid can be considerably extended merely by a simple change of variable. This is demonstrated for a variety of biologically significant examples taken from enzyme kinetics, immunology and ecology.

Notes: Abstract The ability of random fluctuations in selection to maintain genetic diversity is greatly increased when generations overlap. This result has been derived previously using genetic models with very special assumptions about the population age structure. Here we explore its robustness in more realistic population models, with very general age structure or physiological structure. For a range of genetic models (haploid, diploid, single and multilocus) we find that the condition for maintaining genetic diversity generalizes almost without change. Genetic diversity is maintained by selection if a product of the form (generation overlap)×(selection intensity)×(variability in the selection regime) is sufficiently large, where the generation overlap is measured in units of Fisher's reproductive value. This conclusion is based on a local evolutionary stability analysis, which differs from the standard “protected polymorphism” criterion for the maintenance of genetic diversity. Simulation results match the predictions from the local stability analysis, but not those from the protected polymorphism criterion. The condition obtained here for maintaining genetic diversity requires fitness fluctuations that are substantial but well within the range observed in many studies of natural populations.

Notes: Abstract Premised on relatively simple assumptions, mathematical models like those of Monod, Pirt or Droop inadequately explain the complex transient behavior of microbial populations. In particular, these models fail to explain many aspects of the dynamics of aTetrahymena pyriformis-Escherichia coli community. In this study an alternative approach, an individual-based model, is employed to investigate the growth and interactions ofTetrahymena pyriformis andE. coli in a batch culture. Due to improved representation of physiological processes, the model provides a better agreement with experimental data of bacterial density and ciliate biomass than previous modeling studies. It predicts a much larger coexistence domain than rudimentary models, dependence of biomass dynamics on initial conditions (bacteria to ciliate biomasses ratio) and appropriate timing of minimal bacteria density. Moreover, it is found that accumulation ofE. coli sized particles andE. coli toxic metabolites has a stabilizing effect on the system.

Notes: Abstract At the core of contemporarymorphometrics—the quantitative study of biological shape variation—is a synthesis of two originally divergent methodological styles. One contributory tradition is the multivariate analysis of covariance matrices originally developed as biometrics and now dominant across a broad expanse of applied statistics. This approach, couched solely in the linear geometry of covariance structures, ignores biomathematical aspects of the original measurements. The other tributary emphasizes the direct visualization of changes in biological form. However, making objective the biological meaning of the features seen in those diagrams was always problematical; also, the representation of variation, as distinct from pairwise difference, proved infeasible. To combine these two variants of biomathematical modeling into a valid praxis for quantitative studies of biological shape was a goal earnestly sought though most of this century. That goal was finally achieved in the 1980s when techniques from mathematical statistics, multivariate biometrics, non-Euclidean geometry and computer graphics were combined in a coherent new system of tools for the complete regionalized quantitative analysis oflandmark points together with the biomedical images in which they are seen. In this morphometric synthesis, correspondence of landmarks (biologically labeled geometric points, like “bridge of the nose”) across specimens is taken as a biomathematical primitive. The shapes of configurations of landmarks are defined as equivalence classes with respect to the Euclidean similarity group and then represented as single points in David Kendall'sshape space, a Riemannian manifold with Procrustes distance as metric. All conventional multivariate strategies carry over to the study of shape variation and covariation when shapes are interpreted in the tangent space to the shape manifold at an average shape. For biomathematical interpretation of such analyses, one needs a basis for the tangent space compatible with the reality of local biotheoretical processes and explanations at many different geometric scales, and one needs graphics for visualizing average shape differences and other statistical contrasts there. Both of these needs are managed by thethin-plate spline, a deformation function that has an unusually helpful linear algebra. The spline also links the biometrics of landmarks to deformation analysis of the images from which the landmarks originally arose. This article reviews the history and principal tools of this synthesis in their biomathematical and biometrical context and demonstrates their usefulness in a study of focal neuroanatomical anomalies in schizophrenia.

Notes: Abstract A competition model describing tumor-normal cell interaction with the added effects of periodically pulsed chemotherapy is discussed. The model describes parameter conditions needed to prevent relapse following attempts to remove the tumor or tumor metastasis. The effects of resistant tumor subpopulations are also investigated and recurrence prevention strategies are explored.

Notes: Abstract Increasing attention is being paid to the configuration and development of vascular structures and their possible correlations with physiological events. The study of angiogenesis in normal and pathological states as well as in the embryo and adult has provided new insights into the mechanism of vessel growth and organization of the vasculature. Various mathematical branching models have been developed. These constructions are mainly geometrical and only involve a branching phenomenon. We propose the use of a deterministic non-linear model based on physiological laws and hydrodynamics. Growth, branching and anastomosis, the three actual main events occurring in vascular growth, are included in this model. Space growth, including cells and vessels, is defined by a decreasing transformation. Space density and the length of new sprouts are controlled by a set of parameters. The conditions on these parameters are well established, which allows the production of realistic patterns.

Notes: Abstract The quasi-stationary distribution of a population within a system of interacting populations is approximated by a stochastic logistic process. The parameters of this process can be expressed in the parameters of the full system. Using the diffusion approximation, an expression for the expected extinction time is derived from this logistic process. Since the expected extinction time is expressed in the parameters of the full system, the effect of these parameters on the extinction risk can be easily evaluated, which may be of use for studies in ecology, conservation biology and epidemiology. The outcome is compared with simulation results for the case of a prey-predator system.

