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  • Springer  (53,560)
  • Elsevier  (49,415)
  • 2015-2019
  • 2010-2014
  • 1985-1989  (102,975)
  • 1987  (102,975)
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  • 2015-2019
  • 2010-2014
  • 1985-1989  (102,975)
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  • 1
    Electronic Resource
    Electronic Resource
    Entropy balance of white-tailed deer during a winter night (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. 321-327 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The entropy budget of a white-tailed deer (50kg) on a maintenance diet and a full-feed diet in a standing posture in an open field under clear nocturnal skies with an air temperature of −20°C is investigated based on the energetics given by Moen. Entropy inflow into a white-tailed deer due to infra-red radiation and entropy outflows from a deer due to infra-red radiation, convection, evaporation of water and conduction to ingested food are calculated. Also the entropy production due to metabolic heat production is estimated. Net entropy flow into a deer from its environment becomes negative. On the assumption that a white-tailed deer is in a steady state in entropy, the total entropy production in a deer on a maintenance diet becomes +0.46 J/sec/K. Positiveness of the entropy production shows that the Second Law of Thermodynamics certainly holds in a white-tailed deer. The entropy production per effective radiating surface area of a deer on a maintenance diet is 0.32×10−4 J/cm2/sec/K. On the other hand, the entropy production in a deer on a full-feed diet is 0.59 J/sec/K and that per effective surface area is 0.41×10−4 J/cm2/sec/K. Uptake of 1 g of food produces 22 J/K of entropy within the body of a white-tailed deer. Comparison is made with the results for entropy production in a lizard and in plant leaves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460123
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  • 2
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    Book reviews (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. 507-517 
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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/BF02458867
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  • 3
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    Editorial: Software survey section (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), 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/BF02458868
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  • 4
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    The [extended] maximum entropy formalism and the statistical structure of ecosystems (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. 531-538 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Biological adaptability has been proved to be analysable by means of the Maximum Entropy Formalism (MAXENT) in some cases of non-interacting systems. This formalism is extended to the biomass statistical structures of populations exhibiting internal interactions (i.e. predatorprey effects).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460136
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  • 5
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    Theoretical study of a two-dimensional autocatalytic model for calcium dynamics at the extracellular fluid-bone interface (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. 597-613 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The temporal behaviours of the nonlinear substructure of a self-organized compartmental model of calcium metabolism were investigated. The order-two autocatalytic process included in this simple two-dimensional model is compared to some secondary nucleation mechanisms which should take place at the extracellular fluid-bone interface. The model gives rise to complex dynamic behaviours, and multistability properties, involving up to two stable periodic regimes (birhythmicity), were established in different topological configurations. The bifurcations occurring on the boundaries between regions of different qualitative behaviour have been determined. These properties are discussed in relation to the dynamical behaviour of other two-variable models, especially those including the same nonlinearity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460138
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  • 6
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    Linearized oscillations in population dynamics (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. 615-627 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A linearized oscillation theorem due to Kulenović, Ladas and Meimaridou (1987,Quart. appl. Math. XLV, 155–164) and an extension of it are applied to obtain the oscillation of solutions of several equations which have appeared in population dynamics. They include the logistic equation with several delays, Nicholson's blowflies model as described by Gurney, Blythe and Nisbet (1980,Nature, Lond. 287, 17–21) and the Lasota-Wazewska model of the red blood cell supply in an animal. We also developed a linearized oscillation result for difference equations and applied it to several equations taken from the biological literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460139
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  • 7
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    Editorial: Software survey section (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), 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/BF02460142
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  • 8
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    A theoretical approach to the evolution and structural design of enzymatic networks; Linear enzymatic chains, branched pathways and glycolysis of erythrocytes (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. 539-595 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theoretical approach to the explanation of the structural design of metabolic pathway is presented. It is based on the hypothesis that due to natural selection during evolution the cellular metabolism of present-day organisms may be characterized by optimal properties. Two cardinal terms enter the theory: (i) the efficiency of a metabolic pathway and (ii) the evolutionary effort for the change of the kinetic parameters of enzymes by mutations of the corresponding genes. For both quantities simple mathematical expressions are proposed. While the efficiency is related to the reaction rates of the enzymes constituting the metabolic pathway, the evolutionary effort is considered to be a monotonically increasing function of the parameter values. By maximizing the efficiency under the constraint of a fixed evolutionary effort the theory allows the calculation of the optimal parameter distribution as the outcome of evolution processes. The methods developed are applied to the following systems: (a) linear reaction sequences with very low affinities of the enzymes towards substrates, (b) linear sequences consisting of saturable enzymatic reactions, (c) branched metabolic pathways consisting of segments of linear chains and (d) glycolysis of erythrocytes. The conclusion is derived that the optimal distribution of kinetic constants depends strongly on the equilibrium constants of the reactions as well as on the total osmolarity of the metabolic intermediates. Without osmotic constraints the evolutionary effort is mainly spent on the enzymes at the beginning of the chain. Using Michaelis-Menten equations the optimal state is characterized by a decrease of the maximal activities of the enzymes towards the end of the chain. These results are modified if osmotic constraints are taken into account. At the investigation of branched pathways the following results were obtained: firstly, if a certain end product may be synthesized along different pathways those which are thermodynamically more unfavourable (e.g. characterized by a small change of free energy) are eliminated in the course of evolution; secondly, if a branched pathway leads to several important end products those reaction segments which are thermodynamically unfavourable are characterized by a higher evolutionary effort. The application of the theory to a realistic model of glycolysis of erythrocytes leads to a correct description of various functionally important properties of the system, such as the ratio between fluxes through different branches and the ATP/ADP ratio, whereas the theory cannot predict the strong separation of time constants observed in the real glycolytic system. It is concluded that the improvement of the predictive power of the theory necessitates the use of more complex functionals for the efficiency which take into account not only the fluxes but also other system properties such as the stability of the pathway or homoeostatic effects.
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    URL: http://dx.doi.org/10.1007/BF02460137
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  • 9
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    Editorial announcement (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), 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/BF02459954
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  • 10
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    Book reviews (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. iv 
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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/BF02459956
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  • 11
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    Bayesian image processing of data from constrained source distributions—II. valued, uncorrelated and correlated constraints (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. 75-91 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Bayesian image processing formalisms which incorporatea priori information about valued-uncorrelated and valued-correlated (patterned) source distributions are introduced and the corresponding iterative algorithms are derived using the EM technique. Striking improvement in image processing is demonstrated when applying these algorithms to Poisson and Gaussian randomized data in one-dimensional cases.
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    URL: http://dx.doi.org/10.1007/BF02459960
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  • 12
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    Decentralized variable structure control of interconnected multi-input/ multi-output nonlinear systems (1987)
    Springer
    Circuits, systems and signal processing 6 (1987), S. 363-387 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract For a broad class of interconnected nonlinear systems, this paper develops a complete design methodology for decentralized variable structure control. Specifically, the paper sets forth design schemes for local switching surfaces and the related local switched feedback gains which together force the original nonlinear interconnected system to behave as a reduced order interconnected equivalent system having a desired response such as stability, tracking, or prespecified eigenvalues. Also developed is a numerical algorithm for constructing the switched local feedback gains. A simple nonlinear example illustrates the control strategy.
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    URL: http://dx.doi.org/10.1007/BF01600000
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  • 13
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    On decentralized hierarchic stabilization of a large-scale system with constraints (1987)
    Springer
    Circuits, systems and signal processing 6 (1987), S. 391-419 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A new stabilization method of a large-scale dynamic system, consisting of a set of interconnected subsystems, is presented in this paper. The topology of the interconnected subsystems is given as a network containing nodes with only one ingoing link, and none, one, or more outgoing links. Here, when the notion “node” is used a subsystem is assumed, and the links stand for the subsystem interconnections. The stabilization method is made only by the use of local linear state feedback around each subsystem, in order to satisfy constraints given in the problem. The interconnections among the subsystems are assumed to be nonlinear, time-varying. According to the topology of the large-scale system, the method of stabilization is hierarchic, one proceeds from node to node, and is applicable from a computer standpoint. A design algorithm follows directly, and can be made using the Generate and Test method for each subsystem independently, thus enabling designers to use a computer which has a video terminal as a peripheral unit and providing a possibility for interactive applications.
