An Application of the Subordination Chains

MSC 2010: 30C45, 30A20, 34A30

Impact of normalization on miRNA microarray expression profiling.

Profiling miRNA levels in cells with miRNA microarrays is becoming a widely used technique. Although normalization methods for mRNA gene expression arrays are well established, miRNA array normalization has so far not been investigated in detail. In this study we investigate the impact of normalization on data generated with the Agilent miRNA array platform. We have developed a method to select nonchanging miRNAs (invariants) and use them to compute linear regression normalization coefficients or variance stabilizing normalization (VSN) parameters. We compared the invariants normalization to normalization by scaling, quantile, and VSN with default parameters as well as to no normalization using samples with strong differential expression of miRNAs (heart-brain comparison) and samples where only a few miRNAs are affected (by p53 overexpression in squamous carcinoma cells versus control). All normalization methods performed better than no normalization. Normalization procedures based on the set of invariants and quantile were the most robust over all experimental conditions tested. Our method of invariant selection and normalization is not limited to Agilent miRNA arrays and can be applied to other data sets including those from one color miRNA microarray platforms, focused gene expression arrays, and gene expression analysis using quantitative PCR.

A retrospective study of cholinesterase inhibitors for Alzheimer's disease : the effect of cerebrovascular disease on patient outcomes and the impact of biases on the results.

Introduction: La démence peut être causée par la maladie d’Alzheimer (MA), la maladie cérébrovasculaire (MCEREV), ou une combinaison des deux. Lorsque la maladie cérébrovasculaire est associée à la démence, les chances de survie sont considérées réduites. Il reste à démontrer si le traitement avec des inhibiteurs de la cholinestérase (ChEIs), qui améliore les symptômes cognitifs et la fonction globale chez les patients atteints de la MA, agit aussi sur les formes vasculaires de démence. Objectifs: La présente étude a été conçue pour déterminer si la coexistence d’une MCEREV était associée avec les chances de survie ou la durée de la période jusqu’au placement en hebergement chez les patients atteints de la MA et traités avec des ChEIs. Des études montrant de moins bons résultats chez les patients souffrant de MCEREV que chez ceux n’en souffrant pas pourrait militer contre l’utilisation des ChEIs chez les patients atteints à la fois de la MA et la MCEREV. L'objectif d'une seconde analyse était d'évaluer pour la première fois chez les patients atteints de la MA l'impact potentiel du biais de « temps-immortel » (et de suivi) sur ces résultats (mort ou placement en hebergement). Méthodes: Une étude de cohorte rétrospective a été conduite en utilisant les bases de données de la Régie de l’Assurance Maladie du Québec (RAMQ) pour examiner la durée de la période jusqu’au placement en hebergement ou jusqu’au v décès des patients atteints de la MA, âgés de 66 ans et plus, avec ou sans MCEREV, et traités avec des ChEIs entre le 1er Juillet 2000 et le 30 Juin 2003. Puisque les ChEIs sont uniquement indiquées pour la MA au Canada, chaque prescription de ChEIs a été considérée comme un diagnostic de la MA. La MCEREV concomitante a été identifié sur la base d'un diagnostic à vie d’un accident vasculaire cérébral (AVC) ou d’une endartériectomie, ou d’un diagnostic d'un accident ischémique transitoire au cours des six mois précédant la date d’entrée. Des analyses séparées ont été conduites pour les patients utilisant les ChEIs de façon persistante et pour ceux ayant interrompu la thérapie. Sept modèles de régression à risque proportionnel de Cox qui ont varié par rapport à la définition de la date d’entrée (début du suivi) et à la durée du suivi ont été utilisés pour évaluer l'impact du biais de temps-immortel. Résultats: 4,428 patients ont répondu aux critères d’inclusion pour la MA avec MCEREV; le groupe de patients souffrant seulement de la MA comptait 13,512 individus. Pour le critère d’évaluation composite considérant la durée de la période jusqu’au placement en hebergement ou jusqu’au décès, les taux de survie à 1,000 jours étaient plus faibles parmi les patients atteints de la MA avec MCEREV que parmi ceux atteints seulement de la MA (p<0.01), mais les différences absolues étaient très faibles (84% vs. 86% pour l’utilisation continue de ChEIs ; 77% vs. 78% pour la thérapie avec ChEIs interrompue). Pour les critères d’évaluation secondaires, la période jusqu’au décès était plus courte chez les patients avec la MCEREV que sans la MCEREV, mais la période jusqu’au vi placement en hebergement n’était pas différente entre les deux groupes. Dans l'analyse primaire (non-biaisée), aucune association a été trouvée entre le type de ChEI et la mort ou le placement en maison d'hébergement. Cependant, après l'introduction du biais de temps-immortel, on a observé un fort effet différentiel. Limitations: Les résultats peuvent avoir été affectés par le biais de sélection (classification impropre), par les différences entre les groupes en termes de consommation de tabac et d’indice de masse corporelle (ces informations n’étaient pas disponibles dans les bases de données de la RAMQ) et de durée de la thérapie avec les ChEIs. Conclusions: Les associations entre la coexistence d’une MCEREV et la durée de la période jusqu’au placement en hebergement ou au décès apparaissent peu pertinentes cliniquement parmi les patients atteints de la MA traités avec des ChEIs. L’absence de différence entre les patients atteints de la MA souffrant ou non de la MCEREV suggère que la coexistence d’une MCEREV ne devrait pas être une raison de refuser aux patients atteints de la MA l’accès au traitement avec des ChEIs. Le calcul des « personne-temps » non exposés dans l'analyse élimine les estimations biaisées de l'efficacité des médicaments.

