Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

Fractional state space analysis of economic systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Proving a market for a startup befor scaling using the hypothesis-driven entrepreneurship process

The year is 2015 and the startup and tech business ecosphere has never seen more activity. In New York City alone, the tech startup industry is on track to amass $8 billion dollars in total funding – the highest in 7 years (CB Insights, 2015). According to the Kauffman Index of Entrepreneurship (2015), this figure represents just 20% of the total funding in the United States. Thanks to platforms that link entrepreneurs with investors, there are simply more funding opportunities than ever, and funding can be initiated in a variety of ways (angel investors, venture capital firms, crowdfunding). And yet, in spite of all this, according to Forbes Magazine (2015), nine of ten startups will fail. Because of the unpredictable nature of the modern tech industry, it is difficult to pinpoint exactly why 90% of startups fail – but the general consensus amongst top tech executives is that “startups make products that no one wants” (Fortune, 2014). In 2011, author Eric Ries wrote a book called The Lean Startup in attempts to solve this all-too-familiar problem. It was in this book where he developed the framework for The Hypothesis-Driven Entrepreneurship Process, an iterative process that aims at proving a market before actually launching a product. Ries discusses concepts such as the Minimum Variable Product, the smallest set of activities necessary to disprove a hypothesis (or business model characteristic). Ries encourages acting briefly and often: if you are to fail, then fail fast. In today’s fast-moving economy, an entrepreneur cannot afford to waste his own time, nor his customer’s time. The purpose of this thesis is to conduct an in-depth of analysis of Hypothesis-Driven Entrepreneurship Process, in order to test market viability of a reallife startup idea, ShowMeAround. This analysis will follow the scientific Lean Startup approach; for the purpose of developing a functional business model and business plan. The objective is to conclude with an investment-ready startup idea, backed by rigorous entrepreneurial study.

Visual data analysis in air traffic management

Visual data mining, multi-dimensional scaling, POLARMAP, Sammon's mapping, clustering, outlier detection

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods

Analysis of susceptibility to human immunodeficiency virus 1 (HIV-1) by comparative genetics

Summary [résumé français voir ci-dessous] From the beginning of the 20th century the world population has been confronted with the human immune deficiency virus 1 (HIV-1). This virus has the particularity to mutate fast, and could thus evade and adapt to the human host. Our closest evolutionary related organisms, the non-human primates, are less susceptible to HIV-1. In a broader sense, primates are differentially susceptible to various retrovirus. Species specificity may be due to genetic differences among primates. In the present study we applied evolutionary and comparative genetic techniques to characterize the evolutionary pattern of host cellular determinants of HIV-1 pathogenesis. The study of the evolution of genes coding for proteins participating to the restriction or pathogenesis of HIV-1 may help understanding the genetic basis of modern human susceptibility to infection. To perform comparative genetics analysis, we constituted a collection of primate DNA and RNA to allow generation of de novo sequence of gene orthologs. More recently, release to the public domain of two new primate complete genomes (bornean orang-utan and common marmoset) in addition of the three previously available genomes (human, chimpanzee and Rhesus monkey) help scaling up the evolutionary and comparative genome analysis. Sequence analysis used phylogenetic and statistical methods for detecting molecular adaptation. We identified different selective pressures acting on host proteins involved in HIV-1 pathogenesis. Proteins with HIV-1 restriction properties in non-human primates were under strong positive selection, in particular in regions of interaction with viral proteins. These regions carried key residues for the antiviral activity. Proteins of the innate immunity presented an evolutionary pattern of conservation (purifying selection) but with signals of relaxed constrain if we compared them to the average profile of purifying selection of the primate genomes. Large scale analysis resulted in patterns of evolutionary pressures according to molecular function, biological process and cellular distribution. The data generated by various analyses served to guide the ancestral reconstruction of TRIM5a a potent antiviral host factor. The resurrected TRIM5a from the common ancestor of Old world monkeys was effective against HIV-1 and the recent resurrected hominoid variants were more effective against other retrovirus. Thus, as the result of trade-offs in the ability to restrict different retrovirus, human might have been exposed to HIV-1 at a time when TRIM5a lacked the appropriate specific restriction activity. The application of evolutionary and comparative genetic tools should be considered for the systematical assessment of host proteins relevant in viral pathogenesis, and to guide biological and functional studies. Résumé La population mondiale est confrontée depuis le début du vingtième siècle au virus de l'immunodéficience humaine 1 (VIH-1). Ce virus a un taux de mutation particulièrement élevé, il peut donc s'évader et s'adapter très efficacement à son hôte. Les organismes évolutivement le plus proches de l'homme les primates nonhumains sont moins susceptibles au VIH-1. De façon générale, les primates répondent différemment aux rétrovirus. Cette spécificité entre espèces doit résider dans les différences génétiques entre primates. Dans cette étude nous avons appliqué des techniques d'évolution et de génétique comparative pour caractériser le modèle évolutif des déterminants cellulaires impliqués dans la pathogenèse du VIH- 1. L'étude de l'évolution des gènes, codant pour des protéines impliquées dans la restriction ou la pathogenèse du VIH-1, aidera à la compréhension des bases génétiques ayant récemment rendu l'homme susceptible. Pour les analyses de génétique comparative, nous avons constitué une collection d'ADN et d'ARN de primates dans le but d'obtenir des nouvelles séquences de gènes orthologues. Récemment deux nouveaux génomes complets ont été publiés (l'orang-outan du Bornéo et Marmoset commun) en plus des trois génomes déjà disponibles (humain, chimpanzé, macaque rhésus). Ceci a permis d'améliorer considérablement l'étendue de l'analyse. Pour détecter l'adaptation moléculaire nous avons analysé les séquences à l'aide de méthodes phylogénétiques et statistiques. Nous avons identifié différentes pressions de sélection agissant sur les protéines impliquées dans la pathogenèse du VIH-1. Des protéines avec des propriétés de restriction du VIH-1 dans les primates non-humains présentent un taux particulièrement haut de remplacement d'acides aminés (sélection positive). En particulier dans les régions d'interaction avec les protéines virales. Ces régions incluent des acides aminés clé pour l'activité de restriction. Les protéines appartenant à l'immunité inné présentent un modèle d'évolution de conservation (sélection purifiante) mais avec des traces de "relaxation" comparé au profil général de sélection purifiante du génome des primates. Une analyse à grande échelle a permis de classifier les modèles de pression évolutive selon leur fonction moléculaire, processus biologique et distribution cellulaire. Les données générées par les différentes analyses ont permis la reconstruction ancestrale de TRIM5a, un puissant facteur antiretroviral. Le TRIM5a ressuscité, correspondant à l'ancêtre commun entre les grands singes et les groupe des catarrhiniens, est efficace contre le VIH-1 moderne. Les TRIM5a ressuscités plus récents, correspondant aux ancêtres des grands singes, sont plus efficaces contre d'autres rétrovirus. Ainsi, trouver un compromis dans la capacité de restreindre différents rétrovirus, l'homme aurait été exposé au VIH-1 à une période où TRIM5a manquait d'activité de restriction spécifique contre celui-ci. L'application de techniques d'évolution et de génétique comparative devraient être considérées pour l'évaluation systématique de protéines impliquées dans la pathogenèse virale, ainsi que pour guider des études biologiques et fonctionnelles

