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  • Springer  (120,417)
  • 2020-2024
  • 1990-1994  (64,934)
  • 1985-1989  (55,483)
  • 1993  (64,934)
  • 1988  (55,483)
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  • 2020-2024
  • 1990-1994  (64,934)
  • 1985-1989  (55,483)
Year
  • 1
    Electronic Resource
    Electronic Resource
    A mathematical derivation of the P-V relation at end-systole (1988)
    Springer
    Bulletin of mathematical biology 50 (1988), S. 35-41 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A dynamical model of the left ventricle as a thick-walled cylinder contracting radially is used to derive the P-V (pressure-volume) relation in the left ventricular cavity during contraction. It is shown how the mathematical results derived could apply to experimental results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459976
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  • 2
    Electronic Resource
    Electronic Resource
    Stability of discrete one-dimensional population models (1988)
    Springer
    Bulletin of mathematical biology 50 (1988), S. 67-75 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We give conditions for local and global stability of discrete one-dimensional population models. We give a new test for local stability when the derivative is −1. We give several sufficient conditions for global stability. We use these conditions to show that local and global stability coincide for the usual models from the literature and even for slightly more complicated models. We give population models, which are in some sense the simplest models, for which local and global stability do not coincide.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459978
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  • 3
    Electronic Resource
    Electronic Resource
    Sequence comparison with concave weighting functions (1988)
    Springer
    Bulletin of mathematical biology 50 (1988), S. 97-120 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider efficient methods for computing a difference metric between two sequences of symbols, where the cost of an operation to insert or delete a block of symbols is a concave function of the block's length. Alternatively, sequences can be optimally aligned when gap penalties are a concave function of the gap length. Two algorithms based on the ‘candidate list paradigm’ first used by Waterman (1984) are presented. The first computes significantly more parsimonious candidate lists than Waterman's method. The second method refines the first to the point of guaranteeingO(N 2 lgN) worst-case time complexity, and under certain conditionsO(N 2). Experimental data show how various properties of the comparison problem affect the methods' relative performance. A number of extensions are discussed, among them a technique for constructing optimal alignments inO(N) space in expectation. This variation gives a practical method for comparing long amino sequences on a small computer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459948
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  • 4
    Electronic Resource
    Electronic Resource
    On the incompatibility of gompertz or weibull survival dynamics with exponentially distributed individual lifespans (1988)
    Springer
    Bulletin of mathematical biology 50 (1988), S. 187-192 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is well documented, in the biological literature, that many species throughout the animal kingdom exhibit Gompertzian or Weibull-like population level total survival distributions. Many researchers have long assumed, believed, or otherwise postulated that an individual organism, in such a population, survived according to an exponential survival distribution. Using well-known results from reliability theory, it is shown that if every individual in the population has an exponentially distributed lifespan, then a Gompertzian or Weibull-like group/population level dynamics (or any other dynamics with a strictly increasing mortality rate for some interval) is not possible. This implies that, for species with a population level Gompertzian or Weibull (with the mortality rate strictly increasing) survival curve, some or all of the individual organisms must have non-exponentially distributed lifespans.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459951
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  • 5
    Electronic Resource
    Electronic Resource
    Identifiability of DNA distribution from flow cytometric data with cell debris (1988)
    Springer
    Bulletin of mathematical biology 50 (1988), S. 209-225 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In flow cytometric measurement of cell DNA distribution one of the major problems is accounting for the effect of fragmentation in the staining process. This work considers a recent probabilistic model that has been proposed for the fragmentation process and species under which conditions it is possible to uniquely identify the DNA distributions of the original population using flow cytometric data. Attention is given both to the normal and to the polyploid case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458881
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  • 6
    Electronic Resource
    Electronic Resource
    Metastability in a temperature-dependent model system for predator-prey mite outbreak interactions on fruit trees (1988)
    Springer
    Bulletin of mathematical biology 50 (1988), S. 379-409 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The nonlinear behavior of a particular Kolmogorov-type exploitation differential equation system assembled by May (1973,Stability and Complexity in Model Ecosystems, Princeton University Press) from predator and prey components developed by Leslie (1948,Biometrica 35, 213–245) and Holling (1973,Mem. Entomol. Soc. Can. 45, 1–60), respectively, is re-examined by means of the numerical bifurcation code AUTO 86 with model parameters chosen appropriately for a temperature dependent mite interaction on fruit trees. The most significant result of this analysis is that, in addition to the temperature ranges over which the single community equilibrium point of the system iseither globally stableor gives rise to a globally stable limit cycle, there can also exist a range wherein multiple stable states occur. These stable states consist of a focus (spiral point) and a limit cycle, separated from each other in the phase plane by an unstable limit cycle. The ecological implications of such metastability, hysteresis and threshold behavior for the occurrence of outbreaks, the persistence of oscillations, the resiliency of the system and the biological control of mite populations are discussed. It is further suggested that a model of this sort which possesses a single community equilibrium point may be more useful for representing outbreak phenomena, especially in the presence of oscillations, than the non-Kolmogorov predator-prey systems possessing three community equilibrium points, two of which are stable and the other a saddle point, traditionally employed for this purpose.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459707
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  • 7
    Electronic Resource
    Electronic Resource
    A simple mathematical model of the thermal death of microorganisms (1988)
    Springer
    Bulletin of mathematical biology 50 (1988), S. 493-501 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This note is concerned with a simple mathematical model of how a population of bacterial spores decrease with time when subjected to a uniform temperature. The model assumes that there is a Boltzman distribution of energy among water or other molecules surrounding the assumed single lethal target in a spore; it assumes that repair is not possible; and that only molecules with energies above a critical level cause inactivation. The model provides new insight concerning the ‘kill-rate’ of spores during ultra heat treatment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458848
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  • 8
    Electronic Resource
    Electronic Resource
    Effects of survival thresholds upon one-dimensional dynamics of single-species populations (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 1-13 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A simple one-dimensional model of single-species populations is studied by means of computer simulations. Although the model has a rich spectrum of dynamics including chaotic behavior, the introduction of survival thresholds makes the chaotic region so small that it can be hardly observed. Stochastic fluctuations further reduce the chaotic region because they accidentally lead populations to extinction. The model thus naturally explains the observation that the majority of natural populations do not show chaotic behavior but a monotonic return to a stable equilibrium point following a disturbance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460292
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  • 9
    Electronic Resource
    Electronic Resource
    Estimation of the extent of the cutoff region from the spatial distribution of labelling and mitotic indices of intestinal crypts of a fixed length (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 37-73 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Current understanding of the pattern of proliferation within intestinal crypts involves the notion of a cutoff region introduced by Cairnieet al. (Exp. Cell. Res. 39, 539–553, 1965b). (Cells produced above the cutoff are non-cycling, whereas cells produced below the cutoff are cycling.) They contrasted the predicted distribution of proliferation in the extreme cases of a cutoff of width 0 (a sharp cutoff) with one eight cells wide (a slow cutoff) and concluded that the data were better explained by the latter. We have shown that crypt size variation artificially broadens the apparent distribution of proliferating cells in the crypt (Totafurnoet al., Biophys. J. 54, 845–858, 1988). Here we show that the measurement and analysis of crypts of a specified height reduces this artifact. This work introduces the use of distance from the crypt base (in microns) to specify the location of cells within the crypt as an improvement over the cell position ordering traditionally used in the determination of the distribution of proliferating cells. We also show how to explicitly correct for several artifacts in the measurement of the labelling index. We conclude that cell proliferation within the crypt is more localized than previously realized; in fact, a cutoff as slow as eight cells wide is rejected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460294
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  • 10
    Electronic Resource
    Electronic Resource
    Efficient methods for multiple sequence alignment with guaranteed error bounds (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 141-154 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Multiple string (sequence) alignment is a difficult and important problem in computational biology, where it is central in two related tasks: finding highly conserved subregions or embedded patterns of a set of biological sequences (strings of DNA, RNA or amino acids), and inferring the evolutionary history of a set of taxa from their associated biological sequences. Several precise measures have been proposed for evaluating the goodness of a multiple alignment, but no efficient methods are known which compute the optimal alignment for any of these measures in any but small cases. In this paper, we consider two previously proposed measures, and given two computationaly efficient multiple alignment methods (one for each measure) whose deviation from the optimal value isguaranteed to be less than a factor of two. This is the novel feature of these methods, but the methods have additional virtues as well. For both methods, the guaranteed bounds are much smaller than two when the number of strings is small (1.33 for three strings of any length); for one of the methods we give a related randomized method which is much faster and which gives, with high probability, multiple alignments with fairly small error bounds; and for the other measure, the method given yields a non-obviouslower bound on the value of the optimal alignment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460299
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  • 11
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    Orientation by helical motion—I. Kinematics of the helical motion of organisms with up to six degrees of freedom (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 197-212 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The kinematics of helical motion are descirbed for an organism treated as a rigid body with six degrees of freedom relative to the organism's frame of reference, i.e. the organism can translate in the direction of, or rotate around any of, three orthogonal axes fixed to its body. Equations are derived that express the unit vectors of the Frenet trihedron and the torsion and curvature of the trajectory in terms of the organism's translational and rotational velocities. These equations permit description of the radius, pitch, angular velocity and axis of a helical trajectory in terms of the translational and rotational velocities of the organism swimming along that trajectory. The results of this analysis are then used in two later papers that describe how organisms can orient to an external stimulus.
