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  • Springer  (186,269)
  • Wiley-Blackwell  (24,942)
  • 2010-2014
  • 1995-1999  (141,653)
  • 1985-1989  (69,558)
  • 1999  (68,476)
  • 1997  (73,177)
  • 1989  (69,558)
Collection
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  • 2010-2014
  • 1995-1999  (141,653)
  • 1985-1989  (69,558)
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  • 1
    Electronic Resource
    Electronic Resource
    Memory but no suppression in low-dimensional symmetric idiotypic networks (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 223-246 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present a new symmetric model of the idiotypic immune network. The model specifies clones of B-lymphocytes and incorporates: (1) influx and decay of cells; (2) symmetric stimulatory and inhibitory idiotypic interactions; (3) an explicit affinity parameter (matrix); (4) external (i.e. non-idiotypic) antigens. Suppression is the dominant interaction, i.e. strong idiotypic interactions are always suppressive. This precludes reciprocal stimulation of large clones and thus infinite proliferation. Idiotypic interactions first evoke proliferation, this enlarges the clones, and may in turn evoke suppression. We investigate the effect of idiotypic interactions on normal proliferative immune responses to antigens (e.g. viruses). A 2-D, i.e. two clone, network has a maximum of three stable equilibria: the virgin state and two asymmetric immune states. The immune states only exist if the affinity of the idiotypic interaction is high enough. Stimulation with antigen leads to a switch from the virgin state to the corresponding immune state. The network therefore remembers antigens, i.e. it accounts for immunity/memory by switching beteen multiple stable states. 3-D systems have, depending on the affinities, 9 qualitatively different states. Most of these also account for memory by state switching. Our idiotypic network however fails to account for the control of proliferation, e.g. suppression of excessive proliferation. In symmetric networks, the proliferating clones suppress their anti-idiotypic suppressors long before the latter can suppress the former. The absence of proliferation control violates the general assumption that idiotypic interactions play an important role in immune regulation. We therefore test the robustness of these results by abandoning our assumption that proliferation occurs before suppression. We thus define an “escape from suppression” model, i.e. in the “virgin” state idiotypic interactions are now suppressive. This system erratically accounts for memory and never for suppression. We conclude that our “absence of suppression from idiotypic interactions” does not hinge upon our “proliferation before suppression” assumption.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458444
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  • 2
    Electronic Resource
    Electronic Resource
    Book reviews (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 287-291 
    Details
    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/BF02458448
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  • 3
    Electronic Resource
    Electronic Resource
    Editorial: Software survey section (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. I 
    Details
    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/BF02458449
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  • 4
    Electronic Resource
    Electronic Resource
    Upper and lower bounds from the maximum principle. Intracellular diffusion with Michaelis-Menten kinetics (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 325-335 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Analytical bounding functions for diffusion problems with Michaelis-Menten kinetics were recently presented by Anderson and Arthurs, 1985 (Bull. math. Biol. 47, 145–153). Their methods, successful to some extent for a small range of parameters, has the disadvantage of providing a weak upper bound. The optimal approach for the use of one-line bounding kinetics is presented. The use of two-line bounding kinetics is also shown, in order to give, sufficient accuracy in those cases where the one-line approach does not provide satisfactory results. The bounding functions provide excellent upper and lower bounds on the true solution for the entire range of kinetic and transport parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460111
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  • 5
    Electronic Resource
    Electronic Resource
    The threshold of survival for systems in a fluctuating environment (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 311-323 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Thresholds for survival and extinction are important for assessing the risk of mortality in systems exposed to exogeneous stress. For generic, rudimentary population models and the classical resource-consumer models of Leslie and Gallopin, we demonstrate the existence of a survival threshold for situations where demographic parameters are fluctuating, generally, in a nonperiodic manner. The fluctuations are assumed, to be generated by exogenous, anthropogenic stresses such as toxic chemical exposures. In general, the survival threshold is determined by a relationship between mean stress measure in organisms to the ratio of the population intrinsic growth rate and stress response rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460110
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  • 6
    Electronic Resource
    Electronic Resource
    Plant strategies and the dynamics and structure of plant communities (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 409-411 
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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/BF02460116
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  • 7
    Electronic Resource
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    Editorial: Viewpoint (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 415-415 
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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/BF02460080
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  • 8
    Electronic Resource
    Electronic Resource
    Stochastic models for subpopulation emergence in heterogeneous tumors (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 731-747 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A stochastic analog to a deterministic model describing subpopulation emergence in heterogeneous tumors is developed. The resulting system is described by the Fokker-Planck or forward Kolmogorov equation. A finite element approach for the numerical solution to this equation is described. Four biological and clinical scenarios are simulated (emergence of heterogeneity, exclusion of a subpopulation, and induction of drug resistance in both pure and heterogeneous tumors). The results of the simulations show that the stochastic model describes the same basic dynamics as its deterministic counterpart via a convective component, but that for each simulation a distribution of tumor sizes and mixes can also be derived from a diffusive component in the model. These distributions yield estimates for subpopulation extinction probabilities. The biological and clinical relevance of these results are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459658
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  • 9
    Electronic Resource
    Electronic Resource
    Algorithms for the optimal identification of segment neighborhoods (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 39-54 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two algorithms for the efficient identification of segment neighborhoods are presented. A segment neighborhood is a set of contiguous residues that share common features. Two procedures are developed to efficiently find estimates for the parameters of the model that describe these features and for the residues that define the boundaries of each segment neighborhood. The algorithms can accept nearly any model of segment neighborhood, and can be applied with a broad class of best fit functions including least squares and maximum likelihood. The algorithms successively identify the most important features of the sequence. The application of one of these methods to the haemagglutinin protein of influenza virus reveals a possible mechanism for conformational change through the finding of a break in a strong heptad repeat structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458835
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  • 10
    Electronic Resource
    Electronic Resource
    Approximate matching of regular expressions (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 5-37 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Given a sequenceA and regular expressionR, theapproximate regular expression matching problem is to find a sequence matchingR whose optimal alignment withA is the highest scoring of all such sequences. This paper develops an algorithm to solve the problem in timeO(MN), whereM andN are the lengths ofA andR. Thus, the time requirement is asymptotically no worse than for the simpler problem of aligning two fixed sequences. Our method is superior to an earlier algorithm by Wagner and Seiferas in several ways. First, it treats real-valued costs, in addition to integer costs, with no loss of asymptotic efficiency. Second, it requires onlyO(N) space to deliver just the score of the best alignment. Finally, its structure permits implementation techniques that make it extremely fast in practice. We extend the method to accommodate gap penalties, as required for typical applications in molecular biology, and further refine it to search for substrings ofA that strongly align with a sequence inR, as required for typical data base searches. We also show how to deliver an optimal alignment betweenA andR in onlyO(N+logM) space usingO(MN logM) time. Finally, anO(MN(M+N)+N 2logN) time algorithm is presented for alignment scoring schemes where the cost of a gap is an arbitrary increasing function of its length.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458834
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  • 11
    Electronic Resource
    Electronic Resource
    Codon preference and primary sequence structure in protein-coding regions (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 95-115 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The stochastic complexity of a data base of 365 protein-coding regions is analysed. When the primary sequence is modeled as a spatially homogeneous Markov source, the fit to observed codon preference is very poor. The situation improves substantially when a non-homogeneous model is used. Some implications for the estimation of species phylogeny and substitution rates are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458838
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  • 12
    Electronic Resource
    Electronic Resource
    Tutorial on large deviations for the binomial distribution (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 125-131 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present, in an easy to use form, the large deviation theory of the binomial distribution: how to approximate the probability ofk or more successes inn independent trials, each with success probabilityp, when the specified fraction of successes,a≡k/n, satisfies 0〈p〈a〈1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458840
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  • 13
    Electronic Resource
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    Editorial: Software survey section (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. I 
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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/BF02458844
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  • 14
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    A continuous analog for RNA folding (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 167-171 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A linear segment in which a number of pairs of intervals of equal length are identified as potential stems is the subject of a folding problem analogous to inference of RNA secondary structure. A quantity of free energy (or equivalently, energy per unit length) is associated with each stem, and the various types of loops are assigned energy costs as a function of their lengths. Inference of stable structures can then be carried out in the same way as in RNA folding. More important, perturbation of stem lengths and energy densities (modelling various mutational processes affecting nucleotide sequences) allows the delineation of domains of stability of various foldings, through the explicit calculation of their boundaries, in a low-dimensional parameter space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458842
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  • 15
    Electronic Resource
    Electronic Resource
    Prediction of linear and non-linear responses of MGB neurons by system identification methods (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 337-346 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In sensory physiology, various System Identification methods are implemented to formalized stimulus-response relationships. We applied the Volterra approach for characterizing input-output relationships of cells in the medial geniculate body (MGB) of an awake squirrel monkey. Intraspecific communication calls comprised the inputs and the corresponding cellular evoked responses—the outputs. A set of vocalization was used to calculate the kernels of the transformation, and these kernels subserved to predict the responses of the cell to a different set of vocalizations. It was found that it is possible to predict the response (PSTH) of MGB cells to natural vocalizations, based on envelopes of the spectral components of the vocalization. Some of the responses could be predicted by assuming a linear transformation function, whereas other responses could be predicted by non-linear (second order) kernels. These two modes of transformation, which are also reflected by a distinct spatial distribution of the linearvis-à-vis non-linear responding cells, apparently representa new revelation of parallel processing of auditory information.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460112
