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  • Articles  (70,495)
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  • Springer  (70,451)
  • Berkeley Electronic Press (now: De Gruyter)
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  • Articles  (70,495)
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  • 1
    Electronic Resource
    Electronic Resource
    Estimation of the Stochastic Volatility Models by Simulated Maximum Likelihood: C++ Code (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 1, algorithm1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This is documentation for a C++ implementation of the simulated maximum likelihood (SML) estimation method, where the SML algorithm is applied to the stochastic volatility (SV) model. The algorithm and code can easily be adapted to a richer class of SV models, as well as to more general dynamic latent-variable models.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    A Random Walk or Color Chaos on the Stock Market? Time-Frequency Analysis of S&P Indexes (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 2, art2 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: The random-walk (white-noise) model and the harmonic model are two polar models in linear systems. A model in between is color chaos, which generates irregular oscillations with a narrow frequency (color) band. Time-frequency analysis is introduced for evolutionary time-series analysis. The deterministic component from noisy data can be recovered by a time-variant filter in Gabor space. The characteristic frequency is calculated from the Wigner decomposed distribution series. It is found that about 70 percent of fluctuations in Standard & Poor stock price indexes, such as the FSPCOM and FSDXP monthly series, detrended by the Hodrick-Prescott (HP) filter, can be explained by deterministic color chaos. The characteristic period of persistent cycles is around three to four years. Their correlation dimension is about 2.5. The existence of persistent chaotic cycles reveals a new perspective of market resilience and new sources of economic uncertainties. The nonlinear pattern in the stock market may not be wiped out by market competition under nonequilibrium situations with trend evolution and frequency shifts. The color-chaos model of stock-market movements may establish a potential link between business-cycle theory and asset-pricing theory.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    An Approximate Wavelet MLE of Short- and Long-Memory Parameters (1999)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1999, 4, art5 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: By design a wavelet's strength rests in its ability to localize a process simultaneously in time-scalespace. The wavelet's ability to localize a time series in time-scale space directly leads to the computationalefficiency of the wavelet representation of a N £ N matrix operator by allowing the N largest elements of thewavelet represented operator to represent the matrix operator [Devore, et al. (1992a) and (1992b)]. Thisproperty allows many dense matrices to have sparse representation when transformed by wavelets.In this paper we generalize the long-memory parameter estimator of McCoy and Walden (1996) to estimatesimultaneously the short and long-memory parameters. Using the sparse wavelet representation of a matrixoperator, we are able to approximate an ARFIMA model's likelihood function with the series' wavelet coefficientsand their variances. Maximization of this approximate likelihood function over the short and long-memoryparameter space results in the approximate wavelet maximum likelihood estimates of the ARFIMA model.By simultaneously maximizing the likelihood function over both the short and long-memory parameters andusing only the wavelet coefficient's variances, the approximate wavelet MLE provides a fast alternative to thefrequency-domain MLE. Furthermore, the simulation studies found herein reveal the approximate wavelet MLEto be robust over the invertible parameter region of the ARFIMA model's moving average parameter, whereas thefrequency-domain MLE dramatically deteriorates as the moving average parameter approaches the boundariesof invertibility.
    Type of Medium: Electronic Resource
    URL: http://www.bepress.com/snde/vol3/iss4/art5
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  • 4
    Electronic Resource
    Electronic Resource
    Predictive Evaluation of Econometric Forecasting Models in Commodity Futures Markets (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1998, 4, art6 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: The predictive accuracy of various econometric models, including random walks, vector-autoregressive and vector-error-correction models, are investigated using daily futures prices of four commodities (the S&P 500 index, treasury bonds, gold, and crude oil). All models are estimated using a rolling-window approach, and evaluated by both in-sample and out-of-sample performance measures. The criteria considered include system criteria, where we evaluate multiequation forecasting models, and univariate forecast-accuracy criteria. The five univariate criteria are root mean square error (RMSE), mean absolute deviation (MAD), mean absolute percentage error (MAPE), confusion matrix (CM), and confusion rate (CR). The five system criteria used include the trace of second-moment matrix of the forecast-errors matrix (TMSE), the trace of second-moment matrix of percentage-forecast errors (TMAPE), the generalized forecast-error second-moment matrix (GFESM), and a trading-rule profit criterion (TPC) based on a maximum-spread trading strategy. An in-sample criterion, the mean Schwarz information criteria (MSIC), is also computed. Our results suggest that error-correction models perform better in shorter forecast horizons, when models are compared based on quadratic loss measures and confusion matrices. However, the error-correction models which we consider perform better at all forecast horizons (one to five steps ahead) when models are compared based on a profit-maximization loss function. Further, our error-correction model, where the error-correction term is constructed according to a cost-of-carry equilibrium condition, outperforms our alternative error-correction model, which uses the price spreads as the error-correction term.
    Type of Medium: Electronic Resource
    URL: http://www.bepress.com/snde/vol2/iss4/art6
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  • 5
    Electronic Resource
    Electronic Resource
    Using Long-, Medium-, and Short-Term Trends to Forecast Turning Points in the Business Cycle: Some International Evidence (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1998, 2, art2 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper provides rules for anticipating business-cycle recessions and recoveries for countries showing asymmetric cycle durations. Based on a Schumpeterian framework, we analyze business cycles as sums of short-, medium-, and long-term cycles defined for a particular class of unobserved component models. By associating the trend with the low frequencies of the pseudo-spectrum in the frequency domain, manipulation of the spectral bandwidth allows us to define subjective length trends with specific properties. In this paper, we show how these properties can be exploited to anticipate business-cycle turning points, not only historically, but also in a true ex-ante forecasting exercise. This procedure is applied to U.S. post-World War II GNP quarterly data, as well as to another set of European countries.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    A Markov-Chain Sampling Algorithm for GARCH Models (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1998, 2, algorithm1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper describes a GAUSS program of a Markov-chain sampling algorithm for GARCH models proposed by Nakatsuma (1998). This algorithm allows us to generate Monte Carlo samples of parameters in a GARCH model from their joint posterior distribution. The samples obtained by this algorithm are used for Bayesian analysis of the GARCH model. As numerical examples, GARCH models of simulated data and of weekly foreign exchange rate series are estimated and analyzed.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Sectoral Investigation of Asymmetries in the Conditional Mean Dynamics of the Real U.S. GDP (1999)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1999, 4, art2 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: We investigate asymmetries in the conditional mean dynamics of four sectors of the U.S. GDP data. Since the statistical evidence on nonlinearities in the conditional mean could be influenced by the presence of outliers, or by a failure to model conditional heteroskedasticity, we explicitly account for outliers by assuming that the innovations are drawn from the stable family, and model time-varying volatility by a GARCH(1,1) process. We also allow for the possibility of long memory in the series with fractional differencing. Our results indicate only weak evidence of significant nonlinearities in the conditional mean in some sectors of the GDP.
