Centre de Recherche en Mathématiques de la Décision

We present here a new method for solving minimization problems in unbounded domains. We first derive a general principle showing the equivalence between the compactness of all minimizing sequences and some strict sub-additivity conditions. The proof is based upon a compactness lemma obtained with the help of the notion of concentration function of a measure. We give various applications to problems arising in Mathematical Physics. Résumé Nous présentons ici une méthode nouvelle de résolution des problèmes de minimisation dans des domaines non bornés. Nous commençons par établir un principe général montrant l’équivalence entre la compacité de toutes les suites minimisantes et certaines conditions de sous-additivité stricte. La démonstration s’appuie sur un lemme de compacité obtenu à l’aide de la notion de fonction de concentration d’une mesure. Nous donnons diverses applications à des problèmes de physique mathématique.

In this paper (sequel of Part 1) we investigate further applications of the concentration-compactness principle to the solution of various minimization problems in unbounded domains. In particular we present here the solution of minimization problems associated with nonlinear field equations. Résumé Dans cette deuxième partie, nous examinons de nouvelles applications du principe de concentration-compacité à la résolution dedivers problèmes de minimization dans des ouverts non bornés. En particulier nous résolvons des problèmes de minimisation associés aux équations de champ non linéaires.

The use of energy-minimizing curves, known as "snakes" to extract features of interest in images has been introduced by Kass, Witkin and Terzopoulos (1987). A balloon model was introduced by Cohen (1991) as a way to generalize and solve some of the problems encountered with the original method. A 3-D generalization of the balloon model as a 3-D deformable surface, which evolves in 3-D images, is presented. It is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential. We also show properties of energy-minimizing surfaces concerning their relationship with 3-D edge points. To solve the minimization problem for a surface, two simplified approaches are shown first, defining a 3-D surface as a series of 2-D planar curves. Then, after comparing finite-element method and finite-difference method in the 2-D problem, we solve the 3-D model using the finite-element method yielding greater stability and faster convergence. This model is applied for segmenting magnetic resonance images.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We present a simple, purely analytic method for proving the convergence of a wide class of approximation schemes to the solution of fully non linear second-order elliptic or parabolic PDE. Roughly speaking, we prove that any monotone, stable and consistent scheme converges to the correct solution provided that there exists a comparison principle for the limiting equation. This method is based on the notion of viscosity solution of Crandall and Lions and it gives completely new results concerning the convergence of numerical schemes for stochastic differential games.

The deviance information criterion (DIC) introduced by Spiegelhalter et al.(2002) for model assessment and model comparison is directly inspired by linear and generalised linear models, but it is open to different possible variations in the setting of missing data models, depending in particular on whether or not the missing variables are treated as parameters. In this paper, we reassess the criterion for such models and compare different DIC constructions, testing the behaviour of these various extensions in the cases of mixtures of distributions and random effect models.

We discuss problems the null hypothesis significance testing (NHST) paradigm poses for replication and more broadly in the biomedical and social sciences as well as how these problems remain unresolved by proposals involving modified p-value thresholds, confidence intervals, and Bayes factors. We then discuss our own proposal, which is to abandon statistical significance. We recommend dropping the NHST paradigm—and the p-value thresholds intrinsic to it—as the default statistical paradigm for research, publication, and discovery in the biomedical and social sciences. Specifically, we propose that the p-value be demoted from its threshold screening role and instead, treated continuously, be considered along with currently subordinate factors (e.g., related prior evidence, plausibility of mechanism, study design and data quality, real world costs and benefits, novelty of finding, and other factors that vary by research domain) as just one among many pieces of evidence. We have no desire to “ban” p-values or other purely statistical measures. Rather, we believe that such measures should not be thresholded and that, thresholded or not, they should not take priority over the currently subordinate factors. We also argue that it seldom makes sense to calibrate evidence as a function of p-values or other purely statistical measures. We offer recommendations for how our proposal can be implemented in the scientific publication process as well as in statistical decision making more broadly.

In this paper, we introduce a notion of barycenter in the Wasserstein space which generalizes McCann's interpolation to the case of more than two measures. We provide existence, uniqueness, characterizations, and regularity of the barycenter and relate it to the multimarginal optimal transport problem considered by Gangbo and Święch in [Comm. Pure Appl. Math., 51 (1998), pp. 23–45]. We also consider some examples and, in particular, rigorously solve the Gaussian case. We finally discuss convexity of functionals in the Wasserstein space.