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    URL: http://dx.doi.org/10.1007/BF02460302
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  • 12
    Electronic Resource
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    Announcement (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 257-257 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460305
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  • 13
    Electronic Resource
    Electronic Resource
    Orientation by helical motion—III. Microorganisms can orient to stimuli by changing the direction of their rotational velocity (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 231-255 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Organisms that move along helical trajectories change their net direction of motion largely by changing the direction, with respect to the body of the organism, of their rotational velocity (Crenshaw and Edelstein-Keshet, 1993,Bull. math. Biol. 55, 213–230). This paper demonstrates that an organism orients to a stimulus field, such as a chemical concentration gradient or a ray of light, if the components of its rotational velocity, with respect to the, body of the organism, are simple functions of the stimulus intensity encountered by the organism. For example, an organism can orient to a chemical concentration gradient if the rate at which it rotates around its anterior-posterior axis is proportional to the chemical concentration it encounters. Such an orientation can be either positive or negative. Furthermore, it is true taxis—orientation of the axis of helical motion is direct. It is neither a kinesis nor a phobic response—there is no random component to this mechanism of orientation.
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    URL: http://dx.doi.org/10.1007/BF02460304
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  • 14
    Electronic Resource
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    Terminal and intermediate segment lenghts in neuronal trees with finite length (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 277-294 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A basic but neglected property of neuronal trees is their finite length. This finite length restricts the length of a segment to a certain maximum. The implications of the finite length of the tree with respect to the segment length distributions of terminal and intermediate segments are shown by means of a stochastic model. In the model it is assumed that branching is governed by a Poisson process. The model shows that terminal segments are expected to be longer than intermediate segments. Terminal and intermediate segments are expected to decrease in length with incrasing centrifugal order. The results are compared with data fromin vivo pyramidal cells from rat brain and tissue cultured ganglion cells from chicken. A good agreement between data and model was found.
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    URL: http://dx.doi.org/10.1007/BF02460884
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  • 15
    Electronic Resource
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    The geometry of elongating plant cells (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 345-364 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Shape and size of elongating cells were examined in three plant tissues: the adaxial epidermis of the petiole ofZebrina pendula L., the abaxial epidermis ofAnacharis densa L. leaves and the abaxial epidermis of the scale leaf ofAllium cepa L. Based on a few simple assumptions, the expected probability distribution frequencies (pdf) for cell length and number of adjacent walls were calculated. Actual data of cell lengths closely approximated those expected with the pdfs being asymmetrical since there are more younger, shorter cells than older, longer cells. Data for number of lateral walls of real cells were similar to that expected and these walls increase in compensating mechanism exists to maintain a constant range of cell lengths through many cell generations. It is expressed by longer than average new daughter cells dividing relatively soon while shorter than average new daughter cells divide after a relatively long cycle.
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    URL: http://dx.doi.org/10.1007/BF02460887
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  • 16
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    Diffusion driven instability in an inhomogeneous domain (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 365-384 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism for pattern formation in numerous embryological and ecological contexts. However, the possible effects of environmental inhomogeneities has received relatively little attention. We consider a general two species reaction-diffusion model in one space dimension, with one diffusion coefficient a step function of the spatial coordinate. We derive the dispersion relation and the solution of the linearized system. We apply our results to Turing-type models for both embryogenesis and predator-prey interactions. In the former case we derive conditions for pattern to be isolated in one part of the domain, and in the latter we introduce the concept of “environmental instability”. Our results suggest that environmental inhomogeneity could be an important regulator of biological pattern formation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460888
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  • 17
    Electronic Resource
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    Non-uniformities and superimposed competition in a model of an autocatalytic network formed by error-prone self-replicative species (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 417-449 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The particular dynamics of the previously proposed model of a catalytic network formed byn error-prone self-replicative species without and with superimposed competition is analysed. In the first case, two situations are studied in detail: a uniform network in which all the species are inter-coordinated in the same way, and a network with a species differentiated in its catalytic relation with the remaining elements. In the second case, the superimposed competition is introduced at two levels: first, as an asymmetry in one of the network species amplification factor considering a null self-catalytic vector, and secondly, as a non-null self-catalytic vector with no asymmetry in the other propertics of the species. This kind of system does not present complex behaviour and can be adequately deseribed by performing a standard linear analysis, which gives direct information on the asymptotic behaviour of the sytem. Finally, the biological implications of this analysis within the framework of biological evolution are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460890
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  • 18
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    A thermodynamical model of cell distributions in the slug of cellular slime mold (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 451-464 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theoretical model is proposed for the formation of cell distribution patterns in the slug stage of the cellular slime moldDictyostelium discoideum. The equilibrium distribution of two types of cells, prestalk and prespore, is obtained by minimizing the free energy, which is defined in terms of differential chemotaxis, differential cell adhesion and randomness of cell movement. Resulting distributions show various segregation patterns of cell types. The condition for cell sorting is obtained from stability analysis of the set of diffusion equations governing the evolution of cell type distribution and the concentration of chemoattractant. The intensities of differential chemotaxis and random cell movement are quantitatively evaluated from experimental data to show that two cell types can sort themselves completely by these forces.
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    URL: http://dx.doi.org/10.1007/BF02460891
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  • 19
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    Cell migration in multicell spheroids: Swimming against the tide (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 655-674 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Multicell spheroids, small spherical clusters of cancer cells, have become an importantin vitro model for studying tumour development given the diffusion limited geometry associated with many solid tumour growths. Spheroids expand until they reach a dormant state where they exhibit a grossly static three-layered structure. However, at a cellular level, the spheroid is demonstrably dynamic with constituent cells migrating from the outer well-nourished region of the spheroid toward the necrotic central core. The mechanism that drives the migrating cells in the spheroid is not well understood. In this paper we demonstrate that recent experiments on internationalization can be adequately described by implicating pressure gradients caused by differential cell proliferation and cell death as the primary mechanism. Although chemotaxis plays a role in cell movement, we argue that it acts against the passive movement caused by pressure differences.
