Laboratoire de Mathématiques Blaise Pascal

This paper describes a linear matrix inequality (LMI)-based algorithm for the static and reduced-order output-feedback synthesis problems of nth-order linear time-invariant (LTI) systems with n/sub u/ (respectively, n/sub y/) independent inputs (respectively, outputs). The algorithm is based on a "cone complementarity" formulation of the problem and is guaranteed to produce a stabilizing controller of order m/spl les/n-max(n/sub u/,n/sub y/), matching a generic stabilizability result of Davison and Chatterjee (1971). Extensive numerical experiments indicate that the algorithm finds a controller with order less than or equal to that predicted by Kimura's generic stabilizability result (m/spl les/n-n/sub u/-n/sub y/+1). A similar algorithm can be applied to a variety of control problems, including robust control synthesis.

We present the R package missMDA which performs principal component methods on incomplete data sets, aiming to obtain scores, loadings and graphical representations despite missing values. Package methods include principal component analysis for continuous variables, multiple correspondence analysis for categorical variables, factorial analysis on mixed data for both continuous and categorical variables, and multiple factor analysis for multi-table data. Furthermore, missMDA can be used to perform single imputation to complete data involving continuous, categorical and mixed variables. A multiple imputation method is also available. In the principal component analysis framework, variability across different imputations is represented by confidence areas around the row and column positions on the graphical outputs. This allows assessment of the credibility of results obtained from incomplete data sets.

1. Ordered Fields, Real Closed Fields.- 2. Semi-algebraic Sets.- 3. Real Algebraic Varieties.- 4. Real Algebra.- 5. The Tarski-Seidenberg Principle as a Transfer Tool.- 6. Hilbert's 17th Problem. Quadratic Forms.- 7. Real Spectrum.- 8. Nash Functions.- 9. Stratifications.- 10. Real Places.- 11. Topology of Real Algebraic Varieties.- 12. Algebraic Vector Bundles.- 13. Polynomial or Regular Mappings with Values in Spheres.- 14. Algebraic Models of C? Manifolds.- 15. Witt Rings in Real Algebraic Geometry.- Index of Notation.

Let $\\mu_N$ be the empirical measure associated to a $N$-sample of a given\nprobability distribution $\\mu$ on $\\mathbb{R}^d$. We are interested in the rate\nof convergence of $\\mu_N$ to $\\mu$, when measured in the Wasserstein distance\nof order $p>0$. We provide some satisfying non-asymptotic $L^p$-bounds and\nconcentration inequalities, for any values of $p>0$ and $d\\geq 1$. We extend\nalso the non asymptotic $L^p$-bounds to stationary $\\rho$-mixing sequences,\nMarkov chains, and to some interacting particle systems.\n

The dynamics of linear operators is a young and rapidly evolving branch of functional analysis. In this book, which focuses on hypercyclicity and supercyclicity, the authors assemble the wide body of theory that has received much attention over the last fifteen years and present it for the first time in book form. Selected topics include various kinds of 'existence theorems', the role of connectedness in hypercyclicity, linear dynamics and ergodic theory, frequently hypercyclic and chaotic operators, hypercyclic subspaces, the angle criterion, universality of the Riemann zeta function, and an introduction to operators without non-trivial invariant subspaces. Many original results are included, along with important simplifications of proofs from the existing research literature, making this an invaluable guide for students of the subject. This book will be useful for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.

The theory of hyperbolic groups has its starting point in a fundamental paper by M. Gromov, published in 1987. These are finitely generated groups that share important properties with negatively curve

Abstract Physical activity has been associated with lower risks of breast and colorectal cancer in epidemiological studies; however, it is unknown if these associations are causal or confounded. In two-sample Mendelian randomisation analyses, using summary genetic data from the UK Biobank and GWA consortia, we found that a one standard deviation increment in average acceleration was associated with lower risks of breast cancer (odds ratio [OR]: 0.51, 95% confidence interval [CI]: 0.27 to 0.98, P-value = 0.04) and colorectal cancer (OR: 0.66, 95% CI: 0.48 to 0.90, P-value = 0.01). We found similar magnitude inverse associations for estrogen positive (ER +ve ) breast cancer and for colon cancer. Our results support a potentially causal relationship between higher physical activity levels and lower risks of breast cancer and colorectal cancer. Based on these data, the promotion of physical activity is probably an effective strategy in the primary prevention of these commonly diagnosed cancers.