The contributions of rare objects in correspondence analysis

Correspondence analysis, when used to visualize relationships in a table of counts(for example, abundance data in ecology), has been frequently criticized as being too sensitiveto objects (for example, species) that occur with very low frequency or in very few samples. Inthis statistical report we show that this criticism is generally unfounded. We demonstrate this inseveral data sets by calculating the actual contributions of rare objects to the results ofcorrespondence analysis and canonical correspondence analysis, both to the determination ofthe principal axes and to the chi-square distance. It is a fact that rare objects are oftenpositioned as outliers in correspondence analysis maps, which gives the impression that theyare highly influential, but their low weight offsets their distant positions and reduces their effecton the results. An alternative scaling of the correspondence analysis solution, the contributionbiplot, is proposed as a way of mapping the results in order to avoid the problem of outlying andlow contributing rare objects.

Scaled and adjusted restricted tests in multi-sample analysis of moment structures

We extend to score, Wald and difference test statistics the scaled and adjusted corrections to goodness-of-fit test statistics developed in Satorra and Bentler (1988a,b). The theory is framed in the general context of multisample analysis of moment structures, under general conditions on the distribution of observable variables. Computational issues, as well as the relation of the scaled and corrected statistics to the asymptotic robust ones, is discussed. A Monte Carlo study illustrates thecomparative performance in finite samples of corrected score test statistics.

Weighted metric multidimensional scaling

This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods.

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

GPS analysis of human locomotion: further evidence for long-range correlations in stride-to-stride fluctuations of gait parameters.

During free walking, gait is automatically adjusted to provide optimal mechanical output and minimal energy expenditure; gait parameters, such as cadence, fluctuate from one stride to the next around average values. It was described that this fluctuation exhibited long-range correlations and fractal-like patterns. In addition, it was suggested that these long-range correlations disappeared if the participant followed the beep of metronome to regulate his or her pace. Until now, these fractal fluctuations were only observed for stride interval, because no technique existed to adequately analyze an extended time of free walking. The aim of the present study was to measure walking speed (WS), step frequency (SF) and step length (SL) with high accuracy (<1 cm) satellite positioning method (global positioning system or GPS) in order to detect long-range correlations in the stride-to-stride fluctuations. Eight participants walked 30 min under free and constrained (metronome) conditions. Under free walking conditions, DFA (detrended fluctuation analysis) and surrogate data tests showed that the fluctuation of WS, SL and SF exhibited a fractal pattern (i.e., scaling exponent alpha: 0.5 < alpha < 1) in a large majority of participants (7/8). Under constrained conditions (metronome), SF fluctuations became significantly anti-correlated (alpha < 0.5) in all participants. However, the scaling exponent of SL and WS was not modified. We conclude that, when the walking pace is controlled by an auditory signal, the feedback loop between the planned movement (at supraspinal level) and the sensory inputs induces a continual shifting of SF around the mean (persistent anti-correlation), but with no effect on the fluctuation dynamics of the other parameters (SL, WS).

Tying up the loose ends in simple correspondence analysis

Although correspondence analysis is now widely available in statistical software packages and applied in a variety of contexts, notably the social and environmental sciences, there are still some misconceptions about this method as well as unresolved issues which remain controversial to this day. In this paper we hope to settle these matters, namely (i) the way CA measures variance in a two-way table and how to compare variances between tables of different sizes, (ii) the influence, or rather lack of influence, of outliers in the usual CA maps, (iii) the scaling issue and the biplot interpretation of maps,(iv) whether or not to rotate a solution, and (v) statistical significance of results.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.