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    URL: http://dx.doi.org/10.1007/BF01600232
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  • 14
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    Estimation of structured covariances with application to array beamforming (1987)
    Springer
    Circuits, systems and signal processing 6 (1987), S. 421-447 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The estimation of covariance matrices which are structured, for example, of Toeplitz type, from measurement data is considered. The problem is considered in the context of array beamforming, and various methods of estimation are derived and compared, such comparison including consideration of the behavior of the estimate in beamforming applications.
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    URL: http://dx.doi.org/10.1007/BF01600233
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  • 15
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    Formation of the block toeplitz matrix for two-dimensional PLSI Polynomials (1987)
    Springer
    Circuits, systems and signal processing 6 (1987), S. 449-456 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The planar least-squares inverse (PLSI) polynomials are used for stabilization of two-dimensional unstable recursive filters. In order to obtain the PLSI polynomials, the main work involved consists in forming a set of linear equations and then solving them. In this paper we present an efficient and simple method to form the necessary set of linear equations (i.e., the required coefficient matrix) for a chosen pattern and order of the desired PLSI polynomial, starting from the denominator polynomial of a two-dimensional unstable recursive filter.
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    URL: http://dx.doi.org/10.1007/BF01600234
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  • 16
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    System inversion using orthogonal functions (1987)
    Springer
    Circuits, systems and signal processing 6 (1987), S. 347-362 
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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 shows how to use orthogonal functions to invert singular (i.e., generalized state-space) systems. The approach is to express the inverse system itself as a singular system, and then to apply the theory of orthogonal functions to convert that differential-algebraic system to a purely algebraicgeneralized Lyapunov equation whose solution yields the input of the original system given its output. Both left and right inversion are treated. Necessary and sufficient conditions for the existence and uniqueness of the generalized Lyapunov equation are derived, and a generalizedQZ algorithm is given for its efficient solution. It is also shown that the coefficients in the Walsh function expansion may be approximately found using an FFT-type butterfly network. These results provide both an extension in theory, by investigating the properties of a new Lyapunov equation, and an extension in the implementation of system inversion, by providing a scheme which applies to generalized state-space systems and uses an unconventional approach which may prove to be a useful contribution.
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    URL: http://dx.doi.org/10.1007/BF01599999
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  • 17
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    Call for papers (1987)
    Springer
    Circuits, systems and signal processing 6 (1987), S. I 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01600237
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  • 18
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    Decoupling of the overflow and quantization phenomena in orthogonal biquad recursive digital filters (1987)
    Springer
    Circuits, systems and signal processing 6 (1987), S. 457-470 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In digital communication networks, a special class of complex biquad recursive digital filters called orthogonal filters is increasingly being used. The separate effects of the overflow and quantization nonlinearities on these orthogonal filters' responses have been investigated [5], [6]. In this paper we examine the zero-input stability properties of the actual orthogonal filter having both overflow and quantization nonlinearities. The overflow nonlinearities considered include saturation, bit-by-bit inversion, zeroing, and modulo 2 arithmetic. The quantization techniques used may be roundoff, magnitude, or value truncation. An example demonstrates the adverse coupling effect between the overflow and quantization nonlinearities. Two criteria are therefore derived to ensure asymptotic overflowstability of the filter in the presence of quantization. These criteria have been translated to the coefficient plane; various regions corresponding to different minimum wordlengths required to ensure decoupling of the overflow and quantization phenomena have been derived.
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    URL: http://dx.doi.org/10.1007/BF01600235
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  • 19
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    An output error model and algorithm for electromagnetic system identification (1987)
    Springer
    Circuits, systems and signal processing 6 (1987), S. 471-505 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The identification problem for electromagnetic objects excited by transients is discussed. Several classes of models are reviewed, and an output error model is selected. An algorithm for solving the transient identification problem using this model is presented, and some of the issues connected with its use are considered. Examples of the application of this algorithm to electromagnetic data are given.
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    URL: http://dx.doi.org/10.1007/BF01600236
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  • 20
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    The forum (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. iii 
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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/BF02459955
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  • 21
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    Stochastic model of population growth and spread (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. 1-11 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A stochastic model for the population regulated by logistic growth and spreading in a given region of two-or three-dimensional space has been introduced. For many-species population the interactions among the species have also been icorporated in this model. From the random variables that describe stochastic processes of a Wiener type the space-dependent random population densities have been formed and shown to satisfy the Langevin equations. The Fokker-Planck equation corresponding to these Langevin equations has been approximately solved for the transition probability of the population spreading and it has been found that such approximate expressions of the transition probability depend on the solutions of the deterministic equations of the diffusion model with logistic growth and interactions. Also, the stationary or equilibrium solutions of the Fokker-Planck equation together with the special discussion on the pattern of single-species population spreading have been made.
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    URL: http://dx.doi.org/10.1007/BF02459957
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  • 22
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    Hierarchical evolutive systems: A mathematical model for complex systems (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. 13-50 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The notion of an evolutive hierarchical system proposed in this paper is a mathematical model for systems, like organisms, with more or less complex objects. This model, based on category theory, retains the following characteristics of natural systems: they have an internal organization consisting of components with interrelations; they maintain their organization in time though their components are changing; their components are divided into several levels corresponding to the increasing complexity of their own organization, and the system may be studied at any of these levels (e.g. molecular, cellular...). The state of the system at a given instant is modeled by a category whose objects are its components, the state transition by a functor, a complex object by the (direct) limit of a pattern of linked objects (which describes its internal organization). The properties of limits in a category make it possible to ‘measure’ the emergence of properties for a complex object with respect to its components, and to reduce the study of a hierarchical system to that of its components of the lowest degree and their links. Categorical constructions describe the formation of a hierarchical evolutive system stepwise, by means of the operations: absorption of external objects, destruction of some components, formation of new complex objects.
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  • 23
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    Inference algorithms for developmental systems with cell lineages (1987)
    Springer
    Bulletin of mathematical biology 49 (1987), S. 93-123 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An algorithmic formulation is presented for the inference procedure concerning lineage models. The problem is to find lineage rules from observed sequences of tree structures under the assumption that no interactions take place in the course of development and that sufficiently frequent observations are available at equal time intervals. The underlying structural pattern is taken to be a OL system, and the goal is to find propagating and deterministic OL schemes with minimal properties satifsying certain biological reliance criteria. Upper bounds have been found for the complexity of the inference algorithms.
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    URL: http://dx.doi.org/10.1007/BF02459961
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  • 24
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    Non-equilibrium fluctuation in Volterra-Lotka systems (1987)
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    Bulletin of mathematical biology 49 (1987), S. 125-131 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A statistical theory of non-equilibrium fluctuation in Volterra-Lotka systems has been presented on the basis of the technique of statistical linearization of non-linear coupled stochastic differential equations.
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    URL: http://dx.doi.org/10.1007/BF02459962
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    A stochastic dynamical model for the characterization of the geometrical structure of dendritic processes (1987)
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    Bulletin of mathematical biology 49 (1987), S. 135-152 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Under certain basic assumptions the branching pattern of dendrites can be modeled as a Galton-Watson process in varying environment. Using results from graph theory we compute the probability distributions, expectations and variances for biologically significant variables such as the number of (intermediate and terminal) branches, the maximum number of orders, etc., together with the limit behavior of these quantities. Furthermore, the probability measure induced by the Galton-Watson process on the set of all trees is calculated. The measure assigns to any set of branching patterns the probability that it is realized by a certain process, which is completely described through the bifurcation probabilities.
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    URL: http://dx.doi.org/10.1007/BF02459695
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    On reliability analysis of DNA repair systems (1987)
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    Bulletin of mathematical biology 49 (1987), S. 187-216 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Theoretical models for DNA repair mechanisms are constructed. Reliability studies considering the living cell as a repairable system are done. The DNA repair process is discussed along with applications and comparison with available experimental data.
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    Transport of macromolecules in arterial wallin vivo: A mathematical model and analytical solutions (1987)
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    Bulletin of mathematical biology 49 (1987), S. 153-169 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model has been developed to simulatein vivo transmural accumulation of an intravenously injected tracer in the aortic wall of experimental animals. Parameters have been included to represent the following processes that affect tracer distribution: permeation of the blood-tissue interface, diffusion through the layers of the artery wall,convective solute drag through the same, and degradation. Of particular interest for thein vivo situation situation is the inclusion of boundary conditions that account for the variation in the plasma concentration of injected tracer as a function of time. Two analytical solutions are presented. The first describes a system in which two boundaries must be delineated; it pertains if the tracer is allowed to circulate until it enters the avascular media of the artery wall both across its luminal boundary and from the capillaries in its outer layer. The second applies to shorter duration experiments in which entry across only the luminal boundary is considered. A limiting case of the solution for short circulation times is presented, compared with a previously published solution, and examined for its potential utility in parameter estimation. Because of its treatment of time-dependent boundary conditions, the model has unique application toin vivo experiments related to macromolecular transport in atherosclerosis that may otherwise elude proper interpretation.
