PhD Nour Baïz
email: baiz@u707.jussieu.fr

PhD Patricia Dargent-Molina

PhD John D Wark

PhD Jean-Claude Souberbielle

MD, DSc Isabella Annesi-Maesano

Eden Mother

Cord serum 25-hydroxyvitamin D and risk of early childhood transient wheezing and atopic dermatitis

Keywords: Vitamin D, 25-hydroxyvitamin D, Cord blood, Allergic diseases, Wheezing, Atopic dermatitis, Mother-child cohort Abbreviations: 25(OH)D, 25-hydroxyvitamin D, EDEN, Etude des Déterminants

Background: There is increasing evidence of the effect of maternal vitamin D intake during pregnancy on the risk of asthma and allergic outcomes in the offspring. However, studies on the relationship between cord levels of 25-hydroxyvitamin D (25[OH]D) and asthma and allergic diseases are very few.

Objective: Our aim was to investigate the associations between cord serum 25(OH)D levels and asthma, wheezing, allergic rhinitis and atopic dermatitis in the offspring from birth to 5 years.

Methods

: Cord blood samples were collected at birth and were analyzed for levels of 25(OH)D in 239 newborns from the EDEN birth cohort. The children were followed up until age 5 years by symptom ISAAC-based questionnaires (International Study of Asthma and Allergies in Childhood).

Results:

The median cord serum level of 25(OH)D was 17.8 ng/mL (interquartile range: 15.1 ng/mL). Using multivariable-adjusted logistic regression models, a significant inverse association was observed between cord serum 25(OH)D and risk of transient early wheezing and early and late-onset atopic dermatitis, as well as atopic dermatitis by the age of 1, 2, 3 and 5. We found no association between cord serum 25(OH)D levels and asthma and allergic rhinitis at 5 years of age.

Conclusions

: Cord serum 25(OH)D level was inversely associated with the risk of transient early wheezing and atopic dermatitis by the age of 5 years, but no association was found with asthma and allergic rhinitis. Clinical implications: The risk of transient wheezing and atopic dermatitis in childhood is inversely associated with cord 25(OH)D levels. Interventions to increase vitamin D levels in utero and in early life are potential public health interventions to reduce transient wheezing and atopic dermatitis in young children.

Capsule summary:

Although research is required to establish the optimal level, timing and route of exposure, recommendations for adequate vitamin D intake in pregnant women may prevent transient early childhood wheezing and atopic dermatitis.

Introduction

Over the last decade, the prevalence of allergies and asthma in childhood has increased worldwide, particularly in westernized societies. There is increasing evidence that fetal life and early life exposures, along with associated epigenetic changes [START_REF] Bollati | Environmental epigenetics[END_REF], are important determinants of the future development of asthma and allergies throughout life [START_REF] Gillman | Developmental origins of health and disease[END_REF]. Among other environmental factors, prenatal and early life dietary exposures, including vitamin D, have been suggested to play an important role in the development of allergies and asthma in childhood [START_REF] Robison | The effect of prenatal and postnatal dietary exposures on childhood development of atopic disease[END_REF].

Vitamin D deficiency, defined as a circulating level of < 20 ng/mL of 25hydroxyvitamin D (25(OH)D), has become a public health issue [START_REF] Holick | Vitamin D deficiency[END_REF]. It has been largely attributed to dietary, lifestyle and behavioral changes during recent decades [START_REF] Holick | Vitamin D deficiency[END_REF], especially in Western countries. Children as well as pregnant and lactating women are identified as groups vulnerable to vitamin D deficiency [START_REF] Mulligan | Implications of vitamin D deficiency in pregnancy and lactation[END_REF].