This paper examines the relationship between wavelet-based image processing algorithms and variational problems. Algorithms are derived as exact or approximate minimizers of variational problems; in particular, we show that wavelet shrinkage can be considered the exact minimizer of the following problem. Given an image F defined on a square I, minimize over all g in the Besov space B(1)(1)(L (1)(I)) the functional |F-g|(L2)(I)(2)+lambda|g|(B(1)(1 )(L(1(I)))). We use the theory of nonlinear wavelet image compression in L(2)(I) to derive accurate error bounds for noise removal through wavelet shrinkage applied to images corrupted with i.i.d., mean zero, Gaussian noise. A new signal-to-noise ratio (SNR), which we claim more accurately reflects the visual perception of noise in images, arises in this derivation. We present extensive computations that support the hypothesis that near-optimal shrinkage parameters can be derived if one knows (or can estimate) only two parameters about an image F: the largest alpha for which FinEpsilon(q)(alpha )(L(q)(I)),1/q=alpha/2+1/2, and the norm |F|B(q)(alpha)(L(q)(I)). Both theoretical and experimental results indicate that our choice of shrinkage parameters yields uniformly better results than Donoho and Johnstone's VisuShrink procedure; an example suggests, however, that Donoho and Johnstone's SureShrink method, which uses a different shrinkage parameter for each dyadic level, achieves a lower error than our procedure.

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 details a general numerical framework to approximate solutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized problem corresponds to a Kullback--Leibler Bregman divergence projection of a vector (representing some initial joint distribution) on the polytope of constraints. We show that for many problems related to optimal transport, the set of linear constraints can be split in an intersection of a few simple constraints, for which the projections can be computed in closed form. This allows us to make use of iterative Bregman projections (when there are only equality constraints) or, more generally, Bregman--Dykstra iterations (when inequality constraints are involved). We illustrate the usefulness of this approach for several variational problems related to optimal transport: barycenters for the optimal transport metric, tomographic reconstruction, multimarginal optimal transport, and in particular its application to Brenier's relaxed solutions of incompressible Euler equations, partial unbalanced optimal transport, and optimal transport with capacity constraints.

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappé et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.

Bifidobacteria, naturally present in the dominant colonic microbiota, represent up to 25% of the cultivable faecal bacteria in adults and 80% in infants. As probiotic agents, bifidobacteria have been studied for their efficacy in the prevention and treatment of a broad spectrum of animal and/or human gastrointestinal disorders, such as colonic transit disorders, intestinal infections, and colonic adenomas and cancer. The aim of this review is to focus on the gastrointestinal effects of bifidobacteria as probiotic agents in animal models and man. The traditional use of bifidobacteria in fermented dairy products and the GRAS ('Generally Recognised As Safe') status of certain strains attest to their safety. Some strains, especially Bifidobacterium animalis strain DN-173 010 which has long been used in fermented dairy products, show high gastrointestinal survival capacity and exhibit probiotic properties in the colon. Bifidobacteria are able to prevent or alleviate infectious diarrhoea through their effects on the immune system and resistance to colonization by pathogens. There is some experimental evidence that certain bifidobacteria may actually protect the host from carcinogenic activity of intestinal flora. Bifidobacteria may exert protective intestinal actions through various mechanisms, and represent promising advances in the fields of prophylaxis and therapy.

Surface wave methods gained in the past decades a primary role in many seismic projects. Specifically, they are often used to retrieve a 1D shear wave velocity model or to estimate the VS,30 at a site. The complexity of the interpretation process and the variety of possible approaches to surface wave analysis make it very hard to set a fixed standard to assure quality and reliability of the results. The present guidelines provide practical information on the acquisition and analysis of surface wave data by giving some basic principles and specific suggestions related to the most common situations. They are primarily targeted to non-expert users approaching surface wave testing, but can be useful to specialists in the field as a general reference. The guidelines are based on the experience gained within the InterPACIFIC project and on the expertise of the participants in acquisition and analysis of surface wave data.

We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion, which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggest a direct transition between the two phases.

Object recognition, robotic vision, occluding noise removal or photograph design require the ability to perform disocclusion. We call disocclusion the recovery of hidden parts of objects in a digital image by interpolation from the vicinity of the occluded area. It is shown in this paper how disocclusion can be performed by means of a level lines structure, which offers a reliable, complete and contrast-invariant representation of an image, in contrast to edges. Level lines based disocclusion yields a solution that may have strong discontinuities, which is not possible with PDE-based interpolation. Moreover, the proposed method is fully compatible with Kanizsa's (1996) theory of "amodal completion".

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.