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    URL: http://dx.doi.org/10.1007/BF02459696
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  • 28
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    On the heterogeneity of reaction-diffusion generated pattern (1987)
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    Bulletin of mathematical biology 49 (1987), S. 233-252 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Several current reaction-diffusion mechanisms have been proposed as models for morphogenesis in the Turing (1952,Phil. Trans. R. Soc. Lond. B 237, 37–72) sense. We introduce and exploit a quantity, we have termed heterogeneity, which allows us to elaborate the differences between the various models with regard to spatial pattern formation. It is shown that this quantity provides a concise view for the comparison of theoretical models with experimental observations. Two model mechanisms are treated explicitly both for linear and for biased diffusion.
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    URL: http://dx.doi.org/10.1007/BF02459700
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  • 29
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    Optimum capillary number for oxygen delivery to tissue in man (1987)
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    Bulletin of mathematical biology 49 (1987), S. 351-361 
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    ISSN: 1522-9602
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    Notes: Abstract The optimum number of total capillaries in the whole human body was estimated from the analysis of the efficiency for oxygen (O2) transport in the vascular-tissue system. We used a tissue model composed of uniform spheres in which O2 diffuses from the capillary located at the centre of each sphere towards the surrounding tissue consuming O2 at a constant rate. The tissue mass supplied by a single capillary was estimated as the area of positive O2 concentration under a given condition of capillary flow and O2 consumption rate. Total tissue mass was determined as the function of the capillary numbern and the total blood flow. On the other hand, the energy cost required to maintain the vascular system withn terminals was assessed by using the minimum volume model (Kamiya and Togawa,Bull. math. Biophys. 34, 431–438, 1972). The efficiency of the entire vascular-tissue system was evaluated by calculating the ratio of total tissue mass/cost function. The result of the calculation using physiological data of cardiac output and O2 consumption for an average human adult during a heavy exercise revealed the maximum efficiency occurring at the capillary number 3.7×1010 which coincided well with its normal range of physiological estimates (3.2×1010–4.2×1010). We concluded that the entire vascular-tissue system is constructed so as to attain the highest efficiency in O2 transport at its maximum activity.
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    Model of synthesis and release of insulin from rat islet β-cells and the effect of pretreatment with tolbutamide (1987)
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    Bulletin of mathematical biology 49 (1987), S. 379-394 
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    Notes: Abstract A kinetic model involving synthesis of proinsulin in the rough endoplasmic reticulum, maturation through the Golgi apparatus and granules, with conversion to insulin, is proposed to account for data on the amount of insulin and of proinsulin both secreted during various time intervals and remaining in islets. Introducing three compartments for granules makes it possible to account for the measurement of both hot (pulse labeled with tritiated leucine) and cold proinsulin and insulin over a period of 21/2 hr under constant glucose. Data from islets from animals pretreated with tolbutamide are also presented and modeled. The model is then expanded so that it can be successfully applied to available data on the effects of a period of glucose deprivation on secretion of both hot and cold hormone. Parameters have essentially the same values, where they overlap, as were obtained (Landahl and Grodsky, 1982Bull. math. Biol. 44, 399–410) from insulin secretion by perfused rat pancreas stimulated by a variety of temporal patterns of glucose concentration.
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    Sequential and synchronous growth models related to vertex analysis and branching ratios (1987)
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    Bulletin of mathematical biology 49 (1987), S. 413-429 
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    Notes: Abstract Two models of binary tree growth are examined in terms of the Strahler order branching ratio (Rb) and the types of vertex produced during growth, and their inter-relationship. The sequential growth model is that described by Van Pelt and Verwer (1985,Bull. math. Biol. 47, 323–336) in which random growth occurs according to attributed probabilities on terminal or internal segments, one branch at a time. This model generates values ofRb≥3. The synchronous growth model is new and permits more than one segment to branch at a time, again randomly with attributed probabilities. This model generates values ofRb≥2 and in particular, when only terminal branching is permitted, gives 2≤Rb〈3. Such a model might explain the branching in the human bronchial tree, in which 2.5≤Rb≤2.8. Our synchronous model is an alternative to the centrifugal-order-dependent sequential model of Van Pelt and Verwer.
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    Entropy budgets of deciduous plant leaves and a theorem of oscillating entropy production (1987)
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    Bulletin of mathematical biology 49 (1987), S. 449-460 
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    Notes: Abstract From an energy budget of a deciduous plant leaf in moderate conditions, entropy fluxes into or out of the leaf due to solar radiation, infrared radiation, evaporation of water and heat conduction are calculated. Net entropy flow into the leaf is negative. On the assumption that the entropy in the leaf is in a steady state, the entropy production in the typical deciduous leaf in moderate conditions [the solar energy absorbed by both sides of the leaf isE solar=0.0602 (J cm−2 s−1)] becomesS prod=1.8×10−4 (J cm−2 s−1 K−1). The positiveness of the entropy production shows that the Second Law of Thermodynamics certainly holds in the plant leaf. Entropy productions in other conditions are also calculated. The entropy production in the leafS prod becomes a linear function of the solar energy absorbed by the leafE solar:S prod≈-(29.5E solar)×10−4. A theorem is presented: the entropy production in plant leaves oscillates during the period of one day, paralleling the daily solar energy absorbed by leaves.
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    Computational complexity of inferring phylogenies from dissimilarity matrices (1987)
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    Bulletin of mathematical biology 49 (1987), S. 461-467 
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    Notes: Abstract Molecular biologists strive to infer evolutionary relationships from quantitative macromolecular comparisons obtained by immunological, DNA hybridization, electrophoretic or amino acid sequencing techniques. The problem is to find unrooted phylogenies that best approximate a given dissimilarity matrix according to a goodness-of-fit measure, for example the least-squares-fit criterion or Farris'sf statistic. Computational costs of known algorithms guaranteeing optimal solutions to these problems increase exponentially with problem size; practical computational considerations limit the algorithms to analyzing small problems. It is established here that problems of phylogenetic inference based on the least-squares-fit criterion and thef statistic are NP-complete and thus are so difficult computationally that efficient optimal algorithms are unlikely to exist for them.
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    Editorial: Software survey section (1987)
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    Bulletin of mathematical biology 49 (1987), S. I 
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    Oscillatory flow of blood in a stenosed artery (1987)
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    Bulletin of mathematical biology 49 (1987), S. 279-287 
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    Notes: Abstract In order to understand the abnormal flow conditions of blood in a locally constricted blood vessel, the analytical results are obtained for the oscillatory flow of blood which behaves as a Newtonian fluid. It is here assumed that the surface roughness is cosine-shaped and the maximum height of the roughness is very small compared with the radius of the unconstricted tube. Numerical solutions are presented for the instantaneous flow rate, resistive impedance, wall shear stress and phase lag.
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    Pulse waves in prestressed arteries (1987)
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    Bulletin of mathematical biology 49 (1987), S. 289-305 
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    Notes: Abstract In order to better understand the effect of initial stress in blood flow in arteries, a theoretical analysis of wave propagation in an initially inflated and axially stretched cylindrical thick shell is investigated. For simplicity in the mathematical analysis, the blood is assumed to be an incompressible inviscid fluid while the arterial wall is taken to be an isotropic, homogeneous and incompressible elastic material. Employing the theory of small deformations superimposed on a large initial field the governing differential equations of perturbed solid motions are obtained in cylindrical polar coordinates. Considering the difficulty in obtaining a closed form solution for the field equations, an approximate power series method is utilized. The dispersion relations for the most general case of this approximation and for the thin tube case are thoroughly discussed. The speeds of waves propagating in an unstressed tube are obtained as a special case of our general treatment. It is observed that the speeds of both waves increase with increasing inner pressure and axial stretch.