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  • 16
    Electronic Resource
    Electronic Resource
    Diffusion limited immunochemical sensing (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 359-379 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The time-dependent surface coverage of antigen-antibody complexes for a sensor in which antigens are bound to surface immobilized antibodies is determined analytically. Assuming a reversible first order reaction between the antigens and antibodies, a model is derived describing the dynamical response of the sensor. The surface coverage is related explicitly to the antigen concentration which is of special interest in experimental situations. The stationary state and short time behaviour are determined explicitly. Several illustrations of the full solution are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460114
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  • 17
    Electronic Resource
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    An informational approach to reaction times (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 347-358 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Simple reaction time is the minimum time required to respond to a signal such as a steady light or tone. Such a reaction time is taken to be the time required for transmission of a fixed quantity of information, ΔH, from stimulus to subject. That is, information summation replaces energy summation. This information is calculated from consideration of the quantum nature of the stimulus. The theoretically derived equation for reaction time is fitted to experimental data. Piéron's empirical law for reaction time is obtained as an approximation from a proposed informational equation. The exponent in Piéron's law is found to be the same as the exponent in the power law of sensation. Threshold appears to be the smallest stimulus capable of transmitting the quantity of information ΔH.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460113
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  • 18
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    The Third World Conference on Mathematics at the Service of Man (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 413-413 
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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/BF02460117
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  • 19
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    Editorial: Software survey section (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. I 
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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/BF02460118
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  • 20
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    Adaptive superparasitism and host-parasitoid dynamics (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 23-41 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider a host-solitary parasitoid system with three categories of individuals: parasitoids, healthy hosts and parasitized hosts. Parasitoids are assumed to discriminate perfectly between the two kinds of hosts and they can reject those which are already parasitized. If parasitoids systematically accept or reject superparasitism or behave randomly, the system is always unstable. Using an optimal foraging model, we determine the behavior of parasitoids which leads to maximization of the instantaneous reproductive rate. When following this adaptive decision rule, parasitoids accept or refuse superparasitism according to the densities of both healthy and parasitized hosts. We study the dynamics of the system when parasitoids follow the optimal rule and show that under certain conditions it possesses a locally stable equilibrium point. In addition, our model predicts that at equilibrium parasitoids show partial preferences for superparasitism.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459469
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  • 21
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    Chemotherapeutic treatments: A study of the interplay among drug resistance, toxicity and recuperation from side effects (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 205-232 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A system of differential equations for the control of tumor growth cells in a cycle nonspecific chemotherapy is analyzed. Spontaneously acquired drug resistance is taken into account, and a criterion for the selection of chemotherapeutic treatment is used. This criterion purports to describe the possibility of improvement of the patient's health when treatment is discontinued. Contrary to our early results which also take drug resistance into account, in this context strategies of continuous chemotherapy in which rest periods take part may be better than maximum drug concentration throughout the treatment (which appears to be in accordance with clinical practice). This bears out our previous conjecture that when drug resistance is accounted for, the imperfections in the usual modelling of treatment criteria, which in general do not allow for patient recuperation, ruled out the possibility of rest periods in optimal continuous chemotherapy.
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    URL: http://dx.doi.org/10.1007/BF02462001
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  • 22
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    Matrix population model with density-dependent recruitment for assessment of age-structured wildlife populations (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 255-262 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A logistic density-dependent matrix model is developed in which the matrices contain only parameters and recruitment is a function of adult population density. The model was applied to simulate introductions of white-tailed deer into an area; the fitted model predicted a carrying capacity of 215 deer, which was close to the observed carrying capacity of 220 deer. The rate of population increase depends on the dominant eigenvalue of the Leslie matrix, and the age structure of the simulated population approaches a stable age distribution at the carrying capacity, which was similar to that generated by the Leslie matrix. The logistic equation has been applied to study many phenomena, and the matrix model can be applied to these same processes. For example, random variation can be added to life history parameters, and population abundances generated with random effects on fecundity show both the affect of annual variation in fecundity and a longer-term pattern resulting from the age structure.
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    URL: http://dx.doi.org/10.1007/BF02462003
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  • 23
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    Book reviews (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 399-406 
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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/BF02462008
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  • 24
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    Conflicting objectives in chemotherapy with drug resistance (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 707-724 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Spontaneously acquired drug resistance is accounted for, as well as the evolution in time of normal cells. In addition, optimization of conflicting objectives forms the aim of the chemotherapeutic treatment. For general cell growth, some results are given, whereas for the special case of Malthusian (exponential) growth of tumor cells and rather general growth rate for normal cells, the optimal strategy is worked out. The latter, from the clinical standpoint, corresponds to maximum drug concentration throughout the treatment.
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    URL: http://dx.doi.org/10.1007/BF02458426
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  • 25
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    Book reviews (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 787-807 
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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/BF02458430
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  • 26
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    Dynamical consequences of optimal host feeding on host-parasitoid population dynamics (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 809-831 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This study examines the influence of various host-feeding patterns on host-parasitoid population dynamics. The following types of host-feeding patterns are considered: concurrent and non-destructive, non-concurrent and non-destructive, and non-concurrent and destructive. The host-parasitoid population dynamics is described by the Lotka-Volterra continuous-time model. This study shows that when parasitoids behave optimally, i.e. they maximize their fitness measured by the instantaneous per capita growth rate, the non-destructive type of host feeding stabilizes host-parasitoid dynamics. Other types of host feeding, i.e. destructive, concurrent, or non-concurrent, do not qualitatively change the neutral stability of the Lotka-Volterra model. Moreover, it is shown that the pattern of host feeding which maximizes parasitoid fitness is either non-concurrent and destructive, or concurrent and non-destructive host feeding, depending on the host abundance and parameters of the model. The effects of the adaptive choice of host-feeding patterns on host-parasitoid population dynamics are discussed.
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    URL: http://dx.doi.org/10.1007/BF02459994
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  • 27
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    Multi-player matrix games (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 931-952 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Game theory has had remarkable success as a framework for the discussion of animal behaviour and evolution. It suggested new interpretations and prompted new observational studies. Most of this work has been done with 2-player games. That is the individuals of a population compete in pairwise interactions. While this is often the case in nature, it is not exclusively so. Here we introduce a class of models for situations in which more than two (possibly very many) individuals compete simultaneously. It is shown that the solutions (i.e. the behaviour which may be expected to be observable for long periods) are more complex than for 2-player games. The concluding section lists some of the new phenomena which can occur.
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    URL: http://dx.doi.org/10.1007/BF02460000
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  • 28
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    The “clustered structure” of the purines/pyrimidines distribution in DNA distinguishes systematically between coding and non-coding sequences (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 975-992 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method allowing to measure the inhomogeneous distribution of purines/pyrimidines in nucleotide sequences is developed. We show that this measure relates to the coding or non-coding character of the considered sequence. Coding sequences present a near to the random Pu or Py distribution. This property is shared by both protein-coding DNA and functional RNA-coding DNA. Non-coding sequences present a highly clustered inhomogeneity. We propose the hypothesis, corroborated with appropriate computer simulations, that this is due to the action of various transposition events accumulated for long time periods.
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    URL: http://dx.doi.org/10.1007/BF02460002
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  • 29
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    Quantal currents and potential in the three-dimensional anisotropic bidomain model of smooth muscle (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1047-1075 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The potential generated in the smooth muscle of the vas deferens on release of a quantum of transmitter from a varicosity was analyzed using a three-dimensional bidomain continuum model. Current was injected at the origin of the bidomain; this current had the temporal characteristics of the junctional current. The membrane potential, intracellular potential, and extracellular potential, as well as the extracellular current, were then calculated throughout the bidomain at different times. Calculations were performed to show the effect of changing the anisotropy ratios of the intracellular and extracellular conductivities on the spread of current and potential in each of the three dimensions. These results provide a theoretical framework for ascertaining the time course of transmitter interaction at a varicosity following the secretion of a quantum of transmitter.
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    URL: http://dx.doi.org/10.1007/BF02460101
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  • 30
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    An extremum principle for parabolic competition (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1145-1154 
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    ISSN: 1522-9602
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    Notes: Abstract Parabolic growth invariably results in the survival of all competing types. Under the constraint of constant total concentration, there is a unique equilibrium in the simplex interior, which is asymptotically stable inside the whole simplex. The appropriate Lyapunov function is obtained in terms of the excess productivity which is shown to be maximized for the competitive system with fractional order kinetics. Claims to the contrary are refuted.