Uncoupling protein 2 (UCP2) belongs to the mitochondrial anion carrier family and partially uncouples respiration from ATP synthesis when expressed in recombinant yeast mitochondria. We generated a highly sensitive polyclonal antibody against human UCP2. Its reactivity toward mitochondrial proteins was compared between wild type and ucp2(−/−) mice, leading to non-ambiguous identification of UCP2. We detected UCP2 in spleen, lung, stomach, and white adipose tissue. No UCP2 was detected in heart, skeletal muscle, liver, and brown adipose tissue. The level of UCP2 in spleen mitochondria is less than 1% of the level of UCP1 in brown adipose tissue mitochondria. Starvation and LPS treatments increase UCP2 level up to 12 times in lung and stomach, which supports the hypothesis that UCP2 responds to oxidative stress situations. Stimulation of the UCP2 expression occurs without any change in UCP2 mRNA levels. This is explained by translational regulation of the UCP2 mRNA. We have shown that an upstream open reading frame located in exon two of theucp2 gene strongly inhibits the expression of the protein. This further level of regulation of the ucp2 gene provides a mechanism by which expression can be strongly and rapidly induced under stress conditions. Uncoupling protein 2 (UCP2) belongs to the mitochondrial anion carrier family and partially uncouples respiration from ATP synthesis when expressed in recombinant yeast mitochondria. We generated a highly sensitive polyclonal antibody against human UCP2. Its reactivity toward mitochondrial proteins was compared between wild type and ucp2(−/−) mice, leading to non-ambiguous identification of UCP2. We detected UCP2 in spleen, lung, stomach, and white adipose tissue. No UCP2 was detected in heart, skeletal muscle, liver, and brown adipose tissue. The level of UCP2 in spleen mitochondria is less than 1% of the level of UCP1 in brown adipose tissue mitochondria. Starvation and LPS treatments increase UCP2 level up to 12 times in lung and stomach, which supports the hypothesis that UCP2 responds to oxidative stress situations. Stimulation of the UCP2 expression occurs without any change in UCP2 mRNA levels. This is explained by translational regulation of the UCP2 mRNA. We have shown that an upstream open reading frame located in exon two of theucp2 gene strongly inhibits the expression of the protein. This further level of regulation of the ucp2 gene provides a mechanism by which expression can be strongly and rapidly induced under stress conditions. uncoupling protein 1, 2, and 3 brain mitochondrial carrier protein brown adipose tissue gonadal white adipose tissue lipopolysaccharide Fos-choline 12 (N-dodecylphosphocholine) untranslated region open reading frame l-tosylamido-2-phenylethyl chloromethyl ketone 3-(cyclohexylamino)-1-propanesulfonic acid reactive oxygen species phosphate-buffered saline polymerase chain reaction N-hydroxysuccinimide UCP21 belongs to a large family of at least 35 anion carriers that are present in the inner mitochondrial membrane (1El Moualij B. Duyckaerts C. Lamotte-Brasseur J. Sluse F.E. Yeast. 1997; 13: 573-581Crossref PubMed Scopus (93) Google Scholar). Most of these carriers transport key metabolite substrates such as the malate, oxoglutarate, citrate, or products from the oxidative phosphorylation such as ADP3−, ATP4−, or Pi (for review see Ref. 2Kramer R. Palmieri F. Biochim. Biophys. Acta. 1989; 974: 1-23Crossref PubMed Scopus (112) Google Scholar). Since the discovery of ucp2 (3Gimeno R.E. Dembski M. Weng X. Deng N. Shyjan A.W. Gimeno C.J. Iris F. Ellis S.J. Woolf E.A. Tartaglia L.A. Diabetes. 1997; 46: 900-906Crossref PubMed Scopus (0) Google Scholar, 4Fleury C. Neverova M. Collins S. Raimbault S. Champigny O. Levi-Meyrueis C. Bouillaud F. Seldin M.F. Surwit R.S. Ricquier D. Warden C.H. Nat. Genet. 1997; 15: 269-272Crossref PubMed Scopus (1552) Google Scholar) and ucp3 (5Gong D.W. He Y. Karas M. Reitman M. J. Biol. Chem. 1997; 272: 24129-24132Abstract Full Text Full Text PDF PubMed Scopus (738) Google Scholar, 6Vidal-Puig A. Solanes G. Grujic D. Flier J.S. Lowell B.B. Biochem. Biophys. Res. Commun. 1997; 235: 79-82Crossref PubMed Scopus (681) Google Scholar, 7Boss O. Samec S. Paoloni-Giacobino A. Rossier C. Dulloo A. Seydoux J. Muzzin P. Giacobino J.P. FEBS Lett. 1997; 408: 39-42Crossref PubMed Scopus (996) Google Scholar) genes, a subfamily of mitochondrial carriers, related to the well known UCP1 from brown adipose tissue, has emerged in mammals as well as in plants (8Laloi M. Klein M. Riesmeier J.W. Muller-Rober B. Fleury C. Bouillaud F. Ricquier D. Nature. 