Kernel discriminant analysis and clustering with parsimonious Gaussian process models

This work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the eigen-decomposition of the Gaussian processes modeling each class. This allows in particular to use non-linear mapping functions which project the observations into infinite dimensional spaces. It is also demonstrated that the building of the classifier can be directly done from the observation space through a kernel function. The proposed classification method is thus able to classify data of various types such as categorical data, functional data or networks. Furthermore, it is possible to classify mixed data by combining different kernels. The methodology is as well extended to the unsupervised classification case. Experimental results on various data sets demonstrate the effectiveness of the proposed method

Simulating and analyzing order book data: The queue-reactive model

Through the analysis of a dataset of ultra high frequency order book updates, we introduce a model which accommodates the empirical properties of the full order book together with the stylized facts of lower frequency financial data. To do so, we split the time interval of interest into periods in which a well chosen reference price, typically the mid price, remains constant. Within these periods, we view the limit order book as a Markov queuing system. Indeed, we assume that the intensities of the order flows only depend on the current state of the order book. We establish the limiting behavior of this model and estimate its parameters from market data. Then, in order to design a relevant model for the whole period of interest, we use a stochastic mechanism that allows for switches from one period of constant reference price to another. Beyond enabling to reproduce accurately the behavior of market data, we show that our framework can be very useful for practitioners, notably as a market simulator or as a tool for the transaction cost analysis of complex trading algorithms

Lifting vector bundles to Witt vector bundles

Let $p$ be a prime, and let $S$ be a scheme of characteristic $p$. Let $n \geq 2$ be an integer. Denote by $\mathbf{W}_n(S)$ the scheme of Witt vectors of length $n$, built out of $S$. The main objective of this paper concerns the question of extending (=lifting) vector bundles on $S$ to vector bundles on $\mathbf{W}_n(S)$. After introducing the formalism of Witt-Frobenius Modules and Witt vector bundles, we study two significant particular cases, for which the answer is positive: that of line bundles, and that of the tautological vector bundle of a projective space. We give several applications of our point of view to classical questions in deformation theory---see the Introduction for details. In particular, we show that the tautological vector bundle of the Grassmannian $Gr_{\mathbb{F}_p}(m,n)$ does not extend to $\mathbf{W}_2(Gr_{\mathbb{F}_p}(m,n))$, if $2 \leq m \leq n-2$. In the Appendix, we give algebraic details on our (new) approach to Witt vectors, using polynomial laws and divided powers. It is, we believe, very convenient to tackle lifting questions.Comment: Enriched version, with an appendi

Point-record incentives, asymmetric information and dynamic data

Les politiques de sécurité routière utilisent souvent des mécanismes incitatifs basés sur les infractions pour améliorer le comportement des conducteurs. Ces mécanismes sont soit monétaires (amendes, primes d'assurance), soit non monétaires (permis à points). Nous utilisons des données québécoises couvrant une période allant de 1983 à 1996 pour analyser l'efficacité incitative de ces mécanismes. Nous analysons leurs propriétés théoriques par rapport au nombre de points associés aux infractions et par rapport au temps contrat. Ces propriétés sont ensuite testées empiriquement. Nous comparons l'efficacité globale des différents mécanismes incitatifs et nous relions les résultats obtenus avec les propriétés de la relation entre l'effort de conduite prudente et le risque d'infractions. Nous concluons à la présence d'aléa moral dans les données. Par ailleurs, la prime indicée sur les points introduite en 1992 a réduit de 15% la fréquence d'infractions.

Mass transfer in bubble column for industrial conditions—effects of organic medium, gas and liquid flowrates and column design

Most of available gas–liquid mass transfer data in bubble column have been obtained in aqueous media and in liquid batch conditions, contrary to industrial chemical reactor conditions. This work provides new data more relevant for industrial conditions, including comparison of water and organic media, effects of large liquid and gas velocities, perforated plates and sparger hole diameter. The usual dynamic O2 methods for mass transfer investigation were not convenient in this work (cyclohexane, liquid circulation). Steadystate mass transfer of CO2 in an absorption–desorption loop has been quantified by IR spectrometry. Using a simple RTD characterization, mass transfer efficiency and kLa have been calculated in a wide range of experimental conditions. Due to large column height and gas velocity, mass transfer efficiency is high, ranging between 40% and 90%. kLa values stand between 0.015 and 0.050 s−1 and depend mainly on superficial gas velocity. No significant effects of column design and media have been shown. At last, using both global and local hydrodynamics data, mass transfer connection with hydrodynamics has been investigated through kLa/G and kLa/a

On the reliability of an optical fibre probe in bubble column under industrial relevant operating conditions

When bubble columns are operated under industrial relevant conditions (high gas and liquid flow rates, large bubbles and vortices,. . .), local data, and especially bubble size values, are difficult to obtain. However, such data are essential for the comprehension of two-phase flow phenomena in order to design or to improve industrial installations. When high gas flow rates and organic liquids are used, intrusive optic probes are considered. This work investigates different ways to derive reliable local information on gas phase from double optic probe raw data. As far as possible, these results have been compared with global data, easier to measure in such conditions. Local gas hold-up, eG, and bubble frequency, fB, are easily obtained, but bubble velocity and bubble diameter determination is not obvious. For a better reliability, the final treatment that is proposed for velocity and size estimation is based on mean values only: the bubble velocity is considered as the most probable velocity ~v issued from raw signals inter-correlation function and the mean Sauter diameter is calculated through dSM ¼ 3~veG 2f B

Application of the double optic probe technique to distorted tumbling bubbles in aqueous or organic liquid

The optic probe technique is widely used to investigate bubble reactors. To derive values of bubble local velocities and bubble local sizes, a specific signal treatment is usually applied under severe assumptions for bubble path and shape. However, in most industrial reactors, bubble motion is chaotic and no common shape can be assumed. In this work, the reliability of the signal treatment associated with the optic probe technique is examined for distorted and tumbling bubbles. A double-tip optic probe is settled in a glass tank and the rise of bubbles is filmed simultaneously. Several trains of bubbles are studied, interactions between bubbles being gradually increased. Referring to image analysis, several ways to derive mean bubble velocities from optic probe data have been compared. Crenels from front tipand rear tipra w signals are associated and individual bubble velocities are derived. Nevertheless, complete velocity distributions are difficult to obtain, as they depend on the choice of the time within which the bubble is searched on the second tip. Using a simpler approach it is shown that the most probable velocity, calculated through the raw signals inter-correlation, is a correct estimation of the average bubble velocity. Concerning bubble size, bubble chord distributions show too high values due to bubble distortion and deviation. A simplified estimation of bubble mean Sauter diameter, using the most reliable measurements only (i.e., local gas hold-up, local mean bubbling frequency, and most probable bubble velocity), was tested for highly distorted bubbles; this method was validated both in water and cyclohexane

Smooth profinite groups, III: the Smoothness Theorem

Let $p$ be a prime. The goal of this article is to prove the Smoothness Theorem 5.1 (Theorem D), which notably asserts that a $(1,\infty)$-cyclotomic pair is $(n,1)$-cyclotomic, for all $n \geq 1$. In the particular case of Galois cohomology, the Smoothness Theorem provides a new proof of the Norm Residue Isomorphism Theorem. Using the formalism of smooth profinite groups, this proof presents it as a consequence of Kummer theory for fields.Comment: Added index for reader's convenience. Comments welcom