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    URL: http://dx.doi.org/10.1007/BF02460655
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  • 20
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    Book reviews (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 675-691 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02460656
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  • 21
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    Summer School on Nonlinear Systems in Evolutionary and Population Biology (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 693-693 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02460657
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  • 22
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    Consensus functions and patterns in molecular sequences (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 695-713 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In recent years, methods of consensus, developed for the solution of problems in the social sciences, have become widely used in molecular biology. Westudy a method of consensus originally due to Watermanet al. (Waterman, Galas and Arratia. 1984. Pattern recognition in several sequences: consensus and alignment.Bull. math. Biol. 46, 515–527) which is used to identify patterns or features in a molecular sequence where a pattern can vary in position within a given window. We show that some well-known consensus methods of the social sciences, the median and the mean, are special cases of this method for certain choices of the parameters used in it and give a precise account of the parameters for which these special cases arise. We also show that the specific parameters used in the method of Watermanet al. make their method equivalent to the median procedure which is widely used in the social sciences.
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    URL: http://dx.doi.org/10.1007/BF02460669
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  • 23
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    Immune network behavior—I. From stationary states to limit cycle oscilations (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 745-780 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation, B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis, how each of the processes influences the model's behavior. After appropriate nondimensinalization, the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-tye equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior.
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    URL: http://dx.doi.org/10.1007/BF02460672
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    Immune network behavior—II. From oscillations to chaos and stationary states (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 781-816 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two types of behavior have been previously reported in models of immune networks. The typical behavior of simple models, which involve B cells only, is stationary behavior involving several steady states. Finite amplitude perturbations may cause the model to switch between different equilibria. The typical behavior of more realistic models, which involve both B cells and antibody, consists of autonomous oscillations and/or chaos. While stationary behavior leads to easy interpretations in terms of idiotypic memory, oscillatory behavior seems to be in better agreement with experimental data obtained in unimmunized animals. Here we study a series of models of the idiotypic interaction between two B cell clones. The models differ with respect to the incorporation of antibodies, B cell maturation and compartmentalization. The most complicated model in the series has two realistic parameter regimes in which the behavior is respectively stationary and chaotic. The stability of the equilibrium states and the structure and interactions of the stable and unstable manifolds of the saddle-type equilibria turn out to be factors influencing the model's behavior. Whether or not the model is able to attain any form of sustained oscillatory behavior, i.e. limit cycles or chaos, seems to be determined by (global) bifurcations involving the stable and unstable manifolds of the equilibrium states. We attempt to determine whether such behavior should be expected to be attained from reasonable initial conditions by incorporating an immune response to an antigen in the model. A comparison of the behavior of the model with experimental data from the literature provides suggestions for the parameter regime in which the immune system is operating.
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    URL: http://dx.doi.org/10.1007/BF02460673
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  • 25
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    Mathematics in medicine and the life sciences (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 865-867 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02460677
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  • 26
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    Diffusion-enhanced bioreactions: A hypothetical mechanism for plant cell aggregation (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 869-889 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We show that the existence of diffusional resistance due to the presence of a solid phase can have a positive effect on the metabolic reactions of plant cells. In this case the efficiency of metabolic reactions, defined as the ratio of rate of production of biomass of aggregated cells/rate of production of biomass of dispersed cells, can be greater than unity for a certain range of aggregate sizes for both solid spheres (common plant cell aggregates) and hollow spheres (e.g.Volvox aggregates). This means that, under appropriate conditions, plant cells tend to stay in the aggregated form to improve the efficiency of their metabolic reactions. The result of the present analysis provides an explanation as to why aggregates of plant cells are observed under typical culture conditions.
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    Bifurcation of the Hodgkin and Huxley equations: A new twist (1993)
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    Bulletin of mathematical biology 55 (1993), S. 937-952 
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    Notes: Abstract The Hodgkin and Huxley equations model action potentials in squid giant axons. Variants of these equations are used in most models for electrial activity of excitable membranes. Computational tools based upon the theory of nonlinear dynamical systems are used here to illustrate how the dynamical behavior of the Hodgkin Huxley model changes as functions of two of the system parameters.
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    Positive feedback in aquatic ecosystems: The case of the microbial loop (1993)
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    Bulletin of mathematical biology 55 (1993), S. 919-936 
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    Notes: Abstract The description of the “microbial loop” has led to some major changes in our understanding of nutrient cycling within aquatic ecosystems. It now appears that in many settings it is not uncommon for some 50% of phytoplankton production to be diverted into microbial pathways rather than passing up to higher trophic levels. As a result the microbial loop is responsible for enhanced and rapid nutrient cycling at the very base of the food web. Since tight recycling is often associated with unstable positive feedback, we use a model to examine the possible repercussions in more detail. The model simulates the dynamics of the microbial loop and finds it to greatly affect the way in which aquatic primary production responds to nutrient pulses.
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    Optimal maintenance investment of plants and its dependence on environmental conditions (1993)
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    Bulletin of mathematical biology 55 (1993), S. 953-971 
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    Notes: Abstract The maintenance activity of plants is investigated in terms of a simple model. Maximization of a certain biomass fraction we refer to asnonactive biomass is postulated. Optimal behaviour of plants according to this principle is explicitly derived and expressed depending on environmental conditions. Several interesting hypotheses result, e.g. a quadratic law relating specific growth rate and gross rate of photosynthesis. A qualitative comparison with data from the literature is performed, with a special emphasis on the question whether plants stressed by air pollutants repair optimally. Regarding long-term constant environmental conditions, no data were found that contradict optimal behaviour. Exact quantitative testing of the theory is desirable, appropriate experiments are suggested.
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    Growth factors and growth control of heterogeneous cell populations (1993)
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    Bulletin of mathematical biology 55 (1993), S. 993-1011 
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    Notes: Abstract In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocrine and paracrine growth factors in tumor growth.Bull. math. Biol. 53, 639–656). The target population, a generic tumor, was modeled as a single, homogeneous population using the standard Verhulst equation of logistic growth. Mitogenic signals were represented by modifications to the Malthusian growth parameter and adaptational signals were represented by modifications to the carrying capacity. Three growth scenarios were described: (1) normal tissue wound healing, (2) unperturbed tumor growth, and (3) tumor growth in a radiation damaged environment, a phenomenon termed the Tumor Bed Effect (TBE). In this paper, we extend those results to include a “triad” of growth factor controls (autocrine, paracrine and endocrine) and heterogeneity of the target population. The heterogeneous factors in the model represent either intrinsic, epigenetic or environmental differences in both normally differentiating tissues and tumors. Three types of growth are modeled: (1) normal tissue differentiation or wound healing, assuming no communication between differentiated and undifferentiated cell compartments; (2) normal wound healing with feedback inhibition, due to signalling from the differentiated compartment; and (3) the development of hypoxia in a spherical tumor. The signal processing within the triad is discussed for each model and biologically reasonable constraints are defined for limits on growth control.
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    A new method to solve a non-steady-state multispecies biofilm model (1993)
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    Bulletin of mathematical biology 55 (1993), S. 1039-1061 
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    Notes: Abstract A transient multispecies model for quantifying microbial space competition in biofilm is derived from existing models, introducing a new approach to biomass detachment modelling. This model includes inert biomass, substrate diffusion and utilization rate within the biofilm and diffusional layers. It predicts the evolution of biofilm thickness, bulk substrate concentration, species distribution and substrate concentration within the biofilm. A zero-dimensional transient model is described. Its steady-state solution is used to set up initial conditions of the one-dimensional model and case computation towards steady-state solution. Some numerical tools have been developed, enabling fast computation on microcomputers. Simulations show the validity of a zero-dimensional model and perturbated systems are also simulated. Simulations with experimental data give acceptable results.