While the relationship of vitamin D deficiency and rickets is well established [START_REF] Thandrayen | Maternal vitamin D status: implications for the development of infantile nutritional rickets[END_REF], and its association with a wide variety of medical conditions including microbial infections [START_REF] Ginde | Association between serum 25hydroxyvitamin D level and upper respiratory tract infection in the Third National Health and Nutrition Examination Survey[END_REF], cardiovascular diseases [START_REF] Kim | Prevalence of hypovitaminosis D in cardiovascular diseases (from the National Health and Nutrition Examination Survey 2001 to 2004)[END_REF], cancers [START_REF] Trump | Vitamin D: considerations in the continued development as an agent for cancer prevention and therapy[END_REF], autoimmune diseases [START_REF] Kinder | Could combating vitamin D deficiency reduce the incidence of autoimmune disease?[END_REF] and diabetes [START_REF] Ozfirat | Vitamin D deficiency and type 2 diabetes[END_REF] is well documented, only more recently has the role of vitamin D deficiency and insufficiency in asthma [START_REF] Lange | Vitamin D, the immune system and asthma[END_REF][START_REF] Mak | Vitamin D and asthma[END_REF][START_REF] Brehm | Serum vitamin D levels and severe asthma exacerbations in the Childhood Asthma Management Program study[END_REF] and allergic diseases [START_REF] Annesi-Maesano | Perinatal events, vitamin D, and the development of allergy[END_REF] beginning in infancy or childhood [START_REF] Camargo | Cord-blood 25-hydroxyvitamin D levels and risk of respiratory infection, wheezing, and asthma[END_REF][START_REF] Bozzetto | Asthma, allergy and respiratory infections: the vitamin D hypothesis[END_REF][START_REF] Miyake | Dairy food, calcium and vitamin D intake in pregnancy, and wheeze and eczema in infants[END_REF] been debated. In the last couple of decades in the twentieth century and early in the twenty-first century, the vitamin D receptor has been found in a variety of cells, including keratinocytes and numerous cells of the immune system (e.g., dendritic cells, natural killer cells) [START_REF] Rudzki | Frequency and significance of the major and minor features of Hanifin and Rajka among patients with atopic dermatitis[END_REF].

Several lines of evidence demonstrate the effects of vitamin D on pro-inflammatory cytokines, regulatory T cells, and immune responses [START_REF] Hewison | An update on vitamin D and human immunity[END_REF].

Vitamin D is found naturally in very few dietary sources, the only really significant being fatty fish [START_REF] Brown | Vitamin D[END_REF] and vitamin D-fortified foods. The latter are scarce in France. The main source of vitamin D in humans is synthesis from 7-dehydrocholesterol in the skin upon exposure to ultraviolet B solar radiation and conversion to a readily-measurable circulating metabolite, 25-hydroxyvitamin D (25(OH)D) in the liver [START_REF] Brown | Vitamin D[END_REF]. Circulating 25(OH)D is the best index of vitamin D nutritional status [START_REF] Brown | Vitamin D[END_REF]. Low intake of vitamin D and inadequate exposure to sunlight constitute the main causes of vitamin D deficiency. A number of factors may influence the cutaneous synthesis and dietary sources of vitamin D [START_REF] Tsiaras | Factors influencing vitamin D status[END_REF], especially in pregnant women [START_REF] Dror | Association of modifiable and nonmodifiable factors with vitamin D status in pregnant women and neonates in Oakland, CA[END_REF]. These factors include season of the newborn's birth, maternal vitamin D intake, body mass index, constitutive skin pigmentation, latitude, clothing, sunscreen-use, outdoors activities, age [START_REF] Tsiaras | Factors influencing vitamin D status[END_REF][START_REF] Dror | Association of modifiable and nonmodifiable factors with vitamin D status in pregnant women and neonates in Oakland, CA[END_REF] and genetic factors [START_REF] Wang | Common genetic determinants of vitamin D insufficiency: a genome-wide association study[END_REF].