One of the biggest challenges in non-rigid shape retrieval and comparison is the design of a shape descriptor that would maintain invariance under a wide class of transformations the shape can undergo. Recently, heat kernel signature was introduced as an intrinsic local shape descriptor based on diffusion scale-space analysis. In this paper, we develop a scale-invariant version of the heat kernel descriptor. Our construction is based on a logarithmically sampled scale-space in which shape scaling corresponds, up to a multiplicative constant, to a translation. This translation is undone using the magnitude of the Fourier transform. The proposed scale-invariant local descriptors can be used in the bag-of-features framework for shape retrieval in the presence of transformations such as isometric deformations, missing data, topological noise, and global and local scaling. We get significant performance improvement over state-of-the-art algorithms on recently established non-rigid shape retrieval benchmarks.

UNLABELLED: Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC. AVAILABILITY: The software DIY ABC is freely available at http://www.montpellier.inra.fr/CBGP/diyabc.

This paper is devoted to difference of convex functions (d.c.) optimization: d.c. duality, local and global optimality conditions in d.c. programming, the d.c. algorithm (DCA), and its application to solving the trust-region problem. The DCA is an iterative method that is quite different from well-known related algorithms. Thanks to the particular structure of the trust-region problem, the DCA is very simple (requiring only matrix-vector products) and, in practice, converges to the global solution. The inexpensive implicitly restarted Lanczos method of Sorensen is used to check the optimality of solutions provided by the DCA. When a nonglobal solution is found, a simple numerical procedure is introduced both to find a feasible point having a smaller objective value and to restart the DCA at this point. It is shown that in the nonconvex case, the DCA converges to the global solution of the trust-region problem, using only matrix-vector products and requiring at most 2m+2 restarts, where m is the number of distinct negative eigenvalues of the coefficient matrix that defines the problem. Numerical simulations establish the robustness and efficiency of the DCA compared to standard related methods, especially for large-scale problems.

In this article, we give some mathematical results for an isothermal model of capillary compressible fluids derived by Dunn and Serrin in [1] Anderson, DM, McFadden, GB and Wheeler, GB. 1998. Diffuse interface methods in fluid mechanics. Annual Review of Fluid Mech, 30: 139–165. [Crossref], [Web of Science ®] , [Google Scholar]Dunn JE, Serrin J. On the thermodynamics of interstitial working. Arch Rational Mech Anal. 1985; 88(2):95–133), which can be used as a phase transition model. We consider a periodic domain Ω = T d (d = 2 ou 3) or a strip domain Ω = (0,1) × T d −1. We look at the dependence of the viscosity μ and the capillarity coefficient κwith respect to the density ρ. Depending on the cases we consider, different results are obtained. We prove for instance for a viscosity μ(ρ) = νρ and a surface tension the global existence of weak solutions of the Korteweg system without smallness assumption on the data. This model includes a shallow water model and a lubrication model. We discuss the validity of the result for the shallow water equations since the density is less regular than in the Korteweg case.

Importance sampling methods can be iterated like MCMC algorithms, while being more robust against dependence and starting values. The population Monte Carlo principle consists of iterated generations of importance samples, with importance functions depending on the previously generated importance samples. The advantage over MCMC algorithms is that the scheme is unbiased at any iteration and can thus be stopped at any time, while iterations improve the performances of the importance function, thus leading to an adaptive importance sampling. We illustrate this method on a mixture example with multiscale importance functions. A second example reanalyzes the ion channel model using an importance sampling scheme based on a hidden Markov representation, and compares population Monte Carlo with a corresponding MCMC algorithm.

