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  • Articles  (7,204)
  • Springer  (7,137)
  • Blackwell Publishing Ltd  (67)
  • American Geophysical Union (AGU)
  • Annual Reviews
  • 1995-1999  (7,204)
  • 1980-1984
  • 1935-1939
  • 1995  (7,204)
  • Mathematics  (7,204)
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  • Articles  (7,204)
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  • 1995-1999  (7,204)
  • 1980-1984
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  • 1
    Electronic Resource
    Electronic Resource
    CERTAINTY EQUIVALENCE AND LOGARITHMIC UTILITIES IN CONSUMPTION/INVESTMENT PROBLEMS (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We investigate an optimal consumption/investment decision problem with partially observable drift. Logarithmic utilities are shown to be necessary and sufficient for the certainty equivalence principle to hold. For the sufficiency part of the proof, we allow a general stochastic structure about the unobservable drift. On the other hand, a simple Bayesian structure is assumed for the necessity part in order to utilize the Hamilton-Jacobi-Bellman equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00069.x
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  • 2
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    BOOK REVIEW (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Book Review in this Articleeconomic and financial modelling with mathematica, hal R. varian (editor), telos/springer-verlag. new york 1993
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00073.x
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  • 3
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    DEFAULT RISK INSURANCE AND INCOMPLETE MARKETS (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper uses the existence of secondary markets for debt instruments with default risk (e.g. corporate bonds) to define default insurance along the lines of financial economics. It examines whether, in the case of several risk-neutral measures, characteristics of default can be uniquely determined by the prices of contracts involving default-prone securities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00064.x
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  • 4
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    EXISTENCE OF A NONNEGATIVE EQUILIBRIUM PRICE VECTOR IN THE MEAN-VARIANCE CAPITAL MARKET (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We derive a necessary and sufficient condition for the existence of a nonnegative equilibrium price vector under which the total demand and supply of each asset balances in the standard mean-variance capital market. Also, we give an explicit formula for such a price vector. This formula shows that the price of assets is an increasing function of p̄, the weighted average of the requested rate of return of individual investors, which tends to infinity as p̄ approaches the expected rate of return on the market portfolio. Further, we construct a macroeconomic index which gives information about the soundness of the capital market.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00066.x
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  • 5
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    ATTAINABLE CLAIMS IN A MARKOV MARKET (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: It is shown how, even when the market is incomplete, certain contingent claims are attainable: that is, they can be represented as stochastic integrals with respect to the process which describes the evolution of the asset prices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00105.x
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  • 6
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    MULTIVARIATE STABLE FUTURES PRICES (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper introduces new techniques for modeling financial data under the assumption that the data belong to the domain of attraction of a multivariate stable Pareto law. We provide tail estimators for the index of stability parameter a and the corresponding spectral measure. These estimators are then applied to test the associtation of the individual components and to compute estimates of portfolio risk and the covariation of commodities. A practical example is given using DM-dollar and JY-dollar exchange rates data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00106.x
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  • 7
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    BOOK REVIEW (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Book Review in this Article Dynamic Asset Pricing Theory, By Darrell Duffie
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00102.x
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  • 8
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    VOLATILITY STRUCTURES OF FORWARD RATES AND THE DYNAMICS OF THE TERM STRUCTURE (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: For general volatility structures for forward rates, the evolution of interest rates may not be Markovian and the entire path may be necessary to capture the dynamics of the term structure. This article identifies conditions on the volatility structure of forward rates that permit the dynamics of the term structure to be represented by a two-dimensional state variable Markov process. the permissible set of volatility structures that accomplishes this goal is shown to be quite large and includes many stochastic structures. In general, analytical characterization of the terminal distributions of the two state variables is unlikely, and numerical procedures are required to value claims. Efficient simulation algorithms using control variates are developed to price claims against the term structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00101.x
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  • 9
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    OPTION PRICING USING THE TERM STRUCTURE OF INTEREST RATES TO HEDGE SYSTEMATIC DISCONTINUITIES IN ASSET RETURNS (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper demonstrates the use of term-structure-related securities in the design of dynamic portfolio management strategies that hedge certain systematic jump risks in asset return. Option pricing formulas based on the absence of arbitrage opportunities in this context are also developed. the analysis is for the case where assets returns are driven by a finite number of Brownian motions and an m-variate point process. the inclusion of :the additional traded assets in the term structure makes it possible to hedge systematic jumps imbedded in the m variate point process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00070.x
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  • 10
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    OPTIMAL INVESTMENT OF A LIFE INTEREST (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider the problem of a trustee faced with investing a sum of money, the interest from which will be received by one party (the life-tenant) during his lifetime while the capital will go to another party (the survivor) on the death of the life-tenant. We assume mat there are n+ 1 assets in which the trustee may invest—n risky assets of geometric Brownian motion type and one nonrisky asset. Under assumptions as to the utility functions of the two parties, we find the collection of Pareto optimal investment strategies for the trustee together with the corresponding payoffs. We do this by optimizing the payoff of the Lagrangian for the problem. We go on to present the Nash optimal solution for the trustee.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00068.x
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  • 11
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    OPTIMAL PORTFOLIO MANAGEMENT WITH FIXED TRANSACTION COSTS (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We study optimal portfolio management policies for an investor who must pay a transaction cost equal to a fixed Traction of his portfolio value each time he trades. We focus on the infinite horizon objective function of maximizing the asymptotic growth rate, so me optimal policies we derive approximate those of an investor with logarithmic utility at a distant horizon. When investment opportunities are modeled as m correlated geometric Brownian motion stocks and a riskless bond, we show that the optimal policy reduces to solving a single stopping time problem. When there is a single risky stock, we give a system of equations whose solution determines the optima! rule. We use numerical methods to solve for the optima! policy when there are two risky stocks. We study several specific examples and observe the general qualitative result that, even with very low transaction cost levels, the optimal policy entails very infrequent trading.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00071.x
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  • 12