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    Bayesian image processing of data from constrained source distributions—I. non-valued, uncorrelated and correlated constraints (1987)
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    Bulletin of mathematical biology 49 (1987), S. 51-74 
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    Notes: Abstract A series of Bayesian image processing algorithms which incorporate various classes ofa priori source information in treating data which obeys Poisson and Gaussian statistics is derived using maximum entropy considerations. The standard maximum likelihood equations are shown to be a special case of Bayesian image processing when thea priori information about a source distribution φ j is solely that a non-vanishing probability for each element value φ j exists only in some finite interval,a j ≤φ j ≤φ j . Bayesian image processing equations for thea priori source information that all φ j are finite -∞〈φ j 〈∞ and each φ j distribution has a defined mean φ j and a defined variance σ j are derived. The Bayesian image processing equations are also derived when thea priori source information is that all φ j ≥0 and that each φ j distribution has a defined mean φ j and a defined variance σ j . The a priori source distribution constraint that a correlation exists among nearby elements is also considered. The results indicate improvement over standard methods.
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    Announcements (1987)
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    Bulletin of mathematical biology 49 (1987), S. 133-134 
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    Editorial: Software survey section (1987)
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    A probabilistic approach for evaluating a technique for an indirect monitoring of the capillary blood flow to the gastric parietal cells (1987)
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    Bulletin of mathematical biology 49 (1987), S. 171-185 
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    Notes: Abstract The superficial capillary network of the gastric mucosa can be monitored for red blood cell velocity measurements by a microscopic technique. This network, however, reflects the blood flow in capillaries of more physiological interest, namely those passing by the acid-producing cells and emptying into the superficial network. It is, however, not possible to study these capillaries directly and therefore the problem is to determine in what way and to what degree blood flow measurements in the superficial network reflect the capillary flow of interest. A probabilistic approach where the movements of the red blood cells have been analysed, gives indications of determinable relations between observations on the superficial network flow and the flow passing the acid-producing cells.
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    In vivo determination of young's modulus for the human cornea (1987)
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    Bulletin of mathematical biology 49 (1987), S. 217-232 
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    Notes: Abstract The present paper describes a calculation technique to determine a value of Young's modulus for the cornea when the intraocular pressure, the shape of the cornea and the thickness variation along the cornea are known fromin vivo measurements. Twenty-eight persons were examined in both eyes and a mean value of Young's modulus for the cornea was calculated to 2.45×104±0.57×104 N/m2 (S.D.).
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    Time delays produced by essential nonlinearity in population growth models (1987)
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    Bulletin of mathematical biology 49 (1987), S. 253-255 
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    Notes: Abstract It is pointed out that the asymptotic general solution to the ϕ-model equation for a periodic carrying capacityK(t) andt≳r −1 is identical in form to the generalized logistic equation solution with a built-in developmental time delay τ(≲r −1) and associated parameter ranges of primary biological interest. In the case of the ϕ-model equation, the time delay is a purely dynamical consequence of the nonlinear form featured by the population growth rate.
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    A study on the non-linear flow of blood through arteries (1987)
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    Bulletin of mathematical biology 49 (1987), S. 257-277 
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    Notes: Abstract The pulsatile flow of blood through arteries is investigated in this paper by treating the blood vessel as a thin-walled anisotropic, non-linearly viscoelastic, incompressible circular cylindrical shell; nonlinearities of the flow of blood are also paid due consideration. The displacement components of the vessel wall are obtained from the equations of equilibrium which have been linearized by employing the principle of superimposition of a small deformation on a state of known finite deformation. The influence of the wall deformation on the flow properties of blood, has been accounted for by considering suitably formulated continuity conditions. A finitedifference scheme is employed for solving the flow equations together with the boundary and initial conditions by using the locally measured values of pressure and pressure gradient. Numerical results obtained for the velocity profile of blood flowing in a canine middle descending thoracic aorta have been presented through figures.
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    A nonlinear treatment of the protocell model by a boundary layer approximation (1987)
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    Bulletin of mathematical biology 49 (1987), S. 307-320 
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    Notes: Abstract The “protocell” is a mathematical model of a self-maintaining unity based on the dynamics of simple reaction-diffusion processes and a self-controlled dynamics of the surface. In this paper its spatio-temporal behaviour far from the stationary structure is investigated by means of a boundary layer approximation. It is shown in detail how a simplified and mathematically feasible equation can be derived from the original parabolic problem. It turns out that the known instability which is initiated in the linear region around the stationary structure is continued further in the direction to a division by nonlinear dynamics.
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    The kinetics of solute clearance by a single tissue capillary of limited permeability: Explicit solutions of two models and their bounds (1987)
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    Bulletin of mathematical biology 49 (1987), S. 329-349 
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    Notes: Abstract To describe stationary-state kinetics of solute clearance from an interstitial space with an initial uniform concentration, an explicit solution of the Sangren-Sheppard model and a stratagem for an explicit solution of the Johnson-Wilson model are presented. In both cases expressions for computing the exact intravascular and extravascular concentrations at any time and location are complicated and inconvenient. Simpler and far more convenient formulae for determining upper and lower bounds on solute concentrations and on the pseudo-first-order clearance rate ‘constant’ (k) are derived. For the Johnson-Wilson model, the bounds are so tight thatk, for example, can be estimated with considerable accuracy whenever the capillary blood flow exceeds the permeability-surface area product.
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    Parameter estimation in topological analysis of binary tree structures (1987)
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    Bulletin of mathematical biology 49 (1987), S. 363-378 
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    Notes: Abstract Different types of random binary topological trees (like neuronal processes and rivers) occur with relative frequencies that can be explained in terms of growth models. It will be shown how the model parameter determining the mode of growth can be estimated with the maximum likelihood procedure from observed data. Monte Carlo simulations were used to study the distributional properties of this estimator which appeared to have a negligible bias. It is shown that the minimum chi-square procedure yields an estimate that is very close to the maximum likelihood estimate. Moreover, the goodness-of-fit of the growth model can be inferred directly from the chi-square statistic. To illustrate the procedures we examined axonal trees from the goldfish tectum. A notion of complete partition randomness is presented as an alternative to our growth hypotheses.
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    Editorial: Software survey section (1987)
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    Bulletin of mathematical biology 49 (1987), S. I 
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    Solution of large compartmental models using numerical transform inversion (1987)
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    Bulletin of mathematical biology 49 (1987), S. 395-402 
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    Notes: Abstract Compartmental models of biological or physical systems are often described by a system of “stiff” differential equations. In this paper an algorithm for solving a system with linear coefficients is presented that employs numerical inversion of the Laplace transform of the model equations. The inversion algorithms and Gear's backward differentiation method are compared for two stiff test problems and a differential system governing a 27-compartment model of bile acid transport and metabolism. The inversion algorithm is reliable, requires modest computation time on a desktop computer and provides better accuracy than Gear's method, especially for the extremely stiff example.
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    Model geometries for sickled erythrocytes (1987)
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    Bulletin of mathematical biology 49 (1987), S. 403-411 
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    Notes: Abstract Proposed model geometries are described for three types of axisymmetric and four types of flattened sickled erythrocytes. The axisymmetric types are designated as concave-convex, convex-convex and parabolic, while the flattened types carry designations of concave-convex, convex-convex, parabolic and S-shaped. Formulae are provided for the volume and surface area of each type and a figure showing the profile of each is included. Measurements of actual sickled cellsin vitro could be used to find values for the volume and surface area of each type of cell by using parameter values for the appropriate model geometry. These would give close approximations that could be useful in clinical therapies and laboratory investigations for sickle cell anemia. Surface area to volume ratios can also be found to a close approximation for each cell type.
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    Global stability of single-species diffusion volterra models with continuous time delays (1987)
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    Bulletin of mathematical biology 49 (1987), S. 431-448 
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    Notes: Abstract In this paper we consider the stability property of single-species patches connected by diffusion with a within-patch dynamics of Volterra type and with continuous time delays. We prove that this system can only have two kinds of equilibria: the positive and the trivial one. By the assumption that the delay kernels are convex combinations of suitable non-negative and normalized functions, the linear chain trick gives an expanded system of O.D.E. with the same stability properties as the original integro-differential system. Homotopy function techniques provide sufficient conditions for the existence of the positive equilibrium and for its global stability. We also prove the local stability of any positive equilibrium and the local instability both of positive and trivial equilibria. The biological meanings of the results obtained are compared with known results from the literature.