1997; 389: 135-136Crossref PubMed Scopus (210) Google Scholar). The deduced coding sequence for UCP2 predicts 59% identity with UCP1, whereas the predicted UCP3 sequence is 72% identical to UCP2. The common characteristic of these proteins is to uncouple the respiratory chain from ATP synthesis by dissipating the proton electrochemical gradient when overexpressed in yeast mitochondria (for reviews see Refs. 9Boss O. Hagen T. Lowell B.B. Diabetes. 2000; 49: 143-156Crossref PubMed Scopus (389) Google Scholar and 10Ricquier D. Bouillaud F. Biochem. J. 2000; 345: 161-179Crossref PubMed Scopus (750) Google Scholar). They may also transport anions, like the other mitochondrial carriers, but these substrates are currently unknown. Over the last few years, several physiological roles have been proposed for UCP2, based on the expression of its mRNA upon various physiological conditions (for review see Ref. 11Fleury C. Sanchis D. Int. J. Biochem. Cell Biol. 1999; 31: 1261-1278Crossref PubMed Scopus (83) Google Scholar). Genetic studies suggested the novel UCPs might be linked to hyperinsulinemia (4Fleury C. Neverova M. Collins S. Raimbault S. Champigny O. Levi-Meyrueis C. Bouillaud F. Seldin M.F. Surwit R.S. Ricquier D. Warden C.H. Nat. Genet. 1997; 15: 269-272Crossref PubMed Scopus (1552) Google Scholar) or to the resting metabolic rate (12Bouchard C. Perusse L. Chagnon Y.C. Warden C. Ricquier D. Hum. Mol. Genet. 1997; 6: 1887-1889Crossref PubMed Scopus (229) Google Scholar) and consequently to the control of body weight. It was also proposed that UCP2 contributes to the inflammatory response and regulates the production of reactive oxygen species from mitochondria (13Lee F.Y. Li Y. Zhu H. Yang S. Lin H.Z. Trush M. Diehl A.M. Hepatology. 1999; 29: 677-687Crossref PubMed Scopus (144) Google Scholar, 14Negre-Salvayre A. Hirtz C. Carrera G. Cazenave R. Troly M. Salvayre R. Penicaud L. Casteilla L. FASEB. J. 1997; 11: 809-815Crossref PubMed Scopus (683) Google Scholar). Recently, it has been shown thatucp3(−/−) mice exhibited no consistent phenotypic abnormality, despite a reduced proton leak in muscle mitochondria and a higher level of intracellular ROS in muscle. Moreover, double knockoutucp1-ucp3 phenotype was indistinguishable from the singleucp1(−/−) phenotype (15Gong D.W. Monemdjou S. Gavrilova O. Leon L.R. Marcus-Samuels B. Chou C.J. Everett C. Kozak L.P. Li C. Deng C. Harper M.E. Reitman M.L. J. Biol. Chem. 2000; 275: 24129-24132Google Scholar, 16Vidal-Puig A.J. Grujic D. Zhang C.Y. Hagen T. Boss O. Ido Y. Szczepanik A. Wade J. Mootha V. Cortright R. Muoio D.M. Lowell B.B. J. Biol. Chem. 2000; 275: 16258-16266Abstract Full Text Full Text PDF PubMed Scopus (589) Google Scholar). One of the main problems encountered in the physiological studies of the new UCPs is the absence of reliable immunological tools to detect the proteins in vivo. More than 100 publications have described variation of UCP2 mRNA, whereas only seven analyses were performed at the protein level (for reviews see Refs. 9Boss O. Hagen T. Lowell B.B. Diabetes. 2000; 49: 143-156Crossref PubMed Scopus (389) Google Scholar and 10Ricquier D. Bouillaud F. Biochem. J. 2000; 345: 161-179Crossref PubMed Scopus (750) Google Scholar). In the present study, we have addressed this problem by generating antibodies against the complete human UCP2 sequence, rigorously evaluated their specificity and sensitivity, and compared them with commercial antibodies. Mitochondria were prepared either from ucp2(+/+) or ucp2(−/−) mice that were jointly created by the Ricquier and Collins laboratories (17Arsenijevic D. Onuma H. Pecqueur C. Raimbault S. Manning B.S. Miroux B. Goubern M. Alves-Guerra M. Couplan E. Surwit R. Bouillaud F. Richard D. Collins S. Ricquier D. Nat. Genet. 2000; 26: PubMed Scopus Google Scholar). UCP2 protein was without in spleen, lung, stomach, and gonadal but in other UCP2 protein was in at a level in spleen, lung, stomach, and its expression was strongly upon and LPS in lung and of UCP2 mRNA and protein in that the of UCP2 is strongly by an upstream in the exon two of the and acid and antibodies were from and antibody were from and were from and were from antibody was from and and antibodies were from and antibody from mice were mice were generated on an and (17Arsenijevic D. Onuma H. Pecqueur C. Raimbault S. Manning B.S. Miroux B. Goubern M. Alves-Guerra M. Couplan E. Surwit R. Bouillaud F. Richard D. Collins S. Ricquier D. Nat. Genet. 