The use of the symmetries of a physical system in the study of its dynamics has a long history that goes back to the founders of c1assical mechanics. Symmetry-based tech niques are often implemented b

Abstract We develop a framework for the objective selection of a suite of indicators for use in fisheries management. The framework encompasses eight steps, and provides guidance on pitfalls to be avoided at each step. Step 1 identifies user groups and their needs, featuring the setting of operational objectives, and Step 2 identifies a corresponding list of candidate indicators. Step 3 assigns weights to nine screening criteria for the candidate indicators: concreteness, theoretical basis, public awareness, cost, measurement, historic data, sensitivity, responsiveness, and specificity. Step 4 scores the indicators against the criteria, and Step 5 summarizes the results. Steps 3–5 offer technical aspects on which guidance is provided, including scoring standards for criteria and a generalized method for applying the standards when scoring individual indicators. Multi-criterion summarization methods are recommended for most applications. Steps 6 and 7 are concerned with deciding how many indicators are needed, and making the final selection of complementary suites of indicators. Ordinarily, these steps are done interactively with the users of the indicators, thus providing guidance on process rather than technical approach. Step 8 is the clear presentation to all users of the information contained. The discussion also includes the special case in which indicators are used in formal decision rules.

The propagation of acoustic waves in a phononic crystal slab consisting of piezoelectric inclusions placed periodically in an isotropic host material is analyzed. Numerical examples are obtained for a square lattice of quartz cylinders embedded in an epoxy matrix. It is found that several complete band gaps with a variable bandwidth exist for elastic waves of any polarization and incidence. In addition to the filling fraction, it is found that a key parameter for the existence and the width of these complete band gaps is the ratio of the slab thickness, d, to the lattice period, a. Especially, we have explored how these absolute band gaps close up as the parameter d/a increases. Significantly, it is observed that the band gaps of a phononic crystal slab are distinct from those of bulk acoustic waves propagating in the plane of an infinite two-dimensional phononic crystal with the same composition. The band gaps of the slab are strongly affected by the presence of cutoff frequency modes that cannot be excited in infinite media.

This article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain Ω when the control acts on any open and nonempty subset of Ω or on a part of the boundary. In the case of both an internal and a boundary control, the approximate controllability in L P (Ω) for 1 ≦ p < + ∞ is proved when the nonlinearity is globally Lipschitz with a control in L ∞ . In the case of the interior control, we also prove approximate controllability in C 0 (Ω). The proof combines a variational approach to the controllability problem for linear equations and a fixed point method. We also prove that the control can be taken to be of “quasi bang-bang” form.

BACKGROUND: Western Cambodia is the epicentre of Plasmodium falciparum multidrug resistance and is facing high rates of dihydroartemisinin-piperaquine treatment failures. Genetic tools to detect the multidrug-resistant parasites are needed. Artemisinin resistance can be tracked using the K13 molecular marker, but no marker exists for piperaquine resistance. We aimed to identify genetic markers of piperaquine resistance and study their association with dihydroartemisinin-piperaquine treatment failures. METHODS: We obtained blood samples from Cambodian patients infected with P falciparum and treated with dihydroartemisinin-piperaquine. Patients were followed up for 42 days during the years 2009-15. We established in-vitro and ex-vivo susceptibility profiles for a subset using piperaquine survival assays. We determined whole-genome sequences by Illumina paired-reads sequencing, copy number variations by qPCR, RNA concentrations by qRT-PCR, and protein concentrations by immunoblotting. Fisher's exact and non-parametric Wilcoxon rank-sum tests were used to identify significant differences in single-nucleotide polymorphisms or copy number variants, respectively, for differential distribution between piperaquine-resistant and piperaquine-sensitive parasite lines. FINDINGS: Whole-genome exon sequence analysis of 31 culture-adapted parasite lines associated amplification of the plasmepsin 2-plasmepsin 3 gene cluster with in-vitro piperaquine resistance. Ex-vivo piperaquine survival assay profiles of 134 isolates correlated with plasmepsin 2 gene copy number. In 725 patients treated with dihydroartemisinin-piperaquine, multicopy plasmepsin 2 in the sample collected before treatment was associated with an adjusted hazard ratio (aHR) for treatment failure of 20·4 (95% CI 9·1-45·5, p<0·0001). Multicopy plasmepsin 2 predicted dihydroartemisinin-piperaquine failures with 0·94 (95% CI 0·88-0·98) sensitivity and 0·77 (0·74-0·81) specificity. Analysis of samples collected across the country from 2002 to 2015 showed that the geographical and temporal increase of the proportion of multicopy plasmepsin 2 parasites was highly correlated with increasing dihydroartemisinin-piperaquine treatment failure rates (r=0·89 [95% CI 0·77-0·95], p<0·0001, Spearman's coefficient of rank correlation). Dihydroartemisinin-piperaquine efficacy at day 42 fell below 90% when the proportion of multicopy plasmepsin 2 parasites exceeded 22%. INTERPRETATION: Piperaquine resistance in Cambodia is strongly associated with amplification of plasmepsin 2-3, encoding haemoglobin-digesting proteases, regardless of the location. Multicopy plasmepsin 2 constitutes a surrogate molecular marker to track piperaquine resistance. A molecular toolkit combining plasmepsin 2 with K13 and mdr1 monitoring should provide timely information for antimalarial treatment and containment policies. FUNDING: Institut Pasteur in Cambodia, Institut Pasteur Paris, National Institutes of Health, WHO, Agence Nationale de la Recherche, Investissement d'Avenir programme, Laboratoire d'Excellence Integrative "Biology of Emerging Infectious Diseases".