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    PORTFOLIO MANAGEMENT WITH TRANSACTION COSTS: AN ASYMPTOTIC ANALYSIS OF THE MORTON AND PLISKA MODEL (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We examine the Morton and Pliska (1993) model for the optimal management of a portfolio when there are transaction costs proportional to a fixed fraction of the portfolio value. We analyze this model in the realistic case of small transaction costs by conducting a perturbation analysis about the no-transaction-cost solution. Although the full problem is a free-boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00072.x
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  • 13
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    ARBITRAGE IN SECURITIES MARKETS WITH SHORT-SALES CONSTRAINTS (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we derive the implications of the absence of arbitrage in securities markets models where traded securities are subject to short-sales constraints and where the borrowing and lending rates differ. We show that a securities price system is arbitrage free if and only if there exists a numeraire and an equivalent probability measure for which the normalized (by the numeraire) price processes of traded securities are supermartingales. Also, the tightest arbitrage bounds that can be inferred on the price of a contingent claim without knowing agents’preferences are equal to its largest and smallest expected normalized payoff with respect to the supermartingale measures. In the case where the underlying security price follows a diffusion process and where short selling is possible but costly, we derive partial differential equations that must be satisfied by the arbitrage bounds on derivative securities prices, and we determine optimal hedging strategies. We compute the arbitrage bounds on common securities numerically for several values of the borrowing and short-selling costs and show that they can be quite sharp.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00065.x
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  • 14
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    CRITICAL STOCK PRICE NEAR EXPIRATION (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We study the critical price of an American put option near expiration in the Black-Scholes model. Our main result is an estimate for the difference P̄ (t)- K between the critical price at time t and the exercise price as t approaches the maturity of the option.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00103.x
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  • 15
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    TAKEOVERS OF DIFFUSELY HELD FIRMS: A NONSTANDARD APPROACH (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: A common theme in the literature on corporate control is that, when share ownership is diffuse, the free-rider problem prevents raiders from making acquisitions at tender prices below the postacquisition share price. In this paper, we address this question by formulating a nonstandard model of takeovers of diffusely held firms. It is demonstrated that, even when individual shareholdings are infinitesimal relative to firm size, takeovers succeed with positive probability and equilibria exist in which the raider earns substantial per share profits. Further, the Nash equilibria of the game are characterized with regard to raider profit, the aggregate fraction of shares tendered, and the relation between raider profit and the degree of randomization exhibited by shareholder tendering strategies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00067.x
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  • 16
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    ISOLATING THE WILD CARD OPTION (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Many embedded options are difficult to value the wild card option in the Treasury bond futures contract is one of these embedded options. We illustrate how narrow theoretical bounds on the value of this option, relative to the price of the contract, may be obtained in the presence of other embedded options. Simulations suggest that the value of the wild card option is close to zero. This implies that, in this economy, a simpler pricing model of the Treasury bond futures contract, which ignores the wild card option, will result in only a small loss of accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00107.x
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  • 17
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    TAX BASIS AND NONLINEARITY IN CASH STREAM VALUATION (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The value of a future cash stream is often taken to be its net present value with respect to some term structure. This means that a linear formula is used in which each future payment is discounted by a factor deemed appropriate for the date on which the payment will be made. In a money market with taxes and shorting costs, however, there is no theoretical support for the existence of a universal term structure for this purpose. What is worse, reliance on linear formulas can be seriously inaccurate relative to true worth and can lead to paradoxes of disequilibrium. A consistent no-arbitrage theory of valuation in such a market requires instead that taxed and untaxed investors be grouped in separate classes with different valuation operators. Such operators are linear to scale but nonlinear with respect to addition. Here it is established that although these valuation operators provide general bounds applicable across an entire class, individual investors within a tax class can have more special operators because of the influence of existing holdings. These customized valuation operators have the feature of not even being linear to scale. In consequence of this nonlinearity, investors from the same or different tax classes can undertake advantageous trades even when the market is in a no-arbitrage state, but such trade opportunities are limited. Some degree of activity in financial markets can thereby be understood without appeal to differences in utility functions or temporary disequilibrium due to random disturbances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00104.x
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  • 18
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    FACTOR MODELS OF DOMESTIC AND FOREIGN INTEREST RATES WITH STOCHASTIC VOLATILITIES (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider a two-country economy under the nonarbitrage assumption and where volatilities are stochastic. Assuming the existence of state variables, we show that, under some mild volatility assumptions, the model is actually fully specified. In particular, both term structure dynamics and the exchange rate process can be given endogeneously under the risk-neutral probability. We then derive the exact dependence of the zero-coupon bonds and the exchange rate on the underlying state variables. As a result, some closed-form solutions can be proposed for the derivative assets as futures and options written on foreign zero-coupon bonds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00108.x
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  • 19
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    THE GARCH OPTION PRICING MODEL (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This article develops an option pricing model and its corresponding delta formula in the context of the generalized autoregressive conditional heteroskedastic (GARCH) asset return process. the development utilizes the locally risk-neutral valuation relationship (LRNVR). the LRNVR is shown to hold under certain combinations of preference and distribution assumptions. the GARCH option pricing model is capable of reflecting the changes in the conditional volatility of the underlying asset in a parsimonious manner. Numerical analyses suggest that the GARCH model may be able to explain some well-documented systematic biases associated with the Black-Scholes model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00099.x
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  • 20
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    ARBITRAGE AND INFORMATION IN A SEQUENTIAL ECONOMY WITH MANY CREDIT AGENCIES (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper augments the theoretical foundations of organized commodity futures markets and uncovers singular facts about arbitrage and the role of information. Using the term “credit agency” to embrace organized futures markets such as the Chicago Board of Trade as well as independent brokerage houses, we extend the extant theory of temporary equilibrium for an economy with a single credit agency to economies with many credit agencies. In the process, we find that arbitrage with no risk of bankruptcy and with perfect interagency trade information can be incompatible with equilibrium (exact or approximate). On the other hand, the usual regularity assumptions are sufficient for the existence of at least an approximate equilibrium, provided that interagency trade information is imperfect (or risky). However, such imperfect information limits arbitrage so different agencies can have different prices.