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    Book reviews (1997)
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    Bulletin of mathematical biology 59 (1997), S. 1191-1201 
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    Understanding drug resistance for monotherapy treatment of HIV infection (1997)
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    Bulletin of mathematical biology 59 (1997), S. 763-785 
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    Notes: Abstract The purpose of this study was to investigate strategies in the monotherapy treatment of HIV infection in the presence of drug-resistant (mutant) strains. A mathematical system is developed to model resistance in HIV chemotherapy. It includes the key players in the immune response to HIV infection: virus and both uninfected CD4+ and infected CD4+ T-cell populations. We model the latent and progressive stages of the disease, and then introduce monotherapy treatment. The model is a system of differential equations describing the interaction of two distinct classes of HIV—drug-sensitive (wild type) and drug-resistant (mutant)—with lymphocytes in the peripheral blood. We then introduce chemotherapy effects. In the absence of treatment, the model produces the three types of qualitative clinical behavior—anuninfected steady state, andinfected steady state (latency), andprogression to AIDS. Simulation of treatment is provided for monotherapy, during theprogression to AIDS state, in the consideration of resistance effects. Treatment benefit is based on an increase or retention in CD4+ T-cell counts together with a low viral titer. We explore the following treatment approaches: an antiviral drug which reduces viral infectivity that is administered early—when the CD4+ T-cell count is ≥300/mm3, and late—when the CD4+ T-cell count is less than 300/mm3. We compare all results with data. When treatment is initiated during the progression to AIDS state, treatment prevents T-cell collapse, but gradually loses effectiveness due to drug resistance. We hypothesize that it is the careful balance of mutant and wild-type HIV strains which provides the greatest prolonged benefit from treatment. This is best achieved when treatment is initiated when the CD4+ T-cell counts are greater than 250/mm3, but less than 400/mm3 in this model (i.e. not too early, not too late). These results are supported by clinical data. The work is novel in that it is the first model to accurately simultate data before, during and after monotherapy treatment. Our model also provides insight into recent clinical results, as well as suggests plausible guidelines for clinical testing in the monotherapy of HIV infection.
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    Mathematical modeling of adhesion of bacteria to host cell lines (1997)
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    Bulletin of mathematical biology 59 (1997), S. 833-856 
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    Notes: Abstract A mathematical model which describes adhesion of bacteria to host cell lines is presented. The model is flexible enough to account for the following situations: extracellular bacteria are either in exponential or in stationary phase. Adhesion is described as a reversible binding process in which the bacteria attach to or detach from specific receptors uniformly distributed on the cell surface. In turn, attached bacteria can either replicate or, conversely, they are restrained to remain in stationary phase. In the first case, however, we must consider the problem of whether the decrease of unoccupied receptors as adhesion progresses imposes a limit to the replicating capacity of the attached bacteria. The effect exerted by the multiplicity of infection (MOI), i.e. the ratio of the number of bacteria to the number of host cells, on the process of adhesion is also contemplated by the model. This has revealed that experiments performed at the same values of MOI can show completely different levels of adhered bacteria, depending on the number of host cells in the assays. This finding demonstrates that the report of the MOI values is insufficient to characterize comparative studies of bacterial adhesion since it could lead to a misunderstanding of the corresponding data. Simplified models based on the steady-state approximation and in equilibrium analysis by means of a Lagmuir adsorption isotherm for the attached bacteria are also discussed. This allows us to define the adhesion coefficient (β) in a given bacterium-cell system so that, with the exception of those systems where these coefficients cannot be defined, larger values of β are related to a greater adhesion capacity. An overview of the procedures to perform quantitative adhesion data analysis is outlined. Finally, theoretical predictions are compared with experimental results from the literature.
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    A new measure of xenobiotic toxicity to the first-line human defence system from the time-resolved phagocyte luminescence (1997)
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    Bulletin of mathematical biology 59 (1997), S. 897-910 
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    Notes: Abstract A new measure of toxicity based on stochastic modelling of single photon-counting processes, representing time-resolved phagocyte luminescence of xenobiotic-perturbed human neutrophils, has been constructed. The stochastic measure of toxicity has been verified by the QSAR method, and then compared and contrasted with the traditional toxicity measure used in bio- and chemiluminescent research. Phenol and benzene homologues were chosen as perturbers due to their importance from the viewpoint of ecotoxicology and occupational medicine.
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    Dynamics of human milk extraction: A comparative study of breast feeding and breast pumping (1997)
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    Bulletin of mathematical biology 59 (1997), S. 953-973 
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    Notes: Abstract We describe a mathematical model of the flow and deformation in a human teat. Our aim is to compare the theoretical milk yield during infant breast feeding with that obtained through the use of a breast pump. Infants use a peristaltic motion of the tongue, along with some suction, to extract milk, whereas breast pumps use a cyclic pattern of suction only. Our model is based on quasi-linear poroelasticity whereby the teat is modelled as a cylindrical porous elastic material saturated with fluid. We impose a cyclic axial suction pressure difference across the teat and impose a radial compressive force moving along the teat which mimics infant suckling. This is compared to the case of cyclic and steady pumping only which models the action of breast pumps. The results illustrate that there is an optimal time to apply the compressive force during the suction cycle that will increase the flow rate in our theoretical teat. The model and results may be of use in the future design of effective breast pumps.
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    The effect of shear stress on solitary waves in arteries (1997)
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    Bulletin of mathematical biology 59 (1997), S. 993-1012 
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    Notes: Abstract In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materals are depicted in graphical forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissues.
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    Role of fibroblast migration in collagen fiber formation during fetal and adult dermal wound healing (1997)
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    Bulletin of mathematical biology 59 (1997), S. 1077-1100 
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    Notes: Abstract Adult dermal wounds, in contrast to fetal wounds, heal with the formation of scar tissue. A crucial factor in determining the degree of scarring is the ratio of types I and III collagen, which regulates the diameter of the combined fibers. We developed a reaction-diffusion model which focuses on the control of collagen synthesis by different isoforms of the polypeptide transforming growth factor-β (TGFβ). We used the model to investigate the current controversy as to whether the fibroblasts migrate into the wound from the surrounding unwounded dermis or from the underlying subcutaneous tissue. Numerical simulations of a spatially independent, temporal model led to a value of the collagen ratio consistent with that of healthy tissue for the fetus, but corresponding to scarring in the adult. We investigated the effect of topical application of TGFβ and show that addition of isoform 3 reduces scar tissue formation, in agreement with the experiment. However, numerical solutions of the reaction-diffusion system do not exhibit this sensitivity to growth factor application. Mathematically, this corresponds to the observation that behind healing wavefront solutions, a particular healed state is always selected independent of transients, even though there is a continuum of possible positive steady states. We explain this phenomenon using a caricature system of equations, which reflects the key qualitative features of the full model but has a much simpler mathematical form. Biologically, our results suggest that the migration into a wound of fibroblasts and TGFβ from the surrounding dermis alone cannot account for the essential features of the healing process, and that fibroblasts entering from the underlying subcutaneous tissue are crucial to the healing process.
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    Agonist-induced calcium waves in oscillatory cells: A biological example of Burgers' equation (1997)
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    Bulletin of mathematical biology 59 (1997), S. 1125-1144 
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    Notes: Abstract Oscillations in cytosolic Ca2+ concentrations in living cells are often a manifestation of propagating waves of Ca2+. Numerical simulations with a realistic model of inositol 1, 4, 5-trisphosphate (IP3)-induced Ca2+ wave trains lead to wave speeds that increase linearly at long times when (a) IP3 levels are in the range for Ca2+ oscillations, (b) a gradient of phase is established by either an initial ramp or pulse of IP3, and (c) IP3 concentrations asymptotically become uniform. We explore this phenomenon with analytical and numerical methods using a simple two-variable reduction of the De Young-Keizer model of the IP3 receptor that includes the influence of Ca2+ buffers. For concentrations of IP3 in the oscillatory regime, numerical solution of the resulting reaction diffusion equations produces nonlinear wave trains that shows the same asymptotic growth of wave speed. Due to buffering, diffusion of Ca2+ is quite slow and, as previously noted, these waves occur without appreciable bulk movement of Ca2+. Thus, following Neu and Murray, we explore the behavior of these waves using an asymptotic expansion based on the small size of the buffered diffusion constant for Ca2+. We find that the gradient in phase of the wave obeys Burgers' equation asymptotically in time. This result is used to explain the linear increase of the wave speed observed in the simulations.
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    Cell communities and robustness in development (1997)
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    Bulletin of mathematical biology 59 (1997), S. 1183-1189 
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    Notes: Abstract The robustness of patterning events in development is a key feature that must be accounted for in proposed models of these events. When considering explicitly cellular systems, robustness can be exhibited at different levels of organization. Consideration of two widespread patterning mechanisms suggests that robustness at the level of cell communities can result from variable development at the level of individual cells; models of these mechanisms show how interactions between participating cells guarantee community-level robustness. Cooperative interactions enhance homogeneity within communities of like cells and the sharpness of boundaries between communities of distinct cells, while competitive interactions amplify small inhomogeneities within communities of initially equivalent cells, resulting in fine-grained patterns of cell specialization.
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    Cable analysis of a motor-nerve terminal branch in a volume conductor (1999)
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    Bulletin of mathematical biology 61 (1999), S. 1-17 
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    Notes: Abstract An equivalent electrical circuit is given for a branch of an amphibian motor-nerve terminal in a volume conductor. The circuit allows for longitudinal current flow inside the axon as well as between the axon and its Schwann cell sheath, and also for the radial leakage of current through the Schwann cell sheath. Analytical and numerical solutions are found for the spatial and time dependence of the membrane potential resulting from the injection of depolarizing current pulses by external electrodes at one or two separate locations on the terminal. These solutions show that the depolarization at an injection site can cause a hyperpolarization at sites a short distance away. This effect becomes more pronounced in a short terminal with sealed-end boundary conditions. The hyperpolarization provides a possible explanation for recent experimental results, which show that the average quantal release due to a test depolarizing current pulse delivered by an electrode at one site on a nerve terminal is reduced by the application of an identical conditioning pulse at a neighbouring site.