We investigate the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process. Developing a theory that allows for measure–valued trading portfolios, we study existence and uniqueness of a martingale measure. We also study completeness and its relation to the uniqueness of a martingale measure. For the case of a finite jump spectrum we give a fairly general completeness result and for a Wiener–Poisson model we prove the existence of a time–independent set of basic bonds. We also give sufficient conditions for the existence of an affine term structure.

THE SYNTAX OF LINEAR LOGIC The connectives of linear logic Linear logic is not an alternative logic ; it should rather be seen as an extension of usual logic. Since there is no hope to modify the extant classical or intuitionistic connectives, linear logic introduces new connectives. Exponentials : actions vs situations Classical and intuitionistic logics deal with stable truths: if A and A ⇒ B , then B, but A still holds . This is perfect in mathematics, but wrong in real life, since real implication is causal . A causal implication cannot be iterated since the conditions are modified after its use ; this process of modification of the premises (conditions) is known in physics as reaction . For instance, if A is to spend $1 on a pack of cigarettes and B is to get them, you lose $1 in this process, and you cannot do it a second time. The reaction here was that $1 went out of your pocket. The first objection to that view is that there are in mathematics, in real life, cases where reaction does not exist or can be neglected : think of a lemma which is forever true, or of a Mr. Soros, who has almost an infinite amount of dollars. Such cases are situations in the sense of stable truths. Our logical refinements should not prevent us to cope with situations, and there will be a specific kind of connectives ( exponentials , “!” and “?”) which shall express the iterability of an action, i.e. the absence of any reaction ; typically! A means to spend as many dollars as one needs.

This article and the companion paper aim at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since the name was coined in 1995 by merging the words ‘Economics’ and ‘Physics’, this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distribution), microstructure of financial markets (order book modeling), econometrics of financial bubbles and crashes, etc. We discuss the interactions between Physics, Mathematics, Economics and Finance that led to the emergence of Econophysics. We then present empirical studies revealing the statistical properties of financial time series. We begin the presentation with the widely acknowledged ‘stylized facts’, which describe the returns of financial assets—fat tails, volatility clustering, autocorrelation, etc.—and recall that some of these properties are directly linked to the way ‘time’ is taken into account. We continue with the statistical properties observed on order books in financial markets. For the sake of illustrating this review, (nearly) all the stated facts are reproduced using our own high-frequency financial database. Finally, contributions to the study of correlations of assets such as random matrix theory and graph theory are presented. The companion paper will review models in Econophysics from the point of view of agent-based modeling.