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    Analysis of three- and four-compartment models forin vivo radioligand-neuroreceptor interaction (1987)
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    Bulletin of mathematical biology 49 (1987), S. 469-486 
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    Notes: Abstract Currently applied three-copartment models for analyzing kinetic data derived fromin vivo positron emission tomographic (PET) studies of radioligand-neuroreceptor interactions require assumptions which may not be strictly valid. Such assumptions include very rapid kinetics for nonspecific binding and the absence of multiple specific receptors or subtypes. Computer simulations, based on an exact analytical solution of the relevant differential equations, indicate the numerical errors that can arise when the assumptions are invalid. We propose a fourcompartment model which requires fewer assumptions. A simple relationship is derived for expressing the microscopic rate constants of either the three- or four-compartment model as explicit functions of the experimentally-observed macroscopic rate constants. This could eliminate the need for time-consuming, iterative, non-linear, curve-fitting approaches and numerical integration. The usefulness of the four-compartment model is limited, however, by the sensitivity and temporal resolution of current PET imaging devices.
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    Logistic population growth under random dispersal (1987)
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    Bulletin of mathematical biology 49 (1987), S. 495-506 
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    Notes: Abstract Various diffusion processes employed for modelling logistic growth are briefly summarized. A discrete-time, discrete-state space stochastic process for population growth is proposed and analyzed with either Bose-Einstein or Maxwell-Boltzmann statistics for the distribution of offspring in available sites in a restricted region. A diffusion approximation is constructed, which differs from those previously employed. The logistic law is a natural deterministic analog of the diffusion process.
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    Fractional exponential decay in the capture of ligands by randomly distributed traps in one dimension (1987)
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    Bulletin of mathematical biology 49 (1987), S. 487-494 
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    Notes: Abstract In many biophysical and biochemical experiments one observes the decay of some ligand population by an appropriate system of traps. We analyse this decay for a one-dimensional system of randomly distributed traps, and show that one can distinguish three different regimes. The decay starts with a fractional exponential of the form exp[−(t/t 0)1/2], which changes into a fractional exponential of the form exp[−(t/t 1)1/3] for long times, which in its turn changes into a pure exponential time dependence, i.e. exp[−t/t 2] for very long times. With these three regimes, we associate three time scales, related to the average trap density and the diffusion constant characterizing the motion of the ligands.
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    Morphogenesis in an asymmetric medium (1987)
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    Bulletin of mathematical biology 49 (1987), S. 519-530 
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    Notes: Abstract Some key experiments of artificial production ofsitus inversus viscerum are briefly reviewed and a two-step mechanism for the explanation of the systematic asymmetric visceral arrangement in vertebrates is proposed. A two-variable reaction-diffusion system displaying a symmetry-breaking bifurcation is considered, and it is demonstrated that a slight asymmetry of the boundary conditions can give rise to a marked asymmetry in the resulting dissipative structure in both one-and three-dimensional systems. A criterion is formulated allowing classification of reaction-diffusion systems operating in a three-dimensional space with regard to their ability to incorporate slight asymmetries at the boundaries in the form of a chiral dissipative structure.
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    Evolution through group selection (1987)
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    Bulletin of mathematical biology 49 (1987), S. 629-647 
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    International Conference on Mathematical Modelling in Science and Technology (1987)
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    Bulletin of mathematical biology 49 (1987), S. 649-649 
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    Some properties of the multidimensional complex cepstrum and their relationship to the stability of multidimensional systems (1987)
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    Circuits, systems and signal processing 6 (1987), S. 3-30 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Conditions are obtained for the cepstrum of anl 1 sequence having arbitrary support on theM-dimensional lattice to exist also as anl 1 sequence with arbitrary support. These conditions are used to show that the cepstrum of a sequence with support on a half-space will, when it exists, also have support on the same half-space. This result is used, in turn, to describe the support of the cepstrum of a sequence with bounded support on a half-space. The relationship between the existence of the cepstrum and bounded-input, bounded-output (BIBO) stability for all three of these cases is considered. Finally, the derivatives of the inversion operator, the homomorphic transform operator, and its inverse are calculated. These results are also useful in the one-dimensional case.
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    A software environment for digital signal-processing simulations (1987)
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    Circuits, systems and signal processing 6 (1987), S. 31-43 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A signal-processing software system is described which allows the simulation of systems described by block diagrams or signal-flow graphs. A high-level data-flow language describes the interconnection of the components. All configurations of interconnections are allowed, including those containing feedback. Component systems (blocks) are allowed to be multi-input, multi-output, and to be programmed in any language. Blocks are implemented as separate processes running under a UNIX2 operating system. Input and output signals are transferred between blocks via the UNIXpipe facility. Thedata type of a signal is arbitrary in the context of the compiler; within a component or system, signals and internal variables can be either floating point or fixed point. The compiler enforces strong or weak type checking of signals according to the characteristics of the blocks generating and receiving the signals. The invariance of the program to implementation data type is accomplished by the use of abstract data types. Fixed-point simulations having differing number of bits per signal and per internal variable in a block are supported. Special display software is used to allow any signal in the system to be displayed on any graphics device.
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    The numerical solution of some higher-index time-varying semistate systems by difference methods (1987)
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    Circuits, systems and signal processing 6 (1987), S. 61-75 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Necessary and sufficient conditions are given for the solvability of fully implicit index-one and semiexplicit index-two linear time-varying semistate systems of the formA(t)x′+B(t)x=f(t). Using these solvability criteria, we establish the convergence and stability of backward difference formulas (BDF) for solvable semiexplicit index-two systems. In the algebraic variables, these methods exhibit a boundary layer of instability of length 2k, wherek is the order of the method. Finally, we show that the systems considered in this paper belong to a class of problems, solvable by BDF, which strictly contains the systems safely transformable to standard canonical form.
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    On the approximation of the magnitude response of two-dimensional IIR digital filters using linear programming (1987)
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    Circuits, systems and signal processing 6 (1987), S. 45-60 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The design of two-dimensional IIR digital filters is approached using linear-programming techniques. The problem is formulated as an approximation problem and filter frequency response characteristics are represented via the square of the magnitude of the filter transfer function. An appropriate approximation error is minimized leading to a linear problem formulation. The latter problem does not require differential correction methods for its solution, thus resulting in a computationally efficient algorithm. Stability conditions and symmetry considerations are easily accounted for. The linear programming approach assures convergence of the solution to a global minimum, among other advantages over nonlinear methods. Several examples illustrate the strength and effectiveness of the methodology.
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    Stabilization theory for single-input/single-output two-dimensional systems (1987)
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    Circuits, systems and signal processing 6 (1987), S. 77-93 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Necessary and sufficient conditions for output and state feedback stabilization are given for single-input/single-output systems. Extensions are also provided for single-input/multi-output and multi-input/single-output systems. A technique for constructing explicitly a stabilizing controller is presented, and the main differences with respect to the one-dimensional case are clarified. Finally, the existence of “intrinsically unstable” transfer functions, i.e., not allowing stabilizable realizations, is discussed.
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    Single-parameter controlled-variable amplitude change function for digital filtering (1987)
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    Circuits, systems and signal processing 6 (1987), S. 95-106 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A single-parameter controlled-variable amplitude change function has been constructed for digital filtering using multiple units of a prototype filter. The limits of variation are discussed. The technique is shown to be useful not only for the reduction of errors in either the pass band or the stop band of the overall filter, but also for varying the cutoff frequency of the overall filter over a wide range. Hardware implementation problems resulting from a wide variation are shown to be overcome by a modular approach.
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    Introduction to the special issue (1987)
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    Circuits, systems and signal processing 6 (1987), S. 125-126 
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    Topics: Electrical Engineering, Measurement and Control Technology
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    Editorial (1987)
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    Circuits, systems and signal processing 6 (1987), S. 123-123 
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    URL: http://dx.doi.org/10.1007/BF01598953
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    Parameter estimation of continuous-time stationary Gaussian processes with rational spectra (1987)
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    Circuits, systems and signal processing 6 (1987), S. 107-119 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper considers the problem of estimating the parameters of continuous-time stationary Gaussian processes with rational spectra, from uniformly sampled measurements. The sampled process is shown to be an autoregressive moving-average process, and explicit relationships between the parameters of the continuous-time and the sampled processes are derived. These relationships are then used to derive a lower bound on the variances of biased estimates of the continuous-time parameters, and on the generalized variance of such estimates. It is shown by some examples that the bound on the generalized variance depends on the sampling interval in a nonmonotonic manner. In particular, for each specific set of parameters there exists a sampling interval for which the lower bound is minimized.
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    Array resolutions of linear maps (1987)
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    Circuits, systems and signal processing 6 (1987), S. 127-137 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The identification of concurrency is a critical factor in the high-speed calculation of algorithms. This study considers maps onX, a discrete resolution space. We establish a resolution on the space of linear maps onX which exhibit compatibility with array processing. Our results are extended to the partially ordered resolution space setting. While on-line array processing motivates our study, the results also suggest efficient processing procedures for off-line applications.