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    A mathematical model for simulating virus transport through synthetic barriers (1999)
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    Bulletin of mathematical biology 61 (1999), S. 113-140 
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    Notes: Abstract Synthetic barriers such as gloves, condoms and masks are widely used in efforts to prevent disease transmission. Due to manufacturing defects, tears arising during use, or material porosity, there is inevitably a risk associated with use of these barriers. An understanding of virus transport through the relevant passageways would be valuable in quantifying the risk. However, experimental investigations involving such passageways are difficult to perform, owing to the small dimensions involved. This paper presents a mathematical model for analyzing and predicting virus transport through barriers. The model incorporates a mathematical description of the mechanisms of virus transport, which include carrier-fluid flow, Brownian motion, and attraction or repulsion via virus-barrier interaction forces. The critical element of the model is the empirically determined rate constant characterizing the interaction force between the virus and the barrier. Once the model has been calibrated through specification of the rate constant, it can predict virus concentration under a wide variety of conditions. The experiments used to calibrate the model are described, and the rate constants are given for four bacterial viruses interacting with a latex membrane in saline. Rate constants were also determined for different carrier-fluid salinities, and the salt concentration was found to have a pronounced effect. Validation experiments employing laser-drilled pores in condoms were also performed to test the calibrated model. Model predictions of amount of transmitted virus through the drilled holes agreed well with measured values. Calculations using determined rate constants show that the model can help identify situations where barrier-integrity tests could significantly underestimate the risk associated with barrier use.
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    Analysis of intra-uterine fluid motion induced by uterine contractions (1999)
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    Bulletin of mathematical biology 61 (1999), S. 221-238 
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    Notes: Abstract Evaluation of the fluid flow pattern in a non-pregnant uterus is important for understanding embryo transport in the uterus. Fertilization occurs in the fallopian tube and the embryo (fertilized ovum) enters the uterine cavity within 3 days of ovulation. In the uterus, the embryo is conveyed by the uterine fluid for another 3 to 4 days to a successful implantation site at the upper part of the uterus. Fluid movements within the uterus may be induced by several mechanisms, but they seem to be dominated by myometrial contractions. Intra-uterine fluid transport in a sagittal cross-section of the uterus was simulated by a model of wall-induced fluid motion within a two-dimensional channel. The time-dependent fluid pattern was studied by employing the lubrication theory. A comprehensive analysis of peristaltic transport resulting from symmetric and asymmetric contractions is presented for various displacement waves on the channel walls. The results provide information on the flow field and possible trajectories by which an embryo may be transported before implantation at the uterine wall.
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    Replication potential of cells via the protein kinase C-MAPK pathway: Application of a mathematical model (1999)
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    Bulletin of mathematical biology 61 (1999), S. 379-398 
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    Notes: Abstract A mechanistically based mathematical model is used to investigate some of the important factors in priming hepatocytes to enter the G1 phase of the cell cycle. The model considers all of the relevant biochemical mechanisms from signal-receptor binding to the elevation of AP-1(activation protein transcription factor) levels. Focus is centered on the chain of biochemical events governing the sequential activation of protein kinase C (PKC), mitogen-activated protein kinase (MAPK) and AP-1. Factors such as amplitude and duration of growth factors signals, the kinetics of guanosine diphosphate (GDP) to guanosine triphosphate (GTP) conversion, and the negative feedback control mechanisms governing initial steps in cellular replication were theoretically examined. The results of our theoretical assessments support the finding that specific mutations along the PKC-AP1 pathways can have a critical effect on the rate at which cells enter the division cycle.
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    Velocity and stability of solitary planar travelling wave solutions of intracellular [Ca]2+ (1999)
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    Bulletin of mathematical biology 61 (1999), S. 273-301 
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    Notes: Abstract Normal cardiac muscle contraction occurs in response to a rapid rise followed by a slower decay in intracellular calcium concentration. When cardiac muscle cells are loaded with calcium, an intracellular store releases calcium into the cytosol by the process of calcium-induced calcium release (CICR). This release contributes to the rise in intracellular calcium which in turn triggers contraction. We use two qualitative piecewise linear reaction-diffusion models of this behaviour to investigate the speed, stability and waveform of plane waves using singular perturbation techniques.
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    Numerical simulations of stochastic circulatory models (1999)
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    Bulletin of mathematical biology 61 (1999), S. 365-377 
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    Notes: Abstract Properties of two of the stochastic circulatory models theoretically introduced by Smith et al., 1997, Bull. Math. Biol. 59, 1–22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson elimination scheme. The reason for selecting these models was the fact that the probability density functions of the residence time of these models are formally similar to those of the Bateman and gamma-like function models, i.e., the two common deterministic models. Using published data, the analytical forms of the probability density functions of the residence time and the distributions of the simulated values of the residence time were determined on the basis of the deterministic models and the stochastic circulatory models, respectively. The Kolmogorov-Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic circulatory models, provided that parameters of the latter models fulfilled selected conditions.
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    About deterministic extinction in ratio-dependent predator-prey models (1999)
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    Bulletin of mathematical biology 61 (1999), S. 19-32 
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    Notes: Abstract Ratio-dependent predator-prey models set up a challenging issue regarding their dynamics near the origin. This is due to the fact that such models are undefined at (0, 0). We study the analytical behavior at (0, 0) for a common ratio-dependent model and demonstrate that this equilibrium can be either a saddle point or an attractor for certain trajectories. This fact has important implications concerning the global behavior of the model, for example regarding the existence of stable limit cycles. Then, we prove formally, for a general class of ratio-dependent models, that (0, 0) has its own basin of attraction in phase space, even when there exists a non-trivial stable or unstable equilibrium. Therefore, these models have no pathological dynamics on the axes and at the origin, contrary to what has been stated by some authors. Finally, we relate these findings to some published empirical results.
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    Parkinsonian tremor and simplification in network dynamics (1999)
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    Bulletin of mathematical biology 61 (1999), S. 157-177 
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    Notes: Abstract We explore the behavior of richly connected inhibitory neural networks under parameter changes that correspond to weakening of synaptic efficacies between network units, and show that transitions from irregular to periodic dynamics are common in such systems. The weakening of these connections leads to a reduction in the number of units that effectively drive the dynamics and thus to simpler behavior. We hypothesize that the multiple interconnecting loops of the brain’s motor circuitry, which involve many inhibitory connections, exhibit such transitions. Normal physiological tremor is irregular while other forms of tremor show more regular oscillations. Tremor in Parkinson’s disease, for example, stems from weakened synaptic efficacies of dopaminergic neurons in the nigro-striatal pathway, as in our general model. The multiplicity of structures involved in the production of symptoms in Parkinson’s disease and the reversibility of symptoms by pharmacological and surgical manipulation of connection parameters suggest that such a neural network model is appropriate. Furthermore, fixed points that can occur in the network models are suggestive of akinesia in Parkinson’s disease. This model is consistent with the view that normal physiological systems can be regulated by robust and richly connected feedback networks with complex dynamics, and that loss of complexity in the feedback structure due to disease leads to more orderly behavior.
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    Computational experience with a parallel algorithm for tetrangle inequality bound smoothing (1999)
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    Bulletin of mathematical biology 61 (1999), S. 987-1008 
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    Notes: Abstract Determining molecular structure from interatomic distances is an important and challenging problem. Given a molecule with n atoms, lower and upper bounds on interatomic distances can usually be obtained only for a small subset of the $$\frac{{n(n - 1)}}{2}$$ atom pairs, using NMR. Given the bounds so obtained on the distances between some of the atom pairs, it is often useful to compute tighter bounds on all the $$\frac{{n(n - 1)}}{2}$$ pairwise distances. This process is referred to as bound smoothing. The initial lower and upper bounds for the pairwise distances not measured are usually assumed to be 0 and ∞. One method for bound smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality—the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley—Menger determinants. For every quadruple of atoms, each pass of the tetrangle inequality bound smoothing procedure finds upper and lower limits on each of the six distances in the quadruple. Applying the tetrangle inequalities to each of the ( 4 n ) quadruples requires O(n 4) time. Here, we propose a parallel algorithm for bound smoothing employing the tetrangle inequality. Each pass of our algorithm requires O(n 3 log n) time on a CREW PRAM (Concurrent Read Exclusive Write Parallel Random Access Machine) with $$O\left( {\frac{n}{{\log n}}} \right)$$ processors. An implementation of this parallel algorithm on the Intel Paragon XP/S and its performance are also discussed.
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    Membrane skeleton detachment in spherical and cylindrical microexovesicles (1999)
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    Bulletin of mathematical biology 61 (1999), S. 1019-1030 
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    Notes: Abstract We observed that amphiphile-induced microexovesicles may be spherical or cylindrical, depending on the species of the added amphiphile. The spherical microexovesicle corresponds to an extreme local difference between the two monolayer areas of the membrane segment with a fixed area, while the cylindrical microexovesicle corresponds to an extreme local area difference if the area of the budding segment is increased due to lateral influx of anisotropic membrane constituents. Protein analysis showed that both types of vesicles are highly depleted in the membrane skeleton. It is suggested that a partial detachment of the skeleton in the budding region is favoured due to accumulated skeleton shear deformations in this region.
