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  • 1
    Electronic Resource
    Electronic Resource
    On evolutionarily stable sets (1985)
    Springer
    Journal of mathematical biology 22 (1985), S. 105-115 
    Details
    ISSN: 1432-1416
    Keywords: ESS ; evolution ; game dynamics ; population genetics ; sexual populations ; strategies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract As an extension of the concept of an evolutionarily stable strategy (ESS) evolutionarily stable sets are introduced, i.e. sets of equilibrium strategies (EQS) which have much of the properties of an ESS. They are primarily used with evolutionary game models that allow a continuum of EQSs, none of which can be an ESS, but also include common ESSs as a special case. For a large class even of nonlinear models it can be shown that the standard dynamics converge towards some equilibrium point in an ES set if started within a neighbourhood of the set. Important applications of ES sets include e.g. mixed-strategist models and evolutionary game models in sexual populations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276549
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  • 2
    Electronic Resource
    Electronic Resource
    The species censorship problem: A general solution (1990)
    Springer
    Mathematical geology 22 (1990), S. 95-106 
    Details
    ISSN: 1573-8868
    Keywords: evolution ; extinction ; macroevolution ; probability ; species longevity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The longevities of species constituting a statistical population have an underlying distribution whose form and parametric values reflect probabilities of origination and extinction through time. In the case that a part of the population is extant, the form of distribution and its parameters cannot be estimated directly from the longevity data without bias. Longevities of extant “censored” species are truncated and thus do not statistically represent the underlying distribution. The remaining “uncensored” species do not represent the true relative abundances of longevities. These biases can be defined from the probability densities for species longevitys and intervalr between successive originations of species. For realistic densities ofs andr, species with an intermediate longevity are preferentially censored. This simple, general result arises because the probability of censoring a species increases with its longevity, whereas the probability of censoring a given longevity varies with its relative abundance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00890299
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  • 3
    Electronic Resource
    Electronic Resource
    Inverse methods and kinetic models of hydrocarbon generation: III. Case histories for autoclave product analysis (1991)
    Springer
    Mathematical geology 23 (1991), S. 325-347 
    Details
    ISSN: 1573-8868
    Keywords: hydrocarbons ; kinetics ; inverse methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract From a determination of the transformation matrix for three pyrolysis product experimental data sets, an examination is given of both the applicability of the laboratory experimental data to the modeling of oil cracking in a sedimentary basin, and of the appropriateness of an inverse model. The results of the laboratory experimental data sets, which were done under different thermodynamic conditions and using different sources, show that the transformation matrix varies over each data set and also with time. Therefore, it is necessary to check the data sets before applying them to a basin for hydrocarbon modeling. The laboratory experimental data taken at lower temperature and over longer times appear more pertinent for the construction of an oil-cracking kinetic model suitable for geologic conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02065786
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  • 4
    Electronic Resource
    Electronic Resource
    On the efficiency of Gaussian adaptation (1991)
    Springer
    Journal of optimization theory and applications 71 (1991), S. 589-597 
    Details
    ISSN: 1573-2878
    Keywords: Mathematical programming ; Monte Carlo optimization ; stochastic adaptation ; Gaussian adaptation ; evolution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Gaussian Adaptation (GA) is a stochastic process that adapts a Gaussian distribution to a region or set of feasible points in parameter space. As a result of the adaptation, GA becomes a maximum dispersion process extending the sampling over the largest possible volume in parameter space while keeping the probability of finding feasible points at a suitable level. For such a process, a general measure of efficiency is defined and an efficiency theorem is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00941405
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  • 5
    Electronic Resource
    Electronic Resource
    Controllability of Second-Order Differential Inclusions in Banach Spaces with Nonlocal Conditions (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 559-571 
    Details
    ISSN: 1573-2878
    Keywords: nonlocal conditions ; mild solutions ; evolution ; controllability ; fixed points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we establish sufficient conditions for the controllability ofsecond-order differential inclusions in Banach spaces with nonlocalconditions. We rely on a fixed-point theorem for condensing maps due toMartelli.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026447232030
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  • 6
    Electronic Resource
    Electronic Resource
    Evolutionary games (1985)
    Springer
    Journal of optimization theory and applications 46 (1985), S. 605-612 
    Details
    ISSN: 1573-2878
    Keywords: Game theory ; evolutionarily stable strategies ; evolution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with a mathematical game. As the name implies, the game concept is formulated with biological evolution in mind. An evolutionary game differs from the usual game concepts in that the players cannot choose their strategies. Rather, the strategies used by the players are handed down from generation to generation. It is the survival characteristics of a strategy that determine the outcome of the evolutionary game. Players interact and receive payoffs according to the strategies they are using. These interactions, in turn, determine the fitness of players using a given strategy. The survival characteristics of strategy are determined directly from the fitness functions. Necessary conditions for determining an evolutionarily stable strategy are developed here for a continuous game. Results are illustrated with an example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939163
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