    Type of Medium: Electronic Resource
    URL: http://www.bepress.com/snde/vol3/iss4/art2
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  • 8
    Electronic Resource
    Electronic Resource
    Stability Analysis of Continuous-Time Macroeconometric Systems (1999)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1999, 4, art1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: There has been increasing interest in continuous-time macroeconometric models. This research investigates stability of the Bergstrom, Nowman, and Wymer continuous-time model of the U.K. when systemparameters change. This particularly well-regarded continuous-time macroeconometric model is chosen toassure the empirical and potential policy relevance of the results. Stability analysis is important with this modelfor understanding the dynamic properties of the system and for determining which parameters are the mostimportant to those dynamic properties. The main objective of this paper is to determine the boundaries ofparameters at which instability occurs. Two types of boundaries are found: the transcritical bifurcationboundary and the Hopf bifurcation boundary, corresponding to two different ways that instability occurs whenparameter values cross the bifurcation boundary.The existence of the Hopf bifurcation boundary is particularly useful, since Hopf bifurcation may provideexplanations for some cyclical phenomena in macroeconomy. Numerical algorithms are designed to locate thestability boundaries, which are displayed in three-dimensional diagrams. A notable and perhaps surprisingfact is that both types of bifurcations can coexist with this well-regarded U.K. model--in the same neighborhoodof the parameter space.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Should Policy Makers Worry about Asymmetries in the Business Cycle? (1999)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1999, 4, art3 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper reconsiders the conventional use of econometric models, especially identified vector autoregressive models, in guiding monetary policy. The main question I explore is whether these models are seriously flawed because they ignore asymmetries in the business cycles. Toward that end, models that allow for asymmetric business cycles defined by the case where recessions and expansions are not mirror images of each other are estimated. The results suggest that policy makers should worry about asymmetries in business cycles because most econometric models cannot capture empirically important asymmetries. In particular, estimated multiregime models show that the effects of monetary policy are stronger during turning points and outright recessions than in expansions. I conclude that the symmetry/asymmetry question has as much, and maybe even more, practical significance than debates over identification assumptions that have influenced much of the empirical macroeconomic literature over the past 20 years.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Power Properties of Linearity Tests for Time Series (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 1, art2 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper examines the power properties of several linearity tests applied in time-series analysis. The tests are the ones Lee et al.(1993) used in their Monte Carlo study. The main tool used for power comparisons in this paper is the Pitman asymptotic relative efficiency. The results generally strengthen the outcome of the simulations and complement some results in Lee et al. (1993). They also suggest guidelines for designing Monte Carlo experiments for linearity tests.
    Type of Medium: Electronic Resource
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  • 11
    Electronic Resource
    Electronic Resource
    Forecasting Using First-Available Versus Fully Revised Economic Time-Series Data (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 1, dataset1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: First-reported monthly and quarterly time-series data on nine macroeconomic variables from 1960-1993 are given. Features of this so-called "unrevised" or "first-reported data" are discussed, and the data is compared with standard "fully revised" data using Granger causality tests. For the purposes of real-time forecasting, as well as comparing professional forecasts with traditional econometric forecasts, the use of unrevised (or, even better, "real-time") data has a number of advantages over the use of fully revised data.
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    A Kernel Test for Neglected Nonlinearity (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 2, art4 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper develops a new kernel test for neglected nonlinearity in the conditional expectation function, and compares this test to the Ramsey RESET test (1969) and the Neural Net test of Lee, White, and Granger (1993). Like the Neural Test and the Ramsey Reset Test, this Kernel test is a Lagrange Multiplier test based on the R-Square statistic from a regression of the estimated residuals on the regressors, and an additional nonlinear function of the regressors. Unlike the other tests, our test has a two stage approach where in the first stage we estimate the structure of the misspecification and in the second stage we test for whether or not the estimate of the misspecification can better predict the residuals than their mean. This two stage approach can give the researcher guidance on the nature of the misspecification, and should improve the power of the test since the added function in the regression of the residuals is itself an estimate of the conditional expectation of the residuals given the independent variables. In addition, because it uses simple, well known estimation methods it can be implemented by researchers when using linear models.
    Type of Medium: Electronic Resource
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  • 13
    Electronic Resource
    Electronic Resource
    SIMANN: A Global Optimization Algorithm using Simulated Annealing (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 3, algorithm1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper describes SIMANN, a Fortran and GAUSS implementation of the simulated annealing algorithm. The Fortran code was used in "Global Optimization of Statistical Functions with Simulated Annealing" (Goffe, Ferrier, and Rogers 1994). In that paper, simulated annealing was found to be competitive, if not superior, to multiple restarts of conventional optimization routines for difficult optimization problems. This paper compares SIMANN to the DFP algorithm on another optimization problem, namely, the maximum likelihood estimation of a rational expectations model, which was previously studied in the literature. SIMANN again performs quite well, and shows several advantages over DFP. This paper also describes simulated annealing, and gives explicit directions and an example for using the included GAUSS and Fortran code.
    Type of Medium: Electronic Resource
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  • 14
    Electronic Resource
    Electronic Resource
    Inference in TAR Models (1997)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1997, 1, art1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: A distribution theory is developed for least-squares estimates of the threshold in Threshold Autoregressive (TAR) models. We find that if we let the threshold effect (the difference in slopes between the two regimes) become small as the sample size increases, then the asymptotic distribution of the threshold estimator is free of nuisance parameters (up to scale). Similarly, the likelihood ratio statistic for testing hypotheses concerning the unknown threshold is asymptotically free of nuisance parameters. These asymptotic distributions are nonstandard, but are available in closed form, so critical values are readily available. To illustrate this theory, we report an application to the U.S. unemployment rate. We find statistically significant threshold effects.
    Type of Medium: Electronic Resource
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  • 15
    Electronic Resource
    Electronic Resource
    Forecasting Exchange Rates Using Neural Networks for Technical Trading Rules (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1998, 4, art2 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: We examine the performance of artificial neural networks (ANNs) for technical trading rules for forecasting daily exchange rates. The main conclusion of our attempt is that ANNs perform well, and that they are often better than linear models. Furthermore, the precise number of hidden layer units in ANNs appears less important for forecasting performance than is the choice of explanatory variables.
    Type of Medium: Electronic Resource
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  • 16
    Electronic Resource
    Electronic Resource
    The Current Depth-of-Recession and Unemployment-Rate Forecasts (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1998, 4, art5 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Building upon Beaudry and Koop's (1993) analysis, we consider a "current depth of the recession" (CDR) variable in modeling the time-series behavior of the postwar quarterly U.S. unemployment rate. The CDR approach is consistent with the state-dependent behavior in the unemployment rate documented in the business-cycle asymmetry literature. We show that while the CDR effect is significant in-sample, no statistically significant out-of-sample forecast improvement is obtained relative to the linear alternative. Augmenting an AR(2) model by inclusion of the CDR term, however, does not significantly worsen the out-of-sample forecast performance.
    Type of Medium: Electronic Resource
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  • 17
    Electronic Resource
    Electronic Resource
    Endogenous Cycles in Competitive Models: An Overview (1997)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1997, 4, art1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: It is a common assertion that, in a world with perfect markets and rational expectations, endogenous cycles could only arise under very unrealistic assumptions. This paper offers a short discussion on this claim and a review of the relevant contributions to the literature on deterministic fluctuations in competitive models. It is argued that these types of fluctuations are more easily obtained when agents are assumed to be heterogeneous and when the production side of the economy is considered. The paper also discusses the existence of endogenous cycles in models with financial market imperfections and nonconvex technologies.
    Type of Medium: Electronic Resource
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  • 18
    Electronic Resource
    Electronic Resource
    Investigating Cyclical Asymmetries (1997)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1997, 1, art2 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper accomplishes two goals. First, it introduces a powerful nonparametric test of asymmetry to the economics literature, namely, the triples test of Randles et al. (1980). Second, it documents the presence of two specific kinds of asymmetry in U.S. macroeconomic time series. Depth, or asymmetry in the distribution of a (detrended) series, is a feature of numerous economic time series; and steepness, or asymmetry in the distribution of first differences, is a feature of hours, employment, and the unemployment rate, but is absent from real GDP and aggregate industrial production. The pattern of asymmetries found provides guidelines for restricting the set of alternative nonlinear models from which to select in modeling these time series.
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  • 19
    Electronic Resource
    Electronic Resource
    Nonlinearity and Endogeneity in Macro-Asset Pricing (1997)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1997, 3, art1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Linear asset-pricing relations, with macroeconomic factors as state variables, have found wide usein empirical finance. Applications of such relations range from academic studies of market efficiency andmarket anomalies to practical uses such as risk management and estimation of the cost of capital. Theseapplications make two key assumptions: that the relationship is exclusively linear, and that the macroeconomicfactors are exogenous to returns. For the set of macrofactors commonly used in these applications, bothassumptions run counter to economic intuition. We set out to demonstrate that they are also counter toempirical evidence.We carry out this task using tests for linear and nonlinear Granger causality. We find linear and nonlinearfeedback between stock returns and commonly used macroeconomic pricing factors. We also find linear andnonlinear feedback between residuals from linear pricing relations and returns. In addition, there is littleevidence to suggest that neglected autoregressive or autoregressive conditionally heteroskedastic dynamics areresponsible for these findings, implying that the underlying dynamics are complicated. Thus, linearasset-pricing relations omit interesting and potentially useful aspects of the relationship between stock returnsand the macroeconomy.