2000; 26: PubMed Scopus Google Scholar). mice were from and were to of with to or were with 100 of LPS from of of body mice were with the of were at times by of was in and for and the other was for the of mitochondria. The complete UCP2 was by the and and in a by The was by with the of the upstream at and were with the in with 2 and UCP2 was by and and and was of M. B. J. M. J. PubMed Scopus Google a expression related to the family J.W. PubMed Scopus Google Scholar). UCP1, human UCP2 and UCP3 were also a expression of M. a of that in frame with and of the of the UCP1 at was by the and and of UCP2 and UCP3 were by and as and and as They were the and of of UCP2 for was by and and and of expression of expression acid sequence to the of the recombinant and the sequence were on the were from tissue as described D. Bouillaud F. P. G. R. J. Penicaud L. J. Biol. Chem. Full Text PDF PubMed Google Scholar) or from with a of of tissue or of was as described A.M. Bouillaud F. E. Raimbault S. M. Ricquier D. J. Biochem. PubMed Scopus Google Scholar) an and the complete UCP2 as of UCP2 was with a and the was of the membrane with an of UCP2 and the UCP1, human UCP2, and UCP3 were as in the E. and as described B. J. Mol. Biol. PubMed Scopus Google Scholar). were to and in the of acid and the protein was to of or proteins were in and were the last was at and at and at of the at for was with to E. D. Scholar and by on as described B. Casteilla L. S. Raimbault S. S. Ricquier D. Bouillaud F. J. Biol. Chem. Full Text PDF PubMed Google Scholar). The was in with were to the and for UCP2 mRNA and protein were at were in with the 2 and tissue or were in a at and were by of the at for The was at for and the mitochondrial was in of Mitochondria were to of of at and protein was by the acid to the were on a and membrane by for in a and was by the membrane with saline with for at antibodies were in and at The of the antibodies was to the to of the membrane with antibody was at in antibody was with the was for 1, and on were by a and was the from were compared on the of the UCP2 and the UCP1, human UCP2, and UCP3 were as in the E. B. J. Mol. Biol. PubMed Scopus Google Scholar). human UCP2 and acid proteins were on in the of and were two and the with UCP2 antibodies in this The an antibody that we against the UCP1 D. J.P. M. Biochem. J. PubMed Scopus Google toward This antibody detect only of UCP2 The and antibodies a and reactivity toward UCP2. the the antibody was the sensitive toward UCP2 and was times for UCP2 than either UCP1 or and antibodies we against the UCP2, and higher toward UCP2 than the other antibodies and specificity of UCP1, UCP2, and UCP3 in to of protein as antibodies were by was to to in of mitochondrial of protein by antibody of sequence was by the in to of protein as antibodies were by was to to in of mitochondrial of protein by antibody of sequence was by the in a new Since the we was the sensitive antibody and toward human or UCP2, it was to UCP2 in the of UCP2 protein in spleen, stomach, lung, and white adipose tissue this was the detected by the antibody in mitochondria mice we were to detect UCP2 in muscle, heart, liver, and brain mitochondria. other of in liver, and in brain mitochondria The in mitochondria to be UCP1 it in mitochondria from mice shown S. A. C. H. Harper M.E. Kozak L.P. Nature. 1997; PubMed Scopus Google UCP2 in mitochondria from mice theucp2 gene is in these mice shown S. A. C. H. Harper M.E. Kozak L.P. Nature. 1997; PubMed Scopus Google A. A. B. J. J. Biol. Chem. 1999; Full Text Full Text PDF PubMed Scopus Google with and antibodies antibodies proteins than other antibodies in this any in and of them detected other proteins of weight. The antibody strongly toward proteins in and mitochondria 2 The a in spleen, liver, as a in The antibody with a protein in liver, and 2 of these in mitochondria from ucp2(−/−) mice, that these antibodies are to detect UCP2 in vivo. that UCP2 was and times less in lung and stomach, than in spleen mitochondria the of UCP2 protein expressed in we of the of antibody toward shown in of mitochondria the in than of spleen mitochondria. The was times with mitochondria from of the to the that the antibody toward mitochondria than spleen mitochondria Since the detected in to UCP1 and that the antibody was sensitive toward UCP2 than UCP1 we that UCP2 is less in spleen mitochondria than UCP1 is in of UCP2 in of UCP2 of UCP2 was as for UCP2 mRNA and protein levels. are expressed as of was the control 3 2 3 2 3 was as for UCP2 mRNA and protein levels. are expressed as of was the control in a new It has been that and LPS the level of UCP2 mRNA in skeletal muscle and O. Samec S. Dulloo A. Seydoux J. Muzzin P. Giacobino J.P. FEBS Lett. 1997; PubMed Scopus Google Scholar, R. J. A. C. Biochem. Biophys. Res. Commun. PubMed Scopus Google Scholar, H. Yang Lin H.Z. S. G. Diehl A.M. Biochem. Biophys. Res. Commun. PubMed Scopus Google Scholar, S. Sanchis D. B. Ricquier D. FEBS