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    Analytical expression of the purine/pyrimidine codon probability after and before random mutations (1993)
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    Bulletin of mathematical biology 55 (1993), S. 1025-1038 
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    Notes: Abstract Recently, we proposed a new model of DNA sequence evolution (Arquès and Michel. 1990b.Bull. math. Biol. 52, 741–772) according to which actual genes on the purine/pyrimidine (R/Y) alphabet (R=purine=adenine or guanine, Y=pyrimidine=cytosine or thymine) are the result of two successive evolutionary genetic processes: (i) a mixing (independent) process of non-random oligonucleotides (words of base length less than 10: YRY(N)6, YRYRYR and YRYYRY are so far identified; N=R or Y) leading to primitive genes (words of several hundreds of base length) and followed by (ii) a random mutation process, i.e. transformations of a base R (respectively Y) into the base Y (respectively R) at random sites in these primitive genes. Following this model the problem investigated here is the study of the variation of the 8 R/Y codon probabilities RRR,..., YYY under random mutations. Two analytical expressions solved here allow analysis of this variation in the classical evolutionary sense (from the past to the present, i.e. after random mutations), but also in the inverted evolutionary sense (from the present to the past, i.e. before random mutations). Different properties are also derived from these formulae. Finally, a few applications of these formulae are presented. They prove the proposition in Arquès and Michel (1990b.Bull. math. Biol. 52, 741–772), Section 3.3.2, with the existence of a miximal mean number of random mutations per base of the order 0.3 in the protein coding genes. They also confirm the mixing process of oligonucleotides by excluding the purine/pyrimidine contiguous and alternating tracts from the formation process of primitive genes.
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    Complexity of protein folding (1993)
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    Bulletin of mathematical biology 55 (1993), S. 1199-1210 
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    Notes: Abstract It is believed that the native folded three-dimensional conformation of a protein is its lowest free energy state, or one of its lowest. It is shown here that both a two-and three-dimensional mathematical model describing the folding process as a free energy minimization problems is NP-hard. This means that the problem belongs to a large set of computational problems, assumed to be very hard (“conditionally intractable”). Some of the possible ramifications of this results are speculated upon.
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    Memory in idiotypic networks due to competition between proliferation and differentiation (1993)
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    Bulletin of mathematical biology 55 (1993), S. 1133-1182 
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    Notes: Abstract A model employing separate dose-dependent response functions for proliferation and differentiation of idiotypically interacting B cell clones is presented. For each clone the population dynamics of proliferating B cells, non-proliferating B cells and free antibodies are considered. An effective response function, which contains the total impact of proliferation and differentiation at the fixed points, is defined in order to enable an exact analysis. The analysis of the memory states is restricted in this paper to a two-species system. The conditions for the existence of locally stable steady states with expanded B cell and antibody populations are established for various combinations of different field-response functions (e.g. linear, saturation, log-bell functions). The stable fixed points are interpreted as memory states in terms of immunity and tolerance. It is proven that a combination of linear response functions for both proliferation and differentiation does not give rise to stable fixed points. However, due to competition between proliferation and differentiation saturation response functions are sufficient to obtain two memory states, provided proliferation preceeds differentiation and also saturates earlier. The use of log-bell-shaped response functions for both proliferation and differentiation gives rise to a “mexican-hat” effective response function and allows for multiple (four to six) memory states. Both a primary response and a much more pronounced secondary response are observed. The stability of the memory states is studied as a function of the parameters of the model. The attractors lose their stability when the mean residence time of antibodies in the system is much longer than the B cells' lifetime. Neither the stability results nor the dynamics are qualitatively chanbed by the existence of non-proliferating B cells: memory states can exist and be stable without non-proliferating B cells. Nevertheless, the activation of non-proliferating B cells and the competition between proliferation and differentiation enlarge the parameter regime for which stable attractors are found. In addition, it is shown that a separate activation step from virgin to active B cells renders the virgin state stable for any choice of biologically reasonable parameters.
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    1988 Gordon Conference on Theoretical Biology and Biomathematics (1988)
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    Bulletin of mathematical biology 50 (1988), S. 95-95 
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    Computational simulation of activity of cortical-like neural systems (1988)
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    Bulletin of mathematical biology 50 (1988), S. 143-185 
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    Notes: Abstract The kinetic theory of neural systems is extended to include the description of cortical-like neural structures. This fact is accomplished by the introduction of long-distance effects. Collaterally, we have the separation of the description of the excitatory activity from that of the inhibitory one. Also, the description of neural systems with a high level of activity is obtained. The modified theory is used to simulate computationally the activity of cortical-like neural systems.
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    Simulation of cellular compaction and internalization in mammalian embryo development—II. Models for spherical embryos (1988)
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    Bulletin of mathematical biology 50 (1988), S. 121-142 
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    Notes: Abstract A model based upon minimization of surface energy as an explanation for the phenomena of compaction and internalization of cells during mammalian embryo development is generalized for three-dimensional cells. It is shown that, for a spherical embryo, if cells are assumed to be polygonal cones in shape, the simulation of these phenomena for three-dimensional cells is equivalent to simulations of deformations of two-dimensional cells on the surface of a sphere. This equivalence is used to show that in the optimal compacted structure, with no internal cells, the cross-sections of cells in general are not regular polyhedra. Further, the internalization occurs when the number of cells exceeds a critical value which seems to depend on the relative sizes and biophysical properties of cells.
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    Interactions leading to persistence in predator-prey systems with group defence (1988)
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    Bulletin of mathematical biology 50 (1988), S. 517-530 
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    Notes: Abstract In previous work (Freedman and Wolkowicz, 1986;Bull. math. Biol. 48, 493–508) it was shown that in a predator-prey system where the prey population exhibits group defence, it is possible that enrichment of the environment could lead to extinction of the predator population. In this paper a third population is introduced and criteria are derived under which persistence of all populations will occur. In particular, criteria for a superpredator and for a competitor to stabilize the system in the sense of persistence are analyzed.
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    The unstirred layer during osmotic flow into a tubule (1988)
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    Bulletin of mathematical biology 50 (1988), S. 531-545 
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    Notes: Abstract The interaction between osmotic inflow through the wall of a narrow tubule and bulk flow in the tubule is described. Solution are found by a finite difference method, and two approximate analytic solutions are given. Results given here enable more accurate estimates of osmotic permeability to be obtained for the tubule wall. The theory predicts the behaviour of unstirred layers as experimental parameters are varied and enables tubule experiments to be designed so as to reduce unwanted unstirred layer effects.
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    Book reviews (1988)
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    Bulletin of mathematical biology 50 (1988), S. 567-576 
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    Software survey section (1988)
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    Bulletin of mathematical biology 50 (1988), S. I 
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    Stationary mutant distributions and evolutionary optimization (1988)
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    Bulletin of mathematical biology 50 (1988), S. 635-660 
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    Notes: Abstract Molecular evolution is modelled by erroneous replication of binary sequences. We show how the selection of two species of equal or almost equal selective value is influenced by its nearest neighbours in sequence space. In the case of perfect neutrality and sufficiently small error rates we find that the Hamming distance between the species determines selection. As the error rate increases the fitness parameters of neighbouring species become more and more important. In the case of almost neutral sequences we observe a critical replication accuracy at which a drastic change in the “quasispecies”, in the stationary mutant distribution occurs. Thus, in frequently mutating populations fitness turns out to be an ensemble property rather than an attribute of the individual. In addition we investigate the time dependence of the mean excess production as a function of initial conditions. Although it is optimized under most conditions, cases can be found which are characterized by decrease or non-monotonous change in mean excess productions.