Multiseries Lie groups and asymptotic modules for characterizing and solving integrable models

A multiseries integrable model (MSIM) is defined as a family of compatible flows on an infinite-dimensional Lie group of N-tuples of formal series around N given poles on the Riemann sphere. Broad classes of solutions to a MSIM are characterized through modules over rings of rational functions, called asymptotic modules. Possible ways for constructing asymptotic modules are Riemann-Hilbert and ∂̄ problems. When MSIM's are written in terms of the group coordinates, some of them can be contracted into standard integrable models involving a small number of scalar functions only. Simple contractible MSIM's corresponding to one pole, yield the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. Two-pole contractible MSIM's are exhibited, which lead to a hierarchy of solvable systems of nonlinear differential equations consisting of (2 + 1) -dimensional evolution equations and of quite strong differential constraints. © 1989 American Institute of Physics.

Scalar-bipolar asymptotic modules for solving (2+1)-dimensional nonlinear evolution equations with constraints

An infinite hierarchy of solvable systems of purely differential nonlinear equations is introduced within the framework of asymptotic modules. Eacy system consists of (2+1)-dimensional evolution equations for two complex functions and of quite strong differential constraints. It may be interpreted formally as an integro-differential equation in (1+1) dimensions. © 1988.

Differential pharmacologic properties of the two C75 enantiomers: (+)-C75 is a strong anorectic drug. (-)-C75 has antitumour activity

C75 is a synthetic compound described as having antitumoral properties. It produces hypophagia and weight loss in rodents, limiting its use in cancer therapy but identify- ing it as a potential anti-obesity drug. C75 is a fatty acid synthase (FAS) inhibitor and, through its coenzyme A (CoA) derivative, it acts as a carnitine palmitoyltransferase (CPT) 1 inhibitor. Racemic mixtures of C75 have been used in all the previous studies; however, the potential dif- ferent biological activities of C75 enantiomers have not been examined yet. To address this question we synthesized the two C75 enantiomers separately. Our results showed that ( )- C75 inhibits FAS activity in vitro and has a cytotoxic effect on tumor cell lines, without affecting food consumption. (+)-C75 inhibits CPT1 and its administration produces anorexia, suggesting that central inhibition of CPT1 is essential for the anorectic effect of C75. The differential activity of C75 enantiomers may lead to the development of potential new specific drugs for cancer and obesity.

Differential pharmacologic properties of the two C75 enantiomers: (+)-C75 is a strong anorectic drug. (-)-C75 has antitumour activity

C75 is a synthetic compound described as having antitumoral properties. It produces hypophagia and weight loss in rodents, limiting its use in cancer therapy but identify- ing it as a potential anti-obesity drug. C75 is a fatty acid synthase (FAS) inhibitor and, through its coenzyme A (CoA) derivative, it acts as a carnitine palmitoyltransferase (CPT) 1 inhibitor. Racemic mixtures of C75 have been used in all the previous studies; however, the potential dif- ferent biological activities of C75 enantiomers have not been examined yet. To address this question we synthesized the two C75 enantiomers separately. Our results showed that ( )- C75 inhibits FAS activity in vitro and has a cytotoxic effect on tumor cell lines, without affecting food consumption. (+)-C75 inhibits CPT1 and its administration produces anorexia, suggesting that central inhibition of CPT1 is essential for the anorectic effect of C75. The differential activity of C75 enantiomers may lead to the development of potential new specific drugs for cancer and obesity.

Measurement of the inclusive 3-jet production differential cross section in proton-proton collisions at 7 TeV and determination of the strong coupling constant in the TeV range

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Differential expression of HIF-1 alpha in CD44(+)CD24(-/) (low) breast ductal carcinomas

Background: Cancer stem cell (CSC) hypothesis postulates that tumors are maintained by a self-renewing CSC population that is also capable of differentiating into non-self-renewing cell populations that constitute the bulk of tumor. Stem cells renewal and differentiation can be directly influenced by the oxygen levels of determined tissues, probably by the reduction of oxidative DNA damage in hypoxic regions, thus leading to a friendlier microenvironment, regarding to clonal expansion and for resistance to chemotherapeutic regimens. Furthermore, there have been strong data indicating a pivotal role of hypoxic niche in cancer stem cells development. There are evidence that hypoxia could drive the maintenance of CSC, via HIF-1 alpha expression, but it still to be determined whether hypoxia markers are expressed in breast tumors presenting CD44(+)CD24(-/low) immunophenotype. Methods: Immunohistochemical analysis of CD44(+)CD24(-/low) expression and its relationship with hypoxia markers and clinical outcome were evaluated in 253 samples of breast ductal carcinomas. Double-immunolabeling was performed using EnVision Doublestain System (Dako, Carpinteria, CA, USA). Slides were then scanned into high-resolution images using Aperio ScanScope XT and then, visualized in the software Image Scope (Aperio, Vista, CA, USA). Results: In univariate analysis, CD44(+)CD24(-/low) expression showed association with death due to breast cancer (p = 0.035). Breast tumors expressing CD44(+)CD24(-/low) immunophenotype showed relationship with HIF-1 alpha (p = 0.039) and negativity for HER-2 (p = 0.013). Conclusion: Considering that there are strong evidences that the fraction of a tumour considered to be cancer stem cells is plastic depending upon microenvironmental signals, our findings provide further evidence that hypoxia might be related to the worse prognosis found in CD44(+)CD24(-/low) positive breast tumors.

Differential responses of antioxidant enzymes in pioneer and late-successional tropical tree species grown under sun and shade conditions

To investigate the ability of pioneer and late-successional species to adapt to a strong light environment in a reforestation area, we examined the activities of antioxidant enzymes in relation to photosystem chlorophyll a fluorescence and photosynthetic pigment concentration for eight tropical tree species grown under 100% (sun) and 10% (shade) sunlight irradiation. The pioneer (early-succession) species (PS) were Cecropia pachystachya, Croton urucurana, Croton floribundus and Schinus terebinthifolius. The non-pioneer (late succession) species (LS) were Hymenaea courbaril L var. stilbocarpa, Esenbeckia leiocarpa, Cariniana legalis and Tabebuia roseo-alba. We observed a greater decline in the ratio of variable to maximum chlorophyll a fluorescence (F(v)/F(m)) under full sunlight irradiation in the late-successional species than in the pioneer species. The LS species most sensitive to high irradiance were C. legalis and H. courbaril. In LS species, chlorophyll a, chlorophyll b and total chlorophyll concentrations were higher in the shade-grown plants than in plants that developed under full sunlight, but in the PS species C. floribundus and C. pachystachya, we did not observe significant changes in chlorophyll content when grown in the two contrasting environments. The carotenoids/total chlorophyll ratio increased significantly when plants developed under high-sunlight irradiation, but this response was not observed in the PS species S. terebinthifolius and C. pachystachya. The improved performance of the pioneer species in high sunlight was accompanied by an increase in superoxide dismutase (SOD. EC 1.15.1.1) activity, though no light-dependent increase in the activity of ascorbate peroxidase (APX. EC 1.11.1.11) was observed. The activity of catalase (CAT, EC 1.11.1.6) was reduced by high irradiation in both pioneer and late-successional species. Our results show that pioneer species perform better under high-sunlight irradiation than late-successional species, as indicated by increased SOD activity and a higher F IF,, ratio. C. legalis was the LS species most susceptible to photoinhibition under full sunlight conditions. These results suggest that pioneer plants have more potential tolerance to photo-oxidative damage than late-successional species associated with the higher SOD activity found in pioneer species. Reduced photoinhibition in pioneer species probably results from their higher photosynthetic capacities, as has been observed in a previous survey carried out by our group. (C) 2010 Elsevier B.V. All rights reserved.

Existence results for a damped second order abstract functional differential equation with impulses

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions. (C) 2009 Elsevier Ltd. All rights reserved.

The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.