During pregnancy the fetus is exposed to vitamin D through cord blood supply and the ability of 25(OH)D to cross the placenta [START_REF] Salle | Perinatal metabolism of vitamin D[END_REF]. Over the past 2 years, the number of studies, both cross-sectional and prospective, that have investigated the effects of maternal vitamin D intake on the inception and severity of asthma and allergies in the offspring have increased significantly. Most studies have shown that low maternal vitamin D levels (assessed by food frequency questionnaires) increase the risk for asthma [START_REF] Erkkola | Maternal vitamin D intake during pregnancy is inversely associated with asthma and allergic rhinitis in 5-year-old children[END_REF], wheeze [START_REF] Miyake | Dairy food, calcium and vitamin D intake in pregnancy, and wheeze and eczema in infants[END_REF][START_REF] Camargo | Prospective study of maternal intake of vitamin D during pregnancy and risk of wheezing illness in children at age 2 years[END_REF][START_REF] Camargo | Maternal intake of vitamin D during pregnancy and risk of recurrent wheeze in children at 3 y of age[END_REF] allergic rhinitis [START_REF] Erkkola | Maternal vitamin D intake during pregnancy is inversely associated with asthma and allergic rhinitis in 5-year-old children[END_REF] and atopic dermatitis [START_REF] Miyake | Dairy food, calcium and vitamin D intake in pregnancy, and wheeze and eczema in infants[END_REF], but a few suggest an increased risk with high levels [START_REF] Hypponen | Infant vitamin d supplementation and allergic conditions in adulthood: northern Finland birth cohort[END_REF][START_REF] Gale | Maternal vitamin D status during pregnancy and child outcomes[END_REF].

However, the majority of these studies did not use objective measures of maternal vitamin D status. In addition, studies examining the associations between cord blood 25(OH)D concentrations and asthma and allergic diseases [START_REF] Camargo | Cord-blood 25-hydroxyvitamin D levels and risk of respiratory infection, wheezing, and asthma[END_REF] are still very scarce.

The purpose of the present study was to investigate whether the levels of cord serum 25(OH)D, which is considered the best indicator of newborns' vitamin D status, are associated with risk of asthma, wheeze, allergic rhinitis and atopic dermatitis in offspring. Our study was conducted in the French EDEN mother-child cohort. This sample appeared representative of the overall study population.

Methods

Study design and participants

Mother

Women were given an appointment with a study midwife, planned to take place between 24 and 28 gestational weeks, during which an interview on behavioral factors was conducted and biological samples were collected. Further information on the mothers and their newborns, including parity, mode of delivery, newborn's sex and birth weight (measured with electronic Seca scales, Hamburg, Germany [Seca 737 in Nancy and Seca 335 in Poitiers with a 10 g precision]), gestational age and season of birth, were either collected by a questionnaire after birth or extracted from obstetrical and pediatric records. All children were equally receiving vitamin D supplementation during the first three years of life.

Ethics Statement

The ethical committees who approved the study is: Comité Consultatif pour la Protection des Personnes dans la Recherche Biomédicale, Le Kremlin-Bicêtre University hospital, and Commission Nationale de l'Informatique et des Libertés. The study was approved on 12 December 2002. Written consent was obtained from the mother for herself at the beginning of the study and from both parents for the newborn child after delivery.

Cord serum 25(OH)D measurement

Immediately after delivery, cord blood serum samples were collected by research midwives. In order to prevent any contamination with maternal blood, the cord was doubly clamped immediately after birth (vaginal delivery) or after extraction of the fetus through the uterine incision (elective caesarean section); repeatedly rinsed and venous cord blood serum was sampled between the two clamps. Blood samples were centrifuged within 24 hours of collection. The serum was separated and stored at -80°C. Standard operating procedures for each assay were established. Serum 25(OH)D, which is considered to be the indicator of vitamin D status [START_REF] Holick | Vitamin D status: measurement, interpretation, and clinical application[END_REF], was measured by immunochemilumiscent immunoassays performed on the LIAISON platform manufactured by DiaSorin (Sallugia, Italy). This assay measures both 25(OH)D2 and 25(OH)D3 and provides the sum of these two metabolites and does not crossreact with the C3 25(OH)D epimer, which has been shown to complicate the measurement of 25(OH)D in neonates. The intra-and interassay coefficient of variation was <10% whatever the measured concentration.