Lett. PubMed Scopus Google Scholar). mice were either with LPS with 100 of LPS or or for and several were for their UCP2 protein of UCP2 in muscle and in spleen but a increase of UCP2 protein was in and lung mitochondria and mice and two mice were and that UCP2 protein LPS only in lung mitochondria and its level 2 UCP2 protein to its expression level and No change in UCP2 protein was in the control mice with and in stomach, liver, heart, muscle, and spleen of of LPS that UCP2 protein in lung mitochondria the increase of UCP2 protein in lung mitochondria an increase of UCP2 protein of an of protein was also in mice LPS and mice were and for their UCP2 in lung mitochondria. UCP2 12 LPS This that LPS the synthesis of UCP2 protein in of UCP2 protein in lung mitochondria LPS Mitochondria from two or mice were prepared and LPS of UCP2 antibody at of of UCP2 protein open of UCP2 in lung mitochondria of was as were prepared from lung of control mice or The UCP2 was as UCP2 was of the membrane with the in the protein with gene were and UCP2 mRNA level was by UCP2 protein level was and times in lung and stomach, than in spleen UCP2 mRNA in were The between UCP2 protein and mRNA was in conditions. The of UCP2 mRNA in lung and upon and UCP2 mRNA also the LPS LPS UCP2 mRNA in spleen and lung were UCP2 protein in lung 12 times to times the level of UCP2 in spleen despite the of UCP2 protein that were in or the level of UCP2 mRNA with the of UCP2 protein. The between the of UCP2 mRNA and the of UCP2 protein detected in mitochondria as well as the between UCP2 mRNA and protein to expression was at the translational We have shown gene a open reading frame in exon 2 which a of C. A.M. Raimbault S. Miroux B. Fleury C. C. Bouillaud F. Ricquier D. Biochem. Biophys. Res. Commun. 1999; PubMed Scopus Google Scholar) the of UCP2 protein was by the in C. A.M. Raimbault S. Miroux B. Fleury C. C. Bouillaud F. Ricquier D. Biochem. Biophys. Res. Commun. 1999; PubMed Scopus Google we its the expression of UCP2 in were with the expression the complete sequence or the the The in were also to the of the recombinant UCP2 mRNA a higher than UCP2 mRNA UCP2 mRNA level was times higher in with than in spleen, the of UCP2 protein was only times higher in mitochondria than in spleen mitochondria and the between and of ucp2 gene is in spleen than in of with or the production of UCP2 protein and in without in UCP2 mRNA In the absence of UCP2 protein in mitochondria up to times the level of UCP2 in spleen the UCP2 mRNA level only times that the present in strongly inhibits the of UCP2 mRNA and supports the of between UCP2 mRNA and protein in of UCP2 expression in recombinant in of UCP2 in mitochondrial of UCP2 was as for UCP2 mRNA and protein levels. are expressed as of was are in 12 12 was as for UCP2 mRNA and protein levels. are expressed as of was are in in a new The region of known mitochondrial carriers was for the of upstream or the human and of them at least upstream or We and also and 3 by FEBS Lett. PubMed Scopus Google Scholar) were to translational of these mitochondrial that are a than a in their and a of by the between and In to their upstream the mitochondrial carriers that upstream at least two of the conditions described that are to translational regulation are expressed in carrier with an upstream were from the were the by A. A. of and was performed sequence of and was performed sequence of between and human C. A.M. Raimbault S. Miroux B. Fleury C. C. Bouillaud F. Ricquier D. Biochem. Biophys. Res. Commun. 1999; PubMed Scopus Google C. A.M. Raimbault S. Miroux B. Fleury C. C. Bouillaud F. Ricquier D. Biochem. Biophys. Res. Commun. 1999; PubMed Scopus Google H. PubMed Scopus Google G. A. Grujic D. Flier J.S. Lowell B.B. J. Biol. Chem. 1997; 272: Full Text Full Text PDF PubMed Scopus Google D. Fleury C. N. Goubern M. Neverova M. F. J. Raimbault S. Levi-Meyrueis C. Miroux B. Collins S. Seldin M. Richard D. Warden C. Bouillaud F. Ricquier D. J. Biol. Chem. Full Text Full Text PDF PubMed Scopus Google was from the human carrier ucp2 and protein 2 and brain mitochondrial carrier Sanchis and D. R. P. Mol. 1989; PubMed Scopus Google R. P. Mol. 1989; PubMed Scopus Google R.S. J. Biol. Chem. Full Text PDF PubMed Google were from the were the by A. A. of and was performed sequence was from the human carrier ucp2 and protein 2 and brain mitochondrial carrier D. Sanchis and D. in a new were to in UCP2 protein. antibodies Yang S. Lin H.Z. J. E. A. C.H. Diehl A.M. J. Biol. Chem. 1999; Full Text Full Text PDF PubMed Scopus Google Scholar, Neverova M. Warden C.H. FASEB. J. PubMed Scopus Google Scholar, S. Zhu H. Li Y. Lin H. Trush Diehl A.M. Biochem. Biophys. 