Darwinian evolution in games with perfect information

We consider a model of Darwinian evolution in games with perfect information like chess or checkers. The evolution is viewed as a sequence of strategies, each of which wins over its immediate predecessor. We argue that the intelligence level of strategies need not necessarily increase during this type of evolution.     

Aggregate statistical measures and metapopulation dynamics

There are two main types of metapopulation models. Spatially implicit models are analytically tractable but neglect spatial heterogeneities. Spatially explicit models are more realistic but too complex. In this paper, I build a bridge between both approximations. I derive a new metapopulation model using a well-known technique in population genetics. Spatial heterogeneities are captured by an aggregate statistical measure of spatial correlation. When this correlation is zero, i.e., space is homogeneous, the model becomes the well-known Levins' model. As spatial correlation increases, equilibrium patch occupancy decreases from what would be expected under the spatially homogeneous assumption. I proceed by testing how well spatial complexities from a spatially explicit simulation can be encapsulated by such an aggregate statistical measure.     

Some statistical aspects of sampling in morphometry

Morphometry requires, in addition to the accurate counting of points, intersections and transections, meticulous attention to sampling. Methods are described and discussed for ensuring that adequate samples are obtained for a given standard error. For all situations in which stratification is used, the importance of increasing the number of the early strata for reducing the variance is emphasized.     

SCOREM: statistical consolidation of redundant expression measures

Many platforms for genome-wide analysis of gene expression contain ‘redundant’ measures for the same gene. For example, the most highly utilized platforms for gene expression microarrays, Affymetrix GeneChip® arrays, have as many as ten or more probe sets for some genes. Occasionally, individual probe sets for the same gene report different trends in expression across experimental conditions, a situation that must be resolved in order to accurately interpret the data. We developed an algorithm, SCOREM, for determining the level of agreement between such probe sets, utilizing a statistical test of concordance, Kendall''s W coefficient of concordance, and a graph-searching algorithm for the identification of concordant probe sets. We also present methods for consolidating concordant groups into a single value for its corresponding gene and for post hoc analysis of discordant groups. By combining statistical consolidation with sequence analysis, SCOREM possesses the unique ability to identify biologically meaningful discordant behaviors, including differing behaviors in alternate RNA isoforms and tissue-specific patterns of expression. When consolidating concordant behaviors, SCOREM outperforms other methods in detecting both differential expression and overrepresented functional categories.     

Determination of diagnostic species with statistical fidelity measures

Abstract. Statistical measures of fidelity, i.e. the concentration of species occurrences in vegetation units, are reviewed and compared. The focus is on measures suitable for categorical data which are based on observed species frequencies within a vegetation unit compared with the frequencies expected under random distribution. Particular attention is paid to Bruelheide's u value. It is shown that its original form, based on binomial distribution, is an asymmetric measure of fidelity of a species to a vegetation unit which tends to assign comparatively high fidelity values to rare species. Here, a hypergeometric form of u is introduced which is a symmetric measure of the joint fidelity of species to a vegetation unit and vice versa. It is also shown that another form of the binomial u value may be defined which measures the asymmetric fidelity of a vegetation unit to a species. These u values are compared with phi coefficient, chi‐square, G statistic and Fisher's exact test. Contrary to the other measures, phi coefficient is independent of the number of relevés in the data set, and like the hypergeometric form of u and the chi‐square it is little affected by the relative size of the vegetation unit. It is therefore particularly useful when comparing species fidelity values among differently sized data sets and vegetation units. However, unlike the other measures it does not measure any statistical significance and may produce unreliable results for small vegetation units and small data sets. The above measures, all based on the comparison of observed/expected frequencies, are compared with the categorical form of the Dufrêne‐Legendre Indicator Value Index, an index strongly underweighting the fidelity of rare species. These fidelity measures are applied to a data set of 15 989 relevés of Czech herbaceous vegetation. In a small subset of this data set which simulates a phytosociological table, we demonstrate that traditional table analysis fails to determine diagnostic species of general validity in different habitats and large areas. On the other hand, we show that fidelity calculations used in conjunction with large data sets can replace expert knowledge in the determination of generally valid diagnostic species. Averaging positive fidelity values for all species within a vegetation unit is a useful approach to measure quality of delimination of the vegetation unit. We propose a new way of ordering species in synoptic species‐by‐relevé tables, using fidelity calculations.     