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    Time-dependent subpopulation induction in heterogeneous tumors (1988)
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    Bulletin of mathematical biology 50 (1988), S. 681-696 
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    Notes: Abstract Time-dependent induction of clonal heterogeneity in the neoplastic micro-environment is analysed within the context of a competitive ecology. A model that describes a constant source for clonal emergence was analysed by Michelsonet al. (1987) as an extension of a model proposed by Jansson and Revesz (1974). The extended model has been termed the JRE Model. This paper extends these analyses to time-dependent emergence rates which may represent induction in the presence of a cytotoxic agent. If the analysis is constrained to the tumor micro-environment, and if the emergent subpopulation is drug resistant, then the model may describe the induction and emergence of drug resistant subclones in a growing neoplasm. Asymptotic closed form solutions are derived for a class of emergence rate functions which decay asymptotically to a constant mutation rate. This underlying mutation rate may represent spontaneous mutation to the resistant phenotype, and has been analysed stochastically (Coldmanet al., 1985). The asymptotic solutions to the time-dependent model approach the steady state solution for the JRE Model which represents the dynamics observed in the presence of a constant, spontaneous mutation rate. The clinical and biological implications of these results are discussed.
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    Book reviews (1988)
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    Bulletin of mathematical biology 50 (1988), S. 697-700 
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    The Society for Mathematical Biology is pleased to announce an Annual Best Paper Award of $1000 (1988)
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    Bulletin of mathematical biology 50 (1988), S. 701-701 
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    Editorial: Software survey section (1988)
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    Bulletin of mathematical biology 50 (1988), S. I 
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    Preface (1993)
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    Circuits, systems and signal processing 12 (1993), S. 153-154 
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    Topics: Electrical Engineering, Measurement and Control Technology
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    Efficient derivation of the optimal mean-square binary morphological filter from the conditional expectation via a switching algorithm for discrete power-set lattice (1993)
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    Circuits, systems and signal processing 12 (1993), S. 409-430 
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    Notes: Abstract Once designed, implementation of an optimal mean-square binary morphological filter is extremely fast, especially when the erosions are implemented on a suitable parallel processor. On the other hand, optimal filter design involes a computationally burdensome search procedure that can, in practice, be intractable. The present paper provides an algorithm for filter design that is based on the relationship between the optimal morphological filter and the conditional expectation. The algorithm proceeds by changing the conditional expectation into a morphological filter while at the same time increasing the mean-square error by a minimal amount. It does so by switching observations between the 1-set and the 0-set of the conditional expectation. The switching algorithm is extremely efficient in many noise environments, and therefore provides a filter design that can be useful for online structuring-element updating. Owing to the relationship between stack and morphological filters, the algorithm is at once useful for finding optimal binary stack filters.
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    Feedback neural networks: new characteristics and a generalization (1993)
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    Circuits, systems and signal processing 12 (1993), S. 263-278 
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    Notes: Abstract New characteristics of feedback neural networks are studied. We discuss in detail the question of updating of neurons given incomplete information about the state of the neural network. We show how the mechanism of self-indexing for such updating provides better results than assigning ‘don't know’ values to the missing parts of the state vector. Issues related to the choice of the neural model for a feedback network are also considered. Properties of a new complex valued neuron model that generalizes McCulloch-Pitts neurons are examined.
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    Chained eigenstructure assignment for strongly controllable singular systems (1993)
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    Circuits, systems and signal processing 12 (1993), S. 391-407 
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    Notes: Abstract This paper deals with chained eigenstructure assignment for strongly controllable singular systems of the form Êx (t)=Â x(t)+B u(t) with state feedback control of the formu(t)=Kx(t)+w(t). The development of our method depends crucially on the properties of standard form singular systems. The closed-loop system will satisfy the following requirements: regularity, impulse-free response and rankÊ arbitrary eigenvalues assignment. This parametric characterization conveniently organizes the nonunique gain matrixK to modify the dynamic response of the systems. The result can be used for discrete-time descriptor systems, in which a zero-value eigenvalue may well be a desired closed-loop eigenvalue. One illustrative example is included.
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    Statistical performance analysis of a fast stochastic gradient for constrained adaptive time delay estimation (1993)
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    Circuits, systems and signal processing 12 (1993), S. 453-464 
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    Notes: Abstract An efficient bi-state stochastic gradient is proposed for spontaneous constrained time delay estimation. The quantized stochastic gradient is an approximation of the polarity of the instantaneous delay estimation error. It is adjusted in such a way that it has a much higher probability to move in the correct direction at each iteration so as to enable a speed-up in the delay estimate to converge to global minimum in steady state. The performance of the delay estimator is evaluated statistically and an analytical solution for its convergence behavior is established. It is demonstrated that the proposed algorithm has at least a two-fold improvement in convergence speed when compared with the conventional approach, and this is verified by extensive simulation results.
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    Fast algorithms for erasures and error correction in redundant residue number systems (1993)
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    Circuits, systems and signal processing 12 (1993), S. 503-531 
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    Notes: Abstract In this work, we extend the coding theory approach to error control in redundant residue number systems (RRNS). The concept of erasure correction capability in RRNS is introduced. We derive the relationship between the minimum distance and the error detection and error/erasure correction capability. New computationally efficient algorithms are derived for simultaneously correcting single errors and multiple erasures and detecting multiple errors. These algorithms reduce the computational complexity of the previously known algorithms by at least an order of magnitude. Another attractive feature of the algorithms is that all the arithmetic operations are modulo operations. Consequently, the need to process large valued integers is avoided.
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    On real and complex normalizations (1993)
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    Circuits, systems and signal processing 12 (1993), S. 579-587 
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    Notes: Abstract This paper presents a general expression relating the complex-normalized scattering matrix of ann-port network to that of its augmentedn-port network normalizing to then 1 −Ω resistances, where the Darlington equivalent network may be either reciprocal or nonreciprocal.
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    Robustness of representations in multilayer feedforward neural networks (1993)
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    Circuits, systems and signal processing 12 (1993), S. 211-221 
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    Notes: Abstract Recent research has shown that multilayer feedforward networks with sigmoidal activation functions are universal approximators, and that this holds for more general activations as well. The mathematical underpinning for these results has been various: Kolmogorov's resolution of Hilbert's thirteenth problem; the Stone-Weierstrass theorem; approximation of Fourier and Radon integral representations; and convergence of probability measures. This paper • Rigorously establishes the robustness of feedforward network realizations. • Uses a theorem of Wiener and ideas of translation invariant subspaces to provide conditions for universal approximations toL 1 andL 2 functions by networks, for quite general activation functions. The second result extends and simplifies some of the recent results of Stinchcombe and White, at least for the special cases ofL 1 andL 2 functions.
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    The decimation-in-frequency algorithms for a family of discrete sine and cosine transforms (1988)
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    Circuits, systems and signal processing 7 (1988), S. 3-19 
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    Notes: Abstract In this paper we present results in the development of decimation-in-frequency algorithms for a family of discrete sine and cosine transforms. They are closely related to the decimation-in-time algorithms developed by Yip and Rao [1]. The complexity of the algorithms was examined through the number of multiplications and additions as well as the number of different constants required in the transforms. It was found that the decimation-in-frequency approach provides a viable alternative to other fast algorithms for the discrete sine and cosine transforms. In particular, the recursive and modular structure of the algorithms lends itself readily to possible hardware realization.
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    Editorial (1988)
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    Circuits, systems and signal processing 7 (1988), S. 113-113 
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    URL: http://dx.doi.org/10.1007/BF01602092
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    An overview of the special issue: Concurrent architectures for signal processing (1988)
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    Circuits, systems and signal processing 7 (1988), S. 115-118 
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    A size-independent systolic array for matrix triangularization and eigenvalue computation (1988)
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    Circuits, systems and signal processing 7 (1988), S. 173-189 
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    Notes: Abstract A fixed-size systolic array which can efficiently triangularize arbitrarily large matrices is presented. The array performs orthogonal triangularization by applying Givens' rotations in parallel. For matrices larger than the array, the triangularization is accomplished by emulating a large array with the fixed-size array. The distinguishing features of this array are (1) only one type of cell is used, (2) only unidirectional data flow is required, and (3) the array is rectangular shaped. These properties make it more suitable to emulate arbitrarily large arrays by feedback emulation. The array can also efficiently compute the eigenvalues of arbitrarily large matrices by theQR algorithm, because it can also perform theQR decomposition. In the computation the rotation parameters generated during each stage of theQR decomposition are used in the multiplication before the next stage of decomposition.