Notes: Abstract The cytokines are the information superhighway of the immune system. They are an important component of the integrated behavior of the system. In order to be able to have a good understanding of the immune system, we must be able to model the effect of cytokines and their combined effect. This work is a step in that direction. We study the combined effect of two cytokines: interleukin-2 (IL-2) and interleukin-4 (IL-4) on some cells of the immune system. Interleukin-2 and interleukin-4 are important growth and differentiation factors for B and T cells. Interleukin-4 antagonizes the effect of interleukin-2 on B cells and some T cells while it synergizes with interleukin-2 on other T cells. We build a mathematical model of the interaction of both cytokines on T and B cells as a building block toward a model of the Th1/Th2 cross-regulation. The response of a given cell to the combination of interleukin-2 and interleukin-4 is shown to involve competing dynamical effects which can lead to either antagnostic or synergistic combined effect.

Notes: Abstract We propose a mathematical approach to the modelling of self-organizing hierarchies in animal societies. This approach relies on a basic positive feedback mechanism that reinforces the ability of a given individual to win or to lose in a hierarchical interaction, depending on how many times it won or lost in previous interactions. Motivated by experiments carried out on primitively eusocial waspsPolistes, the model, is based on coupled differential equations supplemented with a small stochastic term. Numerical integrations allow many different hierarchical profiles to be obtained depending on the model parameters: (1) the particular form of the probability for an individual to win or lose a fight given its history, (2) the probability of interaction between two individuals, (3) the forgetting strength, which determines the rate at which events in the past are forgotten and no longer influence the force of an individual and (4) two individual recognition parameters, which set the contribution of individual recognition in the process of hierarchical genesis. We compare the results, expressed in terms of a hierarchical index or of the Landau number that describes the degree of linearity of the hierarchy, with various experimental results.

Notes: Abstract The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable. In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsenet al., J. theor. Biol. 177, 113–128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay. Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states—a central property of the model, which is evident from stability and bifurcation analyses. The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders.

Notes: Abstract Populations often exhibit abrupt changes in abundance associated with a smooth, continuous change in some component of their environment, with the abruptness usually attributed to inter-specific interactions or physical extremes. This paper presents a spatially explicit single-species population model in which intra-specific interactions alone are responsible for such an abrupt change. The essential mechanism involves cooperation in both colonization (through enhanced recruitment near other individuals) and mortality (protection through a “safety-in-numbers” interaction). Large fluctuations in population density would likely be observable near the transition region.

Notes: Abstract A mathematical model of the nitrogen transformation cycle in an aquatic environment is studied. Using Pontryagin's maximum principle, a preferential utilization of ammonium to nitrate by phytoplankton is explained and verified by experimental data. A multiparameter bifurcation is given. The model was found to have four types of equilibrium sets. It is shown that a Hopf bifurcation may occur.

Notes: Abstract Parallel computation employing a domain decomposition method was used to calculate precisely without approximations the spatio-temporal distribution of Ca2+ in nerve terminals. The results showed, contrary to expectations, that for equal admitted Ca2+ currents at low (one channel open) and high (four channels open) depolarization, the average Ca2+ concentration at the release area is higher at the low depolarization. These calculations provide additional support for the Ca2+-voltage hypothesis for neurotransmitter release.

Notes: Abstract Type I hypersensitivity, which functions to protect the organism from parasites, is caused by binding of antigen to IgE antibodies pre-attached to the cell surface of tissue mast cells and their circulating counterparts, the basophils. In “allergy,” type I hypersensitivity is inappropriately induced by protein-based foreign substances (such as pollen) or protein components of insect stings, which in the normal course of events would be cleared from the organism without causing any damage. Paradoxically, a successful clinical treatment of allergy involves repeated immunization of allergic persons with low doses of the allergen—immunotherapy. Investigation of the available experimental evidence leads to the conclusion that the phenomena of immunotherapy are best addressed in terms of the interplay among the mechanism(s) of immune memory—Th1/Th2 cross-regulation—and the physical compart-mentalization of the immune system. These conclusions are illustrated with a numerical simulation.

Notes: Abstract In the presence of seasonal forcing, predator-prey models with quadratic interaction terms and weak dissipation can exhibit infinite numbers of coexisting periodic attractors corresponding to cycles of different magnitude and frequency. These motions are best understood with reference to the conservative case, for which the degree of dissipation is, by definition, zero. Here one observes the familiar mix of “regular” (neutrally stable orbits and tori) and chaotic motion typical of non-integrable Hamiltonian systems. Perturbing away from the conservative limit, the chaos becomes transitory. In addition, the invariant tori are destroyed and the neutrally stable periodic orbits becomes stable limit cycles, the basins of attraction of which are intertwined in a complicated fashion. As a result, stochastic perturbations can bounce the system from one basin to another with consequent changes in system behavior. Biologically, weak dissipation corresponds to the case in which predators are able to regulate the density of their prey well below carrying capacity.

Notes: Abstract The standard method for measuringin vitro antibiotic efficacy is based on a point observation of bacterial activity 18 hours after inoculation. The method, while simple, forgoes significant information by ignoring the dynamics of the interations between antibiotic and bacteria. This paper proposes a simple dynamic model describing these interactions. The model consists of two non-linear differential equations of the S-system type. Its parameter values are estimated, through the minimization of residual errors, from data on the effect of the carbapenem antibiotic imipenem onPseudomonas aeruginosa. The model adequately describes the dynamic behavior of the bacterial populations in the presence of the antibiotic: beginning with drug administration, then through the decline of the bacterial population and possibly ending with bacterial resurgence.