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    A technique for the design of systolic arrays with bit-level pipelining (1987)
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    Circuits, systems and signal processing 6 (1987), S. 139-151 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper describes a method for designing systolic structures with bit-level pipelining. The proposed technique starts with the signal flow graph representation of a given algorithm. A new signal flow graph rule, called the gain transfer rule is introduced to achieve bit-level pipelining. Using this approach, systolic arrays with bit-level pipelining are derived for a general recursive digital filter and a convolver. The proposed technique is quite general and has also been applied to obtain systolic structures for other problems such as vector transformation. In comparison with some previously reported designs, the new architectures are characterized by simpler basic processing cells and faster data throughput rate or smaller chip area requirements.
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    Applications of VLSI technology in a massively parallel machine (1987)
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    Circuits, systems and signal processing 6 (1987), S. 191-215 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract NON-VON is a highly parallel non-von Neumann supercomputer presently under construction at Columbia University. The basis for NON-VON's significant cost/performance advantage lies in a highly unusual application of VLSI technology to the realization of massive computational parallelism. This paper outlines the manner in which the emerging technology of VLSI circuits is employed in NON-VON to achieve this advantage. Particular emphasis is given to novel aspects of the design, layout, and operation of the NON-VON processing element, eight of which are to be embedded within each integrated circuit chip.
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    Fault-tolerant VLSI sorters (1987)
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    Circuits, systems and signal processing 6 (1987), S. 153-174 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Parallel sorting algorithms have been proposed for VLSI implementation. Random defects in the silicon wafer and fabrication errors render processors in the wafer faulty, and may cause these algorithms to fail despite a significant number of nonfaulty processors. This paper presents twofault-tolerant pipelined sorting algorithms that would work on a wafer comprised of faulty and nonfaulty processors. Both the algorithms useO(n) processors and requireO(n) time to sortn elements.
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    Construction of a fault-tolerant grid of processors for wafer-scale integration (1987)
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    Circuits, systems and signal processing 6 (1987), S. 175-189 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract With the advent of wafer-scale integration (WSI), the placement of several “processors” on a single VLSI wafer is becoming a realistic possibility. To avoid the problems of a very low yield inherent in any silicon component of (very) large area, redundant components will be used. In this article we examine three different solutions for reconnecting the nonfaulty processors so that the resulting network is a square grid. We then present results of simulations for various percentages of faulty processors, which show that a small amount of redundancy is the interprocessors paths and a simple back-track based algorithm can produce a resulting grid that, while not necessarily optimal, includes most of the nonfaulty processors.
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    Active memory chips: A brief survey and case study (1987)
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    Circuits, systems and signal processing 6 (1987), S. 239-259 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Conventional random access memories are capable only of writing data into and reading data from the storage location corresponding to a given address. The availability of VLSI circuits containing hundreds of thousands of switching devices, however, has recently made practical the implementation of “active” memory chips capable of performing a range of complex operations on their stored data. Such designs are characterized by the extensive intermingling of processing and memory resources within a single chip to achieve the rapid and cost-effective parallel execution of operations relevant to such tasks as image processing, computer graphics, artificial intelligence, and database management. This paper presents a brief survey of a number of active memory chips that have been implemented or proposed, along with a more detailed examination of a particular active memory circuit, the NON-VON 3 primary processing subsystem chip.
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    Designing VLSI network nodes to reduce memory traffic in a shared memory parallel computer (1987)
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    Circuits, systems and signal processing 6 (1987), S. 217-238 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Serialization of memory access can be a critical bottleneck in shared memory parallel computers. The NYU Ultracomputer, a large-scale MIMD (multiple instruction stream, multiple data stream) shared memory architecture, may be viewed as a column of processors and a column of memory modules connected by a rectangular network of enhanced 2×2 buffered crossbars. These VLSI nodes enable the network to combine multiple requests directed at the same memory location. Such requests include a new coordination primitive, fetch- and-add, which permits task coordination to be achieved in a highly parallel manner. Processing within the network is used to reduce serialization at the memory modules. To avoid large network latency, the VLSI network nodes must be high-performance components. Design tradeoffs between architectural features, asymptotic performance requirements, cycle time, and packaging limitations are complex. This report sketches the Ultracomputer architecture and discusses the issues involved in the design of the VLSI enhanced buffered crossbars which are the key element in reducing serialization.
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    Time-frequency window leakage in the short-time Fourier transform (1987)
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    Circuits, systems and signal processing 6 (1987), S. 263-286 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Conventional frequency-domain window-leakage analysis accurately describes the leakage in the short-time Fourier transform only for stationary signals. Leakage in the time-frequency plane from concentrated transient or nonstationary signals can be effectively analyzed by use of a time-frequency window-leakage envelope with rectangular contours. This envelope is obtained from the Wigner distribution of the analysis window, with appropriate corrections for the sidelobe leakage. The time-frequency window-leakage envelope gives insight into the tradeoffs in time-frequency leakage between various windows and allows quick and accurate estimates of the leakage in the short-time Fourier transform. A simple technique for constructing signals with Wigner distributions that are linear transformations of the Wigner distribution of a known signal is developed. With this technique, windows with a variety of time-frequency orientations and leakage behavior can be developed.
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    Asymptotic bias of the high-order autoregressive estimates of sinusoidal frequencies (1987)
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    Circuits, systems and signal processing 6 (1987), S. 287-298 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Fitting a high-order autoregressive model to data is often used to estimate the frequencies of sinusoids from their noisy measurements. This paper analyzes the asymptotic bias of the frequency estimates obtained by this method. It is shown that the bias decreases significantly with increasing model order.
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    General linear nonstationary passive systems: Derivation of the explicit state model (1987)
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    Circuits, systems and signal processing 6 (1987), S. 299-314 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We consider the general nonstationary passive systems modeled by linearRCG (G = gyrator) networks. Such networks in general contain conventional topological degeneracies (i.e., capacitor-only loops and/or inductor-only cutsets) as well as the topological degeneracies due to gyrator positioning in the network. Our central result is the explict demonstration that the existence of topological degeneracies does not impose any obstruction to the existence of the explicit state model, which we derive under no restriction on the topology of the network. We also discuss the conditions for the existence of the state model, its unique solutions, and the continuity of the state vector. The nature of the degeneracies inherent in the formulation is highlighted and it is shown that a gyrator-only subnetwork is accountable for algebraic degeneracies. Since the nature and the existence of topological degeneracies does not have anything to do with whether the element characteristics are linear or nonlinear, passive or active, our results are easy to extend to a large class of nonlinear and/or activeRCG networks.
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    Qualitative analysis of motion properties of semistate models of large-scale systems (1987)
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    Circuits, systems and signal processing 6 (1987), S. 315-334 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper studies the behavior of motions of large-scale (LS) semistate systems (SSS) governed byP i (t)x i =M i (t,x i )x i +f i (t)+h i (t, x), i=1,2,...,s, =(x 1 T x 2 T ⋯x s T )T, where matricesP i (t) are singular. Using Lyapunov's approach and the tools for LS system analysis, a variant of attractivity and ultimate boundedness of appropriate time-variable sets are investigated. The results are based on a specific choice of the aggregate functions. It is assumed that the reduction of equations to a normal form of lower order is inconvenient. The aggregation-decomposition approach used in this paper reduces the dimensionality of an aggregate matrix of the system to the number of its systems. Motion properties of LS systems are deduced from the properties of its isolated subsystems, the character of interconnections, and the conditions imposed on the system aggregate matrix. Sufficient algebraic conditions for the above-mentioned motion properties are developed.
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    Some practical stability criteria for semistate equations (1987)
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    Circuits, systems and signal processing 6 (1987), S. 335-345 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper various conditions guaranteeing the ordinary, uniform, and asymptoticA-stability of semistate equations are given. These results are based on and given in terms of the semi-explicit form of a semistate equation.
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    Another new journal (1987)
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    Stochastic environmental research and risk assessment 1 (1987), S. 1-2 
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    ISSN: 1436-3259
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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    On the annual maximum distribution in dependent partial duration series (1987)
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    Stochastic environmental research and risk assessment 1 (1987), S. 3-16 
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    ISSN: 1436-3259
    Keywords: Annual maximum ; partial duration series ; T-year estimate ; marshall-Olkin bivariate distribution ; Morgenstern bivariate distribution
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract As a basis for development of the annual maximum distribution the so-called partial duration series with Poissonian occurrence times and exponentially distributed peak exceedance values has been selected. The model is generalized by allowing for a Markov dependence between succeeding peak values. Correlation values from p=0 to p=1 can be accounted for by introducing the Marshall-Olkin bivariate exponential distribution, which is presented in detail. The developed distribution function for the annual maximum is throughly analysed and a variety of distribution forms depending on the value of the correlation coefficient and the intensity in the Poisson process is hereby recognized. To a certain extent this might be considered as parallel to the scattering of hydrological regions with different generating mechanisms for the annual maxima.