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    Book review (1999)
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    Bulletin of mathematical biology 61 (1999), S. 1209-1210 
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    Controlling chaos in ecology: From deterministic to individual-based models (1999)
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    Bulletin of mathematical biology 61 (1999), S. 1187-1207 
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    Notes: Abstract The possibility of chaos control in biological systems has been stimulated by recent advances in the study of heart and brain tissue dynamics. More recently, some authors have conjectured that such a method might be applied to population dynamics and even play a nontrivial evolutionary role in ecology. In this paper we explore this idea by means of both mathematical and individual-based simulation models. Because of the intrinsic noise linked to individual behavior, controlling a noisy system becomes more difficult but, as shown here, it is a feasible task allowed to be experimentally tested.
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    Persistence in metabolic nets (1999)
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    Bulletin of mathematical biology 61 (1999), S. 573-595 
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    Notes: Abstract In an attempt to improve the understanding of complex metabolic dynamic phenomena, we have analysed several ‘metabolic networks’, dynamical systems which, under a single formulation, take into account the activity of several catalytic dissipative structures, interconnected by substrate fluxes and regulatory signals. These metabolic networks exhibit a rich variety of self-organized dynamic patterns, with e.g., phase transitions emerging in the whole activity of each network. We apply Hurst’s R/S analysis to several time series generated by these metabolic networks, and measure Hurst exponents H 〈 0.5 in most cases. This value of H, indicative of antipersistent processes, is detected at very high significance levels, estimated with detailed Monte Carlo simulations. These results show clearly the considered type of metabolic networks exhibit long-term memory phenomena.
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    Bulletin of mathematical biology 61 (1999), S. 597-600 
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    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1006/bulm.1998.0092
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    RNA structures with pseudo-knots: Graph-theoretical, combinatorial, and statistical properties (1999)
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    Bulletin of mathematical biology 61 (1999), S. 437-467 
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    Notes: Abstract The secondary structures of nucleic acids form a particularly important class of contact structures. Many important RNA molecules, however, contain pseudo-knots, a structural feature that is excluded explicitly from the conventional definition of secondary structures. We propose here a generalization of secondary structures incorporating ‘non-nested’ pseudo-knots, which we call bi-secondary structures, and discuss measures for the complexity of more general contact structures based on their graph-theoretical properties. Bi-secondary structures are planar trivalent graphs that are characterized by special embedding properties. We derive exact upper bounds on their number (as a function of the chain length n) implying that there are fewer different structures than sequences. Computational results show that the number of bi-secondary structures grows approximately like 2.35n. Numerical studies based on kinetic folding and a simple extension of the standard energy model show that the global features of the sequence-structure map of RNA do not change when pseudo-knots are introduced into the secondary structure picture. We find a large fraction of neutral mutations and, in particular, networks of sequences that fold into the same shape. These neutral networks percolate through the entire sequence space.
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    A hydrostatic Michell framework supports frog lungs (1999)
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    Bulletin of mathematical biology 61 (1999), S. 683-700 
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    Notes: Abstract A braced framework of tubular struts, in the walls and air spaces of frog lungs, suspends the respiratory surface and holds the lung open at zero transmural pressure withstanding imploding forces created by abdominal viscera, much as would the supports of a bell tent. The struts are tubes, having a larger second moment of area than do solid struts of the same cross-sectional area, and so are stronger, and contain pulmonary vessels within a flexible wall. The orthogonal arrangement of the struts in the framework, explained in part by Maxwell’s Lemma and Michell’s Theorem, strengthens the framework and minimizes its weight; orthogonality is maintained as the lungs change size. A model is presented, in which a frog might control pre-and post-pulmonary vascular resistances and, hence, blood volume in the struts, without compromising pulmonary perfusion. Such adjustments could vary the area of lung and the extent of perfused capillaries exposed to pulmonary gas, helping match the lung’s surface area, weight and metabolic load to activity.
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    Theory of fast neurotransmitter release control based on voltage-dependent interaction between autoreceptors and proteins of the exocytotic machinery (1999)
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    Bulletin of mathematical biology 61 (1999), S. 701-725 
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    Notes: Abstract A molecular-level theory is constructed for the control of fast neurotransmitter release, based on recent experimental findings that depolarization shifts presynaptic autoreceptors to a low affinity state and that an autoreceptor must be bound to a transmitter before it can become associated with the exocytotic apparatus. It is assumed that such an association blocks release; experimental support for this assumption is cited. The theory provides mechanisms for key experimental results concerning the essence of the matter, what controls the time course of evoked release? The same general model can account for both evoked and spontaneous release. The new theory can be regarded as a molecular implementation of the (phenomenological) calcium-voltage hypothesis that was suggested earlier.
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    Bulletin of mathematical biology 61 (1999), S. 799-805 
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    Cellular automaton models for competition in patchy environments: Facilitation, inhibition, and tolerance (1999)
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    Bulletin of mathematical biology 61 (1999), S. 625-649 
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    Notes: Abstract We have developed cellular automaton models for two species competing in a patchy environment. We have modeled three common types of competition: facilitation (in which the winning species can colonize only after the losing species has arrived) inhibition (in which either species is able to prevent the other from colonizing) and tolerance (in which the species most tolerant of reduced resource levels wins). The state of a patch is defined by the presence or absence of each species. State transition probabilities are determined by rates of disturbance, competitive exclusion, and colonization. Colonization is restricted to neighboring patches. In all three models, disturbance permits regional persistence of species that are excluded by competition locally. Persistence, and hence diversity, is maximized at intermediate disturbance frequencies. If disturbance and dispersal rates are sufficiently high, the inferior competitor need not have a dispersal advantage to persist. Using a new method for measuring the spatial patterns of nominal data, we show that none of these competition models generates patchiness at equilibrium. In the inhibition model, however, transient patchiness decays very slowly. We compare the cellular automaton models to the corresponding mean-field patch-occupancy models, in which colonization is not restricted to neighboring patches and depends on spatially averaged species frequencies. The patch-occupancy model does an excellent job of predicting the equilibrium frequencies of the species and the conditions required for coexistence, but not of predicting transient behavior.
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    Reaction and diffusion on growing domains: Scenarios for robust pattern formation (1999)
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    Bulletin of mathematical biology 61 (1999), S. 1093-1120 
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    Notes: Abstract We investigate the sequence of patterns generated by a reaction—diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction—diffusion models and consider the case of slow and isotropic domain growth in one spatial dimension. We use a self-similarity argument to predict a frequency-doubling sequence of patterns for exponential domain growth and we find numerically that frequency-doubling is realized for a finite range of exponential growth rate. We consider pattern formation under different forms for the growth and show that in one dimension domain growth may be a mechanism for increased robustness of pattern formation.
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    On the evolution of pure winner and loser effects: A game-theoretic model (1999)
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    Bulletin of mathematical biology 61 (1999), S. 1151-1186 
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    Notes: Abstract The persistence of linear dominance hierarchies is often attributed to higher probabilities of a win after a win or a loss after a loss in agonistic interactions, yet there has been no theory on the evolution of such prior-experience effects. Here an analytic model, based on the idea that contests are determined by subjective perceptions of resource-holding potential (RHP) which animals may revise in the light of experience, demonstrates that winner and loser effects can evolve through round-robin competition among triads of animals drawn randomly from their population, and that the probability of a hierarchy increases with the strength of the combined effect. The effects are pure, in the sense that a contestant observes neither its own RHP nor its opponent’s RHP or RHP perception or win—loss record; and so the strength of an effect is unmodified by the RHPs of particular individuals, but depends on the distribution of RHP among the population at large. The greater the difference between an individual’s and its opponent’s RHP perception, the more likely it is to win a contest; however, if it overestimates its RHP, then the cost of fighting increases with the overestimate. A winner or loser effect exists only if the fitness gain of the beta individual in a hierarchy, relative to that of the alpha, is less than 0.5. Then a loser effect can exist alone, or it can coexist with a winner effect; however, there cannot exist a winner effect without a loser effect.
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    Multiple attractors, saddles, and population dynamics in periodic habitats (1999)
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    Bulletin of mathematical biology 61 (1999), S. 1121-1149 
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    Notes: Abstract Mathematical models predict that a population which oscillates in the absence of time-dependent factors can develop multiple attracting final states in the advent of periodic forcing. A periodically-forced, stage-structured mathematical model predicted the transient and asymptotic behaviors of Tribolium (flour beetle) populations cultured in periodic habitats of fluctuating flour volume. Predictions included multiple (2-cycle) attractors, resonance and attenuation phenomena, and saddle influences. Stochasticity, combined with the deterministic effects of an unstable ’saddle cycle’ separating the two stable cycles, is used to explain the observed transients and final states of the experimental cultures. In experimental regimes containing multiple attractors, the presence of unstable invariant sets, as well as stochasticity and the nature, location, and size of basins of attraction, are all central to the interpretation of data.
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    Decreasing rearranged Fourier series (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 1-19 
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    Keywords: Primary: 42A20 ; Secondary 42C20 ; divergence of Fourier series ; rearrangement of Fourier series
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    Notes: Abstract There exists a continuous function whose Fourier sum, when taken in decreasing order of magnitude of the coefficients, diverges unboundedly almost everywhere.