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    URL: http://dx.doi.org/10.1111/j.1467-9965.1995.tb00100.x
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  • 21
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    Apparent Decline As A Sign Of Improvement? or, Can Less Be More? (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 17 (1995), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Improvement of a system need not be the usual growth expected of dynamic systems. Decreasing variability, an important index of improvement, is discussed. The disappearance of 0.400 hitters from professional baseball can be better understood under such an assumption. Other examples illustrating the apparent paradox are also mentioned.
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    URL: http://dx.doi.org/10.1111/j.1467-9639.1995.tb00715.x
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  • 22
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    Primary Data (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 17 (1995), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article gives a rare insight into the way in which statistical thinking may be introduced in the primary school classroom.
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    URL: http://dx.doi.org/10.1111/j.1467-9639.1995.tb00717.x
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  • 23
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    Probability, Intuition and a Spreadsheet (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 17 (1995), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Probability simulations are a useful way of helping students to challenge their intuitions about chance events. However, tossing dice and coins can be slow and messy, and may mask underlying long-run patterns. This article provides examples of probability simulations on a spreadsheet which overcome some of these difficulties.
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  • 24
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    Secondary Students' Concepts of Probability (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 17 (1995), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Students develop concepts of probability withut formally studying the discipline and some of their concepts are at variance with those taught in the classroom. A sruvey of 200 students in five schools in Missouri was undertaken in an attempt to learn about pre-conceptions. The results are discussed in this article.
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    URL: http://dx.doi.org/10.1111/j.1467-9639.1995.tb00718.x
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  • 25
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    Arm-waving Mathematics: Sound, if Not Rigorous (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 17 (1995), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article suggestes some teachniques, herein referred to as ‘arm-waving’, which utilise analogies, graphs and examples to illustrate the contribution of mathematisc to statistical concepts without a rigorous treatment of the mathematics used.
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    URL: http://dx.doi.org/10.1111/j.1467-9639.1995.tb00719.x
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  • 26
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    Statistical Tools and Statistical Literacy: The Case of The Average (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 17 (1995), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article is intended to serve as a starting point for a dialogue regarding the goals of teaching students about averages and how to assess their emerging knowledge.
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    URL: http://dx.doi.org/10.1111/j.1467-9639.1995.tb00720.x
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  • 27
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    Resampling Stats (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 28
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    Median and Quartiles from Grouped Data (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 17 (1995), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 29
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    Birds of Britain (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 17 (1995), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 30
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    STEPS for Learning Statistics (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 17 (1995), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    NEWS & NOTES (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    BOOK REVIEWS (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Book reviewed in this Article: Statistics An Introduction By Alan Graham Biodiversity - Measurement and Estimation By D L Hawksworth (ed) Practical Methods for Design and Analysis of Complex Surveys By R Lehtonen & E Pahkinen Models in Biology: Mathematics, Statistics and Computing By D Brown & PRothery
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    The ‘Golden Egg’ (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 17 (1995), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: We examine a geometrical construction of a “perfect” egg shape, comparing it with students' conceptions of the ideal shape. Dimensions of birds' eggs are investigated, to find out how egg shapes are related to natural circumstances.
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    Beginning Statistics with Cuisenaire Rods (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Cuisenaire Rods provide a concrete embodiment for teaching mean, median, and mode to middle schoolers. These statistical concepts are traditionally only taught abstractly, but may be better understood via manipulatives.
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    Statistics and the Mathematical Processes (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: The increasing emphasis on what mathematicians do as distinct from what they know in the development of school mathematics curricula presents some interesting possibilities for teachers of statistics. This article looks at these processes and suggests the kind of influence that they may be having on schools.
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    Using Computers to Teach Theoretical Statistics (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    Asking Sensitive Questions in Surveys (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    Don't get t out of proportion! (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    Scoring Patterns in Rugby League (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Tree Slugs (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    An Episode in the History of Measurement (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Setting Objectives in Scientific Studies (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    A Multiple Regression Project (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: The number of calories in a serving of a food item may be determined from the amount of fat, protein, and carbohydrates it contains. Students can uncover this relationship by collecting food data and then performing a multiple regression.
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    Using IT to Investigate World Statistics (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article outlines the development of classroom materials and a number of associated datafiles involving the use of IT.
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    Electrifying Statistics for Your Students (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: The problem of which electricity tariff is the most economical is considered for some different situations. Given the uncertainty of estimating exact usage in advance, various statistical concerns are mentioned, many of which lend themselves to classroom demonstrations.
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    Chinese Dominoes Games (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Play Your Cards Right (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Junior Pinpoint: A Child's Guide to Data Handling (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    World Development Database (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    Pinpoint - datafiles (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Topics: Mathematics
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    Reflections on the Past 15 Years (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    BOOK REVIEWS (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Book review in this ArticleStarting SPSS/PC+and SPSS For Windows A beginner's guide to data analysis By Jeremy J FosterStatistics In Action SMP 16–19 Mathematics School Mathematics ProjectStarting Data Handling More Data Handling Go Further with Data Handling By D Kirkby
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    NEWS NOTES (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    LOOK AHEAD (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Graphing in the Primary School (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Topics: Mathematics
    Notes: This article examines the role of graphical work in data handling in the early years of schooling.