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  • 20
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    Avoiding the Pitfalls: Can Regime-Switching Tests Reliably Detect Bubbles? (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1998, 1, art1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Our paper uses simulation methods to examine the size and power of regime-switching tests for bubbles. We find that even with several hundred observations, the tests show sometimes considerable size distortion. This distortion makes the tests conservative; they understate the significance of the evidence of bubbles. Despite this, the tests display considerable power to detect bubbles even when using the conservative asymptotic critical values. We also find that the frequency with which bubbles collapse has an important influence on the tests' power. An application to monthly Canadian and American stock-price data provides mixed evidence of bubbles.
    Type of Medium: Electronic Resource
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  • 21
    Electronic Resource
    Electronic Resource
    Smooth-Transition GARCH Models (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1998, 2, art1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: The asymmetric response of conditional variances to positive versus negative news has been traditionally modeled with threshold specifications that allow only two possible regimes: low or high volatility. In this paper, the possibility of intermediate regimes is considered and modeled with the introduction of a smooth-transition mechanism in a GARCH specification. One important property of this model is that it permits an on-off ARCH effect, in which a time series can switch from a process with constant variance to a process with time-varying variance. On testing for the existence of a smooth-transition mechanism, there are nuisance parameters that are not identified under the null hypothesis. Nevertheless, it is possible to construct a Lagrange-multiplier test that is ¬2 p -distributed. A Monte Carlo simulation shows that the test has very good size and good power. A smooth-transition GARCH specification is tested and estimated with stock returns and exchange-rate data. While a threshold model is preferred for stock returns, a smooth-transition model is more likely for exchange rates.
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  • 22
    Electronic Resource
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    Characterizing Asymmetries in Business Cycles Using Smooth-Transition Structural Time-Series Models (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1998, 3, art2 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper aims at testing and modeling business-cycle asymmetries within a structural time-series framework, allowing for smooth transition in the parameters characterizing the cyclical component, namely, the damping factor and the frequency. An LM test of linearity is derived, and illustrations are provided with reference to a set of quarterly U.S. industrial production series for two-digit manufacturing industries.
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  • 23
    Electronic Resource
    Electronic Resource
    Monetary Policy with a Nonlinear Phillips Curve and Asymmetric Loss (1999)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1999, 4, art4 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Recent theoretical and empirical work has cast doubt on the hypotheses of a linear Phillips curve and a symmetric quadratic loss function underlying traditional thinking on monetary policy. This paper studies the one-period optimal monetary policy problem under an asymmetric loss function corresponding to the "opportunistic approach" to disinflation and a convex Phillips curve. The policy-inaction range and its properties are derived analytically. Numerical simulations are then used to assess the implications of asymmetric loss for the distributional properties of the equilibrium levels of inflation and unemployment. For parameter values relevant to the U.S., it is found that the asymmetric loss function yields an average inflation rate in excess of the target, and that bias is larger than the standard symmetric loss function. For moderate policy-maker preferences, the asymmetric loss function also yields a smaller gap between average unemployment and the natural rate, and higher (lower) variance of inflation (unemployment) compared to the symmetric benchmark. Calibrating the model to match the observed average unemployment rate requires a high degree of inflation aversion and small asymmetry.
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    The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 3, art2 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: The method of reconstructing an n-dimensional system from observations is to form vectors of m consecutive observations, which for m 2n, is generically an embedding. This is Takens's result. The Jacobian methods for Lyapunov exponents utilize a function of m variables to model the data, and the Jacobian matrix is constructed at each point in the orbit of the data. When embedding occurs at dimension m = n, the Lyapunov exponents of the reconstructed dynamics are the Lyapunov exponents of the original dynamics. However, if embedding only occurs for an m 〉 n, then the Jacobian method yields m Lyapunov exponents, only n of which are the Lyapunov exponents of the original system. The problem is that as currently used, the Jacobian method is applied to the full m-dimensional space of the reconstruction, and not just to the n-dimensional manifold that is the image of the embedding map. Our examples show that it is possible to obtain spurious Lyapunov exponents that are even larger than the largest Lyapunov exponent of the original system.
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    FORTRAN Programs for Running the TR Test: A Guide and Examples (1997)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1997, 4, algorithm1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper provides a guide to two FORTRAN programs, called TRT1.FOR and TRT2.FOR, written to run the two stages of the Ramsey and Rothman (1996) time-reversibility (TR) test. Original FORTRAN source code and executable (on an IBM-compatible PC) versions of the programs are available. The major step in successfully running the programs is setting up two ASCII control files, called TRT1.CNL and TRT2.CNL. Two examples are provided.
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    Optimal Cycles and Chaos: A Survey (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 1, art3 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper surveys the literature on cyclical and chaotic equilibrium paths in deterministic optimal growth models with infinitely lived agents. We focus on discrete time models but also briefly mention results for continuous time models. We start by reviewing those results that have been proved for optimal growth models in reduced form. Then we discuss results for two-sector optimal growth models in primitive form. Finally, we summarize a few results that have been obtained for other variants of the model, including models with recursive preferences and models with heterogeneous agents.
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    If Nonlinear Models Cannot Forecast, What Use Are They? (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 2, art1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper begins with a brief review of the recent experience using nonlinear models and ideas of chaos to model economic data and to provide forecasts that are better than linear models. The record of improvement is at best meager. The remainder of the paper examines some of the reasons for this lack of improvement. The concepts of "openness" and "isolation" are introduced, and a case is made that open and nonisolated systems cannot be forecasted; the extent to which economic systems are closed and isolated provides the true pragmatic limits to forecastability. The reasons why local "overfitting," especially with nonparametric models, leads to worse forecasts are discussed. Models and "representations" of data are distinguished and the reliance on minimum mean-square forecast error to choose between models and representations is evaluated.
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    Detecting Asymmetries in Observed Linear Time Series and Unobserved Disturbances (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 3, art1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper investigates the problem of testing for the symmetry of linear time series driven by asymmetric innovations. In particular, we examine the performance of alternative symmetry tests when innovations are fat tailed. Among the tests considered, only the test based on the tail estimator of the spectral measure yields satisfactory results in the presence of fat-tailed innovations.
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    GARCH for Irregularly Spaced Financial Data: The ACD-GARCH Model (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1998, 4, art4 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: We develop a class of ARCH models for series sampled at unequal time intervals set by trade orquote arrivals. Our approach combines insights from the temporal aggregation for GARCH models discussed byDrost and Nijman (1993) and Drost and Werker (1996), and the autoregressive conditional duration model ofEngle and Russell (1996) proposed to model the spacing between consecutive financial transactions.The class of models introduced here will be called ACD-GARCH. It can be described as a random coefficientGARCH, or doubly stochastic GARCH, where the durations between transactions determine the parameterdynamics. The ACD-GARCH model becomes genuinely bivariate when past asset-return volatilities are allowedto affect transaction durations, and vice versa. Otherwise, the spacings between trades are consideredexogenous to the volatility dynamics. This assumption is required in a two-step estimation procedure. Thebivariate setup enables us to test for Granger causality between volatility and intratrade durations. Undergeneral conditions, we propose several Generalized Method of Moments (GMM) estimation procedures, somehaving a Quasi Maximum Likelihood Estimation (QMLE) interpretation. As illustration, we present anempirical study of the IBM 1993 tick-by-tick data. We find some evidence that volatility of IBM stock pricesGranger-causes intratrade durations. We also find that the persistence in GARCH drops dramatically onceintratrade durations are taken into account.