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    Wavelets as unconditional bases inL p (ℝ) (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 73-85 
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    Keywords: 42C10 ; 46B15 ; 46E30 ; Wavelet ; unimodular wavelet ; unconditional basis
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    Notes: Abstract We present weak sufficient conditions for decay of a wavelet so that the wavelet basis is an unconditional basis in Lp(ℝ), 1 〈p 〈 ∞. We also prove that some unimodular wavelets yield unconditional bases in Lp(ℝ).
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    Compactly supported refinable distributions in Triebel-Lizorkin spaces and besov spaces (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 87-104 
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    Keywords: 42C15 ; 46E35 ; 42B30 ; refinable distribution ; Triebel-Lizorkin space ; Besov space ; multiresolution ; wavelet ; joint spectral radius
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    Notes: Abstract The aim of this article is to characterize compactly supported refinable distributions in Triebel-Lizorkin spaces and Besov spaces by projection operators on certain wavelet space and by some operators on a finitely dimensional space.
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    Positive matrix functions on the bitorus with prescribed Fourier coefficients in a band (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 21-44 
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    Keywords: 42B99 ; 47B35 ; 15A54 ; 60G35 ; Positive extensions ; Toeplitz operators ; matrix functions on bitorus ; Wiener algebra ; band method ; entropy ; almost periodic functions ; ARMA processes
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    Notes: Abstract Let S be a band in Z2 bordered by two parallel lines that are of equal distance to the origin. Given a positive definite ℓ1 sequence of matrices {cj}j∈S we prove that there is a positive definite matrix function f in the Wiener algebra on the bitorus such that the Fourier coefficients $$\widehat{f(k)}$$ equal ck for k ∈ S. A parameterization is obtained for the set of all positive extensions f of {cj}j∈S. We also prove that among all matrix functions with these properties, there exists a distinguished one that maximizes the entropy. A formula is given for this distinguished matrix function. The results are interpreted in the context of spectral estimation of ARMA processes.
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    A sharper stability bound of Fourier frames (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 67-71 
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    Keywords: 42C15 ; Frame ; Frame sequence ; Fourier frame
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    Notes: Abstract Given a real sequence {λn}n∈ℤ. Suppose that $$\left\{ {e^{i\lambda _n x} } \right\}_{n \in \mathbb{Z}}$$ is a frame for L2[−π, π] with bounds A, B. The problem is to find a positive constant L such that for any real sequence {μn}n∈ℤ with ¦μn −λn¦ ≤δ 〈L, $$\left\{ {e^{i\mu _n x} } \right\}_{n \in \mathbb{Z}}$$ is also a frame for L2[−π, π]. Balan [1] obtained $$L_R = \tfrac{1}{4} - \tfrac{1}{\pi }$$ arcsin $$\left( {\tfrac{1}{{\sqrt 2 }}\left( {1 - \sqrt {\tfrac{A}{B}} } \right)} \right)$$ . This value is a good stability bound of Fourier frames because it covers Kadec's 1/4-theorem $$\left( {L_R = \tfrac{1}{4}ifA = B} \right)$$ and is better than $$L_{DS} = \tfrac{1}{\pi }\ln \left( {1 + \sqrt {\tfrac{A}{B}} } \right)$$ (see Duffin and Schaefer [3]). In this paper, a sharper estimate is given.
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    On the stability of wavelet and Gabor frames (Riesz bases) (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
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    Keywords: 26B05 ; 42B10 ; 42C99 ; frame ; Gabor system ; Riesz basis ; stability ; wavelet
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    Topics: Mathematics
    Notes: Abstract If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].
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    On lower bounds of exponential frames (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 185-192 
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    Keywords: 42C15 ; 30A10 ; 94A12 ; lower bound ; exponential frame ; sine-type-function ; irregular sampling
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    Topics: Mathematics
    Notes: Abstract Lower frame bounds for sequences of exponentials are obtained in a special version of Avdonin's theorem on “1/4 in the mean” [1] and in a theorem of Duffin and Schaeffer [4].
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    A necessary condition for Calderón-Zygmund singular integral operators (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 303-308 
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    Keywords: 42B20 ; 42B30 ; Hardy spaces ; Calderon-Zygmund singular integral operator ; multipliers
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    Notes: Abstract Calderón-Zygmund singular integral operators have been extensively studied for almost half a century. This paper provides a context for and proof of the following result: If a Calderón-Zygmund convolution singular integral operator is bounded on the Hardy space H1 (Rn), then the homogeneous of degree zero kernel is in the Hardy space H1(Sn−1) on the sphere.
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    Spectral pairs in cartesian coordinates (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 285-302 
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    Keywords: 42C05 ; 22D25 ; 46L55 ; 47C05 ; spectral pair ; translations ; tilings ; Fourier basis ; operator extensions ; induced representations ; spectral resolution ; Hilbert space
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    Notes: Abstract Let Ω ⊂ℝd have finite positive Lebesgue measure, and let $$\mathcal{L}^2$$ (Ω) be the corresponding Hilbert space of $$\mathcal{L}^2$$ -functions on Ω. We shall consider the exponential functionse λ on Ω given bye λ(x)=e i2πλ·x . If these functions form an orthogonal basis for $$\mathcal{L}^2$$ (Ω), when λ ranges over some subset Λ in ℝ d , then we say that (Ω, Λ) is a spectral pair, and that Λ is a spectrum. We conjecture that (Ω, Λ) is a spectral pair if and only if the translates of some set Ω′ by the vectors of Λ tile ℝd. In the special case of Ω=Id, the d-dimensional unit cube, we prove this conjecture, with Ω′=Id, for d≤3, describing all the tilings by Id, and for all d when Λ is a discrete periodic set. In an appendix we generalize the notion of spectral pair to measures on a locally compact abelian group and its dual.
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    Fourier asymptotics of statistically self-similar measures (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 355-362 
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    Keywords: 28A80 ; 42B10 ; 60G57 ; random self-similar measures ; Fourier dimension ; Salem sets
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    Notes: Abstract In this paper we investigate the pointwise Fourier decay of some selfsimilar random measures. As an application we construct statistically selfsimilar Salem sets. For example, our result shows that a “slight” random perturbation of the classical Cantor set becomes a “nice” set in the sense that its Fourier dimension equals its Hausdorff dimension.
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    Editorial statement (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. v 
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    Topics: Mathematics
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    A necessary and sufficient condition for dual Weyl-Heisenberg frames to be compactly supported (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 409-419 
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    ISSN: 1531-5851
    Keywords: Weyl-Heisenberg frame ; Zak transform ; polynomial matrix ; 42C15
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    Notes: Abstract In this note we consider continuous-time Weyl-Heisenberg (Gabor) frame expansions with rational oversampling. We present a necessary and sufficient condition on a compactly supported function g(t) generating a Weyl-Heisenberg frame for L2 (ℝ) for its minimal dual (Wexler-Razdual) γ0 (t) to be compactly supported. We furthermore provide a necessary and sufficient condition for a band-limited function g(t) generating a Weyl-Heisenberg frame for L2 (ℝ) to have a band-limited minimal dual γ0 (t). As a consequence of these conditions, we show that in the cases of integer oversampling and critical sampling a compactly supported (band-limited) g(t) has a compactly supported (band-limited) minimal dual γ0(t) if and only if the Weyl-Heisenberg frame operator is a multiplication operator in the time (frequency) domain. Our proofs rely on the Zak transform, on the Zibulski-Zeevi representation of the Weyl-Heisenberg frame operator, and on the theory of polynomial matrices.
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    The journal of Fourier analysis and applications 5 (1999), S. 521-522 
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    Rational smoothness and fixed points of torus actions (1999)
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    Transformation groups 4 (1999), S. 127-156 
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    Notes: Abstract We obtain a criterion for rational smoothness of an algebraic variety with a torus action, with applications to orbit closures in flag varieties, and to closures of double classes in regular group completions.
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    Towards spetses I (1999)
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    Transformation groups 4 (1999), S. 157-218 
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    Notes: Abstract We present a formalization, using data uniquely defined at the level of the Weyl group, of the construction and combinatorial properties of unipotent character sheaves and unipotent characters for reductive algebraic groups over an algebraic closure of a finite field. This formalization extends to the case where the Weyl group is replaced by a complex reflection group, and in many cases we get families of unipotent characters for a mysterious object, a kind of reductive algebraic group with a nonreal Weyl group, the “spets”. In this first part, we present the general results about complex reflection groups, their associated braid groups and Hecke algebras, which will be needed later on for properties of “spetses”. Not all irreducible complex reflection groups will give rise to a spets (the ones which do so are called “spetsial”), but all of them afford properties which already allow us to generalize many of the notions attached to the Weyl groups through the approach of “generic groups” (see [BMM1]).
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    Coordinates on Schubert cells, Kostant's harmonic forms, and the Bruhat Poisson structure onG/B (1999)
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    Transformation groups 4 (1999), S. 355-374 
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    Notes: Abstract For the flag manifoldX=G/B of a complex semi-simple Lie groupG, we make connections between the Kostant harmonic forms onG/B and the geometry of the Bruhat Poisson structure. We show that on each Schubert cell, the corresponding Kostant harmonic form can be described using only data coming from the Bruhat Poisson structure. We do this by using an explicit set of coordinates on the Schubert cell.