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    Generalised Geometric Random Variables (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Properties of the random variable representing the number of identical and independent Bernoulli trials necessary to obtain K consecutive successes are investigated. The results are interesting to students in a first course in probability or mathematical statistics.
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    Directory Enquiries? (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    1 st - Class! (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    On Large-Sample Tests Concerning Proportions (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    The World's 100 Largest Cities (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Data are presented here for the hundred largest cities in the World. They form part of a case study to teach students about exploratory data analysis but are of added interest in providing a focus on poverty and underdevelopment in the Third World and the contrast between this and the wealth of the First World.
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    Minitab Menus-Do They Help or Hinder? (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A comparison of the levels of difficulty experienced by students in the use of Minitab through its menu interface and its command language showed no advantavge in using the menus.
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    More equal than other? (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Research Papers at ICOTS 4 (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Book Reviews (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    Topics: Mathematics
    Notes: Book reviewed in this Article: Key Data 1994/5 Edition, Central Statistical Office. Fifty Things to do with Databases and Spreadsheets Centre for Statistical Education
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    NEWS & NOTES (1995)
    Oxford, UK : Blackwell Publishing Ltd
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    ANNOUNCEMENT (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
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    APPROXIMATE COMPLETENESS WITH MULTIPLE MARTINGALE MEASURES (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 5 (1995), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We construct a financial market with countably many securities for which there are two equivalent martingale measures under which the market is approximately complete. Thus, approximate completeness does not in general guarantee unique consistent prices for nonmarketed claims. the construction also produces an economy with two agents and infinitely many traded goods which is in equilibrium but has no equilibrium when a new good (recognized by all as redundant) is tentatively traded.
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    Hypnosis modelling in neural networks (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 1-20 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the framework of the neural network theory effects similar to hypnotic displays are constructed. They are based on the associative paradigm involving non-linear interaction of excitatory and inhibitory channels with synaptic memory. The non-linearity of long-term memorizing processes may cause effects exhibited by blind spots, which are interpreted as the first stage of hypnosis. More complicated phenomena are discussed in terms of a two-layer network.
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    Dynamics of small autocatalytic reaction networks—II. Replication, mutation and catalysis (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 21-61 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Mutation is introduced into autocatalytic reaction networks. The differential equations obtained are neither of repliator-type nor can they be transformed straightway into a linear equation. Examples of low dimensional dynamical systems —n=2, 3 and 4 — are discussed and complete qualitative analysis is presented. Error thresholds known from simple replication-mutation kinetics with frequency independent replication rates occur here as well. Instead of cooperative transitions or higher order phase transitions the thresholds appear here as supercritical or subcritical bifurcations being analogous to first-order phase transitions.
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    Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 63-76 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The non-linear behavior of a differential equations-based predator-prey model, incorporating a spatial refuge protecting a consant proportion of prey and with temperature-dependent parameters chosen appropriately for a mite interaction on fruit trees, is examined using the numerical bifurcation code AUTO 86. The most significant result of this analysis is the existence of a temperature interval in which increasing the amount of refuge dynamically destabilizes the system; and on part of this interval the interaction is less likely to persist in that predator and prey minimum population densities are lower than when no refuge is available. It is also shown that increasing the amount of refuge can lead to population outbreaks due to the presence of multiple stable states. The ecological implications of a refuge are discussed with respect to the biological control of mite pests.
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    Optimal root/shoot-partitioning of carbohydrates in plants (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 99-107 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In many applications of control theory on plant growth models biomass maximization is postulated to avoid analytically unsolvable problems while fruit maximization is commonly considered to be a more realistic criterion. In a special case, we are able to compare these criteria. Iwasa and Roughgarden (1984,Theor. Pop. Biol. 25, 78–105) have investigated a certain class of plant growth models using a fruit maximization criterion. They proved that, in the vegetative growth period, the organs follow a certain path of balanced growth. We show that this path remains optimal when biomass maximization is postulated. This underlines the importance of the balanced growth path found by Iwasa and Roughgarden. Furthermore, our result suggests that in the vegetative growth period the biomass maximization criterion is a good approximation of fruit maximization. In another theoretical control investigation, Schultzeet al. (1983,Oecologia 58, 169–177) derived a different type of balanced growth path. We apply the theory of Iwasa and Roughgarden to an improved version of the model of Schulzeet al. This leads to a new description of balanced growth between root and shoot that reflects non-linearities in the water uptake process and constitutes an interesting hypothesis for further experimental testing.
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    Ion induced deformation of soft tissue (1995)
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    Bulletin of mathematical biology 57 (1995), S. 77-98 
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    Notes: Abstract In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Laiet al. (1990,Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myerset al. (1984,ASME J. biomech. Engng,106, 151–158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to acount for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility, of approximate analytic solutions in certain cases.
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    Memory capacity in large idiotypic networks (1995)
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    Bulletin of mathematical biology 57 (1995), S. 109-136 
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    Notes: Abstract Many models of immune networks have been proposed since the original work of Jerne [1974,Ann. Immun. (Inst. Pasteur) 125C, 373–389]. Recently, a limited class of models (Weisbuchet al., 1990,J. theor. Biol. 146, 483–499) have been shown to maintain immunological memory by idiotypic network interactions. We examine generalizations of these models when the networks are both large and highly connected to study their memory capacity, i.e. their ability to account for immunization to a large number of random antigens. Our calculations show that in these minimal models, random connectivities with continuously distributed affinities reduce the memory capacity to essentially nil.
