The purpose of this paper is to introduce sequential investment strategies that guarantee an optimal rate of growth of the capital, under minimal assumptions on the behavior of the market. The new strategies are analyzed both theoretically and empirically. The theoretical results show that the asymptotic rate of growth matches the optimal one that one could achieve with a full knowledge of the statistical properties of the underlying process generating the market, under the only assumption that the market is stationary and ergodic. The empirical results show that the performance of the proposed investment strategies measured on past NYSE and currency exchange data is solid, and sometimes even spectacular.

Summary:In recent years optimal portfolio selection strategies for sequential investment have been shown to exist. Although their asymptotical optimality is well established, finite sample properties do need the adjustment of parameters that depend on dimensionality and scale. In this paper we introduce some nearest neighbor based portfolio selectors that solve these problems, and we show that they are also log-optimal for the very general class of stationary and ergodic random processes. The newly proposed algorithm shows very good finite-horizon performance when applied to different markets with different dimensionality or scales without any change: we see it as a very robust strategy.

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BackgroundBoundaries that prevent cell movement allow groups of cells to maintain their identity and follow independent developmental trajectories without the need for ongoing instructive signals from surrounding tissues. This is the case of vertebrate rhombomeric boundaries. Analysis in the developing chick hindbrain provided the first evidence that rhombomeres are units of cell lineage. The appearance of morphologically visible rhombomeres requires the segment restricted expression of a series of transcription factors, which position the boundaries and prefigure where morphological boundaries will be established. When the boundaries are established, when the cells are committed to a particular rhombomere and how they are organized within the hindbrain are important questions to our understanding of developmental regionalization.Methodology/Principal FindingsSophisticated experimental tools with high-resolution analysis have allowed us to explore cell lineage restriction within the hindbrain in mouse embryos. This novel strategy is based on knock-in alleles of ubiquitous expression and allows unrestricted clonal analysis of cell lineage from the two-cell stage to the adult mouse. Combining this analysis with statistical and mathematical tools we show that there is lineage compartmentalization along the anteroposterior axis from very early stages of mouse embryonic development.ConclusionsOur results show that the compartment border coincides with the morphological boundary in the mouse hindbrain. The restriction of the cells to cross rhombomeric boundaries seen in chick is also observed in mouse. We show that the rhombomeric boundaries themselves are involved in cell movement restriction, although an underlying pre-pattern during early embryonic development might influence the way that cell populations organize.

Common property resource, Concern for resource preservation, Early extinction, Endogenous and exogenous scarcity, Experimental design, C91, C92, H41, D64,

Although the histogram is the most widely used density estimator, it is well{known that the appearance of a constructed histogram for a given bin width can change markedly for di erent c hoices of anchor position. In this paper we construct a stability index G that assesses the potential changes in the appearance of histograms for a given data set and bin width as the anchor position changes. If a particular bin width choice leads to an unstable appearance, the arbitrary choice of any one anchor position is dangerous, and a di erent bin width should be considered. The index is based on the statistical roughness of the histogram estimate. We s h o w via Monte Carlo simulation that densities with more structure are more likely to lead to histograms with unstable appearance. In addition, ignoring the precision to which the data values are provided when choosing the bin width leads to instability. W e p r o vide several real data examples to illustrate the properties of G. Applications to other binned density estimators are also discussed.

We analyze and discuss how a generic software to produce biplot graphs should be designed. We describe a data structure appropriate to include the biplot description and we specify the algorithm(s) to be used for several biplot types. We discuss the options the software should offer to the user in two different environments. In a highly interactive environment the user should be able to specify many graphical options and also to change them using the usual interactive tools. The resulting graph needs to be available in several formats, including high quality format for printing. In a web-based environment, the user submits a data file or listing together with some options specified either in a file or using a form. Then the graphic is sent back to the user in one of several possible formats according to the specifications. We review some of the already available software and we present an implementation based in XLISP-STAT. It can be run under Unix or Windows, and it is also part of a service that provides biplot graphs through the web.