Health outcomes

Children were followed up from birth to age 5 years. At the age of 1, 2, 3 and 5 years, parents completed questionnaires including questions on asthma, wheeze, allergic rhinitis and atopic dermatitis, based on the validated International Study of Asthma and Allergies in Childhood (ISAAC) phase-I questionnaire [START_REF]Worldwide variations in the prevalence of asthma symptoms: the International Study of Asthma and Allergies in Childhood (ISAAC)[END_REF][START_REF] Williams | Worldwide variations in the prevalence of symptoms of atopic eczema in the International Study of Asthma and Allergies in Childhood[END_REF]. For each year, asthma was defined as parental report of doctor-diagnosis of asthma plus either one or more attacks of wheeze or asthma medication in the last 12 months. Wheeze was defined as present if the parents answered ''yes'' to the question ''Has your child had wheezing or whistling in the chest in the preceding 12 months?''. Parental report of wheezing has been shown to be a sensitive and specific outcome when using physician assessment as the criterion standard [START_REF] Neto | Validation of a questionnaire for epidemiologic studies of wheezing in infants[END_REF]. Allergic rhinitis was defined as sneezing, nasal congestion, or rhinitis, other than with respiratory infections, accompanied by eye itching and tearing during the previous 12 months [START_REF] Asher | International Study of Asthma and Allergies in Childhood (ISAAC): rationale and methods[END_REF]. And atopic dermatitis was defined as atopic dermatitis diagnosed by a doctor in the last 12 months.

Given the uncertainty of allergic rhinitis and asthma diagnoses in early childhood [START_REF]Expert Panel Report 3 (EPR-3): Guidelines for the Diagnosis and Management of Asthma-Summary Report 2007[END_REF], analyses were performed on allergic rhinitis and asthma from age 4 to 5 (positive answers to the previous questions in the 5 year-questionnaire). Lifetime prevalence of wheeze and atopic dermatitis at 1, 2, 3 and 5 years were analyzed.

Additionally, the data on wheezing from 1 to 5 years of age were used to categorize the children as never wheezers, early transient wheezers, late-onset wheezers, or persistent wheezers according to Martinez et al. [START_REF] Martinez | Asthma and wheezing in the first six years of life. The Group Health Medical Associates[END_REF]. Similarly, we distinguished between early-and late-onset atopic dermatitis, e.g. atopic dermatitis up to age 2 years and thereafter.

Other Variables

We collected information on potential confounders related to offspring health outcomes, including newborn sex, birth weight, gestational age, season at birth, number of older siblings at birth (0, 1 -2, ≥ 3), exclusive breastfeeding for ≥ 4 months (yes or no), maternal age at delivery (< 25 years, 25-34 years, or > 34 years), pre-pregnancy maternal body mass index (18.5 -24.9, 25.0 -29.9, 30.0 -34.9 and 35.0 -39.9 kg/m²), maternal and paternal history of allergies (yes or no), maternal and paternal education level (primary or less, secondary, and university degree or higher), household income (≤ 2300 versus > 2300 Euros per month, median income of the study population), city of residence (Nancy or Poitiers), any smoking during pregnancy (yes or no), environmental tobacco smoke exposure of the child from birth to age of 3 (yes or no), dampness in housing (0 -3 years) (yes or no), and day care attendance in the first year of life (yes or no). Maternal and paternal allergic history was obtained regarding physician-diagnosed allergic diseases such asthma, rhinitis, eczema and food allergies.

Statistical analyses

The sample was described using frequencies of categorical variables and means and standard deviations of continuous variables. The characteristics of the mother-newborn pairs We fitted logistic regression models to examine the associations between cord serum 25(OH)D level as a continuous variable and asthma and allergic rhinitis reported from 4 to 5 years and wheeze and atopic dermatitis by the age of 1, 2, 3 and 5 years, as well as the wheezing and atopic dermatitis patterns.

In order to identify confounding factors, bivariate analysis between potential confounders and each health outcome were performed. In a first step, all variables associated with one health outcome with a p<0.30 were retained. In a second step, confounders affecting at least 20% of the coefficient estimates of the investigated association between vitamin D and the health outcome were selected and included in the multivariate models. In addition to the inclusion of confounders based on their statistically significant association with health outcomes, we selected other adjustment variables, on the basis of their known relationship to 25(OH)D concentrations, independently of any association with exposures and regardless of whether they changed the effect estimates significantly. They included: child's sex [START_REF] Almqvist | Impact of gender on asthma in childhood and adolescence: a GA2LEN review[END_REF], prepregnancy body mass index [START_REF] Patel | Associations between pre-pregnancy obesity and asthma symptoms in adolescents[END_REF], and birthweight [START_REF] Agosti | Allergic manifestations in very low-birthweight infants: a 6-year follow-up[END_REF]. As a result, the adjustments included:

Results

Characteristics of the mother-child pairs

Children with both cord serum 25(OH)D data and complete questionnaires from birth to 5 years of age were included in this analysis (n = 239). Included children did not differ significantly from other children with complete questionnaires up to 5 years of age but without measurement of cord serum 25(OH)D (n = 901) with respect to all characteristics, except for season of birth and city of residence (Table I).

In our study population, no mothers reported type 2 diabetes diagnosed prior to pregnancy or chronic illnesses apart from asthma, eczema and other allergic diseases, such as rhinitis and food allergies.

Health outcomes in the offspring

By the age of 1, 2, 3 and 5 years, 24.7%, 32.6%, 35.1% and 38.9% of all children had experienced wheezing, respectively, and 10%, 13.4%, 14.2% and 25% had had atopic dermatitis, respectively. From age 4 to 5, 8% of all children had asthma and 7.5% had allergic rhinitis. The prevalences of early transient, late-onset and persistent wheezing patterns were 28.5%, 11.7% and 4.2%, respectively. The prevalences of early-onset and late-onset atopic dermatitis were 34.7% and 20.5%, respectively.

Newborns' cord serum levels of 25(OH)D

Relationship of cord serum 25(OH)D and outcomes by the age of 5 years

The associations between cord serum 25(OH)D levels and risk of different wheezing patterns, atopic dermatitis by the age of 1, 3 and 5 years, different atopic dermatitis patterns, and asthma and allergic rhinitis at 5 years of age are presented in table II. Without adjustment, a significant inverse association was observed between cord serum 25(OH)D concentration (per 5 ng/mL increase) and the risk of early transient wheezing and atopic dermatitis by the age of 3 and 5 years and early and late-onset of atopic dermatitis. After multivariable adjustment, the previously observed significant inverse associations persisted (OR for early transient wheezing, per 5 ng/mL increase of cord serum 25(OH)D concentration: 0.67 (0.54-0.81); OR for atopic dermatitis by the age of 1, 3 and 5 years : 0.84 (0.71-1.00), 0.82 (0.68-0.97), 0.75 (0.63-0.88), respectively; and OR for early and late-onset atopic dermatitis: 0.73 (0.62-0.90), 0.75 (0.60-0.94), respectively). The adjusted inverse association along with the confidence intervals and the regression line, between cord serum 25(OH)D concentration and risk of atopic dermatitis by the age of 5 years is shown in Figure 2. The graph represents the predicted probability of atopic dermatitis by the age of 5 years for each observed value of cord serum 25(OH)D concentration in the multivariate model.

In contrast, no significant association was observed between cord serum 25(OH)D level and asthma and allergic rhinitis prevalence. To further investigate this null finding, we stratified each of these outcomes according to maternal history of allergy. In all models, cord serum 25(OH)D levels had no association according to either atopic or non-atopic maternal status (all P > 0.20).

Discussion

Main findings

In this prospective birth cohort study of French mother-child pairs, we found that cord serum concentration of 25(OH)D was negatively associated with early transient wheezing, atopic dermatitis by the age of 1, 3 and 5 and early and late-onset atopic dermatitis. However, cord serum 25(OH)D levels were not associated with risk of other wheezing phenotypes, asthma and allergic rhinitis at 5 years of age.

In literature

To date, there is sparse information on vitamin D status and wheezing and atopic dermatitis. The few studies that have investigated the association between maternal vitamin D status and risk of wheezing [START_REF] Devereux | Maternal vitamin D intake during pregnancy and early childhood wheezing[END_REF] and atopic dermatitis [START_REF] Miyake | Dairy food, calcium and vitamin D intake in pregnancy, and wheeze and eczema in infants[END_REF] in childhood are limited by the fact that vitamin D intake was based only on food frequency questionnaires [START_REF] Miyake | Dairy food, calcium and vitamin D intake in pregnancy, and wheeze and eczema in infants[END_REF][START_REF] Camargo | Maternal intake of vitamin D during pregnancy and risk of recurrent wheeze in children at 3 y of age[END_REF]. Although such methods have been validated and are representative of intake over a period of time, most of these observational studies did not have direct serological measures of 25(OH)D levels to accurately confirm vitamin D status. However, all studies adjusted for total energy intake and for other nutrients associated with healthy diets.

Additionally, a study in 2008 found that vitamin D supplementation significantly improved skin symptoms in children with winter-related atopic dermatitis [START_REF] Sidbury | Randomized controlled trial of vitamin D supplementation for winter-related atopic dermatitis in Boston: a pilot study[END_REF]. And in adults, Oren et al. [START_REF] Oren | Vitamin D and atopic disorders in an obese population screened for vitamin D deficiency[END_REF] also found a protective effect of vitamin D on atopic dermatitis. These results

raise interesting questions about the potential role of vitamin D in the pathogenesis of atopic dermatitis.

Regarding the relationship between early transient wheezing and vitamin D deficit, Martinez et al. [START_REF] Martinez | Asthma and wheezing in the first six years of life. The Group Health Medical Associates[END_REF] found evidence that, in most cases, infant wheeze is a transient condition, not associated with increased risk of asthma or allergies later in life. In transient wheezer infants, a reduced airway caliber seems to be the predisposing factor to wheeze in association with viral infections. In our study, the inverse association between cord serum 25(OH)D levels and early transient wheezing is consistent with Camargo et al. findings [START_REF] Camargo | Cord-blood 25-hydroxyvitamin D levels and risk of respiratory infection, wheezing, and asthma[END_REF] of an inverse relationship between cord blood 25(OH)D levels and respiratory infections.

Potential mechanisms

Cord vitamin D may play a protective role against transient wheezing through its effects on the immune function [START_REF] Liu | Toll-like receptor triggering of a vitamin D-mediated human antimicrobial response[END_REF][START_REF] Adams | Unexpected actions of vitamin D: new perspectives on the regulation of innate and adaptive immunity[END_REF]. The molecular effects of vitamin D in the skin have been well documented in experimental studies. Vitamin D receptor (VDR) expression in the skin was first confirmed after rats injected with radio-labeled 1,25-dihydroxyvitamin D (1,25(OH)2D), the active form of 25(OH)D, demonstrated radioactivity concentrated in the nuclei of the epidermis along with a variety of other tissues [START_REF] Stumpf | Target cells for 1,25dihydroxyvitamin D3 in intestinal tract, stomach, kidney, skin, pituitary, and parathyroid[END_REF]. 1,25(OH) enhances keratinocyte differentiation, as well as have either stimulatory or suppressive effects on keratinocyte growth that is concentration dependent [START_REF] Gurlek | Modulation of growth factor/cytokine synthesis and signaling by 1alpha,25-dihydroxyvitamin D(3): implications in cell growth and differentiation[END_REF].

In addition, there is evidence to suggest that vitamin D decreases inflammatory responses in epidermal keratinocytes [START_REF] Zhang | Regulatory effects of 1,25dihydroxyvitamin D3 and a novel vitamin D3 analogue MC903 on secretion of interleukin-1 alpha (IL-1 alpha) and IL-8 by normal human keratinocytes and a human squamous cell carcinoma cell line (HSC-1)[END_REF][START_REF] Komine | The action of a novel vitamin D3 analogue, OCT, on immunomodulatory function of keratinocytes and lymphocytes[END_REF][START_REF] Fukuoka | RANTES expression in psoriatic skin, and regulation of RANTES and IL-8 production in cultured epidermal keratinocytes by active vitamin D3 (tacalcitol)[END_REF]. In vitro treatment of dendritic cells (DCs) with 1,25(OH)2D or vitamin D analogues led to decreased IL-12 and enhanced IL-10. These cytokine effects, along with inhibitory effects on DC maturation, promote tolerogenic properties and suppressor T cell induction [START_REF] Adorini | Dendritic cells as key targets for immunomodulation by Vitamin D receptor ligands[END_REF]. A short treatment course of 1,25(OH)2D in mice induced tolerogenic DCs and increased regulatory T cells [START_REF] Gregori | Regulatory T cells induced by 1 alpha,25-dihydroxyvitamin D3 and mycophenolate mofetil treatment mediate transplantation tolerance[END_REF]. As a result, vitamin D may promote regulatory T cells that are known to play an important role in the prevention of atopic dermatitis development [START_REF] Agrawal | The role of regulatory T cells in atopic dermatitis[END_REF] by playing a pivotal role in immune suppression and being crucial to the control of allergic responses.

Vitamin D also has a beneficial effect on the permeability barrier in the epidermis. Bikle et al. examined mice null for the expression of 25(OH)D-1α-hydroxylase. Lower levels of multiple proteins necessary for formation of the stratum corneum, including filaggrin, were observed in the null mice compared to the wild type controls [START_REF] Bikle | Regulation of 1,25-dihydroxyvitamin D production in human keratinocytes by interferon-gamma[END_REF]. Following skin barrier disruption, null mice had a significantly delayed barrier recovery compared to wild type mice [START_REF] Bikle | Regulation of 1,25-dihydroxyvitamin D production in human keratinocytes by interferon-gamma[END_REF].

Another potential role for vitamin D is suggested by the work of Schauber et al. [START_REF] Schauber | Antimicrobial peptides and the skin immune defense system[END_REF] , who found that 1,25(OH)2D enables keratinocytes to recognize and respond to microbes through action on the Toll-like receptor 2 and leads to upregulation of cathelicidin, an antimicrobial peptide. As a result, vitamin D may promote the production of antimicrobial peptides that have the ability to enhance immunity and protect skin from bacterial infections.

Consequently, given the fact that the pathogenesis of atopic dermatitis involves both epidermal barrier and immunologic dysfunction, vitamin D may have a protective role against atopic dermatitis and the development of a variety of other skin disorders as well.

Strengths and limitations

First, this is one of the few birth cohort studies to have measured vitamin D levels in cord blood as opposed to estimating infant levels based on vitamin D levels in pregnant women [START_REF] Gale | Maternal vitamin D status during pregnancy and child outcomes[END_REF] or maternal intake of vitamin D during pregnancy [START_REF] Miyake | Dairy food, calcium and vitamin D intake in pregnancy, and wheeze and eczema in infants[END_REF][START_REF] Erkkola | Maternal vitamin D intake during pregnancy is inversely associated with asthma and allergic rhinitis in 5-year-old children[END_REF][START_REF] Camargo | Maternal intake of vitamin D during pregnancy and risk of recurrent wheeze in children at 3 y of age[END_REF][START_REF] Devereux | Maternal vitamin D intake during pregnancy and early childhood wheezing[END_REF]. Additionally, newborns's vitamin D status was assessed by measuring serum levels of 25-hydroxyvitamin D, which is considered the best circulating biomarker of vitamin D metabolic status. The analyses were performed on the continuous 25(OH)D variable, since the often used categorization of vitamin D levels is still arbitrary and without consensus. An additional strength of our prospective investigation consists in the robustness of the results as children were drawn from a cohort and their parents were able to provide information on possible confounders, thus diminishing the probability of biased or confounded results. In addition, we collected outcome data at different ages, providing more robust measures of potential health effects than single time-point outcomes could provide. The definition of health outcomes was based on the validated ISAAC questions.

Our study also has some limitations. Information on offspring health outcomes was obtained from parental report through self-administered questionnaires, which could result in misclassification. We could not obtain vitamin D data from all eligible newborns with complete information at age 5 years, which may have introduced selection bias. Because of the sample size of our study, although the change-in-estimate (CE) criterion ≥ 10% is a conventional one [START_REF] Tong | Identification of confounders in the assessment of the relationship between lead exposure and child development[END_REF], a more conservative criterion ≥ 20% was used in order to select potential confounders. In addition, the absence of significant associations between asthma, heightened awareness of the carcinogenic effect of sun exposure [START_REF] Wright | Solar UVR exposure, concurrent activities and sun-protective practices among primary schoolchildren[END_REF]. Finally, subjects were followed only to age 5 years, at which age asthma may be evolving from being infectionrelated to being predominantly related to allergy. Similarly, wheezing in the preschool years is not necessarily indicative of allergic disease as we know that wheeze may be induced by viral infection [START_REF] Jartti | Allergic sensitization is associated with rhinovirus-, but not other virus-, induced wheezing in children[END_REF]. In light of recent findings on the role of vitamin D, and its effects on asthma and allergic diseases, studies of vitamin D may enhance the understanding, prevention and treatment of these increasingly common conditions in childhood. Further research is required to establish the optimal level (or range) of vitamin D that decreases both the risk for development and severity of these disorders, but also the timing and route of exposure to vitamin D.

Conclusion

  -child pairs were recruited in the EDEN (Etude des Déterminants pré et post natals du développement et de la santé de l′Enfant) prospective Birth Cohort Study (http://eden.vjf.inserm.fr). The primary aim of the EDEN Cohort is to identify prenatal and early postnatal nutritional, environmental and social determinants associated with children's health and their normal and pathological development. Pregnant women seen for a prenatal visit at the departments of Obstetrics and Gynecology of the University Hospital of Nancy and Poitiers before their twenty-fourth week of amenorrhea were invited to participate. Enrolment started in February 2003 in Poitiers and September 2003 in Nancy; it lasted 27 months in each centre. Women with speaking and writing abilities in French, who did not suffer from type 2 diabetes diagnosed prior to pregnancy, and did not plan to deliver outside the university hospital or move out of the region within 3 years, were included in the study. Multiple pregnancies were excluded. Among eligible women, 55% (2002 women) agreed to participate (1034 women in Nancy and 968 in Poitiers). Of the 2002 mother-child pairs included in the EDEN study, 1140 of them had complete data by the child's age of 5 years. Among the 1140 participants, measurements of cord serum 25(OH)D performed at birth were available in 239 children. The final sample for analysis consisted of 239 mother-child pairs.

  in our study sample (n = 239) were compared to the sample of mother-newborn pairs of children without measurement of cord serum 25(OH)D (n = 901). We used Chi-square tests for categorical data, T-tests for normally-distributed data and Mann-Whitney U tests for skewed data.

  city, maternal age at delivery, maternal pre-pregnancy body mass index (BMI), any smoking during pregnancy, any passive smoke exposure during the first 3 years of life, number of siblings, household income, newborn's sex and weight, season of birth (calendar-based), and exclusive breastfeeding for ≥ 4 months. Multiple logistic regression analysis was used to adjust for confounding factors. Estimations of crude and adjusted odds ratios (ORs) and their 95% confidence interval (CI) of asthma, wheeze, allergic rhinitis and atopic dermatitis, at different time point, per 5 ng/mL increase of cord serum 25(OH)D concentration were made by means of logistic regression analysis.To further explore the associations between asthma and allergic rhinitis and cord vitamin D, we examined effect modification of the association of these outcomes with cord serum 25(OH)D, by stratifying the cohort according to maternal history of allergy and testing the interaction term (namely continuous 25(OH)D*maternal history of allergy). All statistical analyses were performed using SAS statistical software version 9.2 (SAS Institute Inc, Cary, North Carolina). P-values < 0.05 were considered statistically significant for all analyses.

Figure 1

 1 Figure 1 shows the distribution of cord blood serum 25(OH)D concentrations. The mean

allergic rhinitis and 25 (

 25 OH)D concentrations may be due to the low prevalences of these outcomes, consequently limiting the power to detect a relationship between 25(OH)D and the outcome. An often-cited limitation of serologic studies is the reliance on a single 25(OH)D measurement per subject. It would have been interesting to measure serum 25(OH)D levels during childhood. The half-life of serum 25(OH)D is approximately 2 to 3 weeks (57), which suggests that the measured concentrations reflect maternal-fetal status during the final months of pregnancy and first months of life. All children in our study were receiving vitamin D supplement during the first three years of life, so difference between children vitamin D levels may depend on diet along with food diversification and on sun-related behaviors, despite

  In summary, our data indicate an inverse association between cord serum 25(OH)D levels and the risk of early transient wheezing and atopic dermatitis in young children. In contrast, we found no apparent association between cord serum 25(OH)D concentrations and other wheezing phenotypes, asthma and allergic rhinitis at 5 years of age. If these associations are causal, interventions to increase vitamin D levels in utero and in early life could reduce the risk of transient wheezing and atopic dermatitis in early childhood. Increased exposure to sunlight and increased intake of foods high in vitamin D (not necessarily supplementation) in both pregnant women and infants are potential public health interventions.

  0.77 (0.69-0.95), P ‡ = 0.01 0.94 (0.77-1.[START_REF] