Abstract:
I describe the implementation of a two-step algorithm to be used in conjunction with SLINK to enable the simulation of a large number of marker loci linked to a trait locus and conditional on trait values in families, with the possibility for the loci to be in linkage disequilibrium. SLINK is used in the first step to simulate genotypes at the trait locus conditional on the observed trait values, and also to generate an indicator of the descent path of the simulated alleles. In the second step, marker alleles or haplotypes are generated in the founders, conditional on the trait locus genotypes simulated in the first step. Then the recombination process between the marker loci takes place conditionally on the descent path and on the trait locus genotypes. This two-step implementation is often computationally faster than other software that are designed to generate marker data linked to, and possibly associated with, a trait locus.Because the proposed method uses SLINK to simulate the segregation process, it benefits from its flexibility: the trait may be qualitative with the possibility of defining different liability classes (which allows for the simulation of gene-environment interactions or even the simulation of multi-locus effects between unlinked susceptibility regions) or it may be quantitative and normally distributed. In particular, this implementation is the only one available that can generate a large number of marker loci conditional on the set of observed quantitative trait values in pedigrees.In recent literature, algorithms and software were developed to simulate the segregation process of marker loci that are in linkage disequilibrium (LD), some allowing for the possibility for the markers to also be associated with a trait [1-3]. These tools were developed to answer important methodological questions and to help determine empirically the properties of family-based statistical tests, and they should be well received especially now that whole genome as

Abstract:
Les sciences sociales tiennent leur légitimité de leur capacité à produire, éprouver et si possible exporter des catégories. Outils d’analyse des réalités qu’elles prétendent rendre lisibles, ces catégories sont historiquement construites. Elles fournissent aux chercheurs autant de grilles de lecture du monde social. Ces outils peuvent-ils voyager sans perdre de leur pertinence théorique et de leur efficience pratique ? En d’autres termes, ces concepts qui permettent d’appréhender et de saisi...

Abstract:
Dans le préambule d’un rapport rédigé à la fin des années 1880, l’ingénieur ottoman Franghia Bey souligne que les souffrances des habitants de Jérusalem, dont le manque d’eau est la principale cause, ont fait que depuis plus de dix ans, parmi toutes les questions qui intéressent la Ville Sainte, celle de la distribution de l’eau tient sans contredit le premier rang dans la préoccupation de l’opinion publique ; à mesure que les jours s’écoulent le besoin en devient plus pressant, plus impéri...

Abstract:
In the foreword to a report written at the end of the 1880s, the Ottoman engineer Franghia Bey stresses that “the suffering of the inhabitants of Jerusalem, the main cause of which is the lack of water, has made public opinion rank water supply highest among all the issues which involve the Holy City for more than ten years; as the days go by, the need becomes more pressing, more urgent.” From its source in the nearby Gihon which supplied the city at its beginnings, to the distant Golan plate...

Abstract:
The study of the birational properties of algebraic $k$ tori began in the sixties and seventies with work of Voskresenkii, Endo, Miyata, Colliot-Thelene and Sansuc. There was particular interest in determining the rationality of a given algebraic $k$ tori. As rationality problems for algebraic varieties are in general difficult, it is natural to consider relaxed notions such as stable rationality, or even retract rationality. Work of the above authors and later Saltman in the eighties determined necessary and sufficient conditions to determine when an algebraic torus is stably rational, respectively retract rational in terms of the integral representations of its associated character lattice. An interesting question is to ask whether a stably rational algebraic $k$ torus is always rational. In the general case, there exist examples of non-rational stably rational $k$ varieties. Algebraic $k$ tori of dimension $r$ are classified up to isomorphism by conjugacy classes of finite subgroups of GL$_r(\mathbb{Z})$. This makes it natural to example the rationality problem for algebraic $k$ tori of small dimensions. In 1967, Voskresenskii proved that all algebraic tori of dimension 2 are rational. In 1990, Kunyavskii determined which algebraic tori of dimension 3 were rational. In 2012, Hoshi and Yamasaki determined which algebraic toriof dimensions 4 and 5 were stably (respectively retract) rational with the aid of GAP. They did not address the rationality question in dimensions 4 and 5. In this paper, we show that all stably rational algebraic $k$ tori of dimension 4 are rational, with the possible exception of 2 undetermined cases. Hoshi and Yamasaki found 7 retract rational but not stably rational dimension 4 algebraic $k$ tori. We give a non-computational proof of these results.

Abstract:
Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast linear time algorithms. The popular piecewise linear model can determine where the data goes up or down and at what rate. Unfortunately, when the data does not follow a linear model, the computation of the local slope creates overfitting. We propose an adaptive time series model where the polynomial degree of each interval vary (constant, linear and so on). Given a number of regressors, the cost of each interval is its polynomial degree: constant intervals cost 1 regressor, linear intervals cost 2 regressors, and so on. Our goal is to minimize the Euclidean (l_2) error for a given model complexity. Experimentally, we investigate the model where intervals can be either constant or linear. Over synthetic random walks, historical stock market prices, and electrocardiograms, the adaptive model provides a more accurate segmentation than the piecewise linear model without increasing the cross-validation error or the running time, while providing a richer vocabulary to applications. Implementation issues, such as numerical stability and real-world performance, are discussed.

Abstract:
The running maximum-minimum (max-min) filter computes the maxima and minima over running windows of size w. This filter has numerous applications in signal processing and time series analysis. We present an easy-to-implement online algorithm requiring no more than 3 comparisons per element, in the worst case. Comparatively, no algorithm is known to compute the running maximum (or minimum) filter in 1.5 comparisons per element, in the worst case. Our algorithm has reduced latency and memory usage.

Abstract:
Iterated hash functions process strings recursively, one character at a time. At each iteration, they compute a new hash value from the preceding hash value and the next character. We prove that iterated hashing can be pairwise independent, but never 3-wise independent. We show that it can be almost universal over strings much longer than the number of hash values; we bound the maximal string length given the collision probability.

Abstract:
The Dynamic Time Warping (DTW) is a popular similarity measure between time series. The DTW fails to satisfy the triangle inequality and its computation requires quadratic time. Hence, to find closest neighbors quickly, we use bounding techniques. We can avoid most DTW computations with an inexpensive lower bound (LB_Keogh). We compare LB_Keogh with a tighter lower bound (LB_Improved). We find that LB_Improved-based search is faster for sequential search. As an example, our approach is 3 times faster over random-walk and shape time series. We also review some of the mathematical properties of the DTW. We derive a tight triangle inequality for the DTW. We show that the DTW becomes the l_1 distance when time series are separated by a constant.

Abstract:
The Dynamic Time Warping (DTW) is a popular similarity measure between time series. The DTW fails to satisfy the triangle inequality and its computation requires quadratic time. Hence, to find closest neighbors quickly, we use bounding techniques. We can avoid most DTW computations with an inexpensive lower bound (LB Keogh). We compare LB Keogh with a tighter lower bound (LB Improved). We find that LB Improved-based search is faster. As an example, our approach is 2-3 times faster over random-walk and shape time series.