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    Equivariant Chow groups for torus actions (1997)
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    Transformation groups 2 (1997), S. 225-267 
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    Notes: Abstract We study Edidin and Graham's equivariant Chow groups in the case of torus actions. Our main results are: (i) a presentation of equivariant Chow groups in terms of invariant cycles, which shows how to recover usual Chow groups from equivariant ones; (ii) a precise form of the localization theorem for torus actions on projective, nonsingular varieties; (iii) a construction of equivariant multiplicities, as functionals on equivariant Chow groups; (iv) a construction of the action of operators of divided differences on theT-equivariant Chow group of any scheme with an action of a reductive group with maximal torusT. We apply these results to intersection theory on varieties with group actions, especially to Schubert calculus and its generalizations. In particular, we obtain a presentation of the Chow ring of any smooth, projective spherical variety.
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    A family of affine Weyl group representations (1997)
    Springer
    Transformation groups 2 (1997), S. 375-390 
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    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we explicitly determine the virtual representations of the finite Weyl subgroups of the affine Weyl group on the cohomology of the space of affine flags containing a family of elementsn t in an affine Lie algebra. We also compute the Euler characteristic of the space of partial flags containingn t and give a connection with hyperplane arrangements.
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    URL: http://dx.doi.org/10.1007/BF01234541
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    Weakly symmetric spaces and bounded symmetric domains (1997)
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    Transformation groups 2 (1997), S. 351-374 
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    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetG be a connected, simply-connected, real semisimple Lie group andK a maximal compactly embedded subgroup ofG such thatD=G/K is a hermitian symmetric space. Consider the principal fiber bundleM=G/K s →G/K, whereK s is the semisimple part ofK=K s ·Z K 0 andZ K 0 is the connected center ofK. The natural action ofG onM extends to an action ofG 1=G×Z K 0 . We prove as the main result thatM is weakly symmetric with respect toG 1 and complex conjugation. In the case whereD is an irreducible classical bounded symmetric domain andG is a classical matrix Lie group under a suitable quotient, we provide an explicit construction ofM=D×S 1 and determine a one-parameter family of Riemannian metrics Ω onM invariant underG 1. Furthermore,M is irreducible with respect to Ω. As a result, this provides new examples of weakly symmetric spaces that are nonsymmetric, including those already discovered by Selberg (cf. [M]) for the symplectic case and Berndt and Vanhecke [BV1] for the rank-one case.
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    URL: http://dx.doi.org/10.1007/BF01234540
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    Weighted norm inequalities for geometric fractional maximal operators (1999)
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 45-66 
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    ISSN: 1531-5851
    Keywords: 42B25 ; Fractional maximal operator ; weighted norm inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For 0 ≤α 〈 ∞ let Tαf denote one of the operators $$M_{\alpha ,0} f(x) = \mathop {\sup }\limits_{I \mathrel\backepsilon x} \left| I \right|^\alpha \exp \left( {\frac{1}{{\left| I \right|}}\int_I {\log \left| f \right|} } \right),M_{\alpha ,0}^* f(x) = \mathop {\lim }\limits_{r \searrow 0} \mathop {\sup }\limits_{I \mathrel\backepsilon x} \left| I \right|^\alpha \left( {\frac{1}{{\left| I \right|}}\int_I {\left| f \right|^r } } \right)^{{1 \mathord{\left/ {\vphantom {1 r}} \right. \kern-\nulldelimiterspace} r}} .$$ We characterize the pairs of weights (u, v) for which Tα is a bounded operator from Lp(v) to Lq(u), 0 〈p ≤q 〈 ∞. This extends to α 〉 0 the norm inequalities for α=0 in [4, 16]. As an application we give lower bounds for convolutions ϕ ⋆ f, where ϕ is a radially decreasing function.
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    URL: http://dx.doi.org/10.1007/BF01274188
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    On discrete and continuous norms in Paley-Wiener spaces and consequences for exponential frames (1999)
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 193-201 
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    ISSN: 1531-5851
    Keywords: Primary 30D15 ; 42C15 ; Secondary 30D10 ; 42C30 ; Paley-Wiener space ; entire functions of exponential type ; exponential frames ; discrete norms ; sampling theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is well known that for certain sequences {tn}n∈ℤ the usual Lp norm ∥·∥p in the Paley-Wiener space PW τ p is equivalent to the discrete norm ‖f‖p,{tn}:=(∑ n=−∞ ∞ |f(tn)|p)1/p for 1 ≤ p = 〈 ∞ and ‖f‖∞,{tn}:=sup n∈ℤ|f(tn| for p=∞). We estimate ∥f∥p from above by C∥f∥p, n and give an explicit value for C depending only on p, τ, and characteristic parameters of the sequence {tn}n∈ℤ. This includes an explicit lower frame bound in a famous theorem of Duffin and Schaeffer.
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    URL: http://dx.doi.org/10.1007/BF01261609
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    Fractal differential equations on the Sierpinski gasket (1999)
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 203-284 
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    ISSN: 1531-5851
    Keywords: Primary 31C45 ; 42C99 ; Fractal differential equations ; analysis on fractals ; Sierpinski gasket ; eigenfunctions of the Laplacian ; wave propagation on fractals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let Δ denote the symmetric Laplacian on the Sierpinski gasket SG defined by Kigami [11] as a renormalized limit of graph Laplacians on the sequence of pregaskets Gm whose limit is SG. We study the analogs of some of the classical partial differential equations with Δ playing the role of the usual Laplacian. For harmonic functions, biharmonic functions, and Dirichlet eigenfunctions of Δ, we give efficient algorithms to compute the solutions exactly, we display the results of implementing these algorithms, and we prove various properties of the solutions that are suggested by the data. Completing the work of Fukushima and Shima [8] who computed the Dirichlet eigenvalues and their multiplicities, we show how to construct a basis (but not orthonormal) for the eigenspaces, so that we have the analog of Fourier sine series on the unit interval. We also show that certain eigenfunctions have the property that they are a nonzero constant along certain lines contained in SG. For the analogs of the heat and wave equation, we give algorithms for approximating the solution, and display the results of implementing these algorithms. We give strong evidence that the analog of finite propagation for the wave equation does not hold because of inconsistent scaling behavior in space and time.
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    URL: http://dx.doi.org/10.1007/BF01261610
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    Injectivity sets for spherical means on the Heisenberg group (1999)
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 363-372 
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    ISSN: 1531-5851
    Keywords: Primary 43A80 ; Secondary 44A12 ; spherical means ; Heisenberg group ; twisted spherical means ; Laguerre functions ; hypergeometric functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that the boundary of a bounded domain is a set of injectivity for the twisted spherical means on ℂ n for a certain class of functions on ℂ n . As a consequence we obtain results about injectivity of the spherical mean operator in the Heisenberg group and the complex Radon transform.
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    URL: http://dx.doi.org/10.1007/BF01259377
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    Wavelets, generalized white noise and fractional integration: The synthesis of fractional Brownian motion (1999)
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 465-494 
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    ISSN: 1531-5851
    Keywords: Fractional ARIMA ; midpoint displacement technique ; fractional Gaussian noise ; fractional derivative ; generalized functions ; self-similarity ; Primary 60G18 ; secondary 41A58 ; 60F15.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We provide an almost sure convergent expansion of fractional Brownian motion in wavelets which decorrelates the high frequencies. Our approach generalizes Lévy's midpoint displacement technique which is used to generate Brownian motion. The low-frequency terms in the expansion involve an independent fractional Brownian motion evaluated at discrete times or, alternatively, partial sums of a stationary fractional ARIMA time series. The wavelets fill in the gaps and provide the necessary high frequency corrections. We also obtain a way of constructing an arbitrary number of non-Gaussian continuous time processes whose second order properties are the same as those of fractional Brownian motion.
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    URL: http://dx.doi.org/10.1007/BF01261639
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    Modified Wigner bispectrum and its generalizations (1997)
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    Circuits, systems and signal processing 16 (1997), S. 27-40 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The Wigner bispectrum of multicomponent signals is studied, and its modified and reduced forms are introduced. A generalization of the presented forms to the Wigner higher-order spectra (WHOS), in the case of multicomponent signals, is provided. From our previous work it is known that cross terms removal (reduction) is possible for odd-order spectra with equal numbers of conjugated and nonconjugated terms. Here, we extend the analysis to even-order spectra. The theory is illustrated by examples.
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    URL: http://dx.doi.org/10.1007/BF01183173
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    On identifiability and information-regularity in parametrized normal distributions (1997)
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    Circuits, systems and signal processing 16 (1997), S. 83-89 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We describe methods to establish identifiability and information-regularity of parameters in normal distributions. Parameters are considered identifiable when they are determined uniquely by the probability distribution and they are information-regular when their Fisher information matrix is full rank. In normal distributions, information-regularity implies local identifiability, but the converse is not always true. Using the theory of holomorphic mappings, we show when the converse is true, allowing information-regularity to be established without having to explicitly compute the information matrix. Some examples are given.