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    Nonplanar switchable arrays (1988)
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    Circuits, systems and signal processing 7 (1988), S. 213-234 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract On-line signal processing and automatic control applications give rise to numerous examples of computationally intense algorithms. Architectures which are algorithmically specialized and provide massive parallelism are necessary to cope with such computational requirements. Systolic arrays, which feature parallelism, local communications, and VLSI compatability appear to match up well with these computational requirements. This paper summarizes recent research on a general class of nonplanar systolic arrays. These arrays feature closed-loop data flow. The arrays may be switched dynamically to facilitate I/O simplicity and to accommodate iterative calculations without intermediate I/O interdiction. The closed-loop data flows also facilitate restructuring of the array to accommodate specific algorithmic requirements. The potential for multiuser, multialgorithm operation is also enhanced. Matrix operations are used as examples in the development. Algorithms as diversified as the Riccati equation, LU factorization, the Faddeev algorithm, FFT calculation, and controllability Grammians can be implemented on the nonplanar architectures.
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    Efficient systolic structures forLU decomposition and system of linear equations (1988)
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    Circuits, systems and signal processing 7 (1988), S. 275-287 
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    Notes: Abstract In this paper two new systolic structures forLU decomposition of an invertible matrix, having 100% and 50% hardware efficiency, are proposed. In comparison, a previously proposed structure forLU decomposition [1] has a hardware efficiency of only 33%. Utilizing one of the proposed systolic structure forLU decomposition, an integrated systolic structure for solving a system of linear equations is also derived. This is unlike other reported systolic structures for solving a system of linear equations, which are obtained by interconnecting heterogeneous subsystems, requiring complicated data realignment. These improvements in the proposed designs have been brought about by giving due consideration to the input/output data flow pattern between various subcomputations.
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    Minimization of transient signals in recursive time-varying digital filters (1988)
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    Circuits, systems and signal processing 7 (1988), S. 345-359 
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    Notes: Abstract Changing the coefficient set of a recursive digital filter during operation results in a transient signal at the filter output. The amplitude of this transient signal may exceed the amplitude of the output signal before and well after the change of coefficients. This effect is rather disturbing in some applications, such as the processing of audio signals. It is shown how these transients can be minimized without increasing the computational complexity of the filter by the use of a properly chosen set of intermediate coefficients.
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    Author's comment to “on decentralized hierarchic stabilization of a large-scale system with constraints” (1988)
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    Circuits, systems and signal processing 7 (1988), S. 409-411 
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    Call for papers (1988)
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    Circuits, systems and signal processing 7 (1988), S. I 
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    On the detection of a signal in colored noise (1988)
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    Circuits, systems and signal processing 7 (1988), S. 467-479 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A modeling approach is used in the detection of a random signal in colored noise. The received sequence is modeled as a regressive/autoregressive time series, and the presence or absence of the desired signal is determined through a hypothesis testing procedure. The test is based on the construction of anF-statistic using likelihood functions. The statistic can be easily incorporated into the computation of the probability of a false alarm, such as required in the processing of radar signals. Results based on simulated data and actual radar data are presented.
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    A variational principle for nonconservative power systems (1988)
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    Circuits, systems and signal processing 7 (1988), S. 413-424 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Recent results for nonconservative dynamical systems involve a variational principle of the Hamilton type. In this approach the velocity of variation and the variation of velocity are not commutative as in the case of mechanics governing conservative dynamical systems. In this paper we adapt the above approach to power systems which include the effects of transfer conductances. For such power systems we show that if certain noncommutative rules (which are consistent with the ones used for the variation of velocities in nonconservative dynamical systems) are used, then it is possible to employ a variational principle of the Hamilton type to derive the classical model for power systems. Numerous simulations of specific postfault multimachine power systems have verified that the above noncommutative rules are indeed satisfied for the types of power systems which we consider. The present results give additional understanding for the types of energy functions that have recently been used in transient stability studies of power systems. In these works, several attributes of energy functions have been ascertained by means of simulations and heuristic reasoning, rather than analysis (e.g., path-dependent terms of energy functions have been approximated by making linear trajectory assumptions).
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    Call for Papers (1988)
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    Circuits, systems and signal processing 7 (1988), S. I 
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    VLSI array processors' block implementation of IIR digital filters (1988)
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    Circuits, systems and signal processing 7 (1988), S. 511-511 
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    Covariance decompositions via elementary transformations. Applications to filtering (1988)
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    Circuits, systems and signal processing 7 (1988), S. 21-55 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper depicts the connection between algorithms for the factorization of covariance matrices, a basic operation in linear estimation, and whitening or modeling filters. General algorithms for arbitrary covariances are presented and related to the four fundamental types of cascade filters: feed-forward and feed-back tapped delay line or ladder filter. Systolic implementations of the algorithms and realizations of the associated filters illustrate the correspondence between algorithms and filters. Finally, fast algorithms for special covariances are introduced through two important examples: constant-parameter tapped delay line and ladder filter.
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    Improvement in adaptive noise canceling using a nonlinear filter based on the pontryagin minimum principle (1988)
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    Circuits, systems and signal processing 7 (1988), S. 57-78 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper introduces a new nonlinear filter that is used for adaptive noise canceling. The derivation and convergence properties of the filter are presented. The performance, as measured by the root mean square error between the signal and its estimate, is compared with that of the commonly used least mean square (LMS) algorithm. It is shown, through simulation, that the proposed nonlinear noise canceler has, on the average, better performance than the LMS canceler. The proposed adaptive noise canceler is based on the Pontryagin minimum principle and the method of invariant imbedding. The computational time for the proposed method is about 10% of that of the LMS, in the studied cases, which is a substantial improvement.
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    VLSI array processors' block implementation of IIR digital filters (1988)
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    Circuits, systems and signal processing 7 (1988), S. 79-94 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract VLSI systolic and wavefront array processors' architectures for the block implementation of infinite impulse response digital filters with very high sample rates are presented. The proposed systolic array processor achieves the maximum possible throughput rate and requires only local data transfers. The asynchronous wavefront array processor operates at the same maximum throughput rate and, moreover, it is characterized by a substantial reduced latency. The throughput rate of the proposed array processor structures is a linear function of the block lengthL and theoretically it may be arbitrary high; however, it is limited only by a number of practical implications.
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    Call for papers (1988)
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    Circuits, systems and signal processing 7 (1988), S. I 
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    Topics: Electrical Engineering, Measurement and Control Technology
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    Fault prediction for analog circuits (1988)
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    Circuits, systems and signal processing 7 (1988), S. 95-109 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The main problems that are the major concern in network testing are fault detection, fault location, and fault prediction. In this paper a multiple-fault-prediction algorithm is proposed for analog circuits with inaccessible nodes. The components in the circuits may be nominals or may be deviated from the nominals within a prescribed tolerance. In the proposed prediction algorithm, the component values are evaluated according to the consecutive voltage measurements that are continuously monitored at the accessible test points at each periodic maintenance. The component values are used to locate the faulty components and/or to predict the components that are about to fail.