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    A kinetic model of coronary reactive hyperemic response to transient ischemia (1995)
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    Bulletin of mathematical biology 57 (1995), S. 137-156 
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    Notes: Abstract A kinetic model is proposed to delineate the factors that determine the coronary reactive hyperemic response (RHR) to transient ischemia. The model comprises of myocardial-interstitial (M) and vascular (V) compartments. Vasodilator metabolites (VM) are produced in the M compartment during the interval of coronary occlusion. The rate of VM production is dependent on the flow rate during the ischemic period, the ratio of excess flow above the control level (R) to the loss of flow during occlusion period (D), the amount of oxygen stored and the degree of vasodilation in the V compartment prior to occlusion. Following a complete release of occlusion, VM are transported from the M to V compartment and are washed out or degraded with time. The time course of RHR is determined by the coronary patency which is proportional to VM concentration in the V compartment. Based on a set of numerical constants, the model is tested by simulating RHR to the various occlusion manoeuvres: a pair of 10 sec occlusions separated by brief release, a 15 sec release followed by a second brief occlusion, a brief release of an occlusion followed by restriced inflow and a period of restricted inflow after occlusion. The simulated results fit the experimental R/D and RH durations data of canine hearts. Factors that determine the impairment of RH capacity in coronary stenosis are suggested in terms of the model scheme.
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    Kinetic study of an enzyme-catalysed reaction in the presence of novel irreversible-type inhibitors that react with the product of enzymatic catalysis (1995)
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    Bulletin of mathematical biology 57 (1995), S. 157-168 
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    Notes: Abstract In the present paper a kinetic study is made of the behaviour of a Michaelis-Menten enzyme-catalysed reaction in the presence of irreversible inhibitors rendered unstable in the medium by their reaction with the product of enzymatic catalysis. A general mechanism involving competitive, non-competitive, uncompetitive and mixed irreversible inhibition with one or two steps has been analysed. The differential equation that describes the kinetics of the reaction is non-linear and computer simulations of its dynamic behaviour are presented. The results obtained show that the systems studied here present kinetic co-operativity for a target enzyme that follows the simple Michaelis-Menten mechanism in its action on the substrate, except in the case of an uncompetitive-type inhibitor.
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    Bulletin of mathematical biology 57 (1995), S. 169-173 
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    On the estimation of alternative pathways of fatty acid oxidation in the liverIn vivo (1995)
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    Bulletin of mathematical biology 57 (1995), S. 191-203 
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    Notes: Abstract The relative contributions of mitochondrial β-oxidation and peroxisomal β-oxidation and peroxisomal ω-oxidation to the oxidation of a given fatty acidin vivo can be quantitated by an isotopic method. The approach requires infusion of a fatty acid labelled on two specific carbon atoms (e.g. [1-14C] and [11-14C] palmitate) to an isotopic steady state, with subsequent isolation and degradation of an acetylated conjugate as a product of the liver cytosolic acetyl CoA pool and of ketone bodies as a product of the liver mitochondrial acetyl CoA pool.
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    Correlations of rates of insulin release from islets and plateau fractions for β-cells (1995)
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    Bulletin of mathematical biology 57 (1995), S. 229-246 
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    Notes: Abstract Pancreatic β-cells in intact islets of Langerhans perfused with various glucose concentrations exhibit periodic bursting electrical activity (BEA) consisting of active and silent phases. The fraction of the time spent in the active phase is called the plateau fraction and appears to be strongly correlated with the rate of release of insulin from islets as glucose concentration is varied. Here this correlation is quantified and a theoretical development is presented in detail. Experimental rates of insulin release are correlated with “effective” plateau fractions over a range of glucose concentrations. There are a number of different models for BEA in pancreatic β-cells and a method is developed here to quantify the dependence of a glucose dependent parameter on glucose concentration. As an example, the plateau fractions computed from the Sherman-Rinzel-Keizer model are matched with experimental plateau fractions to obtain a relationship between the model's glucose-dependent parameter, β, and glucose concentration. Knowledge of the relationships between β and glucose concentration and between experimental measurements of rates of insulin release and plateau fractions permits the determination of theoretical rates of insulin release from the model.
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    The development of concentration gradients in a suspension of chemotactic bacteria (1995)
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    Bulletin of mathematical biology 57 (1995), S. 299-344 
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    Notes: Abstract When a suspension of bacterial cells of the speciesBacillus subtilis is placed in a chamber with its upper surface open to the atmosphere complex bioconvection patterns are observed. These arise because the cells: (1) are denser than water; and (2) usually swim upwards, so that the density of an initially uniform suspension becomes greater at the top than the bottom. When the vertical density gradient becomes large enough, an overturning instability occurs which ultimately evolves into the observed patterns. The reason that the cells swim upwards is that they are aerotactic, i.e. they swim up gradients of oxygen, and they consume oxygen. These properties are incorporated in conservation equations for the cell (N) and oxygen (C) concentrations, and these are solved in the pre-instability phase of development whenN andC depend only on the vertical coordinate and time. Numerical results are obtained for both shallow- and deep-layer chambers, which are intrinsically different and require different mathematical and numerical treatments. It is found that, for both shallow and deep chambers, a thin boundary layer, densely packed with cells, forms near the surface. Beneath this layer the suspension becomes severely depleted of cells. Furthermore, in the deep chamber cases, a discontinuity in the cell concentration arises between this cell-depleted region and a cell-rich region further below, where no significant oxygen concentration gradients develop before the oxygen is fully consumed. The results obtained from the model are in good qualitative agreement with the experimental observations.