Notes: Abstract We have studied an ecological system of two species, which we denotestrong andweak, respectively, that compete for a single food resource. This system is modelled as a three component reaction-diffusion process. In the presence of a solitary pulse of increased resources, the weaker competitor can diffuse toward this surplus, gaining a competitive advantage and hence persisting in contraposition with the classical Lotka-Volterra result. An exact analytical solution has been found through a quantum mechanical analogy. A stability analysis of this solution against changes in different parameters has been carried out.

Notes: Abstract Collapsible-tube flow with self-excited oscillations has been extensively investigated. Though physiologically relevant, forced oscillation coupled with self-excited oscillation has received little attention in this context. Based on an ODE model of collapsible-tube flow, the present study applies modern dynamics methods to investigate numerically the responses of forced oscillation to a limit-cycle oscillation which has topological characteristics discovered in previous unforced experiments. A devil's staircase and period-doubling cascades are presented with forcing frequency and amplitude as control parameters. In both cases, details are provided in a bifurcation diagram. Poincaré sections, a frequency spectrum and the largest Lyapunov exponents verify the existence of chaos in some circumstances. The thin fractal structure found in the strange attractors is believed to be a result of high damping and low stiffness in such systems.

Notes: Abstract In this work, we show that a one-dimensional model of the blood flow across the lungs can reproduce the evolution of a bolus versus the time. Solving the differential equation governing the bolus concentration in the framework of this model, we determine the solution which fulfills Gaussian initial boundary conditions. An effective parameter related to the ratio of a diffusion coefficient to the square of the mean speed of the flow is defined. The determination of its numerical values following a semi-empirical approach enables us to know accurately the mean transit time and the cardiac output. The results have been compared to other methods, and were found in good agreement. Such an approach could be of interest in all studies where the knowledge of flow—including micro-circulation—is needed.

Notes: Abstract How two species interact during and after colonization influences which of them will be present in each stage of succession. In the tolerance model of ecological succession in a patchy environment, empty patches can be colonized by any species, but the ability to tolerate reduced resource levels determines which species will exclude the other. Here, we analyze a meta-population model of the possible roles of competition in colonization and succession, using non-linear Markov chains as a mathematical framework. Different kinds of competition affect the final equilibrial, abundances of the species involved in qualitatively different ways. An explicit criterion is given to determine which interactions have stronger effects on the final equilibrial levels of the weaker, species. Precise conditions are stated for the co-existence of both species. Both species are more likely to co-exist in the presence of an intermediate disturbance frequency.

Notes: Abstract This work addresses the design of LoG filters in the frequency domain within a structure formed by the cascade of quasi-Gaussian and discrete Laplacian filters. The main feature of such a structure is that it requires half the number of convolutions of the classical structure in which the LoG transfer function is expressed as the sum of two separable transfer functions of 1-D Gaussian and LoG type. Such a perspective allows one to rephrase the design of IIR and FIR filters for edge detection as a frequency domain approximation problem solvable by standard digital filter design tools. The zero-phase IIR solutions have a good performance at low orders and approximation errors practically independent of the aperture parameter. The characteristics of the nearly linear-phase IIR filters solving the problem suggest the consideration of linear-phase FIR filters with zeros constrained on the unit circle. The use of such filters leads to remarkable computational savings with respect to the filters designed by impulse response sampling. The agreement between the edge values obtained by the filters designed according to the scheme proposed in this work and those obtained by standard techniques is very good.

Notes: Abstract This paper is a brief historical review of linear singular systems, followed by a survey of results on their solution and properties. The frequency domain and time domain approaches are discussed together to sketch an overall picture of the current status of the theory.

Notes: Abstract We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for Lp-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering.

Notes: Abstract Beurling's algebra $A^*=\{f:\sum_{k=0}^{\infty} \sup_{k\le |m|} |\hat f (m)| 〈 \infty \}$ is considered. A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener's algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means. Certainly, both algebras are used in some other areas. A* has many properties similar to those of A, but there are certain essential distinctions. A* is a regular Banach algebra, its space of maximal ideals coincides with $[-\pi,\pi],$ and its dual space is indicated. Analogs of Herz's and Wiener-Ditkin's theorems hold. Quantitative parameters in an analog of the Beurling-Pollard theorem differ from those for A. Several inclusion results comparing the algebra A* with certain Banach spaces of smooth functions are given. Some special properties of the analogous space for Fourier transforms on the real axis are presented. The paper ends with a summary of some open problems.

Notes: Abstract We construct an algebra of left-invariant pseudodifferential operators on SU(2). We require only that the symbols be homogeneous and C2. For Fourier-bandlimited symbols, we derive the expected formulae for composition and commutators and construct an orthonormal basis of common approximate eigenvectors that could be used to study spectral theory. Some remarks on applications to matrices of operators are made.

Notes: Abstract A novel and complete method is presented for constructing the generalized Bezout identity in polynomial form of the transfer matrix from its state-space representation of a reachable and observable system. As a result, one can easily apply well-developed synthesis and analysis theories to systems described in the frequency domain.

Notes: Abstract The aim of this paper is to obtain the uncertain value set in the complex plane for systems with real and complex parameters that are known to lie inside a ball in a weightedl p-norm. It generalizes previously available results and may be used to test the robust stability of polynomials whose coefficients lie in a weighted lp-ball.