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    The Decomposition of Economic Relationships by Time Scale Using Wavelets: Expenditure and Income (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1998, 1, art2 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Economists have long known that time scale matters, in that the structure of decisions as to the relevant time horizon, degree of time aggregation, strength of relationship, and even the relevant variables differ by time scale. Unfortunately, until recently it was difficult to decompose economic time series into orthogonal time-scale components except for the short and long run, in which the former is dominated by noise. This paper uses wavelets to produce an orthogonal decomposition of some economic variables by time scale over six different time scales. The relationship of interest is the permanent income hypothesis. We confirm that time-scale decomposition is very important for analyzing economic relationships and that a number of anomalies previously noted in the literature are explained by these means. The analysis indicates the importance of recognizing variations in phase between variables when investigating the economic relationships.
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    Information-Theoretic Analysis of Serial Dependence and Cointegration (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1998, 3, art1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper is devoted to presenting wider characterizations of memory and cointegration in time series, in terms of information-theoretic statistics such as the entropy and the mutual information between pairs of variables. We suggest a nonparametric and nonlinear methodology for data analysis and for testing the hypotheses of long memory and the existence of a cointegrating relationship in a nonlinear context. This new framework represents a natural extension of the linear-memory concepts based on correlations. Finally, we show that our testing devices seem promising for exploratory analysis with nonlinearly cointegrated time series.
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    EmmPack 1.01: C/C++ Code for Use with Ox for Estimation of Univariate Stochastic Volatility Models with the Efficient Method of Moments (1997)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1997, 3, algorithm1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Econometric estimation using simulation techniques, such as the efficient method of moments, may be time consuming. The use of ordinary matrix-programming languages such as GAUSS, MATLAB, Ox, or S-PLUS will often cause extra delays. For the efficient method of moments implemented to estimate stochastic volatility models, this will surely be the case; therefore, the author made a C/C++ library containing the bulk of the procedures needed in the implemention of the efficient method of moments technique for a broad range of univariate stochastic volatility models. As a side effect of the efficient method of moments, EGARCH models with a variety of non-normal distributions can be estimated with this package. Implementations have been made for the Intel Pentium platform linked under Windows and for the IBM RS/6000 platform under AIX. The library is dynamically linked to Ox under Windows and statically linked under AIX. The speed improvements are considerable compared with pure Ox code. This paper serves as a manual for this library. It describes the efficient method of moments for this specific case of stochastic volatility models, and it describes the program. Some examples are given from other work of the author. Technicalities are given in the appendices.
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    Early News is Good News: The Effects of Market Opening on Market Volatility (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1998, 4, art3 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: In this paper, we examine the characteristics of market opening news and its impact on the estimated coefficients of the conditional volatility models of the GARCH class. We find that the differences between the opening price of one day and the closing price of the day before have different characteristics when considering various stock-market indices on which options are actively traded. The impact of a suitable positive-valued transformation of these differences has the effects of modifying the direct impact of daily innovations on volatility and reducing the estimated overall persistence of such innovations. The overall contribution of the variable is evaluated in an out-of-sample forecasting exercise, where we obtain significant improvements above the simple GARCH model.
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    On Cycles and Chaos in Economics (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 1, art1 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
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    A Fast Algorithm for the BDS Statistic (1997)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1997, 2, algorithm1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: The BDS statistic has proved to be one of several useful nonlinear diagnostics. It has been shown to have good power against many nonlinear alternatives, and its asymptotic properties as a residual diagnostic are well understood. Furthermore, extensive Monte Carlo results have proved it useful in relatively small samples. However, the BDS test is not trivial to calculate, and is even more difficult to deal with if one wants the speed necessary to make bootstrap resampling feasible. This short paper presents a fast algorithm for the BDS statistic, and outlines how these speed improvements are achieved. Source code in the C programming language is included.
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    Finite Sample Properties of the Efficient Method of Moments (1997)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1997, 2, art2 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Gallant and Tauchen (1996) describe an estimation technique, known as Efficient Method ofMoments (EMM), that uses numerical methods to estimate parameters of a structural model. The technique usesas matching conditions (or moments, in the GMM jargon) the gradients of an auxiliary model that fits a subsetof variables that may be simulated from the structural model.This paper presents three Monte Carlo experiments to assess the finite sample properties of EMM. The first onecompares it with a fully efficient procedure (Maximum Likelihood) by estimating an invertible moving-average(MA) process. The second and third experiments compare the finite sample properties of the EMM estimatorswith those of GMM by using stochastic volatility models and consumption-based asset-pricing models. Theexperiments show that the gains in efficiency are impressive; however, given that both EMM and GMM share thesame type of objective function, finite sample inference based on asymptotic theory continues to lead, in somecases, to "over rejections," even though they are not as significant as in GMM.
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    Testing the Expectations Theory of the Term Structure of Interest Rates Using Model-Selection Methods (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1998, 4, art1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: In this paper, we propose a model-selection approach to testing the expectations theory of the term structure of interest rates. Our method is based on the posterior information criterion (PIC) developed and analyzed by Phillips and Ploberger (1994, 1996) and extended to provide order estimation of cointegrating rank by Chao and Phillips (1997). This methodology has the advantage that issues of order selection--i.e., the determination of lag length and cointegrating rank in a vector autoregression--and hypothesis testing are treated within the same framework. Applying our procedure to interest-rate data from the International Financial Statistics, we find the expectations theory to be inconsistent with the data.
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    Nonlinear Dynamics and European GNP Data (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1998, 1, art3 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: The aim of this paper is to assess whether the data-generation process of the GDP can be interpreted by means of a nonlinear model instead of a linear one. We model the first differences of logarithmic real GDP data with constant parameters for those European countries (France, Germany, Italy, U.K., Denmark, Sweden, and Norway) which have long-term time series. Since the linear autoregressive model is rejected, an alternative nonlinear model has been specified: it turns out that the annual European GDPs can adequately be described by means of a nonlinear model with constant parameters.
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    A Visual Goodness-of-Fit Test for Econometric Models (1998)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 3.1998, 3, art3 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper designs a visual goodness-of-fit test based on the probability integral transformation of the residuals of an estimated model. We illustrate the method with histograms and correlograms of transformed series for different distributions of disturbances in simulated models. An application of the proposed test to the modeling of daily stock-market returns is also presented.
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    A Check on the Robustness of Hamilton's Markov Switching Model Approach to the Economic Analysis of the Business Cycle (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 1, replication1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This note explores the robustness of Hamilton's (Econometrica, 1989) two-regime Markov switching model framework for capturing business-cycle patterns. Applying his exact specification to a revised version of real GNP, I find parameter estimates that are similar to those he reported only when I use the same sample period (1952-1984) and a particular set of starting values for the maximum likelihood procedure. Two other local maxima exist that have higher likelihood values, and neither correspond to the conventional recession-expansion dichotomy. In fact, when the sample period is extended, there is no longer a local maximum near the parameter set reported by Hamilton. Exploring the model and data further, I reject cross-regime restrictions of Hamilton specification, but also find that relaxing these restrictions increases the number of local maxima. However, a parsimonious three-regime model for GNP growth is more robust and plausible, especially when each regime is required to last more than one quarter.
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    Saddle Path Stability, Fluctuations, and Indeterminacy in Economic Growth (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 2, art3 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: We present a macroeconomic growth model in which investment in physical capital exhibits positive externalities which raise the stock of knowledge. Treating physical capital and knowledge as two separate variables, we show that the model can generate endogenous growth. It is demonstrated that there exist at most two balanced growth paths (BGPs) with endogenous growth. If the BGP is unique it is always saddle-point stable. If there are two BGPs, the first is always stable in the saddle point sense, whereas the second cannot be a saddle point. Instead, the second is either totally stable, giving rise to local indeterminacy, or completely unstable. Further, we can demonstrate that a Hopf bifurcation may occur at the second BGP, leading to persistent fluctuations. Besides local indeterminacy, the model may also give rise to global indeterminacy.