2000; PubMed Scopus Google antibodies against the UCP2 P. M. M. J. E. J. Gimeno R.E. Tartaglia L.A. FEBS Lett. 1999; 79-82Crossref PubMed Scopus Google or antibodies A. Hirtz C. Carrera G. Cazenave R. Troly M. Salvayre R. Penicaud L. Casteilla L. FASEB. J. 1997; 11: 809-815Crossref PubMed Scopus (683) Google Scholar, C. F. R. T. M. Zhang PubMed Scopus Google Scholar, D. P. Carrera G. N. Levi-Meyrueis C. Fleury C. Pecqueur C. M. M. Casteilla L. Ricquier D. Biochem. Biophys. Res. Commun. 1997; 235: PubMed Scopus Google Scholar) were to detect the protein either by or A. C.H. Lin H.Z. Yang F.Y. Diehl A.M. Hepatology. 1999; 29: PubMed Scopus Google Scholar, H. Biochem. Biophys. Res. Commun. PubMed Scopus Google Scholar, P. M. M. M. Penicaud L. Casteilla L. J. FEBS Lett. PubMed Scopus Google Scholar, H. Lin H.Z. Yang S. Diehl A.M. 1999; Full Text Full Text PDF PubMed Scopus Google Scholar). The identification of UCP1, UCP2, or UCP3 was by with the tissue of the mRNA. It was also that with and the the identification of the as UCP1, UCP2, or UCP3 P. M. M. J. E. J. Gimeno R.E. Tartaglia L.A. 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UCP2 protein is times less expressed in mitochondria than in spleen the of UCP2 mRNA in is the increase of UCP2 protein in lung and upon or LPS is by an increase of UCP2 mRNA. of in ucp2 gene times the expression of UCP2 protein in without any at the mRNA of with a and the expression of the UCP2 and of the or the of the upstream also the expression of UCP2 the ucp2 gene is at translational level by an upstream regulation of the ucp2 UCP2 mRNA is highly expressed in spleen, lung, stomach, and but is expressed in the other Since UCP2 protein was only in the its mRNA was highly it is that the tissue specificity of ucp2 gene expression is partially at the whereas the level of UCP2 protein is by translational The mechanism by which UCP2 protein synthesis is exon and the LPS an of UCP2 exon 2 the increase of UCP2 protein in lung it is that of the the at the and only few of them the at the UCP2 It is that UCPs also upstream Since a between mRNA and protein expression has been also suggested for UCP3 by 1999; PubMed Scopus Google be mRNA of UCP2, or S. Samec S. Seydoux J. N. Dulloo FEBS Lett. 1999; PubMed Scopus Google Scholar) and A. A. B. J. J. Biol. Chem. 1999; Full Text Full Text PDF PubMed Scopus Google Scholar) studies on muscle mitochondria and mitochondria from mice, They that ucp2 gene was strongly mitochondrial proton In UCP2 protein in the of the translational regulation of ucp2 it is that UCP2 mRNA the expression of the protein It is that UCP1 is a proton highly expressed in brown adipose tissue mitochondria. In UCP1 protein up to of mitochondrial proteins D. G. Bouillaud F. J. J. FEBS Lett. PubMed Scopus Google and its on its and its by LPS UCP2 protein in lung but only of the mitochondrial that either proteins the or have the UCP2 and UCP3 are by M. M. Gimeno R.E. Dembski M. P. Zhang M. P. Tartaglia L.A. J. Biol. Chem. 1999; Full Text Full Text PDF PubMed Scopus Google Scholar, T. E. M. M. FEBS Lett. 1999; PubMed Scopus Google Scholar, E. M. Fleury C. S. Sanchis D. J. Ricquier D. Goubern M. Bouillaud F. J. 1999; PubMed Scopus Google it is that UCP2 is in whereas UCP1 is by in mitochondria. the other also that the of the new UCPs is to by a mitochondrial A. Hirtz C. Carrera G. Cazenave R. Troly M. Salvayre R. Penicaud L. Casteilla L. FASEB. J. 1997; 11: 809-815Crossref PubMed Scopus (683) Google (13Lee F.Y. Li Y. Zhu H. Yang S. Lin H.Z. Trush M. Diehl A.M. Hepatology. 1999; 29: 677-687Crossref PubMed Scopus (144) Google and Yang S. Zhu H. Li Y. Lin H. Trush Diehl A.M. Biochem. Biophys. 2000; PubMed Scopus Google Scholar) have proposed that UCP2 regulates the production of reactive oxygen species by uncoupling the respiratory as suggested by Biochim. Biophys. Acta. PubMed Scopus Google Scholar). In studies on mice A.J. Grujic D. Zhang C.Y. Hagen T. Boss O. Ido Y. Szczepanik A. Wade J. Mootha V. Cortright R. Muoio D.M. Lowell B.B. J. Biol. Chem. 2000; 275: 16258-16266Abstract Full Text Full Text PDF PubMed Scopus (589) Google Scholar) mice (17Arsenijevic D. Onuma H. Pecqueur C. 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PubMed Scopus Google that UCP2 have any in conditions but is when the level of intracellular reactive oxygen species is In this translational regulation of UCP2 might a based on the large of UCP2 mRNA the lung and the as two UCP2 an Since are to and the of UCP2 might be to the from oxidative by or We are to Onuma for in the ucp2(−/−) L. P. Kozak for the of M. and J. E. for the expression D. Sanchis for the of UCP3 M. and A. for and for reading of the