Notes: Abstract This paper describes a new approach—a Fixed-Level Least Squares (FLLS) method for linear-phase FIR filter design. It is intended for rejection of the Gibbs phenomenon through the introduction of a set of equally spaced fixed levels in the transition band and subsequent redefinition of the approximated and weighted functions. Detailed mathematical solutions of the problem as well as many examples are given. The results in graphical form are shown as an output of the FLLS software model.

Notes: Abstract In this paper we examine order reduction of parabolic systems using modal truncation. The parabolic distributed system is first approximated using the Galerkin method. The system matrices have a special structure that allows us to find the approximate spectrum of the parabolic system. To do this we compute approximate inverses of tridiagonal, diagonally dominant symmetric matrices. The approximation leads to algorithms of orderO(n), as opposed to traditional algorithms of orderO(n), wheren is the order of the system. Finally, an example is presented to illustrate the proposed algorithm.

Notes: Abstract We give results concerning the problem of approximating the input-output maps of nonlinear discrete-time approximately finite-memory systems. Here the focus is on the linear dynamical parts of the approximating structures, and we give examples showing that these linear parts can be derived from asingle prespecified function that meets certain conditions. This is done in the context of an approximation theorem in which attention is focused on what we call “basic sets.” We also consider the related but very different problem of approximating nonlinear functionals using lattice operations or the usual linear ring operations. For this problem we give criteria, not just sufficient conditions, for approximation on compact subsets of reflexive Banach spaces (any Hilbert space is a reflexive Banach space).

Notes: Abstract New calibration methods are presented for bearing estimation with sensor location uncertainties, which are based on eigenvalue decomposition of the sample covariance matrix and three or more nondisjoint sources in known bearings. The methods can be applied to arbitrary arrays, including linear arrays, require fewer computations, and are suitable for low signal-to-noise ratio (SNR) cases. Computer simulations are given to illustrate the performance of the proposed methods.

Notes: Abstract A doubly recursive algorithm for time domain convolution with a piecewise linear weighting function is presented that combines the speed of a recursive (IIR) digital filter with the flexibility and ease of design of a nonrecursive (FIR) digital filter. The approach approximates the desired FIR weighting function by a sum-of-triangles weighting function. ForL triangles (or triangle pairs for a linear phase filter) the algorithm is of orderLN. The approximation improves with the number of triangles. A significant advantage of the algorithm compared to FFT filtering or direct convolution is that there is no necessity of a tradeoff between frequency response accuracy and computation time per output point as the data spacing decreases in the filtered signal. The computational complexity is dependent on the number of triangles chosen, not the width of the weighting function, so the algorithm is especially effective for filters with an inherently wide FIR weighting function.

Notes: Abstract A solution of the problem of correlation analysis of stochastic amplitude-angle modulated signals is presented. The solution is obtained on the basis of the theory of linear stochastic processes for the general case of nonstationary correlated Gaussian noises in both modulation channels. These noises are regarded as the results of a linear filtration of Gaussian white noise processes. As an example of the analysis a case of band-pass modulation noises is considered.

Notes: Abstract Two-dimensional (2-D) periodically shift-variant (PSV) digital filters are considered. These filters have applications in processing video signals with cyclostationary noise, scrambling digital images, and 2-D multirate signal processing. The filters are formulated in the form of a Givone-Roesser (GR) state-space model with periodic coefficients. This PSV model is then presented in block form as a shift-invariant system that also has the same GR state-space form. This block form has reduced computations and ease of analysis. An algorithm is developed that transforms any given 2-D PSV GR system to its equivalent shift-invariant model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the shift-invariant model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. The established results are illustrated with an example.

Notes: Abstract In a recent paper a method is described for constructing certain approximations to a general element in the closure of the convex hull of a subset of an inner product space. This is of interest in connection with neural networks. Here we give an algorithm that generates simpler approximants with somewhat less computational cost.

Notes: Abstract In this paper, we gave an exponential estimate for the solutions of singular systems of differential equations with a delay and establish a comparison inequality for the systems. Based on this we estabish the criteria for asymptotic stability for the composite singular systems.

Notes: Abstract This paper presents the VLSI architectures for three-level correlator design based on 1-μm CMOS technology. The architecture performs very high speed, real-time, three-level cross-correlation of signals. Two architectures, one for serial incoming samples of signals (serial data) and the other for stored signal samples (parallel data), are described in the paper.

Notes: Abstract This paper gives the existence of and bounds for the branch voltages and currents in a given infinite network, which on each branch are related by a maximal monotone resistance function. We give a simpler proof than that of Minty, with smaller bounds, in the finite network case.

Notes: Abstract An efficient procedure is presented for computing the frequency-response templates of uncertain rational transfer functions depending on two independent interval polynomials. It consists of a modified Cohen-Sutherland algorithm for the intersection test of two rectangles and a pivoting algorithm. Because the proposed procedure traces out the boundary of a frequency-response template directly, it is, in general, more efficient than the previously proposed algorithms.

Notes: Abstract In this paper, a novel VLSI algorithm for the computation of a two-dimensional discrete cosine transform is proposed. The 2D-DCT equation can be expressed by the sum of high order cosine functions, and the algorithm can be realized by combining a highly efficient first order recursive structure with some simplified matrix multiplications, which results in highly regular hardware architecture and simple routing. The algorithm has temporal and spatial locality of connection and can be segmentized for pipeline operations, so the computation time is greatly reduced. Owing to the simplicity in hardware structure, it is especially good for VLSI implementation.