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    On a stochastic description of the time-space behaviour of extratropical cyclonic precipitation fields (1987)
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    Stochastic environmental research and risk assessment 1 (1987), S. 37-52 
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    ISSN: 1436-3259
    Keywords: Cyclonic precipitation ; mathematical modeling ; simulation
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A stochastic description is developed for extratropical cyclonic precipitation fields at synoptic and meso scales as they are typically observed by radars over the Earth. This description attempts to account I) for the synoptic scale behavior of a cyclonic storm (its birth, its synoptic scale motion trajectory, and its dissipation) II) for the synoptic-scale organizational structure of subsynoptic precipitation areas (rainbands, precipitation cores and raincells) within a cyclonic storm; and III) for the behavior of subsynoptic precipitation areas, in terms of their births, their spatial configuration evolutions, their motions, and their deaths (dissipation). The precipitation cores and the raincells are taken as the building blocks of the subsynoptic precipitation, areas within a cyclonic rainfield.
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    A review on stochastic differential equations for applications in hydrology (1987)
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    Stochastic environmental research and risk assessment 1 (1987), S. 81-100 
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    ISSN: 1436-3259
    Keywords: Stochastic differential equations ; Itô calculus ; Stratovovich integrals ; Jump integrals
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Fundamentals of the theory of stochastic calculus and stochastic differential equations (SDE's) which are finding increasing application in water resources engineering are reviewed. The basics of probability theory, mean square calculus and the Wiener, white Gaussian and compound Poisson processes are given in preparation for a discussion of the general Itô SDE with drift, diffusion and jump discontinuity terms driven by Gaussian white noise and compound Poissionian impulses. Also discussed are stochastic integration and the derivation of moment equations via the Itô differential rule. The lierature of SDE's is reviewed with an emphasis on the more accessible sources.
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    The discrete Hurst range for skew independent two-valued inflows (1987)
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    Stochastic environmental research and risk assessment 1 (1987), S. 53-66 
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    ISSN: 1436-3259
    Keywords: Hurst range ; conditioned exchangeable, variables
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A new theoretical interpretation is proposed for Hurst's empirical law which is applicable to discrete-valued inflows and is consistent with the existing interpretation for continuous-valued inflows. This is applied to independent net inflows {X r} having values +1 and −1 with unequal probabilities. With the aid of a new result on the exchangeability of symmetrically conditioned exchangeable variables, values of the resulting range are obtained and tabulated. It is found that the effect of skewness is very slight for skewness values between (about) 3 and −3, and that Hurst's own approximation, the “conditioned range”, is remarkably accurate.
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    Pattern analysis on mixed-mode hydrometric data (1987)
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    Stochastic environmental research and risk assessment 1 (1987), S. 67-80 
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    ISSN: 1436-3259
    Keywords: pattern analysis ; mixed-mode data ; event-covering ; discretization ; hydrometric data
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a pattern analysis technique that has been successfully applied to a set of hydrometric network data collected in British Columbia, Canada. This technique can extract information from a set of observed heterogeneous multivariate data. The data are represented as n-tuples of mixed discrete and continuous values. The technique is capable of screening out statistically irrelevant information. It is also able to detect inherent subgroups in the data through adopting an event-covering approach. The subgroup characteristics represent important empirical understanding even though there may be considerable probabilistic variation within each individual subgroup.
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    Stochastic models in hydrology (1987)
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    Stochastic environmental research and risk assessment 1 (1987), S. 17-36 
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    ISSN: 1436-3259
    Keywords: Stochastic hydrology ; multivariate analysis ; information extraction ; information transfer ; structure of time series ; time series analysis ; spatial characteristics ; simulation of processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A stochastic approach to the analysis of hydrologic processes is defined along with a discussion of causes of tendency, periodicity and stochasticity in hydrologic series. Sources of temporal non-stationarity are described along with objectives and methods of analysis of processes and, in general, of information extraction from data. Transferred information as measured by correlation coefficients is compared with the transferable information as measured by entropy coefficients. Various multivariate approaches to hydrologic stochastic modeling are classified in light of complexities of spatial/temporal hydrologic processes. Alternatives of time series structural decomposition and modeling are compared. A special approach to modeling of space properties further contributes to approximate simulations of spatial/temporal processes over large areas. Several aspects of stochastic models in hydrology are concisely reviewed.
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    URL: http://dx.doi.org/10.1007/BF01543907
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    A stochastic differential equation approach to soil moisture (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 101-116 
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    ISSN: 1436-3259
    Keywords: Soil moisture ; stochastic processes ; stochastic differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The dynamics of water within the unsaturated root zone of the soil are represented by a pair of stochastic differential equations (SDE's), one representing the so-called “surplus” state of the moisture and the other the “deficit” condition. The inputs to the model are the climatically controlled random infiltration events and evapotranspiration which are modeled as a compound Poisson process and a Wiener (Brownian motion) process, respectively. The solutions to these SDE's are not in “close-form” but sample functions are obtained by numerical integration. The moment properties of the soil moisture evolution process have also been derived analytically including the mean, variance, covariance and autocorrelation functions. To illustrate the model, climatic parameters representing the “surplus” and “deficit” cases and properties of clay loam soil have been used to numerically derived the corresponding sample functions. With proper selection of all the parameters, physically realistic sample trajectories can be obtained for the model.
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    URL: http://dx.doi.org/10.1007/BF01543806
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    On predicting upland erosion losses from rainfall depth (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 127-134 
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    ISSN: 1436-3259
    Keywords: Upland erosion ; annual erosion losses
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Point rainfall triggers the complex processes of overland flow and surface erosion. The probability density functions of rainfall duration and intensity are coupled with a physically based dynamic formulation of rainfall-runoff-sediment transport relationships for upland areas. When considering a single storm, rainfall depth alone is a poor predictor of sediment transport because of the dispersion introduced by the effect of rainfall intensity. On a long terms basis, however, the total amount of rainfall can be used to predict total erosion losses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543808
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    An extended theory of equi-risk line for a general release rule (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 117-126 
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    ISSN: 1436-3259
    Keywords: equi-risk line ; detention pond ; urban runoff ; frequency analysis ; flood risk
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The expression of equi-risk line derived by the authors represents the relationship between discharge capacityy 0 u and storage capacityz 0 u to keep flood frequency under a certain risk level represented by the return periodT, i.e.,z 0/z 0 u ={(y 0 u −y 0 u )/y 0 u } S , wherey 0 u andz 0 u areT-year probability peak discharge and total volume of a hydrograph. The shape parametersS is evaluated in this paper for various release rules of the storage facilities and correlations of durations and peaks of hydrographs. The expression forS is: $$S = S_\infty + (S_0 - S_\infty )\exp ( - \sqrt p )$$ , whereS 0 andS ∞ are the values ofS forp=0 and ∞, andp is the exponent of a general storage-release relation,q=az' p, wherea is the storage constant, andz' andq are the volume of stored water and the corresponding release. The values ofS 0 andS ∞ are expressed in terms of the correlation coefficient ρ of durations and peaks of inflow hydrographs.
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    URL: http://dx.doi.org/10.1007/BF01543807
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    On predicting upland erosion losses from rainfall depth (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 135-140 
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    ISSN: 1436-3259
    Keywords: Upland erosion ; annual soil losses
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Annual erosion losses from 135 experimental plots under a variety of soil types, vegetation cover densities and conservation practices in Iraq have been measured over a period of four years. The first three years of this data set demonstrate that annual erosion losses can be predicted from annual rainfall depths. The results obtained from regression analysis were then validated with the fourth year of soil erosion data. These results corroborate the theoretical findings of the companion paper in that long term erosion losses can be predicted from the total amount of rainfall.