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    URL: http://dx.doi.org/10.1007/BF01183177
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    Two-dimensional model-based power spectrum estimation for nonextendible correlation bisequences (1997)
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    Circuits, systems and signal processing 16 (1997), S. 141-163 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The extendibility of estimated correlation bisequences from an available sampled data array is described in terms of the generating functions of associated block Toeplitz with Toeplitz block (BTTB) matrices. The periodogram-based correlation bisequences are shown to be extendible. It is shown that the method of resultants and subresultants is convenient for generating the nonlinear constraints in the optimization problem which is solved iteratively for power spectrum estimation. A nontrivial example illustrates the concepts developed.
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    URL: http://dx.doi.org/10.1007/BF01183272
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    A multiresolutional approach to 3D object recognition (1997)
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    Circuits, systems and signal processing 16 (1997), S. 217-239 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A multiresolutional approach is presented for effectively recognizing three-dimensional (3D) objects. The approach is both pose and scale invariant. A multiresolutional model base is constructed, and multiscale edges of the object are detected using the wavelet transform. The minimum alignment between model base and object is realized by the linear mapping scheme.
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    URL: http://dx.doi.org/10.1007/BF01183276
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    Fractal interpolation functions and data compression for tracking (1997)
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    Circuits, systems and signal processing 16 (1997), S. 59-67 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The potential for data compression in using fractal interpolation functions (FIFs) is realized by the construction of a set of multirate filters. The filter tap weights are determined by optimizing the energy contents of a preselected set of frequency bands. This filter bank implementation of the FIF is successfully used to compress data simulated in a tracking environment.
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    URL: http://dx.doi.org/10.1007/BF01183175
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    On cyclically time-varying autoregressive digital filters (1997)
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    Circuits, systems and signal processing 16 (1997), S. 91-106 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A first-order autoregressive filter is altered by changing the constant gain to two or more gains that cyclically alternate in time. The advantages of this system are shown, and the relation to linear autoregressive moving average difference equations of higher order is derived.
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    URL: http://dx.doi.org/10.1007/BF01183178
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    Fast implementation of the forward positional acceleration of robots via the distributed arithmetic technique (1997)
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    Circuits, systems and signal processing 16 (1997), S. 165-195 
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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 refers to the fast implementation of the positional forward acceleration of the end effector of revolute robotic arms with spherical wrists, using the distributed arithmetic technique. The acceleration of the end effector is calculated by a cascade configuration of two pipelined arrays that calculate the Jacobian matrix and its time derivative, as well as the centrifugal-Coriolis and linear accelerations. These partial accelerations are then added in the adder tree. The building blocks of the arrays are the distributed arithmetic-based circuits that implement the matrix-vector multiplications involved in the calculations. The digit-serial configuration of the proposed implementation of the positional forward acceleration of the end effector is described. The serial and the parallel configurations may result as special cases of the digit-serial configuration. The proposed distributed arithmetic (DA) implementation of the positional forward acceleration may be applied, after appropriate modifications, to the general case of robots having either revolute or prismatic joints, with any type of wrist.
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    URL: http://dx.doi.org/10.1007/BF01183273
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    Locations and amplitudes of the extrema of the sinx/x function (1997)
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    Circuits, systems and signal processing 16 (1997), S. 241-245 
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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 addresses the calculation of the extrema of the sin x/x function. First the Newton-Raphson method is used, which allows us to obtain the extrema locations very fast through the use of a recursion formula. Then a second approach is proposed, which gives the extrema locations and the extrema amplitudes in the form of series expansions. Simple, accurate algebraic expressions are derived.
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    URL: http://dx.doi.org/10.1007/BF01183277
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    Unicursal resistive networks (1997)
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    Circuits, systems and signal processing 16 (1997), S. 307-324 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We give some existence results for a resistive network in which the components are neither voltage nor current controlled; that is, they are merely unicursal. In fact we allow coupling. Degree arguments give existence and bounds. We study several ways of avoiding the requirement of eventual passivity. No-gain and passive multiterminal elements are included. The results are extended to infinite networks.
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    URL: http://dx.doi.org/10.1007/BF01246715
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    A new approach for estimating spectra from randomly sampled sequences (1997)
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    Circuits, systems and signal processing 16 (1997), S. 375-386 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Random sampling is one of the methods that can overcome the Nyquist limit when evaluating a frequency spectrum of a signal. However, the computational complexity becomesN 2 as the FFT cannot be used. A new approach, called hybrid additive random sampling, is proposed. This new scheme is devised by concatenating random sampling sequences in such a way that symmetry is created in the transform kernel for reducing the computational effort while the anti-alias property is maintained. A savings of the least 75% in computation is achieved. The sampling scheme is also found to be suitable for parallel implementation. In this paper, the algorithms for generating the sampling sequence and evaluating the spectrum are described in detail. The performances of the scheme in terms of noise, accuracy, etc., are compared with genuine random sampling and another approach proposed previously. The advantages and limitations are included.
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    URL: http://dx.doi.org/10.1007/BF01246719
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    Stress wave propagation when the elastic coefficients vary with depth (1999)
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    Circuits, systems and signal processing 18 (1999), S. 27-42 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Of concern is the propagation of distortionless surface waves in a medium that may be nonuniform relative to depth. Distortionless wave propagation in inhomogeneous media was discussed by V. Burke, R. J. Duffin and D. Hazony, inQuart. Appl. Math., 183–194 (1976). Accordingly, the media could be modeled by a distributed electrical ladder network, nonuniform along the axis. We give a two-dimensional development based on Hooke's law and Newton's law which leads to the well-known case of Rayleigh waves in homogeneous media. It will be seen that the available pool of propagation modes greatly increases when high-pass propagation is included. The emphasis is on media where the elastic coefficients track one another as a function of depth. Special cases are studied in detail showing that as a disturbance travels along the surface, it may assume a broadband phase change, which translates into a shape distortion in the time domain, which is periodic with distance. Applications may be found in acousto-optics, in situ monitoring of elongated bodies, high-frequency SAW filters, microstrips, and any situations where surface waves are used in an environment of high precision or relatively large distances.
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    URL: http://dx.doi.org/10.1007/BF01206543
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    Linear stabilizing controllers for electrically driven flexible-joint robots with uncertain parameters (1999)
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    Circuits, systems and signal processing 18 (1999), S. 131-147 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This study presents a linear output-based controller for stabilizing a rigid-link flexible-joint electrically driven (RLFJED) robot manipulator. The proposed controller ensures local exponential stability under some uncertainty conditions. It is assumed that the velocity signals from the link side are not measurable. The controller is analyzed by using tools for pole placement by an output-feedback in the framework of the linear system theory. Some useful structural properties of the systems under consideration have been studied. Applications of the results to the set-point regulation control problem are considered.
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    URL: http://dx.doi.org/10.1007/BF01206679
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    Optimality of a direct adaptive controller in the presence of model mismatch and bounded disturbances (1999)
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    Circuits, systems and signal processing 18 (1999), S. 205-223 
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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 consider an adaptive controller with vanishing gain and excitation of the reference signal. We use the burst recovery concept to show that all signals in the adaptive loop remain uniformly bounded. We also show that the mean-square performance converges so that the adaptive system is optimal in the sense that the parameter estimation error and the one-step ahead prediction error are uncorrelated in the mean despite the presence of the unmodeled dynamics.
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    URL: http://dx.doi.org/10.1007/BF01225695
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    Cycloid decompositions of finite Markov chains (1999)
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    Circuits, systems and signal processing 18 (1999), S. 191-204 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Finite homogeneous Markov chains ξ, which admit invariant probability distributions, can be defined by the cycloids { $$\bar C_k $$ } (closed polygonal lines whose consecutive edges have various orientations that do not necessarily determine a common direction for $$\bar C_k $$ ) occurring in their graphs. These Markov chains are called cycloid chains, and the corresponding finite-dimensional distributions are linear expressions on the cycloids { $$\bar C_k $$ } with the real coefficients αk. Then the collection {{ $$\bar C_k $$ }, {αk}}, called the cycloid decomposition of ξ, gives a minimal description of the finite-dimensional distributions that, except for a choice of the maximal tree, uniquely determines the chain ξ. Furthermore, the cycloid decompositions have an interpretation in terms of the transition probability functions expressing the same essence as the known Chapman-Kolmogorov equations.
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    URL: http://dx.doi.org/10.1007/BF01225694
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    Linear systems in a saturated mode and convergence as gain becomes large of asymptotically stable equilibrium points of neural nets (1999)
    Springer
    Circuits, systems and signal processing 18 (1999), S. 241-267 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We study solutions of the “linear system in a saturated mode” $$\begin{array}{*{20}c} {(M)} & {x' \in Tx + c - \partial I_{D^n } x.} \\ \end{array} $$ We show that a trajectory is in a constant face of the cubeD n on some interval (0,d]. We answer a question about comparing the two systems: (M) and $$\begin{array}{*{20}c} {(H)} & {\begin{array}{*{20}c} {Cu' = T\upsilon + c - R^{ - 1} u,} & {\upsilon = G(\lambda } \\ \end{array} u)} \\ \end{array} $$ . As λ→∞, limits ofv corresponding to asymptotically stable equilibrium points of (H) are asymptotically stable equilibrium points of (M), and the converse is also true. We study the assumptions to see which are required and which may be weakened.
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