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    Topological and phenomenological classification of bursting oscillations (1995)
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    Bulletin of mathematical biology 57 (1995), S. 413-439 
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    Notes: Abstract We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (inMathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the phenomenological character of different types of bursting, addressing the issue of how well the bursting can be characterized given the limited amount of information often available in experimental settings.
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    Bulletin of mathematical biology 57 (1995), S. 499-506 
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    Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions (1995)
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    Bulletin of mathematical biology 57 (1995), S. 461-486 
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    Notes: Abstract To ensure its sustained growth, a tumour may secrete chemical compounds which cause neighbouring capillaries to form sprouts which then migrate towards it, furnishing the tumour with an increased supply of nutrients. In this paper a mathematical model is presented which describes the migration of capillary sprouts in response to a chemoattractant field set up by a tumour-released angiogenic factor, sometimes termed a tumour angiogenesis factor (TAF). The resulting model admits travelling wave solutions which correspond either to successful neovascularization of the tumour or failure of the tumour to secure a vascular network, and which exhibit many of the characteristic features of angiogenesis. For example, the increasing speed of the vascular front, and the evolution of an increasingly developed vascular network behind the leading capillary tip front (the brush-border effect) are both discernible from the numerical simulations. Through the development and analysis of a simplified caricature model, valuable insight is gained into how the balance between chemotaxis, tip proliferation and tip death affects the tumour's ability to induce a vascular response from neighbouring blood vessels. In particular, it is possible to define the success of angiogenesis in terms of known parameters, thereby providing a potential framework for assessing the viability of tumour neovascularization in terms of measurable quantities.
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    Nonlinear Approximation by Trigonometric Sums (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 29-48 
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    Notes: Abstract We investigate the $L_p$ -error of approximation to a function $f\in L_p({\Bbb T}^d)$ by a linear combination $\sum_{k}c_ke_k$ of $n$ exponentials $e_k(x):= e^{i\langle k,x\rangle}=e^{i(k_1x_1+\cdots+k_dx_d)}$ on ${\Bbb T}^d,$ where the frequencies $k\in {\Bbb Z}^d$ are allowed to depend on $f.$ We bound this error in terms of the smoothness and other properties of $f$ and show that our bounds are best possible in the sense of approximation of certain classes of functions.
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    Uniformly Elliptic PDEs with Bounded, Measurable Coefficients (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 237-259 
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    Notes: Abstract Let $L[\,\cdot\,]$ be a nondivergent linear second-order uniformly elliptic partial differential operator defined on functions with domain $\Omega.$ Consider the question, "When is a function u a solution of $L[u] = 0$ on $\Omega$ ?" The naive answer, "u is a solution of $L[u] = 0$ on $\Omega$ if $u\in C^2(\Omega)$ and $L[u](x) = 0$ for all $x\in\Omega,$ " is clearly too limited. Indeed, if the coefficients of L are in $W^{1,2}\cap L^{\infty},$ then L can be rewritten in divergence form for which the notion of a "weak" solution can be applied. In this case there could be infinitely many functions that are "weak" but not classical solutions. More importantly, even if the coefficients of L are just bounded and measurable, the recent results of Krylov permit us to construct "solutions" of $L[u] = 0$ on $\Omega,$ and these "solutions" are generally no better than continuous; the "weak" solutions previously mentioned can be obtained by this construction, too. The preceding discussion provides us with an adequate extrinsic definition of solution (i.e., given a function u we either prove that it is or is not the result of such a construction) that has been used by several authors, but one that is not particularly satisfying or illuminating. Our major contribution in this paper is to show the following. I. There is an intrinsic definition of solution that is equivalent to the extrinsic one. II. Furthermore, the intrinsic definition is just the (now) well-known Crandall-Lions viscosity solution, modified in a natural way to accommodate measurable coefficients.
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    A Weighted Tauberian Theorem (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 397-406 
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    Notes: Abstract We prove a Tauberian theorem of the form $\phi * g (x)\sim p(x)w(x)$ as $x \to \infty,$ where p(x) is a bounded periodic function and w(x) is a weighted function of power growth. It can be used to study the weighted average of the form $(T^\alpha (\hbox {ln }T)^\beta)^{-1}\int _0^T h(t) \, dt.$
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    Neuronal growth via hybrid system of self-growing and diffusion based grammar rules: I (1995)
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    Bulletin of mathematical biology 57 (1995), S. 205-227 
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    Notes: Abstract The formation of neuronal networks requires axonal growth towards target neutons. A simple set of grammar rules is introduced to describe axonal growth towards target cells situated both at short and long distances from the growing neuron. Growth for short distances is descrbed by growth following the highest gradient of a chemical compound (which is spread by diffusion from the targets). This approach fails to describe long-distance growth, which is addressed by adopting a graph grammar theory for growing trees. With these rules a flexible tool to draw network of neurons by computer can be developed.
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    Interlocking triads of growth control in tumors (1995)
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    Bulletin of mathematical biology 57 (1995), S. 345-366 
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    Notes: Abstract A pair of growth control triads are used to describe coincident tumor growth and liver regeneration after partial hepatectomy. The models are extensions of previous growth control models which describe tumor growth in an unperturbed host (Michelson and Leith, 1991,Bull. math. Biol. 53, 639–656; idem, 1992, Proceedings of the Third International Conference on Communications and Control, Vol. 2, pp. 481–490; idem, 1992,Bull. math. Biol. 55, 993–1011; idem,J. theor. Biol. 169, 327–338). The linkage between the two triads depends upon systemic signals carried by soluble factors, and mathematical descriptors based upon biological first principals are proposed. The sources of the growth factors, their targets and the processing of their signals are investigated. Analyses of equilibrium in the constant coefficients case and simulated growth curves for the dynamic system are presented, and the effects of growth factor-induced mitogenesis and angiogenesis are discussed in particular. A case is made for early and late responses in the coupled control system. The biology of the signal processing paradigm is placed within a new theoretical context and discussed with regard to tumor adaptation, liver differentiation and the development of a tumor hypoxic fraction.