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    URL: http://dx.doi.org/10.1007/BF01543809
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    Multivariate contemporaneous ARMA model with hydrological applications (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 141-154 
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    ISSN: 1436-3259
    Keywords: Contemporaneous ARMA models ; maximum likelihood estimation ; multivariate modelling ; stochastic hydrology ; time series analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In order to allow contemporaneous autoregressive moving average (CARMA) models to be properly applied to hydrological time series, important statistical properties of the CARMA family of models are developed. For calibrating the model parameters, efficient joint estimation procedures are investigated and compared to a set of uivariate estimation procedures. It is shown that joint estimation procedures improve the efficiency of the autoregressive and moving average parameter estimates, but no improvements are expected on the estimation of the mean vector and the variance covariance matrix of the model. The effects of the different estimation procedures on the asymptotic prediction error are also considered. Finally, hydrological applications demonstrate the usefulness of the CARMA models in the field of water resources.
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    URL: http://dx.doi.org/10.1007/BF01543810
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    A linearly regressive Gamma Markov process (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 155-160 
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    ISSN: 1436-3259
    Keywords: Gamma Markov ; estimation ; maximum likelihood estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The linearly regressive Gamma Markov sequence is being increasingly used as a model for geophysical phenomena, one of the reasons being that it is possible to determine the distribution of (weighted or otherwise) cumulative sums of such a sequence. In this paper we show briefly how to simulate such a sequence and its seasonal extension; we also show how to estimate its parameters. It is shown that the estimates obtained by the method of moments do not have a high efficiency, whereas those obtained by a modified maximum likelihood method have an efficiency close to unity.
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    URL: http://dx.doi.org/10.1007/BF01543811
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    The inverse problem and ground water management (1987)
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    Stochastic environmental research and risk assessment 1 (1987), S. 161-168 
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    ISSN: 1436-3259
    Keywords: Inverse problem ; groundwater management ; groundwater response function ; stochastic control ; consistent parameter estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The response of groundwater basins to natural and anthropogenic inputs depends on many interrelated factors such as the values of groundwater flow and mass transport parameters. This work presents a theoretical analysis of the impact of parameter uncertainty on groundwater management decisions. It is shown that under classical, Bayesian, and deterministic assumptions about the parameter structure, the resulting management decisions could be very different. This underscores the importance of adopting the proper parameter structure and the need for using consistent methods to solve the inverse problem.
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    URL: http://dx.doi.org/10.1007/BF01543888
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    A feature based method for tracking mesoscale rainfall areas in radar images (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 185-198 
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    ISSN: 1436-3259
    Keywords: Pattern matching ; tracking ; rainfall ; mesoscale ; radar
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a new feature-based matching algorithm for tracking mesoscale precipitation phenomena in radar image sequences. Distinct rainfall areas are identified in each image and characterized by a feature vector of shape descriptors, which provide a mathematical representation of the spatial characteristics of each identified area. Rainfall areas observed in consecutive images are matched by comparing the relative values of the features. Two match scoring algorithms are developed to generate the initial estimates of correct matches, which are then updated by likelihood measures based on relative location. The method is applied to mesoscale rainfall areas observed in sequences of radar-derived images of rainfall activity over Southwestern Ontario during the summers of 1980 and 1981.
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    URL: http://dx.doi.org/10.1007/BF01543890
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    The two-component extreme value distribution for flood frequency analysis: Derivation of a new estimation method (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 199-208 
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    ISSN: 1436-3259
    Keywords: Extreme value distribution ; two-component distribution ; maximum entropy principle ; parameter estimation ; regional estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The two component extreme value (TCEV) distribution has recently been shown to account for most of the characteristics of the real flood experience. A new method of parameter estimation for this distribution is derived using the principle of maximum entropy (POME). This method of parameter estimation is suitable for application in both the site-specific and regional cases and appears simpler than the maximum likelihood estimation method. Statistical properties of the regionalized estimation were evaluated using a Monte Carlo approach and compared with those of the maximum likelihood regional estimators.
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    URL: http://dx.doi.org/10.1007/BF01543891
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    A first-order approximation to stochastic optimal control of reservoirs (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 169-184 
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    ISSN: 1436-3259
    Keywords: Stochastic control and programming ; real-time hydrologic forecasting ; reservoir theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A new approximate method of solution for stochastic optimal control problems with many state and control variables is introduced. The method is based on the expansion of the optimal control into the deterministic feedback control plus a caution term. The analytic, small-perturbation calculation of the caution term is at the heart of the new method. The developed approximation depends only on the first two statistical moments of the random inputs and up to the third derivatives of the cost functions. Its computational requirements do not exhibit the exponential growth exhibited by discrete stochastic DP and can be used as a suboptimal solution to problems for which application of stochastic DP is not feasible. The method is accurate when the cost-to-go functions are approximately cubic in a neighbourhood around the deterministic trajectory whose size depends on forecasting uncertainty. Furthermore, the method elucidates the stochastic optimization problem yielding insights which cannot be easily obtained from the numerical application of discrete DP.
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    URL: http://dx.doi.org/10.1007/BF01543889
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    Transport and sedimentation of particles in a fluid flow (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 209-216 
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    ISSN: 1436-3259
    Keywords: Transport ; sedimentation ; random walk ; Markov chain in continuous time ; distribution of maximum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A simple two-dimensional random walk model is developed for the motion of a particle in a fluid flow. Some earlier results for the persistent injection of particles into the flow are extended, and the distribution of the maximum number of particles in suspension over the period (0,t) is derived.
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    URL: http://dx.doi.org/10.1007/BF01543892
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    Statistical aspects of flow in a random network of channels (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 217-240 
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    ISSN: 1436-3259
    Keywords: Transport of fluid ; random network ; macro-permeability ; micro-geometry ; statistical mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a detailed statistical analysis of Hagen-Poiseuille flow in plane random isotropic networks of interconnected channels. The emphasis is on statistico-geometrical features of networks that affect macroscopic permeability. It is shown that permeability of a network depends on its average co-ordination number, the first two moments of the channel length distribution and other explicitly identifiable geometrical features. Distributions of flow rates in channels and average flow rates are established by minimization of the rate of energy dissipation. Theoretical developments are interpreted in the context of classical statistical mechanics. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network.
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    URL: http://dx.doi.org/10.1007/BF01543893
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    Announcements (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 280-280 
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    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543099
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    Development of stochastic partial differential equations for subsurface hydrology (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 241-262 
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    ISSN: 1436-3259
    Keywords: Martingale ; stochastic-convective ; stochastic-relativist ; spectral-integral ; perturbative ; statistical-mechanical
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The use of stochastic models in subsurface hydrology is growing at a logistic pace. To tie together a number of different stochastic methodologies for deriving subsurface transport equations, we have put together a brief review of some of the more common techniques. Our attention is confined to a few select methodologies so that we might delve in detail into assumptions required by the various approaches and their strengths and weaknesses. The methods reviewed include: Martingale, stochastic-convective, stochastic-relativist, spectral-integral, perturbative, statistical-mechanical, and generalized hydrodynamics. Within this list, we also have included a few stochastic methodologies which have been used solely to develop expressions for the dispersion tensor.
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    URL: http://dx.doi.org/10.1007/BF01543097
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    On a general class of stochastic partial differential equations (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 297-302 
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    ISSN: 1436-3259
    Keywords: Stochastic PDE ; Zakai equation ; nonlinear filtering ; distributed systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract We shall consider in this article a general class of stochastic PDE which in particular covers the Zakai equation of nonlinear filtering and natural formulations of distributed systems involving control variables. We use only fixed point arguments, hence we get uniqueness results. In the case of the Zakai equation, Galerkin approximations have been considered by Pardoux (1979) to derive the existence of the solution
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    URL: http://dx.doi.org/10.1007/BF01543101
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    Semigroup solutions to stochastic unsteady groundwater flow subject to random parameters (1987)
    Springer
    Stochastic environmental research and risk assessment 1 (1987), S. 281-296 
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    ISSN: 1436-3259
    Keywords: Stochastic groundwater flow ; semigroups ; random in time Gaussian process ; random physical parameters ; stochastic partial differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Two methods for the solution of partial differential equations (PDE) for the general case of random in time physical parameters are presented and their application to the solution of unsteady regional groundwater flow equations are illustrated. The first method is the semigroup approach which directly offers a solution without resorting to “closure approximations” (hierarchy techniques), perturbation techniques, or Montecarlo simulation techniques. The semigroup approach can also handle the general stochastic problem when randomness also appears as initial conditions, boundary conditions or forcing terms. The second method is an approximation scheme to obtain the semigroup solution in complex cases and permits the solution of equations with more than one random coefficient.
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    URL: http://dx.doi.org/10.1007/BF01543100
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