Notes: Abstract We examine a generalized matched-filter problem in which the interference is a nonstationary process generated by passing white noise through a general linear time-varying filter. First a matched filter is constructed by transforming the problem into an equivalent formulation involving stationary interference and a time-varying propagation channel. Whereas the response of a time-invariant matched filter is sampled at its peak, the response of this time-varying matched filter is normalized before sampling to account for variations in the signal power. Next a matched filter is constructed using a spectral characterization of the nonstationary interference. This construction is then used to formulate a simplified solution for the case where the rate of variation in the nonstationary interference is sufficiently small. The different solutions are illustrated by a numerical example.

Notes: Abstract The purpose of this paper is to investigate the approximation capability of elliptic basis function (EBF) neural networks. The main results are: (1) A necessary and sufficient condition for a functionS′ (R 1) to be qualified as an activation function in the hidden layer of an EBF neural network is given. (2) Every nonzero functionG ε L 2(R n ) is qualified to be an activation function in the elliptic neural network to approximate any function in L2(Rn). (3) As applications, we give new proofs of the theorems concerning the approximation capability of affine basis function (ABF) neural networks and generalized radial basis function (GRBF) neural networks (including radial basis function neural networks) with arbitrary activation functions. In particular, we solve the problem of the approximation capability of sigma-pi neural networks.

Notes: Abstract The frequency response of linear interval systems under PID controllers is analyzed. A two-stage elimination algorithm is presented to describe the boundary of the response in the complex plane. Illustrative examples are included.

Notes: Abstract This article deals with a new intelligent analog circuit design system. Unlike previous design methods, this approach introduces a formal circuit representation for both the numerical and heuristic knowledge of the design system. The predicate logic circuit representation is proposed as a new formal analog circuit description language. The language's syntax and semantics provide a precise symbolic description of analog circuit functionality at higher levels of hierarchy and network component connectivities, together with CMOS transistor sizes as the lowest level of hierarchy. It is shown how sentence conversion rules of language grammer can be used to derive transistor level circuits from input performance specifications. Language sentences have the form of clauses. In addition to clause representation, a frame representation to reflect VLSI design hierarchy is also introduced. An original bidirectional inference mechanism with elements of hypothesis has been introduced to infer designs from the knowledge in clause and frame representations. The unique feature of this circuit knowledge representation is its ability to automate the analog CMOS circuit design process. The design methodology is described in detail. The proposed iterative closed loop design system adopts an expert system approach to provide topological synthesis, uses a SPICE circuit simulator to evaluate the circuit performance, and uses a new diagnostic expert system to provide advice on how to improve the design. The implementation of the methodology and associated experimental results for simple CMOS operational amplifier designs are also presented.

Notes: Abstract An understanding of the comparative statics of biological communities is important both as a means of explaining the long-term effects of changes in environmental conditions, and as a framework for viewing community time trajectories. A general formulation of community dynamics is presented here which, given full information about a particular community's dynamic behavior, describes the impact of a change in environmental conditions on the community steady state. However, since such full information is often lacking in studies of biological communities, various approaches to partial information analysis of comparative statics are presented and compared, including a generalized protocol for isocline analysis. The suggested isocline protocol is shown to be a useful tool for both full and partial information analyses, as well as for both general and partial equilibrium studies.

Notes: Abstract Fujita's diagrams in phyllotaxis, showing the frequencies of divergence angles as a function of these angles for low phyllotactic patterns such as (2, 1) and (3, 2), which are approximately normal curves centered at the limitdivergence angle of 137.51°, are shown to be puzzling when compared to results and observations in the field. An analysis of these diagrams is proposed, in the context of Fujita's methodology, of data from other sources, of a mathematical theorem on lattices, and of the contact pressure theory of phyllotaxis.

Notes: Abstract It is shown that a representative Fisher-Wright model withn(≥3) diallelic loci admits a necessary condition for existence of a time-independent steady-state probability distribution. This necessary condition states that a global integral depending on the phenotype fitness functions of natural selection must be larger than a certain quantity depending on the parameters associated with genetic drift.

Notes: Abstract Equations for the time-dependent concentrations of all species involved in the general mechanism of human plasminogen activation proposed by Wohlet al. (J. biol. Chem. 255, 2005–2013, 1980) have been derived. These equations are valid for the whole course of the reaction: for both the transient phase and the steady state. In addition, we compare our results with the ones obtained by the above-mentioned authors for the steady state assuming rapid equilibrium conditions. Finally, we propose a method for the determination of all velocity constants.

Notes: Abstract A special class of interval graphs is defined and characterized, and an algorithm is given for their construction. These graphs are motivated by an important representation of DNA called restriction maps by molecular biologists. Circular restriction maps are easily included.

Notes: Abstract Over the past 25 years stepwise improvement in the cure of disseminated cancers has been good, fair or very poor depending on the particular cancer one is discussing. “Cancer chemotherapy provides variably effective treatment for the majority of forms of human cancer and curative treatment for some 12 categories.” We have been slow to gain and learn how to apply quantitative information on the biologic phenomena that underlie the responsiveness, or lack of responsiveness, of many different cancers to single drugs and combinations of drugs delivered in different ways. I am of the opinion that continuing development and integration of rational biomathematical models based on principles already identified, and testing them for compatibility with much already available experimental and clinical data, will lead to models that will help in planning more effective treatment regimens for cancers now classified as moderately refractory or very refractory to chemotherapy. Some of the critical variables are considered briefly. My advice, for what it is worth, is “try to be sure that the biologic concepts that you use in modeling are almost as good as the arithmetic.”