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    Tests for Nonlinearity in EMS Exchange Rates (1996)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1996, 3, art3 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper tests for nonlinearity in EMS exchange rates using the bispectrum. The early experience of the ERM witnessed numerous realignments. We find that exchange rates follow a linear process over the period 1979-1987, consistent with the predictions of the realignment target zone model, where a stabilizing nonlinearity is absent. But from 1987-1992, no realignments occurred, and many currencies conformed to a nonlinear process, consistent with the credible target zone model where an inherent nonlinearity stabilizes exchange rates. However, the Italian lira and the Irish pound follow a linear process, which suggests that a target zone has not proven effective in stabilizing exchange rates.
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    A Nonlinear Analysis of Forward Premium and Volatility (1997)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 1.1997, 4, art2 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: In this paper we investigate the relationship between risk premium and a time-varying conditional variance of spot rate using weekly Swiss franc/US dollar exchange-rate data. First, we apply an EGARCH-in-mean framework to test the unbiasedness hypothesis of the forward rate with a volatility dependent risk premium. The corresponding estimates point to no significant influence of volatility on the risk premium, and reject the unbiasedness hypothesis. Second, we apply a seminonparametric, nonlinear impulse-response analysis to the spot-rate change and the forward premium. This framework allows us to analyze the risk premium/volatility relationship without using a specific, parametric model such as EGARCH-in-mean. The latter analysis confirms the negative EGARCH-in-mean results with respect to the risk premium/volatility relationship, although the volatility dynamics estimated is clearly different from that implied by the EGARCH estimate. Moreover, the forward premium has a nonlinear dynamic influence on the spot rate, whereas the converse is not true.
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    Technical Trading Rules and the Size of the Risk Premium in Security Returns (1997)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 2.1997, 2, art1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Among analysts, technical trading rules are widely used for forecasting security returns. Recent literature provides evidence that these rules may provide positive profits after accounting for transaction costs. This would be contrary to the theory of the efficient market hypothesis which states that security prices cannot be forecasted from their past values or other past variables. This paper uses the daily Dow Jones Industrial Average Index from 1963 to 1988 to examine the linear and nonlinear predictability of stock market returns with simple technical trading rules, by using the nearest neighbors and the feedforward network regressions. Evidence of nonlinear predictability is found in the stock market returns by using the past returns and the buy and sell signals of the moving average rules.
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    Coupling of a slow and a fast oscillator can generate bursting (1985)
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    Bulletin of mathematical biology 47 (1985), S. 1-21 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A general mechanism underlying bursting is proposed and described. It consists of two coupled nonlinear oscillators with different frequencies, where the slower oscillator alternatively switches the faster one on and off. This mechanism is shown to work in an extended Bonhoefer-van der Pol oscillator as well as in a modified version of the Hodgkin-Huxley equations.
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    Analytical bounding functions for diffusion problems with michaelis-menten kinetics (1985)
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    Bulletin of mathematical biology 47 (1985), S. 145-153 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Pointwise upper and lower bounds for the solution of a class of nonlinear diffusion problems with Michaelis-Menten kinetics are presented. Simple analytical bounding curves are obtained and for an illustrative case the calculated values bound the recent numerical solution of P. Hiltmann and P. Lory, 1983.Bull. math. Biol. 45, 661–664.
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    Cell mass concentration variance resulting from fluctuations in the incoming nutrient concentration to a chemostat (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 337-342 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The cellular response in terms of steady-state variance of cell mass concentration to fluctuations in incoming nutrient concentration to a chemostat has been examined. A white noise process is assumed to describe incoming nutrient concentration fluctuations and the variance of cell mass concentration has been found to depend on cell yield (a lumped measure of nutrient concentration fluctuation magnitude and lifetime) and two system time constants.
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    Chaotic dynamics of information processing: The “magic number seven plus-minus two” revisited (1985)
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    Bulletin of mathematical biology 47 (1985), S. 343-365 
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    ISSN: 1522-9602
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    Notes: Abstract In a well-known collection of his essays in cognitive psychology Miller (The Psychology of Communication. Penguin, 1974) describes in detail a number of experiments aiming at a determination of the limits (if any) of the human brain in processing information. He concludes that the ‘channel capacity’ of human subjects does not exceed a few bits or that the number of categories of (one-dimensional) stimuli from which unambiguous judgment can be made are of the order of ‘seven plus or minus two’. This ‘magic number’ holds also, Miller found, for the number of random digits a person can correctly recall on a row and also the number of sentences that can be inserted inside a sentence in a natural language and still be read through without confusion. In this paper we propose a dynamical model of information processing by a self-organizing system which is based on the possible use of strange attractors as cognitive devices. It comes as an amusing surprise to find that such a model can, among other things, reproduce the ‘magic number seven plus-minus two’ and also its variance in a number of cases and provide a theoretical justification for them. This justification is based on the optimum length of a code which maximizes the dynamic storing capacity for the strings of digits constituting the set of external stimuli. This provides a mechanism for the fact that the ‘human channel’, which is so narrow and so noisy (of the order of just a few bits per second or a few bits per category) possesses the ability of squeezing or ‘compressing’ practically an unlimited number of bits per symbol—thereby giving rise to a phenomenal memory.
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    The extension of two-dimensional cable theory to arteries and arterioles (1985)
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    Bulletin of mathematical biology 47 (1985), S. 409-424 
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    Notes: Abstract Electrical polarization of an artery or an arteriole may be modeled by the use of equations developed for two-dimensional cable theory. Two special cases have previously been solved: those corresponding to the case in which the radius is either zero (one-dimensional cable theory) or infinite. This paper presents the general solution.
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    On the computation of the tertiary structure of globular proteins—IV. Use of secondary structure information (1985)
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    Bulletin of mathematical biology 47 (1985), S. 367-407 
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    Notes: Abstract The distance geometry approach for computing the tertiary structure of globular proteins emphasized in this series of papers (Goelet al., J. theor. Biol. 99, 705–757, 1982) is developed further. This development includes incorporation of some secondary structure information—the location of alpha helices in the primary sequence—in the algorithm to compute the tertiary structure of alpha helical globular proteins. An algorithm is developed which estimates the interresidue distances between chain-proximate helices. These distances, in conjunction with the global statistical average distances obtainable from a database of real proteins and determined by the primary sequence of the protein under study, are used to determine the tertiary structure. Five proteins, parvalbumin, hemerythrin, human hemoglobin, lamprey hemoglobin, and sperm whale myoglobin, are investigated. The root mean square (RMS) errors between the calculated structures and those determined by X-ray diffraction range from 4.78 to 7.56 Å. These RMSs are 0.21–2.76 Å lower than those estimated without the secondary structure information. Contact maps and three-dimensional backbone representations also show considerable improvements with the introduction of secondary structure information.
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    Editorial: Software survey section (1985)
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    Bulletin of mathematical biology 47 (1985), S. I 
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    The unidirectional flux transient as a tool for quantifying parallel diffusional pathways through membranes. Exact solution for two pathways (1985)
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    Bulletin of mathematical biology 47 (1985), S. 425-434 
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    Notes: Abstract If a plane membrane consists of patches, each with a given area and a given diffusion coefficient, then the transient of the total unidirectional flux of a diffusing substance (as defined experimentally by Ussing) is predictable. Here the inverse problem is studied: given only the observed transient of the total unidirectional diffusion flux, the unknown membrane heterogeneity transverse to the flux is to be quantified. The ratio of the arithmetic and of the harmonic means (both area-weighted) of the diffusion coefficients, evaluated over the membrane, is expressed in terms of the observed transient alone and is used to characterize the heterogeneity. A unique exact solution of the inverse problem for two kinds of patches is obtained in closed form. A singular limit of this solution pertains to currently postulated models of endothelial membranes, for which a characteristically shaped transient is predicted.