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    Optimal population stabilization and control using the Leslie matrix model (1995)
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    Bulletin of mathematical biology 57 (1995), S. 381-399 
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    Notes: Abstract We consider the problem of optimal stabilization and control of populations which follow the Leslie model dynamics, within state space and control systems theory and methodology. Various types of culling strategies are formulated and introduced into the Leslie model as control inputs, and their effect on global asymptotic stability is investigated. Our new approach provides answers to several unexplored problems. We show that in general it is possible to achieve a desired stable equilibrium population level, through the design of a class ofshifted-proportional stabilizing culling policies. Further, we formulate general non-linear constrained opitmization problems, for obtaining the cost-optimal policy among this generally infinite class of such stabilizing policies. The theoretical findings are illustrated through the solution of the problem over an infinite planning horizon for a numerical example. A comparative study of the costs and dynamic effects of various culling strategies also supports the mathematical results.
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    A data assimilation technique applied to a predator-prey model (1995)
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    Bulletin of mathematical biology 57 (1995), S. 593-617 
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    Notes: Abstract A new approach for data assimilation, which is based on the adjoint method, but allows the computer code for the adjoint to be constructed directly from the model computer code, is described. This technique is straightforward and reduces the chance of introducing errors in the construction of the adjoint code. Implementation of the technique is illustrated by applying it to a simple predator-prey model in a model fitting mode. A series of identical twin numerical experiments are used to show that this data assimilation approach can successfully recover model parameters as well as initial conditions. However, the ease with which these values are recovered is dependent on the form of the model equations as well as on the type and amount of data that are available. Additional numerical experiments show that sufficient coefficient and parameter recoveries are possible even when the assimilated data contain significant random noise. Thus, for biological systems that can be described by ecosystem models, the adjoint method represents a powerful approach for estimating values for little-known biological parameters, such as initial conditions, growth rates, and mortality rates.
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    Building activity and longevity of queenless groups of the Oriental hornet,Vespa orientalis (1995)
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    Bulletin of mathematical biology 57 (1995), S. 441-460 
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    Notes: Abstract The effect of group size on behavioral parameters of the Oriental hornet,Vespa orientalis, was assessed experimentally under laboratory conditions. Hornet groups of various sizes (ranging from 1 to 100 individuals per group) comprised of young individuals (0–24 hr of age) devoid of a queen were placed in artificial breeding boxes (ABBs). The following three quantitative parameters were evaluated: the amount and rate of building as a function of the number of hornets in the group, the rate of oviposition as, related to group size and the longevity of hornets as a function of their group size. The probability for the occurrence of these events was similarly considered and additional behavioral parameters were only assessed qualitatively. Results of this investigation revealed a relation between the three mentioned quantitative behavioral parameters and the number of hornets per group. The number of hornets per group was positively related to the extent of building, the number of cells built by a group is $$2\pi \sqrt {group size} $$ , but negatively related to the rate of building. As for the delay of building, a non-monotone relation was found. The relation between number of hornets per group and the oviposition delay was found to be non-monotone; the number of hornets per group and their longevity were found to be inversely related. Discrepanices were recorded on the very small (1–2 individuals) or very large (100 individuals) hornet groups.
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    Fuzzy classification of nucleotide sequences and bacterial evolution (1995)
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    Bulletin of mathematical biology 57 (1995), S. 527-537 
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    Notes: Abstract A new method for reconstructing evolutionary relationship among bacteria by use of rRNA sequence data is proposed. The method is based on the concept of fuzzy classification of probabilitiesp(i), p(i/j) andp(i/j*) (i=A,G,C,U) of each sequence. The resulting partition tree shares common features of previous works but has some new peculiarities.
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    Bulletin of mathematical biology 57 (1995), S. 619-630 
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    Gyrotaxis: Interaction between algae and flagellates (1995)
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    Bulletin of mathematical biology 57 (1995), S. 631-650 
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    Notes: Abstract We describe the behaviour of motile microorganisms (e.g. flagellates) attracted by “gyrotaxis” to a sinking, non-motile particle (e.g. an algal cell). The model is based on the application of Stokes' solution for the flow field around the settling cell. The volume within which the flagellate is attracted to the sinking particle is determined from the trajectories of the flagellate. The model of gyrotaxis has several applications; these include the colonization of sinking marine snow particles with motile microoganisms and suspension feeding by protozoa.
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    Effect of dimensionality on Lotka-Volterra predator-prey dynamics: Individual based simulation results (1995)
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    Bulletin of mathematical biology 57 (1995), S. 507-526 
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    Notes: Abstract The effect of varying habitat dimensionality on the dynamics of a model predator-prey system is examined using an individual-based simulation. The general results are that in one dimension fluctuations in abundance of prey and predators occur over a large range of spatial scales (extinctions occur over many spatial scales). In two dimensions (and low mobilities of prey and predators) the dynamics become more predictably periodic at local scales and constant at larger scales due to statistical stabilization. In three dimensions, the model can become “phase-locked” with prey and predators displaying oscillations in abundance over large spatial scales.
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    Dicarboxylic acid fluxes during gluconeogenesis. No channelling of mitochondrial oxalacetate (1995)
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    Bulletin of mathematical biology 57 (1995), S. 557-568 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A rather complete model of the gluconeogenic pathway was used, with the known separate pools of mitochondrial and cytosolic oxalacetate, malate and aspartate. The fumarase, malate dehydrogenase and glutamate oxalacetate transaminase reactions were assumed to be isotopically actively reversible, but none at isotopic equilibrium. Malate was assumed to exchange actively between the mitochondrial and cytosol, while aspartate exchange was more limited, in agreement with the known electrogenic nature of aspartate export from the mitochondria. This model was fit to14C data obtained in hepatocyte studies, and to the whole rat14C data obtained by Heath and Rose (Biochem J. 227, 851–876, 1985). The latter data were easily fit to our model, when a single mitochondrial oxalacetate pool was assumed. However, invoking two mitochondrial oxalacetate pools, as proposed by Heath and Rose, with the oxalacetate formed via pyruvate carboxylase preferentially channelled to gluconeogenesis, could not be fit with the known differences in scrambling in glucose and glutamate produced from L[3-14C]lactate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460783
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  • 96
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    Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 569-591 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Oscillatory secretion of insulin has been observed in many different experimental preparations ranging from pancreatic islets to the whole pancreas. Here we examine the mathematical features underlying a possible model for oscillatory secretion from the perifused, insulin-secreting cell line, HIT-15. The model includes the kinetics of uptake of glucose by GLUT transporters, the rate of glucose metabolism within the cell, and the effect of glucose on the rate of insulin secretion. Putative feedback by insulin on the rate of glucose transport into the cells is treated phenomenologically and leads to insulin oscillations similar to those observed experimentally in HIT cells. The resulting set of ordinary differential equations is simplified by time-scale analysis to a two-variable set of ordinary differential equations. Because of this simplification we can explore, in great detail, the characteristics of the oscillations and their sensitivity to parameter variation using phase plane analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460784
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  • 97
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    Sperm motility in the presence of boundaries (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 679-699 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The fluid dynamics of sperm motility near both rigid and elastic walls is studied using the immersed boundary method. Simulations of both single and interacting organisms are presented. In particular, we find that nearby organisms originally undulating with a 90° phase shift may adjust their relative swimming velocities and phase-lock. Comparisons with previous analytical results are also discussed. The tendency of a near-wall to attract organisms is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461846
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  • 98
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    Contributions of memory B cells to secondary immune response (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 713-731 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The secondary immune response is one of the most important features of immune systems. During the secondary immune response, the immune system can eliminate the antigen, which has been encountered by the individual during the primary invasion, more rapidly and efficiently. Both T and B memory cells contribute to the secondary response. In this paper, we only concentrate on the functions of memory B cells. We explore a model describing the memory contributed by the specific long-lived clone which is maintained by continued stimulation with a small amount of antigens sequestered on the surfaces of the follicular dendritic cells (FDC). The behavior of the secondary response provided by the model can be compared with experimental observations. The model shows that memory B cells indeed play an important role in the secondary response. It is found that a single memory cell in a long-lived clone may not be long-lived. In the present note, the influences of relevant parameters on the secondary response are also explored.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461848
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  • 99
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    Reproduction rate, feeding process, and liebig limitations in cell populations—II (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 749-782 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A biological system consisting of a population of cells suspended in a liquid substrate is considered. The general problem addressed in the paper is the derivation of the kinetic pattern of population growth as a statistical effect of a very large number of elementary interactions between a single cell and the molecules of nutrient in substrate. Solution of the problem is obtained in the form of equation expressing the population growth ratec as a function of substrate concentration,C s. The analytical expression derived is applied to a real bacterial population (Escherichi coli) and kinetic patterns are theoretically computed. The major findings, expressed roughly, without nuances, are: (i) the concentration of nutrient at the cell membrane,C c, can only be equal to either 0 (for theC s below some threshold valueC *) orC s (forC s〉C *); (ii) the Michaelis-Menten-Monod kinetics observed in experiments is an artifact: the pure (not contaminated by foreign factors) dependence ofc onC s is actually such that the functionc=c(C s) has practically linear increase whenC s〈C *, and is constant,c=c(C *)=const, whenC s〉C *; (iii) the Liebig principle is strictly fulfilled: up to a feasible accuracy of observation, under no circumstances can population growth be limited (controlled) by more than one substrate component—replacement of a limiting component for another one is an instant event rather than a gradual process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461850
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  • 100
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    Idiotypic regulation of B cell differentiation (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 841-881 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We study the equilibrium properties of idiotypically interacting B cell clones in the case where only the differentiation of B cells is affected by idiotypic interactions. Furthermore, we assume that clones may recognize and be stimulated by self antigen in the same fashion as by antiantibodies. For idiotypically interacting pairs of non-autoreactive clones we observe three qualitatively different dynamical regimes. In the first regime, at small antibody production an antibody-free fixed point, the virgin state, is the only attractor of the system. For intermediate antibody production, a symmetric activated state replaces the virgin state as the only attractor of the system. For large antibody production, finally, the symmetric activated state gives way to two asymmetric activated states where one clone suppresses the other clone. If one or both clones in the pair are autoreactive there is no virgin state. However, we still observe the switch from an almost symmetric activated state to two asymmetric activated states. The two asymmetric activated states at high antibody production have profoundly different implications for a self antigen which is recognized by one of the clones of the pair. In the attractor characterized by high autoantibody concentration the self antigen is attacked vigorously by the immune system while in the opposite steady state the tiny amount of autoantibody hardly affects the self antigen. Accordingly, we call the first state the autoimmune state and the second the tolerant state. In the tolerant state the autoreactive clone is down-regulated by its anti-idiotype providing an efficient mechanism to prevent an autoimmune reaction. However, the antibody production required to achieve this anti-idiotypic control of autoantibodies is rather large.
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    URL: http://dx.doi.org/10.1007/BF02458297
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