Notes: Abstract A discussion of the bases of physiological pharmacokinetics is followed by a brief review of the fundamental mass balance equations of the models. Some examples are outlined, together with a listing of published reviews which give many more references and detailed examples. Finally, some thoughts on future research directions are presented.

Notes: Abstract The use of stochastic simulation languages in cell kinetics research is discussed. Two special purpose simulation languages; CELLSIM and CELLGROW are described and example problems are presented.

Notes: Abstract Mathematical models predicting tissue doses of chemical toxicants can be either highly complex or simple, depending upon the end results needed. As an example of a highly complex mathematical model, the Miller Model of the distribution of reactive gases in human and animal lungs is described. The Miller Model accounts for the convection, the radial and axial diffusion, and the chemical reactions of gases as an inhaled breath passes down the airways. The geometry and physiology of human and animal lungs are used to calculate the convection and diffusion likely in each generation or bifurcating series of airways commencing with the trachea and extending 24 generations in humans. The chemical reactivity of ozone, an air pollutant, is accounted for by simulating second-order chemical reactions with the fluid lining materials of the lung and tissue biological molecules. The flux of ozone into three compartments (pulmonary tissue, overlying liquid layer and capillary blood) in each generation of the lung is calculated to provide molecular doses of ozone reaching each region of the lung. These results of calculated molecular dose are then used to construct dose-response curves for a variety of biological endpoints. A much simpler model is also described which recognizes the saturable or Michaelis-Menten type of kinetics controlling the removal of nickelous ion (nickel) from the lung. This model is used to calculate the chronic lung burden of the human lung for occupational, environmental and cigarette smoking exposure scenarios. In both the complex Miller Model and the simpler nickel lung burden model, the results can be used to calculate molecular doses at the potential site of action of these environmental chemicals and to unify a wide variety of studies. The predictions made are more likely to be valid since multiple investigators using a variety of animal species have participated in generation of the primary data. As a methodology, mathematical modeling based on physiological, physicochemical and anatomical principles provides a means of eliminating non-scientific considerations from the important process of regulating and recognizing toxic or cancer causing chemicals in the human environment.

Notes: Abstract This paper presents a brief review of applications of kinetic simulation of multi-enzyme networks to the study of antimetabolite drugs used as anticancer agents. Kinetic models consist of systems of nonlinear differential equations that describe changes in concentrations of cellular metabolites with respect to time. Such models have been used to predict the effect of changes in activity of enzymes, or changes in enzyme kinetic parameters, on sensitivity to inhibition. Kinetic simulation has provided insight into several aspects of the biochemical pharmacology of antimetabolites, including drug sensitivity and resistance, and drug-drug interactions. Two specific studies are described in detail. The first concerns the importance of the ratio of competing enzymes in determining the selectivity of inhibitors of one of the competing enzymes, studied by a simple model. The second case study examines the effect of alternative biosynthetic pathways, thede novo and salvage pathways of pyrimidine nucleotide biosynthesis, on the selectivity of antipyrimidine drugs, as studied by a detailed model of 27 reactions of pyrimidine metabolism.

Notes: Abstract General (deterministic) ordinary differential equations for the representation of cancer growth are presented when the growth is perturbed due to the action of a chemotherapeutic agent. The Verhulst-Pearl equation is introduced as a particular example of a growth equation applicable to human tumors. An optimal control problem with general performance criterion and state equation is formulated and shown to possess a novel feedback control relationship. This relationship is used in two continuous drug delivery problems involving the Verhulst-Pearl equation.

Notes: Abstract Complex networks of biological processes are analogous to electrical circuits. For each step in a biological or electrical network, flow is dependent on the driving force and the conductivity of the step. The relationship between biological flows and their driving forces can therefore be expressed as relationships between analogous currents and voltages. The time dependence of approach to equilibrium or a steady state is determined by the rates of depletion of material in various compartments. Electrical capacitance is therefore analogous to compartment volume. Once these generalized concepts of flow, force and capacitance are recognized, it becomes clear that computer programs designed for analysis of electrical circuits may be used for simulation of biological networks. A set of simple mathematical descriptions of the individual steps and a diagram showing how the steps are arranged with respect to each other are all that is necessary to perform a simulation; there is no need for computer programming skills or differential equations. The use of SPICE2 for simulation of the cellular and plasma pharmacokinetics of cytosine arabinoside (araC) is described as an example. A network model is developed which considers cellular pharmacokinetics (membrane transport, intracellular phosphorylation and dephosphorylation), and plasma pharmacokinetics following infusions of araC.

Notes: Abstract Developments in computer hardware and software are making significant improvements in the availability of simulation for biomedical researchers. This paper reviews past and present techniques for digital computer simulation and looks at improvements likely in the near future. In the area of hardware, personal computers are making computing and simulation more widely available and at the same time, supercomputers and special-purpose numerical processors are making it possible to solve larger problems. Software developments for simulation are reducing the time, effort and special skills required to produce a simulation program. A new hierarchical linker is proposed to make it easy to synthesize a global model by combining existing submodels. In the more distant future, computer models may be constructed graphically and with the assistance of intelligent programs capable of analysis and information retrieval.

