On the most rational algorithm of recognition

The aim of the present paper is to present some applications of the information theory to the problem of the algorithms of recognition. In all these considerations, a qualitative quantitative measure of the information is used to give a generalisation of Landa's algorithm of recognition.     

On the option interpretation of rational harvesting planning

We consider the determination of the harvesting strategy maximizing the present expected value of the cumulative yield from the present up to extinction. By relying on a combination of stochastic calculus, ordinary nonlinear programming, and the classical theory of diffusions, we show that if the underlying population evolves according to a logistic diffusion subject to a general diffusion coefficient, then there is a single threshold density at which harvesting should be initiated in a singular fashion. We derive the condition which uniquely determines the threshold and show that harvesting should be initiated only when the option value of further preserving another individual falls below its opportunity cost. In this way, we present a real option interpretation of rational harvesting planning. We also consider the comparative static properties of the value of the harvesting opportunity and state a set of usually satisfied conditions under which increased stochastic fluctuations (demographic or environmental) decrease the expected cumulative yield from harvesting and increase the optimal harvesting threshold, thus postponing the rational exercise of the irreversible harvesting decision. Received: 19 January 1999 / Revised version: 2 July 1999 / Published online: 16 February 2000     

Regret and the rationality of choices

Regret helps to optimize decision behaviour. It can be defined as a rational emotion. Several recent neurobiological studies have confirmed the interface between emotion and cognition at which regret is located and documented its role in decision behaviour. These data give credibility to the incorporation of regret in decision theory that had been proposed by economists in the 1980s. However, finer distinctions are required in order to get a better grasp of how regret and behaviour influence each other. Regret can be defined as a predictive error signal but this signal does not necessarily transpose into a decision-weight influencing behaviour. Clinical studies on several types of patients show that the processing of an error signal and its influence on subsequent behaviour can be dissociated. We propose a general understanding of how regret and decision-making are connected in terms of regret being modulated by rational antecedents of choice. Regret and the modification of behaviour on its basis will depend on the criteria of rationality involved in decision-making. We indicate current and prospective lines of research in order to refine our views on how regret contributes to optimal decision-making.     

The rationality of prejudices

We model an N-player repeated prisoner's dilemma in which players are given traits (e.g., height, age, wealth) which, we assume, affect their behavior. The relationship between traits and behavior is unknown to other players. We then analyze the performance of "prejudiced" strategies--strategies that draw inferences based on the observation of some or all of these traits, and extrapolate the inferred behavior to other carriers of these traits. Such prejudiced strategies have the advantage of learning rapidly, and hence of being well adapted to rapidly changing conditions that might result, for example, from high migration or birth rates. We find that they perform remarkably well, and even systematically outperform both Tit-For-Tat and ALLD when the population changes rapidly.     

On the two-locus sampling distribution

Two methods are discussed for evaluating the distribution of the configuration of unlabeled gametic types in a random sample of size n from the two-locus infinitely-many-neutral-alleles diffusion model at stationarity. Both involve finding systems of linear equations satisfied by the desired probabilities. The first approach, which is due to Golding, is to include additional probabilities in the system that allow some members of the sample to be specified at only one locus. The second approach, which is new, considers the joint distribution of the sample configuration and the number of recombination events since the time of the most recent common ancestor. The first approach is used for numerical computation, whereas the second approach is used to derive a two-locus version of Hoppe's urn model. The latter permits efficient simulation of the two-locus sampling distribution, provided the recombination parameter is not too large.Supported in part by NSF grants DMS-8704369 and DMS-8902991     