The Keller-Segel system describes the collective motion of cells which are attracted by a chemical substance and are able to emit it. In its simplest form it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. It is known that, in two space dimensions, for small initial mass, there is global existence of solutions and for large initial mass blow-up occurs. In this paper we complete this picture and give a detailed proof of the existence of weak solutions below the critical mass, above which any solution blows-up in finite time in the whole Euclidean space. Using hypercontractivity methods, we establish regularity results which allow us to prove an inequality relating the free energy and its time derivative. For a solution with sub-critical mass, this allows us to give for large times an “intermediate asymptotics” description of the vanishing. In self-similar coordinates, we actually prove a convergence result to a limiting self-similar solution which is not a simple reflect of the diffusion.

“An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout

MOTIVATION: Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques. RESULTS: We propose a novel approach based on a machine learning tool named random forests (RF) to conduct selection among the highly complex models covered by ABC algorithms. We thus modify the way Bayesian model selection is both understood and operated, in that we rephrase the inferential goal as a classification problem, first predicting the model that best fits the data with RF and postponing the approximation of the posterior probability of the selected model for a second stage also relying on RF. Compared with earlier implementations of ABC model choice, the ABC RF approach offers several potential improvements: (i) it often has a larger discriminative power among the competing models, (ii) it is more robust against the number and choice of statistics summarizing the data, (iii) the computing effort is drastically reduced (with a gain in computation efficiency of at least 50) and (iv) it includes an approximation of the posterior probability of the selected model. The call to RF will undoubtedly extend the range of size of datasets and complexity of models that ABC can handle. We illustrate the power of this novel methodology by analyzing controlled experiments as well as genuine population genetics datasets. AVAILABILITY AND IMPLEMENTATION: The proposed methodology is implemented in the R package abcrf available on the CRAN. CONTACT: jean-michel.marin@umontpellier.fr SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.