ALBERT

Notes: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.

Notes: Abstract Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.

Notes: Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Layapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopf's bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.

Notes: Abstract It was hypothesized in an earlier work that sensory perception can occur only when the perceiving system is uncertain about the nature of the event being perceived. In the absence of any uncertainty, perception will not take place. The response of the sensory afferent neuron (impulse transmission rate) was calculated using Shannon's measure of uncertainty or entropy. It will now be shown that when the event being perceived is the position and momentum of a particle, Shannon's measure of uncertainty leads to the Heisenberg Uncertainty relationship.

Notes: Abstract It is not unusual for several classifications to be given for the same collection of objects. We present a method, called majority rule, which can be used to define a consensus of these classifications. We also discuss some mathematical properties of this consensus tree.

Notes: Abstract The dependence of the spatial concentration profiles of morphogens on a characteristic dimension is obtained by continuation techniques for Gierer and Meinhardt's activator-inhibitor model of morphogenesis. The study of the behaviour of the system during growth, where the linear and exponential increase of the characteristic dimension is considered, revealed that more complex patterns of morphogen spatial concentrations appear regularly in a reproducible way.

Notes: Abstract Computer models have been used by various authors to simulate both the growth of normal cellular tissue and the development of cancerous cells within normal tissue. As these models were the result of considerable idealization, the purpose of the present paper is to propose a model in which the degree of simplification is relaxed: the features of simultaneous growth, and cell growth whose rate depends on the free absorbing periphery of the cell are introduced. Simulation experiments have been conducted using the model, and the results are presented.

Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for a nonlinear model of heat conduction in the human head. Accurate variational solutions are obtained in illustrative calculations. The effect of nonlinearity is seen to be significant from a comparison with the linearized model.

Notes: Abstract A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.

Notes: Abstract The irreversible Michaelis-Menten reaction is studied by the use of the method of multiple scales. Three stages of the reaction are identified, one of which is studied in detail. The results are compared with those of two earlier analyses.

Notes: Abstract A numerical study of the coupled nerve fibre problem is given which verifies and extends the perturbation theory of Luzader. Pulses on adjacent fibres can couple together with two possible stable pulse separations.

Notes: Abstract A possible mechanism for effects of microwave radiation on the auditory system is the generation of field-induced forces at interfaces that divide materials of dissimilar electrical properties. A general expression for these “Maxwell stresses” is derived and then used to calculate the approximate magnitude of field-induced force within the organ of Corti during microwave exposure. Comparison of the results with data on the force needed to excite cochlear hair cells indicates auditory responses could be evoked by this mechanism at power densities near the threshold of rf hearing sensations.

Notes: Abstract A definition of homogeneity for neural networks is given which permits their construction as group quotients. The significance of this for neural dynamics is discussed.

Notes: Abstract The left ventricle is represented as a cylinder contracting both radially and longitudinally. A simple method is indicated to derive an expression for the rate of change of the kinetic energy of this three-dimensional model, which quantity can be used as an index for the study of the contractile behaviour of the myocardium. An application to the study of muscle mechanics is also indicated.

Notes: Abstract A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.

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 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 The theory of computational complexity and certain explicitly-stated hypotheses imply limitations on the information processing power of biological systems. Parallelism, special purpose organization, and analog mechanisms may provide speedup critical for life processes, but have little power in the face of exponential growth. We show that “polynomially simulatable” biological systems cannot exhibit dynamic behavior which produces the solution of an intractable problem. The argument implies that parallelism does not allow biological systems to defeat the exponential explosion, but rather is important because it allows polynomial time algorithms to be used more efficiently.

Notes: Abstract A correlation matrix analysis is applied to the base sequence of MS2 and ϕX174 in comparison with sets of simulated sequences with different degrees of constaint Significant differences between a codified sequence, and a statistical one in terms of the “correlation matrix” for sets of different length cannot be found. This result is analysed in terms of nucleotide sequences with different levels of informational content.

Notes: Abstract A method of calculating the volume of a tree distal to a cut at the origin of a branch, using branching, diameter and length ratios, has been developed. The method was applied to bronchial tree casts from human, dog, sheep, hamster, and rat lungs. It was found that the exponenta in the equation weight=k×diameter a is approximately equal to 3.0 in sheep lung casts, as found by Hooper (1977), but it is greater than 3.0 in casts from the other four species.

Notes: Abstract In this note we examine a continuous time version of a compartmental model introduced in a discrete time setting by S. R. Bernard. The model allows for more than one particle to leave the system at any time. This introduces additional randomness into the system, over the pure death system and this is reflected in the variance function.

Notes: Abstract The mean first passage time for free diffusion can be derived directly by solving a simple analogue steady state problem. In this problem the diffusion starting region is considered as a time independent source of diffusing particles and the diffusion target assumes the behaviour of a perfectly absorbing sink. It is shown here that the transit time between the source and the sink, which in this particular problem is equal to the ratio between the holdup of the system and the total flux, is identical to the Brownian movement concept of the mean first passage time for free diffusion. This established identity considerably facilitates the derivation and investigation of the timing of diffusion in complicated structures such as those commonly found in living organisms.