On the geographical distribution of the Juglandaceae

The present paper aims to discuss the geog raphical distribution of the Juglandaceae on the basis of unity of the phylogeny and the process of dispersal in the plants. The paper is divided into the following three parts: 1. The systematic positions and the distribution patterns of nine living genera in the family Juglandaceae (namely, Engelhardia, Oreomunnea, Alfaroa, Pterocarya, Cyclocarya, Juglans, Carya, Annamocarya and Platycarya) are briefly discussed. The evolutional relationships between the different genera of the Juglandaceae are elucidated. The fossil distribution and the geological date of the plant groups are reviewed. Through the analysis for the geographical distribution of the Juglandaceous genera, the distribution patterns may be divided as follows: A. The tropical distribution pattern a. The genera of tropical Asia distribution: Engelhardia, Annamocarya. b. The genera of tropical Central America distribution: Oreomunnea, Alfaroa. B. The temperate distribution pattern c. The genus of disjunct distribution between Western Asia and Eastern Asia: Pterocarya. d. The genus of disjunct distribution between Eurasia and America: Juglans. e. The genus of disjunct distribution between Eastern Asia and North America: Carya. f. The genera whose distribution is confined to Eastern Asia: Cyclocarya, Platycarya. 2. The distribution of species According to Takhtajan’s view point of phytochoria, the number of species in every region are counted. It has shown clearily that the Eastern Asian Region and the Cotinental South-east Asian Region are most abundant in number of genera and species. Of the 71 living species, 53 are regional endemic elements, namely 74.6% of the total species. The author is of the opinion that most endemic species in Eurasia are of old endemic nature and in America of new endimic nature. There are now 7 genera and 28 species in China, whose south-western and central parts are most abundant in species, with Province Yunnan being richest in genera and species. 3. Discussions of the distribution patterns of the Juglandaceae A. The centre of floristic region B. The centre of floristic regions is determined by the following two principles: a. A large number of species concentrate in a district, namely the centre of the majority; b. Species of a district can reflect the main stages of the systematic evolution of the Juglandaceae, namely the centre of diversity. It has shown clearly that the southern part of Eastern Asian region and the northern part of Continental South-east Asian Region (i.c. Southern China and Northern Indo-China) are the main distribution centre of the Juglandaceae, while the southern part of Sonora Region and Caribbean Region (i.c. South-western U.S.A., Mexico and Central America) are the secondary distribution centre. As far as fossil records goes, it has shown that in Tertiary period the Juglandaceae were widely distributed in northern Eurasia and North America, growing not only in Europe and the Caucasus but also as far as in Greenland and Alaska. It may be considered that the Juglandaceae might be originated from Laurasia. According to the analysis of distribution pattern for living primitive genus, for example, Engelhardia, South-western China and Northern Indo-China may be the birthplace of the most primitive Juglandaceous plants. It also can be seen that the primitive genera and the primitive sections of every genus in the Juglandaceae have mostly distributed in the tropics or subtropics. At the same time, according to the analysis of morphological characters, such as naked buds in the primitive taxa of this family, it is considered that this character has relationship with the living conditions of their ancestors. All the evidence seems to show that the Juglandaceae are of forest origin in the tropical mountains having seasonal drying period. B. The time of the origin The geological times of fossil records are analyzed. It is concluded that the origin of the Juglandaceae dates back at least as early as the Cretaceous period. C. The routes of despersal After the emergence of the Juglandaceous plant on earth, it had first developed and dispersed in Southern China and Indo-China. Under conditions of the stable temperature and humidity in North Hemisphere during the period of its origin and development, the Juglandaceous plants had rapidly developed and distributed in Eurasia and dispersed to North America by two routes: Europe-Greenland-North America route and Asia-Bering Land-bridge-North America route. From Central America it later reached South America. D. The formaation of the modern distribution pattern and reasons for this formation. According to the fossil records, the formation of two disjunct areas was not due to the origin of synchronous development, nor to the parallel evolution in the two continents of Eurasia and America, nor can it be interpreted as due to result of transmissive function. The modern distribution pattern has developed as a result of the tectonic movement and of the climatic change after the Tertiary period. Because of the continental drift, the Eurasian Continent was separated from the North American Continent, it had formed a disjunction between Eurasia and North America. Especially, under the glaciation during the Late Tertiary and Quaternary Periods, the continents in Eurasia and North America were covered by ice sheet with the exception of “plant refuges”, most plants in the area were destroyed, but the southern part of Eastern Asia remained practically intact and most of the plants including the Juglandaceae were preserved from destruction by ice and thence became a main centre of survival in the North Hemisphere, likewise, there is another centre of survival in the same latitude in North America and Central America. E. Finally, the probable evolutionary relationships of the genera of the Juglanda-ceae is presented by the dendrogram in the text.     

On a property of the exponential distribution

If t is an independent exponentially distributed random variable, the distribution p = [t - x] is a modified geometric distribution, similar to the result of HAWKINS and KOTZ (1976), x is uniform.     

On the size distribution of live genera

This article deals with the theoretical size (number of species) distribution of live genera, arising from a simple model of macroevolution in which speciations and extinctions are assumed to occur independently and at random, and in which new genera are formed by the random splitting of existing genera. Mathematically, the distribution is that of the state of a homogeneous birth-and-death process after an exponentially distributed time. An ordinary differential equation for the generating function of the distribution is derived and solved and a recurrence relation for computing the probabilities in the distribution presented. Some properties of the distribution, including asymptotic behaviour, are examined and the distribution of the time since establishment of a genus of a given size derived. Fitting the distribution to empirical taxon size distributions by maximum likelihood is discussed and two examples are presented.     

On the statistical distribution of mutant bacteria

A problem in probability is stated with included the problem of the distribution of bacterial mutants as a special case. This problem is solved exactly but since the resulting expressions are too complicated for practical use, various approximate expressions for the distribution are considered, especially for the bacterial mutation case. Research sponsored by the Office of Naval Research while the author was at the California Institute of Technology.     

On the galactosyl distribution of commercial galactomannans

A simple method was developed that enabled the enzymatic determination of the galactose distribution in galactomannans. endo-Mannanase of Aspergillus niger was used to degrade the galactomannan polymers and the degradation products were determined with high-performance anion-exchange chromatography. A whole range of commercial high-to-low substituted galactomannans was analyzed in this way. It was found that differences in the anion-exchange chromatograms reflected dissimilarities in the distribution of galactose and could be used directly to discern these dissimilarities. The differences among the various elution profiles were used to construct a similarity distance tree. In addition to this approach, the absolute amount of non-substituted mannose released by the enzyme was found to be a good discriminating factor. In this way, galactomannans with regular, blockwise, and randomly distributed galactose could be discerned. All guars and the highly substituted gum of Prosopis juliflora were found to have a blockwise distribution of galactose. For different batches of tara gum both random and blockwise distributions were found. Among batches of locust bean gum the greatest variation was observed: both random, blockwise, and ordered galactose distributions were present. Cassia gum was found to have a highly regular distribution of galactose.     

On the distribution of plant abundance data

Plant abundance data are often analysed using standard statistical procedures without considering their distributional features and the underlying ecological processes. However, plant abundance data, e.g. when measured in biodiversity monitoring programs, are often sampled using a hierarchical sampling procedure, and since plant abundance data in a hierarchical sampling procedure are typically both zero-inflated and over-dispersed, the use of a standard statistical procedure is sub-optimal and not the best possible practice in the modelling of plant abundance data. Two distributions (the zero-inflated generalised binomial distribution and the zero-inflated bounded beta distribution) are suggested as possible distributions for analysing either discrete, continuous, or ordinal hierarchically sampled plant cover data.