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    Systolic processing for dynamic programming problems (1988)
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    Circuits, systems and signal processing 7 (1988), S. 119-149 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we investigate systolic processing for problems formulated in dynamic programming. These problems are classified as monadic-serial, polyadic-serial, monadic-nonserial, and polyadic-nonserial. Problems in serial formulations can be implemented easily in systolic arrays; however, nonserial problems may have to be transformed into a serial one before an efficient implementation can be found. monadic-serial dynamic programming problem can be solved as the search of an optimal path in a multistage graph and can be computed as a string of matrix multiplications. Three efficient systolic-array designs are presented. A polyadic-serial dynamic programming problem can be solved by either a divide- and-conquer algorithm or the search of optimal solutions in a serial AND/OR-graph. We have evaluated the asymptotically optimal architecture for divide- and-conquer algorithms and have developed efficient methods of mapping a regular AND/OR-graph into systolic arrays. Cases are studied for transforming a problem in a nonserial formulation into a serial one.
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    A systolic architecture for optimal filter design support (1988)
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    Circuits, systems and signal processing 7 (1988), S. 151-172 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A prototype filter design is reviewed to underscore the computational problems arising in such designs. A purely systolic-array architecture is presented. This array provides the computational support necessary for filter design. Due to a simple and novel data steering technique the array is capable of carrying out a number of important matrix operations such as factorization, inversion of factors, and matrix-matrix multiplication. Another interesting attribute is the array's ability to maximally overlap computations of multiphase algorithms. In this study we demonstrate the execution of a dense matrix factorization phase and a factor inversion phase on the array with no need for intraphase or interphase I/O. We show that these phases (which are the backbone of an optimal filtering algorithm) are completed in the optimal count of aboutn time units. The array employs 2n n−n simple processing elements (PEs) that are active every other time unit. It is shown that the functions of two adjacent PEs can be merged and assigned to a single PE thus maximizing PE utilization. A possible design of a “merged” PE is given.
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    Geometric problems on two-dimensional array processors (1988)
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    Circuits, systems and signal processing 7 (1988), S. 191-211 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Parallel algorithms for solving geometric problems on two array processor models—the mesh-connected computer (MCC) and a two-dimensional systolic array—are presented. We illustrate a recursive divide- and-conquer paradigm for MCC algorithms by presenting a time-optimal solution for the problem of finding thenearest neighbors of a set of planar points represented by their Cartesian coordinates. The algorithm executes on a√n×√n MCC, and requires an optimalO(√n) time. An algorithm for constructing theconvex hull of a set of planar points and anupdate algorithm for thedisk placement problem on ann 2/3×n 2/3 two-dimensional systolic array are presented. Both these algorithms requireO(n 2/3) time steps. The advantage of the systolic solutions lies in their suitability for direct hardware implementation.
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    Automatic design and partitioning of systolic/wavefront arrays for VLSI (1988)
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    Circuits, systems and signal processing 7 (1988), S. 235-252 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we show how systolic/wavefront arrays can be automatically designed and partitioned to solve problems of arbitrary size. Buffer memory and control of a resulting array is regular and simple, and is generated automatically. Also, the throughput of the array is matched with the I/O speed of the host to which it is to be attached. The approach strongly relies upon classical concepts in signal processing, such as signal flow graphs and state transition functional behavior. Some illustrative examples are included.
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    Call for papers (1988)
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    Circuits, systems and signal processing 7 (1988), S. I 
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    Efficient VLSI array processing structures for adaptive quadratic digital filters (1988)
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    Circuits, systems and signal processing 7 (1988), S. 253-273 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we introduce a class of efficient architectures for adaptive quadratic digital filters. These architectures are based on the LMS algorithm and use the rank compressed lower-upper (LU) triangular deomposition method. These architectures exhibit high parallelism as well as great modularity and regularity. We also consider affiliated VLSI array processing structures and compare these in terms of hardware cost and data throughput delay. For comparison purposes, the distributed arithmetic structures of adaptive quadratic filters are also included in the paper. Finally, the convergence performance of the adaptive quadratic filters is tested via benchmark simulation examples.
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    ARMA modeling of fourth-order cumulants and phase estimation (1988)
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    Circuits, systems and signal processing 7 (1988), S. 291-325 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A new procedure is proposed for ARMA modeling of fourth-order cumulants and trispectrum estimation of non-Gaussian stationary random processes. The new procedure is applied to the identification of nonminimum phase systems for both phase and magnitude response estimation. It is demonstrated by means of comprehensive simulation examples that the ARMA approach exhibits improved performance over conventional trispectrum methods. ARMA model order selection criteria based on fourth-order cumulants are presented and their performance evaluated. The computational complexity of the ARMA and conventional trispectrum methods is also examined. The new procedure does not require knowledge of the non-Gaussian distribution.
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    On adaptive beamforming in correlated noise (1988)
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    Circuits, systems and signal processing 7 (1988), S. 327-343 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper deals with the problem of adaptive beamforming in the presence of fully coherent (correlated) noise sources. Two different techniques are developed for minimizing the effects of coherent interference. The first method employs spatial interpolation of the array aperture, followed by spatial smoothing in order to decorrelate the desired signal and the interference. The second technique is based on a simple algebraic transformation for restoring the rank of the array signal correlation matrix, which is normally rank deficient in such situations. This technique is shown to work for nonuniform adaptive arrays as well. Extensive computer simulation results are presented to illustrate the effectiveness of the proposed techniques.
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    Zeros and poles of linear periodic multivariable discrete-time systems (1988)
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    Circuits, systems and signal processing 7 (1988), S. 361-380 
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    Notes: Abstract In this paper the notions of transmission zero, invariant zero, and structural zero (that is the geometric notion of zero) are extended to linear periodic discrete-time systems, as well as the notion of pole. Their meaning is clarified and their relationships stressed, thus extending the time-invariant theory. In particular, the invariant zeros and the structural zeros are shown to coincide, together with their multiplicities, and the former are shown to be independent of a linear state feedback. Moreover, the nonzero transmission zeros, the nonzero invariant zeros, and the nonzero poles are shown to be independent of time, together with their multiplicities. Some of these results are obtained with the help of the notions of reachability subspace and inner controllable subspace, which constitute a further development of the geometric theory for this class of systems.
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    Errata (1988)
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    Circuits, systems and signal processing 7 (1988), S. 411-411 
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    On the optimal filtering problem for the cubic sensor (1988)
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    Circuits, systems and signal processing 7 (1988), S. 381-408 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We consider the problem of optimal filtering of a scalar diffusion process measured by a monotone nonlinear sensor in a low-noise channel. The specific sensors considered are of the formh n(x)=¦x¦n sgn(x). This case represents a wide class of sensors with a critical inflection point, since it is the leading term in Taylor's expansion of the measurement function in the critical region. We give for the first time a formal asymptotic approximation of the conditional and of the mean square estimation errors of the optimal filter as interpolation formulas. We also construct an asymptotic approximation to the optimal filter and compare its performance with that of a constant gain filter.
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    HIV spread in the San Francisco cohort: Scaling of the effective logistic rate for seropositivity (1988)
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    Bulletin of mathematical biology 50 (1988), S. 345-349 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A simple scaling (semigroup) property is manifest in the functional form of the effective logistic rate for the increase in the HIV seropositive fraction in the San Francisco (City Clinic) cohort. Witht i=4.5 years, this scaling property—r→λ-2r undert→[λt+(λ−1)t i] for all parameter values λ≧1—encapsulates the effects of relevant biological and sociological changes in the key epidemiological variables during the 8-year seropositive rise period, 1978–1985 inclusive.
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    Subcellular distribution of compounds in biosystems (1988)
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    Bulletin of mathematical biology 50 (1988), S. 367-378 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Using plausible assumptions a description of the distribution of externally added low molecular weight solutes in individual subcellular regions of biosystems is reduced to a compartmental system of specific structure having, in general, only numerical solutions. Frequently occurring application of biologically active substances in low doses, however, elicits the conditions (i.e. undirectional membrane transport involving accumulation, instantaneous and linear binding to macromolecules and metabolism obeying first order kinetics) that enable one to solve the system explicitly. Equations have been derived, describing the time course of drug concentration in any subcellular phase of arbitrary biosystem having membranes of similar composition, including tissues with a cellular structure (degenerate case). Accuracy of the description is tested on the relationship between physicochemical and biological properties of drugs, bioactivity being used to monitor the concentration in the receptor region.