Notes: Abstract In this paper three stochastic models are developed for a class of two-compartment systems to analyse the randomness of the leaving process of the particles in the system. Results in closed form for the distribution of the leaving process of the particles in the system are given both for general and exponential sojourn time distributions and also in association with forward recurrence time distributions with and without Poisson input.

Notes: Abstract Two simple models are proposed and analysed, in which it is shown that the formation of a new polymer, resulting from an “error” in the template action mechanism of production of an old polymer, may compromise the stability of the initial system under specific conditions, in the context of prebiotic evolution. Autocatalysis is shown to be a “selective advantage”, enabling the “mutant” to dominate in concentration and even replace the initial polymer. The addition of a third molecule playing the role of a catalyst causes hysteresis effects.

Notes: Abstract The problem of extinction of the prey population in a microbial predator-prey interaction in a chemostat has been examined. Usual deterministic lumped parameter models were used for the dynamics of the chemostat for large numbers of the two populations; the generalized birth and death stochastic process was employed for the description of the random variations at small prey numbers. Extinction probabilities of the prey population were calculated for different holding times and chemostat volumes, and their dependence upon the growth parameters of the two populations was studied. It was found that extinction was possible when the Monod model was used for the specific growth rate of the predators as a function of the prey number density. On the other hand, the decrease of the feeding activity of the predators at low prey densities predicted by the multiple saturation model acts as a regulatory factor that prevents extinction of the prey. In view of the fact that extinction of the prey has never been observed in the laboratory, the latter model seems more appropriate to describe the dynamics of microbial predation.

Notes: Abstract During exposures of the eye to light, the choroidal circulation may have a regulatory influence on the retinal temperature. This is investigated using a mathematical model and a finite-difference technique. It is predicted that the choroidal blood flow a small effect on retinal temperature, which may be important.

Notes: Abstract A probabilistic model of a spatially localized, mutually exitatory (inhibitory) population of neurons is formulated to help explain average evoked potential and post-stimulus time histogram measurements. The model is based on the stochastic activity of single neurons within interactive masses of neurons which exhibit co-operative behavior. Macrostate variables corresponding to the above measurements are related through the model to features of neural operation at the individual and ensemble level. Steady-state solution are obtained and their physiological implications are discussed.

Notes: Abstract We consider a one-compartment system with stochastic transfer rate characterized either by Gaussian or by two-level jump process and study the time evolution of the (statistical) moments of the (random) amount of the substance present in the system. The effect of the coloured as well as of the white noise is investigated and it is found that the presence of stochasticity in the transfer rate parameter increases the relaxation time of the system. Finally, we obtain the conditions for the stability of the system in the moment sense.

Notes: Abstract A model is described in which damage to a single intracellular locus can lead to a tumorigenic transformation. Assuming a large number of independent intracellular loci to be at risk and assuming that damage to a locus sufficient to cause a tumorigenic transformation occurs with probability greater than zero for all doses greater than zero, leads to the use of the Weibull distribution to characterize the probability of a nonspontaneous tumorigenic cellular transformation occurring after exposure to a given dose of carcinogen. The excess lifetime tumor incidence (i.e., the proportion of tumor bearers) above the spontaneous incidence is used as an estimate of the non-spontaneous incidence and is characterized by a tumor incidence function that represents the probability of occurrence of one or more non-spontaneous tumorigenic cellular transformations amongN(D) independent surviving cells per individual, after exposure to a doseD of carcinogen. The tumor incidence function is fitted to published data for the excess tumor incidence after exposure of animals or humans to ionizing radiation and after exposure of animals to chemical carcinogens.

Notes: Abstract This paper deals with a stochasticn-compartment irreversible system with a non-homogeneous Poisson input and arbitrary residence time for each of the compartments. Results relating to the number of particles present in each of the compartments as well as the total number of particles present in the system at any time are derived. Further, explicit expressions for the auto covariance function for each compartment and the cross-covariance function between any two compartments with a given time lag are obtained. As a particular case, then-compartment irreversible system is analyzed with homogeneous Poisson input and exponential residence time distribution for each of the compartments. The possible applications of the model are discussed.

Notes: Abstract This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.

Notes: Abstract The relationships that define the structure of a given ecosystem, social system, or even a physiological function can only exist if certain parameters are confined to a certain range of values. As the values change and exceed this given range the relationships are forced to change, and so produce a new pattern of relationships. The concept of a dynamic structure captures this potential for structural change in relation to a set of parameters. The precise definition of structure and allowable transformation constitutes the definition of a category. The total range of parameters associated with all the relevant structures provides a parameter space which is assumed to be a manifold. Maps with extra structure from the manifold to the category define dynamic structures. The domain of differential dynamic systems is the manifold, and a flow or movement across the manifold is associated with a series of structural transformations in the category. In some cases a structure outruns its parameter range, to be faced with an obstruction—an absence of possible transformations. Ways of studying such “obstructions” are considered along with the related problem of extending a dynamic structure beyond a previously given set of parameters. The cost or resistance of transformations is also studied. The concepts of dynamic structures are illustrated by the structural change of food webs and they are used in a necessarily qualitative fashion to study dominance structures of social orders and finally to speculate on the qualitative nature of evolutionary change of functional aspects of organisms.