Some statistical issues in microarray gene expression data

In this paper we discuss some of the statistical issues that should be considered when conducting experiments involving microarray gene expression data. We discuss statistical issues related to preprocessing the data as well as the analysis of the data. Analysis of the data is discussed in three contexts: class comparison, class prediction and class discovery. We also review the methods used in two studies that are using microarray gene expression to assess the effect of exposure to radiofrequency (RF) fields on gene expression. Our intent is to provide a guide for radiation researchers when conducting studies involving microarray gene expression data.     

Information measures: statistical confidence limits and inference

This paper presents tested statistical methods for reducing sampling bias in, for assigning approximate confidence bounds to, and for testing hypotheses about information-theoretic measures used in the study of animal communication and in behavioral sequence analysis. These procedures are also applicable in fields other than animal behavior, including psychology and ecology. Results of a Monte Carlo evaluation of the methods, including comparison of these techniques with possible alternative procedures, are presented.     

Session-to-session variations in external load measures during small-sided games in professional soccer players

The aims of this study were 1) to analyse session-to-session variations in different external load measures and 2) to examine differences in within-session intervals across different small-sided game (SSG) formats in professional players. Twenty professional soccer players (mean ± SD; age 28.1 ± 4.6 years, height 176.7 ± 4.9 cm, body mass 72.0 ± 7.8 kg, and body fat 10.3 ± 3.8%) participated in 3v3, 4v4, and 6v6 SSGs under different conditions (i.e., touch limitations and presence of goalkeepers vs. free touch and ball possession drill) over three sessions. Selected external load measures—including total distance (TD), high-intensity running (HIR, distance covered > 14.4 km^.h^-1), high-speed running (HSR, distance covered > 19.8 km^.h^-1), and mechanical work (MW, accelerations and deceleration > 2.2 m^.s²)—were recorded using GPS technology during all SSG sessions. Small to large standardized typical errors were observed in session-to-session variations of selected measures across SSGs. TD^.min^-1 showed less variability, having a coefficient of variation (CV) of 2.2 to 4.6%, while all other selected external load measures had CV values ranging from 7.2% to 29.4%. Trivial differences were observed between intervals in TD^.min^-1 and HIR^.min^-1 for all SSGs, as well as in HSR^.min^-1 and MW^.min^-1 for most SSG formats. No reductions or incremental trends in session-to-session variations were observed when employing touch limitations or adding goalkeepers. The increased noise observed in higher speed zones (e.g., high-speed running) suggests a need for more controlled, running-based conditional drills if the aim is greater consistency in these measures.     

Some ethical issues arising from polio eradication programmes in India

The World Health Organisation's programme for the eradication of poliomyelitis as currently practised in India raises many ethical issues. In this paper we concentrate on just two. The first is the balance to be struck between the risks and benefits generated by the eradication programme itself. The issue of risks and benefits arises in relation to the choice between two different vaccine types available for polio programmes: oral polio vaccine (OPV) and inactivated polio vaccine (IPV). OPV is the vaccine currently used in the eradication campaign in India. We argue that given the current risks/benefits profile of this vaccine, there is an urgent need to review the programme and take remedial action to address existing problems (at least in India). The second issue we discuss is the fact that there is little effort to gain the informed consent of the parents of vaccinated children, as they are not currently told about the potential limitations of OPV or the possibility of vaccine-induced harm. We suggest that such a policy might be justifiable, given the importance of polio eradication, but only if there is a system of compensation for vaccine-induced harm as part of the eradication programme itself. There is a real danger that if these issues are not addressed then public trust in the eradication programme and vaccination programmes as a whole will be lost.     

Some statistical considerations in the determination of thresholds in ELISA

The presentation of quantitative results from ELISAs is very variable, and, in particular, the positive-negative threshold or critical value is poorly defined. A simple statistical model is presented which demonstrates how this value may be determined. Depending on what assumptions are made it is possible to estimate the necessary parameters in several different ways. These methods generally form a hierarchy, and greater precision can be achieved by combining variances from several plates. More problematical is the determination of the negative control, and indeed its definition. The results of a series of ELISAs taken from a study of polyphagous predators of the cereal aphid S. avenae are used to illustrate the methods. The ELISAs were done over a period of three months using 86 plates. Recommendations are made for the numbers and levels of controls to be used in future studies.     