Notes: Abstract Modeling is a ubiquitous and often misunderstood enterprise in which data from diverse disciplines are analyzed by techniques from other diverse disciplines in an attempt to confirm or falsify a set of hypotheses about the real world. Guidelines are offered for designing models to match the goals of modeling biological systems. Techniques for the construction and interpretation of models are discussed. The requirements for credibility of models are detailed, and tests are suggested for their validation.

Notes: Abstract Presentations and discussions at the symposium illustrate some general issues in biomedical modeling for cancer research. Given the motivations for modeling and assumptions concerning who should be involved in the modeling process, one can identify some basic needs to be met in supports to modelers. These concern both the models themselves and ways of presenting them to users. In conclusion, some thoughts are offered on economic and educational issues that may affect the infusion of modeling into biomedical research.

Notes: Abstract A global kinetic analysis of a model consisting of an autocatalytic zymogen-activation process, in which an irreversible inhibitor competes with the zymogen for the active site of the proteinase, and a monitoring coupled reaction, in which the enzyme acts upon one of its substrates, is presented. This analysis is based on the progress curves of any of the two products released in the monitoring reaction. The general solution is applied to an important particular case in which rapid equilibrium conditions prevail. Finally, we suggest a procedure to predict whether the inhibition or activation route dominates in the steady state of the system. These results generalize our previous analysis of simpler mechanisms.

Notes: Abstract In this work, treating the artery as a thick-walled cylindrical shell made of an incompressible, isotropic and elastic solid, utilizing the large deformation theory and the stress-strain relation proposed by Demiray (1976b,Trans. ASME Ser. E, J. Appl. Mech.,98, 194–197), an explicit expression for the pulse speed is obtained and the effect of lumen pressure and the axial stretch on wave speed is discussed. Numerical results indicate that the wave speed increases with lumen pressure but decreases with the axial stretch. The results of the present model are compared with our previous work (Demiray, 1988,J. Biomech. 21, 55–58) on the same subject.

Notes: Abstract For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of then-locus genetic system moves on the surface of the product space ofn higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.

Notes: Abstract Most recent models of the immune network are based upon a phenomenological log bell-shaped interaction function. This function depends on a single parameter, the “field”, which is the sum of all ligand concentrations weighted by their respective affinities. The typical behavior of these models is dominated by percolation, a phenomenon in which a local stimulus spreads globally throughout the network. The usual reason for employing a log bell-shaped interaction function is that B cells are activated by cross-linking of their surface immunoglobulin receptors. Here we formally derive a new phenomenological log bell-shaped function from the chemistry of receptor cross-linking by bivalent ligand. Specifying how this new function depends on the ligand concentrations requires two fields: a binding field and a cross-linking field. When we compare the activation functions for ligand-receptor pairs with different affinities, the one-field and the two-field functions differ markedly. In the case of the one-field activation function, its graph is shifted to increasingly higher concentration as the affinity decreases but keeps its width and height. In the case of the two-field activation function, the graph of a low-affinity interaction is nested within the graphs of all higher-affinity interactions. We show that this difference in the relations among activation functions for different affinities radically changes the network behavior. In models that described B cell proliferation using the one-field activation function, network behavior was dominated by low-affinity interactions. Conversely, in our new model, the high-affinity interactions are the most significant. As a consequence, percolation is no longer the only typical network behavior.

Notes: Abstract The dynamics of a microbial community consisting of a eucaryotic ciliateTetrahymena pyriformis and procaryoticEscherichia coli in a batch culture is explored by employing an individual-based approach. In this portion of the article, Part I, population models are presented. Because both models are individual-based, models of individual organisms are developed prior to construction of the population models. The individual models use an energy budget method in which growth depends on energy gain from feeding and energy sinks such as maintenance and reproduction. These models are not limited by simplifying assumptions about constant yield, constant energy sinks and Monod growth kinetics as are traditional models of microbal organisms. Population models are generated from individual models by creating distinct individual types and assigning to each type the number of real individuals they represent. A population is a compilation of individual types that vary in a phase of cell cycle and physiological parameters such as filtering rate for ciliates and maximum anabolic rate for bacteria. An advantage of the developed models is that they realistically describe the growth of the individual cells feeding on resource which varies in density and composition. Part II, the core of the project, integrates models into a dynamic microbial community and provides model analysis based upon available data.

Notes: Abstract Mathematical models are developed for the chemotherapy of AIDS. The models are systems of differential equations describing the interaction of the HIV infected immune system with AZT chemotherapy. The models produce the three types of qualitative clinical behavior: anuninfected steady state, aninfected steady state (latency) and aprogression to AIDS state. The effect of treatment is to perturb the system from progression to AIDS back to latency. Simulation of treatment schedules is provided for the consideration of treatment regimes. The following issues of chemotherapy are addressed: (i) daily frequency of treatment, (ii) early versus late initiation of treatment and (iii) intermittent treatment with intervals of no treatment. The simulations suggest the following properties of AZT chemotherapy: (i) the daily period of treatment does not affect the outcome of the treatment, (ii) treatment should not begin until after the final decline of T cells begins (not until the T cell population falls below approximately 300 mm−3) and then, it should be administered immediately and (iii) a possible strategy for treatment which may cope with side effects and/or resistance, is to treat intermittently with chemotherapy followed by interruptions in the treatment during which either a different drug or no treatment is administered. These properties are revealed in the simulations, as the model equations incorporate AZT chemotherapy as a weakly effective treatment process. We incorporate into the model the fact that AZT treatment does not eliminate HIV, but only restrains its progress. The mathematical model, although greatly simplified as a description of an extremely complex process, offers a means to pose hypotheses concerning treatment protocols, simulate alternative strategies and guide the qualitative understanding of AIDS chemotherapy.

Notes: Abstract A stochastic cellular automata model for the population dynamics of the army antEciton burchelli on Barro Colorado Island in Panama is set up. It is simulated on the computer and shown to give good agreement with biological data. It is analysed using two approximations akin to the mean field approximation in statistical mechanics, and good agreement with the simulations is obtained. Finally, the role of distance between successive statary phase bivouacs is discussed with regard to the rate of colony growth. There are two aspects of the biological system studied here that make it of general importance. First, the population is structured, since the size of each colony of army ants is crucial. Second, the spatial behaviour of the population, as in many others, is not diffusion-like, although it is random. This has implications for the kind of model that is chosen.

Notes: Abstract An analytical model for thermal damage of retinal tissue due to absorption of laser energy by finite-sized melanin granules is developed. Since melanin is the primary absorber of visible and near-IR light in the skin and in the retina, bulk heating of tissue can be determined by superposition of individual melanin granule effects. Granules are modeled as absorbing spheres surrounded by an infinite medium of water. Analytical solutions to the heat equation result in computations that are quick and accurate. Moreover, the model does not rely on symmetric beam profiles, and so arbitrary images can be studied. The important contribution of this model is to provide a more accurate biological description of submillisecond pulse exposures than previous retinal models, while achieving agreement for longer pulses. This model can also be naturally extended into the sub-microsecond domain by including vaporization as a damage mechanism. It therefore represents the beginning of a model which can be applied across the entire pulse duration domain.

Notes: Abstract Most of the elastic tubes found in the mammalian body will collapse from a distended circular cross section and when collapsed may undergo flow-induced oscillations. A mathematical model describing fluid flow in a collapsible tube is analysed using the software package AUTO-86. AUTO-86 is used for continuation and bifurcation problems in systems of non-linear ordinary differential equations. The model is a third-order lumped-parameter type and is based on the classical “Starling resistor”; it describes the unsteady flow behaviour and, in particular, the experimentally observed self-excited oscillations, in a way which is simple enough to give physical understanding, yet still firmly based on fluid mechanical principles. Some of the bifurcation types found in this model bear close resemblance to the types suggested by experimental observations of self-excited oscillations in collapsible tubes; they thus shed some light on the various topological changes which occur in practice, particularly in view of the fact that some of the points found numerically are diffcult to achieve experimentally, while the existence of others can only be inferred indirectly and uncertainly from experiment.

Notes: Abstract A solution algorithm yielding the pressure and flow-rate distributions for steady flow in an arbitrary, tree-like network is provided. Given the tree topology, the conductance of each segment and the pressure distribution at the boundary nodes, the solution is obtained from a simple recursion based on perfect Gauss elimination. An iterative solution method using this algorithm is suggested to solve for the pressure and flow-rate distributions in an arbitrary diverging-converging (arterial-venous) network consisting of two tree-like networks which are connected to each other at the capillary nodes. A number of special solutions for tree-like networks are obtained for which the general algorithm is either simplified or can be replaced by closed form solutions of the pressure and flow-rate distributions. These special solutions can also be obtained for each tree of diverging-converging networks having particular topologies and conductance distributions. Sample numerical results are provided.

Notes: Abstract Previous game-theoretic models of reciprocity have assumed that populations are large and organisms effectively sessile. This paper analyzes an iterated prisoner's dilemma among non-sessile organisms in a finite population, on the assumption that an individual's chance of remaining in one place is not influenced by a partner's behavior. This mode of interaction is suitable for analyzing potentially cooperative behaviors that are secondary to the advantage of group formation, e.g. allogrooming among social mammals. The analysis yields necessary conditions for stable reciprocity in terms of three parameters, namely, a benefit/cost ratio, the probability of further interaction and the probability of partner retention. The results suggest that, in highly mobile organisms such as fish, birds and mammals, reciprocity may be stable only if the population is small and the relative benefit and future interaction probability are both large.

Notes: Abstract We consider the kinetics of an autocatalytic reaction network in which replication and catalytic actions are separated by a translation step. We find that the behaviour of such a system is closely related to second-order replicator equations, which describe the kinetics of autocatalytic reaction networks in which the replicators act also as catalysts. In fact, the qualitative dynamics seems to be described almost entirely be the second-order reaction rates of the replication step. For two species we recover the qualitative dynamics of the replicator equations. Larger networks show some deviations, however. A hypercyclic system consisting of three interacting species can converge toward a stable limit cycle in contrast to the replicator equation case. A singular perturbation analysis shows that the replication-translation system reduces to a second-order replicator equation if translation is fast. The influence of mutations on replication-translation networks is also very similar to the behavior of selection-mutation equations.

Notes: Abstract In this work, we studied the propagation of non-linear waves in a pre-stressed thin elastic tube filled with an inviscid fluid. In the analysis, analogous to the physiological conditions of the arteries, the tube is assumed to be subject to a uniform pressureP 0 and a constant axial stretch ratio λz. In the course of blood flow it is assumed that a large dynamic displacement is superimposed on this static field. Furthermore, assuming that the displacement gradient in the axial direction is small, the non-linear equation of motion of the tube is obtained. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is investigated. It is shown that the governing equations reduce to the Korteweg-deVries equation which admits a solitary wave solution. The result is discussed for some elastic materials existing in the literature.