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    URL: http://dx.doi.org/10.1007/BF02459706
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    Book reviews (1988)
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    Bulletin of mathematical biology 50 (1988), S. 411-419 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459708
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    The osmotic permeability of a tubule wall (1988)
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    Bulletin of mathematical biology 50 (1988), S. 547-558 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The influence of unstirred layers in osmotic experiments designed to measure the osmotic permeability of a tubule wall is considered. Results are given in the form of a set of graphs whose axes are closely related to observed and known experimental parameters. These enable osmotic permeability values to be obtained which are closer to the true values.
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    URL: http://dx.doi.org/10.1007/BF02458852
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    The fractal dimension of EEG as a physical measure of conscious human brain activities (1988)
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    Bulletin of mathematical biology 50 (1988), S. 559-565 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In our previous paper we have given a neuroglia modulated neuronal network model which may display chaotic behaviours under certain parametric values. This work is an attempt to correlate the functions of conscious human brains with the chaotic states shown by the EEG patterns under different physiological conditions. Some of the difficulties and precautions of this kind of work are discussed.
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    URL: http://dx.doi.org/10.1007/BF02458853
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    Critical issues in tumor microcirculation, angiogenesis and metastasis (1988)
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    Bulletin of mathematical biology 50 (1988), S. 577-577 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458855
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    On the validity of the steady state assumption of enzyme kinetics (1988)
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    Bulletin of mathematical biology 50 (1988), S. 579-593 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By estimating relevant time scales, a simple new condition can be found that ensures the validity of the steady state assumption for a standard enzyme-substrate reaction. The generality of the approach is demonstrated by applying it to the determination of validity criteria for the steady state assumption applied to an enzyme-substrate-inhibitor system.
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    URL: http://dx.doi.org/10.1007/BF02460092
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    Algorithms for task allocation in ants. (A study of temporal polyethism: Theory) (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 891-918 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present an algorithm for allocating individual ants to tasks that relies solely on task change being caused by the unavailability of work. We prove that such an algorithm will allocate the correct number of individuals to each job. Furthermore, we can demonstrate that if such an algorithm is used then an age structure emerges over the ants performing the various tasks. This matches closely with the weak temporal structure over tasks that is observed in Sendova-Franks and Franks (1993. Division of labour in ants nests within highly variable environments. (A study of temporal polyethism: experimental).Bull. math. Biol. 55, 75–96).
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    URL: http://dx.doi.org/10.1007/BF02460691
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    Book reviews (1993)
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    Bulletin of mathematical biology 55 (1993), S. 1013-1024 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460697
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    Logical identification of all steady states: The concept of feedback loop characteristic states (1993)
    Springer
    Bulletin of mathematical biology 55 (1993), S. 973-991 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Biological regulatory systems can be described in terms of non-linear differential equations or in logical terms (using an “infinitely non-linear” approximation). Until recently, only part of the steady states of a system could be identified on logical grounds. The reason was that steady states frequently have one or more variable located on a threshold (see below); those steady states were not detected because so far no logical status was assigned to threshold values. This is why we introduced logical scales with values 0,1θ, 12θ, 2, ..., in which1θ,2θ, ... are the logical values assigned to the successive thresholds of the scale. We thus have, in addition to the regular logical states,singular states in which one or more variables is located on a threshold. This permits identifyingall the steady states on logical grounds. It was noticed that each feedback loop (or reunion of disjointed loops) can be characterized by a logical state located at the thresholds at which the variables of the loop operate. This led to the concept ofloop-characteristic state, which, as we will see, enormously simplifies the analysis.The core of this paper is a formal demonstration that among the singular states of a system, only loop-characteristic states can be steady. Reciprocally, given a loop-characteristic state, there are parameter values for which this state is steady; in this case, the loop is effective (i.e. it generates multistationarity if it is a positive loop, homeostasis if it is a negative loop). This not only results in the above-mentioned radical simplification of the identification of the steady states, but in an entirely new view of the relation between feedback loops and steady states.
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    URL: http://dx.doi.org/10.1007/BF02460695
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    A necessary and sufficient condition for right coprime factorization of nonlinear feedback systems (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 489-492 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this short note, we establish a simple, yet precise, necessary and sufficient condition for the “right coprime factorization” of a nonlinear feedback control system. As a consequence, we also obtain similar conditions for the “stable right coprime factorizations ” of the nonlinear feedback control system.
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    URL: http://dx.doi.org/10.1007/BF01223323
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    Analysis of a PRSA generator (1993)
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    Circuits, systems and signal processing 12 (1993), S. 557-566 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The pseudorandom sequence of arrays (PRSA) and a method to generate it was reported earlier by the authors. This paper presents another method to generate a PRSA. The mathematical recursion describing the PRSA and some of its properties are discussed.
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    URL: http://dx.doi.org/10.1007/BF01188094
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    An improvement on the digital redesign method based on the block-pulse function approximation (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 37-49 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper proposes an effective method to improve the digital redesign method via the block-pulse function approach. The coefficients of the block-pulse function expansion are exactly evaluated such that the desired digitally redesigned feedback gain and forward gain will be obtained. A numerical example is given to demonstrate the effectiveness of the proposed method.
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    URL: http://dx.doi.org/10.1007/BF01183146
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    Interval-analysis techniques in linear systems: An application in power systems (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 51-60 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we apply the technique of interval analysis to get bounds on the initial value response of a linearized single machine infinite bus problem when a parameter is varied. It is generally believed that responses for parameter variations in an interval should lie within the responses for the extremums of the parameter variations. This is not generally true and our example demonstrates this. The interval-analysis technique permits getting the overall bound on the response. Further experimentation also revealed that the method has some limitations particularly involving lightly damped long-term dynamics. The technique is useful in finding the robustness of a particular design such as the power system stabilizer for parameter variations.
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    URL: http://dx.doi.org/10.1007/BF01183147
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    Comparative performance study of SVD-based and QRD-based high-order Yule-Walker methods for frequency estimation (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 105-117 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The high-order Yule-Walker (HOYW) method of sinusoidal frequency estimation based on a singular value decomposition (SVD) is known to have excellent statistical performance. Here, we show that the SVD-based step of the HOYW method can be replaced by a computationally more convenient QR decomposition (QRD)-based step, without affecting the asymptotic properties of the frequency estimates.
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    URL: http://dx.doi.org/10.1007/BF01183150
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    Estimation and setting starting values in ARMA algorithms (1993)
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    Circuits, systems and signal processing 12 (1993), S. 85-103 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract For the given observations set of the ARMA (autoregressive moving average) process, the likelihood function depends, not only on model parameters, but on the starting values of the input and output. Therefore, it is called theconditional likelihood function. Theunconditional likelihood function can be obtained in two ways. The first is to set the starting values to zero, as is often done, and the second is to set them to the properly estimated values. The difference between these two types of likelihood functions is significant when the given data sequence is short, and any of the zeros of the moving average part is close to the boundary of the unit circle. In this paper the direct method of starting value estimation and its application to two off-line ARMA estimation algorithms, the maximum likelihood (ML) algorithm and the iterative inverse filtering (ITIF) algorithm, is proposed. Experimental results prove both increased efficiency and stability of these algorithms. The importance of setting the starting values properly is also significant when the recursive algorithm, with previously estimated parameters, has to be restarted. The advantage of the proposed reinitialization method is shown on the recursive lattice algorithm working in the block mode.
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    URL: http://dx.doi.org/10.1007/BF01183149
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    Editorial (1993)
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    Circuits, systems and signal processing 12 (1993), S. 151-151 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189870
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