Unscheduled DNA synthesis: Some statistical thoughts

Statistical interpretation of results of experiments involving unscheduled DNA synthesis is examined from a design standpoint. Most appropriate methods currently in use are evaluated and some modifications and extensions are suggested. Concerns about replication and/or interaction errors are evaluated and methods for their appropriate handling are discussed. It is suggested that methods incorporating both dose-response and heterogeneity statistics should be considered in treating results from unscheduled DNA synthesis experiments. Proper designs for such experiments are emphasized.Abbreviations ANOVA analysis of variance - MSE mean square error - UDS unscheduled DNA synthesis     

Some statistical properties of the miniature endplate potentials

I will demonstrate that series of miniature endplate potentials (m.e.p.ps) showing a high proportion of so-called giant m.e.p.ps (g.m.e.p.ps) have different statistical structures from series where the proportion of g.m.e.p.ps is low. The nature of the different structures will be discussed on the basis of two statistical models, one for the distribution of the m.e.p.p. amplitudes and one for the series of point events occurring in time.     

Some statistical properties of an index of multiple traits

Summary Hazel (1943) defined a selection index that maximizes the correlation, R_IH, between the index, I=b_iX_i and its aggregate genetic value, H=a_ig_i, where the b_i's are the derived coefficients of the observed traits, X_i, the a_i's are their relative economic values and the g_i's are their respective breeding values. This is called an optimum index. The expected value of the index is not H but rather K=b_ig_i. The ratio of R_HI/R_KI is always less than or equal to 1.0. With selection on I, the ratio of the change in K to the change in H is the true heritability of the indez, that is, h _I ² =(K)/H. This is not the same as R _IH ² , which serves only as the predictor of the change in H with selection on I. If the index, I, itself is considered as a unit trait, studies can then be made of correlated response in I when selection is based only on a single trait in the index. I is then called a performance index. This approach provides for additional insight into the question of the failure of selection to make gains in total performance over many generations.Journal Paper No. J-8176 of the Iowa Agriculture and Home Economics Experiment Station, Project 1711. Editor's Note: This paper and one closely similar (Lin and Allaire T.A.G. 51, 1–3 (1977) were independently derived and reviewed by different corresponding editors. The earlier paper, however, lacks numerical examples and a possible application as discussed in the present paper.     

Statistical measures for defining an individual's degree of independence within state-dependent dynamic games

Background  

For organisms living or interacting in groups, the decision-making processes of an individual may be based upon aspects of both its own state and the states of other organisms around it. Much research has sought to determine how group decisions are made, and whether some individuals are more likely to influence these decisions than others. State-dependent modelling techniques are a powerful tool for exploring group decision-making processes, but analyses conducted so far have lacked methods for identifying how dependent an individual's actions are on the rest of the group.     

Some fundamental aspects of information dynamics

Zusammenfassung Mechanisierte Sprachübersetzung, Speichern von Information und Mustererkennung stellen drei Sonderfälle der allgemeinen Operationen Lernen, Ordnen und Erkennen dar. Die Automatisierung solcher Operationen bildet nicht nur ein an und für sich interessantes Problem, sondern eine dringliche Notwendigkeit, sollen die universellen Gro Brechenanlagen nicht an der Komplexität ihrer inneren Organisation (soft-ware) ersticken. Als vielleicht einfachstes dieser drei — im Grunde nie getrennt auftretenden — Vorgänge, wird das Problem der Wiedererkennung betrachtet, d.h. dasjenige der Abbildung eines kontinuierlichen Ensembles reeller, metrischer Objekte auf eine endliche, diskrete Struktur ohne Metrik, wie sie beispielsweise das Innere einer digitalen Rechenanlage darstellt. Der notwendige Übergang vom heute einzig üblichen Speicher zum eigentlichen Gedächtnis hängt unter anderem von der Lösung dieses Problems ab. Seine Untersuchung hebt die grundsätzliche Bedeutung der Umgebung einzelner Objekte — ihres Kontextes — hervor, welche Umgebung im diskreten Raum das notwendige Äquivalent zum Kontinuum darstellt. Dies führt zu einer neuen Betrachtung des Paradoxon von Brillouin, und zur notwendigen Benützung dynamischer Methoden bei der Verarbeitung von Information, anders gesagt bei ihrer Überführung aus der bildhaft-kontinuierlichen Form in die diskrete, und zurück. Womit zumindest eine mögliche Definition nicht-trivialer Informationsverarbeitung gegeben ist.