Notes: Abstract The preceding paper (Thorn, 1981) has shown that in a linear pharmacokinetic system with a multimodal impulse response the peak drug level may sometimes be smaller with slower rates of injection. This paper presents two theorems on this paradoxical injection rate effect where the injection is a constant infusion of finite duration. The first theorem establishes a graphical method for determining whether a given impulse response will give a paradoxical injection rate effect; and the second establishes that the maximum paradoxical increase in peak drug level is by a factor of two. It is further shown that in order to approach this maximum paradoxical increase the impulse response must contain two isolated, sharp, narrow pulses of approximately equal area. Some examples of bimodal arterial dye-dilution curves from the literature are discussed as impulse responses; and there is also a discussion of the behavior of drug level maxima and minima at different injection rates.

Notes: Abstract This paper presents three theorems on the peak drug levels that result from injection into a linear pharmacokinetic system. As a preliminary, the “rate of injection” is defined in terms of time expansion or time contraction of the injection function (input). The first theorem then states that the peak drug level will not be greater when the rate of injection is slow than when it is fast, if the impulse response is unimodal. The second theorem sets limits for the time of the maximum drug level, in relation to the time of the maximum of the (unimodal) impulse response and the duration of the input. The third theorem defines conditions which assure a definitely lower peak drug level if the rate of injection is slower. A graphical method is suggested for determining the times and magnitudes of the peak drug levels that result from constant infusions of a fixed dose at different rates. An example is provided to show that if the impulse response is multimodal then the peak drug level may sometimes increase with a decrease in the injection rate.

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.

Notes: Abstract The present paper deals with the bifurcation analysis of a simple food chain model consisting of components like detritus, nutrients, microorganisms, phytoplankton and zooplankton in an aquatic environment. The food chain model is described by a system of differential equations. If the length of the food chain (LFCH) is equal to 3 or 4, then an asymptotically stable equilibrium exists. For LFCH=5 or 6 the non-trivial equilibrium is unstable and the food-chain model has periodic orbits.

Notes: Abstract We develop a macroscopic model for delivering drug to brain tumors. The model accounts for bulk convective and diffusive transport across the blood-brain barrier and through the interstitial space. Through mathematical analysis and simulations, we assess the effects of changing parameters (within physiological bounds) on drug delivery. We find that there is an optimal treatment for convective drug delivery to the center of the tumor. We interpret this phenomenon in terms of traffic flow. The implications of our analyses on existing chemotherapeutic protocols are discussed.

Notes: Abstract The concept of shape space proposed by Perelson and Oster (1979,J. Theor. Biol. 81, 645–670) has been a useful tool for theoretical immunologists, who have invoked it to model idiotypic binding, which plays a significant role in mathematical models of immune networks. The actual construction of such a space from its definition requires specialized experimental information, which is not completely available. In this article, we discuss, with illustrative examples, how graphical representations similar to the idea of shape space can be derived by analyzing real affinity matrices, and the relative merits of such representations to approximations that might be obtained by the approach of Perelson and Oster. We also give directions for future research with a view toward applications.

Notes: Abstract A novel intact circular dsDNA supercoil is proposed as an alternative to the conventional DNA supercoil, so that the two complementary strands of ssDNA circles are separable without any covalent bond breakage. This new structure can be visualized by using two tubings: one black and one clear. Twist the black tubing a number of times and connect its two ends. Do the same for the clear tubing. Then wrap the two tubings together. This forms the separable or novel supercoil. On the other hand, the conventional supercoil can be modeled by twisting the black and clear tubings together and then connect their respective ends, so that the two tubings are not separable unless one of them is cut. Experimentally, in the absence of any enzyme, many intact plasmid dsDNA circles give two bands on agarose gel electrophoresis under a certain given condition, while the same plasmid molecules after cutting once by a restriction enzyme give only one band under the same, condition. In the case of intact pUC19 plasmids, these two bands can then be, recovered and sequenced separately, using two primers in opposite directions. Each band gives mostly one sequence which is complementary to that of the other band. The combination of the above theoretical model and experimental results strongly suggests that there is an alternative structure of DNA which does not have the usual difficulty of unwinding, rewinding and requiring numerous covalent bond breakages and ligations during semiconservative replication.

Notes: Abstract In this paper, a closed-form identification of possibly nonminimum phase multichannel moving average (MA) processes is derived by exploiting the eigenstructures of the observation cumulant matrices using the ESPRIT algorithm. The proposed approach allows the combination of statistics of different orders for better performance and offers reduced computation complexity when compared with existing iterative approaches. Simulations are also presented to demonstrate the performance of the proposed algorithm.