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    Editor's comments (1985)
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    Bulletin of mathematical biology 47 (1985), S. 435-435 
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    Sequence similarity (‘Homology’) searching for molecular biologists (1985)
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    Bulletin of mathematical biology 47 (1985), S. 437-474 
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    Notes: Abstract Major types of sequence similarity searching (often, and incorrectly, called ‘homology’ searching) are reviewed and examples of each are presented. The features and limitations of each type of program, and individual implementations of each type are discussed. Two pairs of sequences are used as examples to show how implementations of each type differ in their results and their presentation. Both local and global alignment programs are examined, and the programs reviewed run on many different types of computer architectures, from laboratory computers such as the IBM PC, minicomputers such as the VAX, to large mainframe computers such as DEC-10/20 series.
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    The existence of stable equilibria in Volterra predator-prey systems represented by loop graphs (1985)
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    Bulletin of mathematical biology 47 (1985), S. 489-494 
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    Notes: Abstract Criteria for the existence of globally stable equilibria in classical Volterra predator-prey systems represented by loop graphs are provided by comparing the community matrix with a matrix belonging to matrix classS W .
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    Pattern regulation in reaction-diffusion systems-the problem of size invariance (1985)
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    Bulletin of mathematical biology 47 (1985), S. 475-487 
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    Notes: Abstract Ordinary reaction-diffusion mechanisms do not account for size invariance properties of morphogenetic fields. We show that such a failure results from ignoring cell individuality. By considering purely topological factors, such as the number of intercellular contacts or the extent of the cell surface in contact with neighbouring cells, size invariance exists in reaction-diffusion systems. Our results are general, model independent and may be applied to any multi-unit ensemble exhibiting coherent behaviour.
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    Effects of twist on pulse waves in arteries (1985)
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    Bulletin of mathematical biology 47 (1985), S. 495-502 
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    Notes: Abstract The artery is treated as a thick-walled cylindrical shell. Using the large deformation theory, an analytical expression for the pulse wave speed is obtained and the effect of twist on the wave speed is discussed. Numerical results indicate that although phase velocity increases with pressure, it decreases with increasing twist angle.
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    Effects of the shape of stenosis on the resistance to blood flow through an artery (1985)
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    Bulletin of mathematical biology 47 (1985), S. 545-550 
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    Notes: Abstract The effect of the shape of stenosis on the resistance to blood flow through an artery with mild local narrowing has been studied. It is shown that the resistance to flow decreases as the shape of stenosis changes and the maximum resistance is attained in the case of symmetric stenosis.
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    A method for numbering binary rooted and unrooted phylogenies and their hypothetical taxonomic units (1985)
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    Bulletin of mathematical biology 47 (1985), S. 535-543 
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    Notes: Abstract A set of 2n−2 relations (edges) and a set ofn−1 hypothetical taxonomic units (HTUs) derive from the estimation of a binary phylogeny of a set ofn operational taxonomic units (OTUs). We propose an easy way for numbering thesen−1 hypothetical taxonomic units, as well as for then−2 interior points of an unrooted binary phylogeny. We also present an alternative method to the one proposed by Rohlf (Bull. math. Biol. 45, 33–40, 1983) for numbering the π i=1 n (2i−3) possible rooted binary phylogenies and the π i=1 n−1 (2i−3) possible unrooted binary phylogenies conerning a set ofn operational taxonomic units. An illustrative example of the method is presented. It is hoped that some studies in phylogenetics will become more accessible, from the viewpoint of computational economy, by the use of this method.
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    Mathematical modeling of opiate binding to mouse brain membrane (1985)
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    Bulletin of mathematical biology 47 (1985), S. 503-512 
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    Notes: Abstract The heterogeneity of rat brain opiate receptors was examined by analyzing competition data. The binding of three prototypical tritiated opioid agonists, [3H]-dihydromorphine ([3H]-DHM), [3H]-D-ala2-D-leu5-enkephalin ([3H]-DADLE), and [3H]-ethylketocyclazocine ([3H]-EKC) was determined in the presence of varying concentrations of each of these unlabeled ligands, generating nine displacement curves. A computer program was then used to find the best fit of a model system to these data, assuming two, three or four independent binding sites. The best fit was a four-site model. One of these sites is specific for DHM; two are relatively selective for DHM and DADLE respectively, but also bind EKC. The remaining site binds only EKC with high affinity. These results, together with displacement data using naloxone, FK33824, and D-ala2-met5-enkephalinamide, are discussed in terms of current opiate receptor models.
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    Capillary operators—II (1985)
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    Bulletin of mathematical biology 47 (1985), S. 651-668 
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    Notes: Abstract This work continues with an examination of capillary exchange models as operators, namely the operatorsO k andK αk relating extravascular and intravascular concentration to input for the Krogh cylinder model of a single capillary, a model basic to many organ models. Fundamental algebraic and analytic properties are presented: the operators belong to a commutative Banach algebra; an addition theorem holdsK αk +K βk =K α+β,k ; the operatorK αk has an inverse;K αk -1 , (as an operator on LebesgueL p space or on the locally integrable functions); partial derivatives are given forK αk [f](t) andO k [f](t) (sensitivity functions); and inequalities are established for the derivatives. Dominance relations between model curves are inferred. Error bound formulas are presented forK andO as bounds on ‖K αk f-K βl f‖ p and ‖O k f-O l f‖ p for allL p . Consequent limitations on relative errors are shown. The implications for operators on a finite time interval are deduced.
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    A theoretical analysis for determining the nonlinear hydraulic permeability of a soft tissue from a permeation experiment (1985)
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    Bulletin of mathematical biology 47 (1985), S. 669-683 
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    Notes: Abstract The nonlinear nature of the hydraulic permeability, as well as the corresponding pressure and displacement fields, in a soft tissue are studied for steady-state permeation. From a two-phase continuum model analytical expressions are derived that can be used with the results from a permeation experiment to determine the dependence of the permeability on the strain. In the process it is found that, because of the compaction of the tissue arising from fluid flow, it is necessary to distinguish between the apparent and intrinsic permeability. The former, which is an averaged quantity, is the permeability usually obtained in permeation studies. However, as shown from the analysis, it can differ substantially from the latter, which is the local permeability in the tissue.
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    Editorial: Software survey section (1985)
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    Bulletin of mathematical biology 47 (1985), S. I 
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    Editor's comments (1985)
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    Bulletin of mathematical biology 47 (1985), S. 695-695 
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    Chaotic phenomena (1985)
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    Bulletin of mathematical biology 47 (1985), S. 697-738 
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    Effects of the torso boundary and internal conductivity interfaces in electrocardiography: An evaluation of the ‘Infinite medium’ approximation (1985)
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    Bulletin of mathematical biology 47 (1985), S. 685-694 
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    Notes: Abstract The analytic, eccentric spheres model of the torso was used to examine the validity of approximating the ‘infinite medium’ potential by integrating ‘finite medium potentials’ over the torso surface. Although idealized, the analytic model is sophisticated enough for all important torso conductivity and geometry parameters to be preserved in the formulation. The model generates both ‘finite medium’ potentials (for which the torso is surrounded by air) and also ‘infinite medium’ potentials (for which the outermost layer of the torso extends outward to infinity). The finite medium torso potentials were integrated over the torso surface in accordance with the approximation used by many investigators in an effort to make the surface distribution more representative of the primary cardiac sources. The resulting potential distribution was compared with the true infinite medium potential, in which the effects of internal inhomogeneities (secondary sources) were taken into account. The difference between the two representations was found to be significant, and caution should be used when interpreting such data.
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    An environ analysis for nonlinear compartment models (1985)
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    Bulletin of mathematical biology 47 (1985), S. 739-748 
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    Notes: Abstract Environ analysis, an input-output analysis for models of ecological systems, has been previously formulated for linear systems. This note has a twofold purpose: first, we indicate that a variation of parameters technique can be applied, at least in principle, to computeboth input and output environs; and second, we show that this technique may be used for computation of environs in nonautonomous, nonlinear compartment models. This nonlinear theory, obtained as a direct extension of dynamical system developments, allows the traditional environ partitioning of compartmental storages and flows. An example of a nonlinear nutrient-producer-consumer system whose output environs can be computed asymptotically is presented to illustrate these concepts.
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    Dependence of tetanic hyperpolarization on pump conductance in the cyanide-treatedXenopus node (1985)
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    Bulletin of mathematical biology 47 (1985), S. 749-755 
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    Notes: Abstract Prolonged exposure to cyanide leads to a delayed but reversible disappearance of tetanic hyperpolarization in theXenopus node (G. M. Schoepfle,Am. J. Physiol. 231, 1033–1038, 1976). This effect is attributed to a pronounced decline in the absolute values of the ATP and ADP concentrations, such that the ATP-driven ion translocation is no longer possible, regardless of the existing values for (Na)i, (K)i and the (ATP)/(ADP) ratio. Mathematically, this would imply a vanishing of a constant pump conductance gp in the exression for electrogenic pump current densitityJ p, whereJ p=g p (V m −E p) in whichV m is membrane potential andE p is an ATP-and sodium-dependent e.m.f.
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    Stress-strain behavior for curved exponential strips (1985)
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    Bulletin of mathematical biology 47 (1985), S. 757-764 
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    Notes: Abstract For the two-parameter (A, α) exponentially-stiffening constituitive relation, typical of many biological materials, it is shown that the uniaxial stress-strain behavior of an initially curved strip is significantly changed by the residual bending stresses. Closedform theoretical results depend on the thickness to radius ratio (h/R) and the relative strain level ε(h/R). The bending stresses tend to obscure accurate measurement ofA and α unless care is taken. However, it is shown that by changing co-ordinates to (dℝ/d∈, ℝ)-space, bothA and α can be recovered from the high stress data, and α alone can be recovered from the low stress data. This has practical application to the mechanics of cornea, sclera, and heart muscle.
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    A mathematical note on the fahraeuslindqvist effect in power law fluid (1985)
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    Bulletin of mathematical biology 47 (1985), S. 765-769 
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    Notes: Abstract An axisymmetric flow of a power law fluid through circular tubes under constant pressure gradient with the flow parameters varying radially is analyzed theoretically. The main finding is that for the Fahraeus-Lindqvist (F-L) effect to occur, it is necessary to have at least one of the parametersK (consistency) andn (index) as a discontinuous function ofr in the absence of wall slip; and with slip condition the parameters could be continuous functions ofr under specific conditions. In both the cases the existence of more than one discontinuity cannot be ruled out. The results obtained are consistent with experimental findings of blood flow through narrow tubes.
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    Zygotic algebra for two linked loci with sexually different recombination rates (1985)
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    Bulletin of mathematical biology 47 (1985), S. 771-782 
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    Notes: Abstract This is a study of the properties of a zygotic algebra of two linked autosomal loci with different recombination rates in males and females, without selection or mutation and with random mating. The above-mentioned zygotic algebra contains a genetic subalgebra. A canonical basis of this subalgebra is constructed and the train roots are calculated.
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    Third International Summer School on Mathematical Modelling in Physiology and Clinical Medicine (1985)
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    Bulletin of mathematical biology 47 (1985), S. 799-799 
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    The possible role of solitonic processes during A to B conformational changes in DNA (1985)
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    Bulletin of mathematical biology 47 (1985), S. 783-789 
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    Notes: Abstract Among the conformations which the DNA molecule can adopt, the transition beween the A and B families, controlled by water content (relative humidity), seems to be implicated in the transcription process. Focusing on the main structural difference involved (tilting of base normals with respect to the helix axis), a model is constructed, solitary wave solutions of the resulting equation of motion are demonstrated and possible experimental implications indicated.
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    On the distribution of the time required to remove white balls from an URN (1985)
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    Bulletin of mathematical biology 47 (1985), S. 791-797 
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    Notes: Abstract Balls are removed one-at-a-time at equal time intervals from an urn initially containingw 0 white balls and a large number b of black balls and each black or white ball is immediately replaced by a black ball. The distribution of the number of white balls remaining aftert iterations (under certain limiting operations) is taken from the literature. The problem is to use this result to find the time required to remove a fixed number of white ballsw 1 from the urn. We then find the mean and variance of this distribution and also look at the special case whenw 1 =w 0.
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    An equation for flow in the renal proximal tubule (1986)
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    Bulletin of mathematical biology 48 (1986), S. 29-57 
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    Notes: Abstract Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.
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    Seventeenth Annual Meeting of the Classification Society of North America (1986)
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    Bulletin of mathematical biology 48 (1986), S. 105-105 
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    Bulletin of mathematical biology 48 (1986), S. I 
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    Dominance of geometric overelastic factors in pulse transmission through arterial branching (1986)
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    Bulletin of mathematical biology 48 (1986), S. 97-103 
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    Notes: Abstract The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.
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    Galerkin's finite element-Laplace transform technique to transient heat migration in human skin and subcutaneous tissues (1986)
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    Bulletin of mathematical biology 48 (1986), S. 125-136 
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    Notes: Abstract Galerkin's finite element-Laplace transform technique (GAFELTTE) has been used to study transient temperature distribution in human skin and subcutaneous tissues. This study incorporates heat conduction, heat carried by perfusion of blood in the capillary beds and metabolic heat generation in the tissues. Different values of various quantities have been considered in all three parts, namely epidermis, dermis and subcutaneous tissues, depending on physiological considerations. The GAFELTTE provides interface temperatures for a wide range of the values of skin surface temperatures. These values have been used to obtain temperature profiles in the region considered. Steady-state temperature distribution has been deduced from the solution obtained by GAFELTTE and has been compared with the results obtained by using different methods.
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    Multiple stable equilibria in a predator-prey system (1986)
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    Bulletin of mathematical biology 48 (1986), S. 137-148 
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    Notes: Abstract Necessary and sufficient conditions are given for three equilibria to occur in a predatorprey model and conditions are given for two of these to be stable. The existence of two stable equilibria requires predator intraspecific competition for either space or food, and the lower the prey growth rate the stronger this predator self-regulation must be. A prey growth rate that is skewed to the right, the ability of a few predators to survive at low prey densities, and predators with high searching effectiveness, long handling times, and large maximum per capita rate of increase all make two stable equilibria more likely.
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    Servocontrol of the heart rate in homeothermic animals: On recognizing butterfly catastrophy models in biology (1986)
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    Bulletin of mathematical biology 48 (1986), S. 107-124 
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    Notes: Abstract Drawing evidence from a variety of cardiovascular studies on the heart rate in homeothermic animals, the author establishes the following thesis. The servocontrol (i.e. the autonomic and reflex control) by the medulla oblongata of the heart (rate) is a negative feedback dynamic which is isomorphic (i.e. ‘diffeomorphic’) to the dyamic underlying the heat rate control in those animals (cf. Kuyk,Bull. math. Biol. 46, 81–102, 1984). In fact, unlike in the heat rate case, the qualitative evidence supporting this thesis can not be fully complemented by quantitative data stemming from experiments, because of a lack of pertinent experiments—which, indeed, should measuresimultaneously the heart rate state parameter and thefour control parameters at the input side of the medulla. The results of some of the existing experiments on animal preparations can nevertheless be adduced to recognize that this dynamic can be graphed by the five-dimensional butterfly catastrophe type. The theory leads to new ways of looking at experiments in the field and/or setting up such experiments in the future.
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    Simulation of cellular compaction and internalization in mammalian embryo development as driven by minimization of surface energy (1986)
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    Bulletin of mathematical biology 48 (1986), S. 167-187 
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    Notes: Abstract A model based upon minimization of surface energy is proposed as an explanation for compaction and internalization of cells during mammalian embryo development. The model is used to simulate and graphically display these phenomena on a computer.
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    Topological properties of binary trees grown with order-dependent branching probabilities (1986)
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    Bulletin of mathematical biology 48 (1986), S. 197-211 
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    Notes: Abstract This paper describes a growth model for binary topological trees. The model defines the branching probability of all segments in the tree. The branching probability of a segment is formulated as a function of two variables, one indicating its type (intermediate or terminal), the other representing its order, i.e. the topological distance to the root segment. The function is determined by two parameters, namely the ratio of branching probabilities of intermediate and terminal segments and the strength of the order dependency, implemented in an exponential form. Expressions are derived for the calculation of symmetry properties of the partitions and it is indicated which part of the parameter domain results in predominantly symmetrical trees.
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    Pattern formation and morphogenesis: A reaction-diffusion model (1986)
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    Bulletin of mathematical biology 48 (1986), S. 213-228 
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    Notes: Abstract The problem of cellular differentiation and consequent pattern generation during embryonic development has been mathematically investigated with the help of a reaction-diffusion model. It is by now a well-recognized fact that diffusion of micromolecules (through intercellular gap junctions), which is dependent on the spatial parameter (r), serve the purpose of ‘positional information’ for differentiation. Based on this principle the present model has been constructed by coupling the Goodwin-type equations for RNA and protein synthesis with the diffusion process. The homogeneous Goodwin system can exhibit stable periodic solution if the value of the cooperativity as measured by the Hill coefficient (ρ) is greater than 8, which is not biologically realistic. In the present work it has been observed that inclusion of a negative cross-diffusion can drive the system into local instability for any value of ρ and thus a time-periodic spatial solution is possible around the unstable local equilibrium, eventually leading to a definite pattern formation. Inclusion of a negative cross-diffusion thus makes the system biologically realistic. The cross-diffusion can also give rise to a stationary wave-like dissipative structure.
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    Editorial: Software survey section (1986)
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    Bulletin of mathematical biology 48 (1986), S. I 
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    SCoP: An interactive simulation control program for micro- and minicomputers (1986)
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    Bulletin of mathematical biology 48 (1986), S. 427-441 
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    Notes: Abstract A nes software system is described for building simulation programs on micro- and minicomputers. Model equations are written as C subroutines, compiled and linked to the SCoP package to produce a menu-driven, interactive program. The system maintains a database of names, values, and units for all model parameters and variables. Run-time options include several methods for interactive parameter modification and both graphic and tabular outputs, with output values presented as they are calculated. Simulation output values can be compared with experimental data graphically and a companion program SCoPFit is provided for formal optimization of parameter values.
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    Global stability of partially closed food-chains with resources (1986)
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    Bulletin of mathematical biology 48 (1986), S. 455-468 
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    Notes: Abstract We consider the existence and global stability of aq-member equilibrium (1≤q≤n) in partially closed food-chains of lengthn having an abiotic component as resource. We observe that such existence demands bounds of resource supply rate and these bounds are weighted sums of interaction coefficients. Particular results of global sector-stability of partially feasible equilibria of simple food-chains obeying Lotka-Volterra dynamics are shown. Lastly the elasticity of such food-chains when a new species is introduced at the highest trophic level is investigated.
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    Global stability in time-delayed single-species dynamics (1986)
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    Bulletin of mathematical biology 48 (1986), S. 485-492 
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    Notes: Abstract Criteria are established for three classes of models of single-species dynamics with a single discrete delay to have a globally asymptotically stable positive equilibrium independent of the length of delay.
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    Predator-prey systems with group defence: The paradox of enrichment revisited (1986)
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    Bulletin of mathematical biology 48 (1986), S. 493-508 
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    Notes: Abstract The main concern of this paper is with survival or extinction of predators in models of predator-prey systems exhibiting group defence of the prey. It is shown that if there is no mutual interference among predators, enrichment could result in their extinction. However, if there is mutual interference, the predator population survives (at least deterministically).
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    A class of general stochastic compartmental systems (1986)
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    Bulletin of mathematical biology 48 (1986), S. 509-523 
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    Notes: Abstract In this paper a general class of semi-Markov compartmental systems is studied. Two models for different input processes are analysed. Attention has been paid to the recurrence times associated with each compartment and to the distribution of the number of particles in each compartment. As an example, a three-compartment system is discussed to study the movement between three health states of patients with chronic diseases.
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    Optimized homology searches of the gene and protein sequence data banks (1986)
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    Bulletin of mathematical biology 48 (1986), S. 569-583 
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    Notes: Abstract A strategy is presented for searching the gene and protein sequence data banks which combines the use of two previously described algorthms. The implementation of this strategy is thoroughly evaluated with respect to sensitivity, specificity and speed. The establishment of standard benchmarks for comparing programs that rearch the sequence data banks for homology is proposed.
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    Receptors and functional linkage in membrane permeability: A quantum mechanical model (1986)
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    Bulletin of mathematical biology 48 (1986), S. 545-567 
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    Notes: Abstract During functional linkage, ligand receptors are coupled to other receptors and to the cell's metabolic-transport apparatus. The linkage guides the cellular processing of matter, energy and information. Previous conceptions of functional linkage have used the ideas of classical physics appropriate to macroscopic objects. This study presents an initial quantum mechanical model of functional linkage in the case of ligands moving through lipid bilayers and hydrophilic transmembrane channels (‘pores’) of molecular dimensions. On the basis of permeability data, energy surfaces consisting of piecewise-constant potential regions are used to model the lipid bilayers and transmembrane channels. The centre-of-mass wavefunction for a ligand on such energy surfaces is analysed and the permeability coefficients calculated from the wavefunction's transmission characteristics. It is found that quasi-bound states in the several ligand-binding regions of a bilayer or pore system can functionally link to facilitate the passage of the molecule across the permeability barrier. Appearance of the linkage is a sensitive function of the ligand's energy. If the centre-of-mass energies are distributed as in a thermalized fluid, the flux via the quantum functional linkage can equal or exceed that of a classical flux for proton transport through rigid pores in which the intrasite barriers are relatively high (0.25–1 eV) and narrow (0.1–1 Å). The functional linkage plays a less important role in bilayer (rather than pore) energy surfaces and at higher molecular weights. If the ligand-receptor interaction is accompanied by energy transfer to or from ligands, the flux via the quantum functional linkage can equal or exceed the classically expected flux at all relevant ligand molecular weights. These findings are discussed in relation to earlier work and the limitations of the model emphasized.
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    A nonlinear measure of subalignment similarity and its significance levels (1986)
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    Bulletin of mathematical biology 48 (1986), S. 617-632 
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    Notes: Abstract A new measure of subalignment similarity is introduced. Specifically, similaritys(l,c) is defined as the logarithm to the basep of the probability of findingc or fewer mismatches in a subalignment of lengthl, wherep is the probability of a match. Previous algorithms can not use this measure to find locally optimal subalignments because, unlike Needleman-Wunsch and Sellers similarities, this measure is nonlinear. A new pattern recognition algorithm is described for finding all locally optimal subalignments of two nucleotide sequences. The DD algorithm can uses(l, c) or any other reasonable similarity function to assess the relative interest of subalignments. The DD algorithm searches only the diagonal graph, which lacks insertions and deletions. This search strategy greatly decreases the computation time and does not require an arbitrary choice of gap cost. The paths of the resulting DD graph usually draw attention to likely locations for insertions and deletions. A heuristic formula is derived for estimating significance levels fors(l, c) in the context of the lengths of the two aligned sequences. The DD algorithm has been used to find interesting subalignments between the nucleotide sequences for human and murine interleukin 2.
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    Entropy balance of white-tailed deer during a winter night (1987)
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    Bulletin of mathematical biology 49 (1987), S. 321-327 
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    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.
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    Book reviews (1987)
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    Bulletin of mathematical biology 49 (1987), S. 507-517 
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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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    The [extended] maximum entropy formalism and the statistical structure of ecosystems (1987)
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    Bulletin of mathematical biology 49 (1987), S. 531-538 
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    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).
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    Theoretical study of a two-dimensional autocatalytic model for calcium dynamics at the extracellular fluid-bone interface (1987)
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    Bulletin of mathematical biology 49 (1987), S. 597-613 
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    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.
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    Linearized oscillations in population dynamics (1987)
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    Bulletin of mathematical biology 49 (1987), S. 615-627 
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    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.
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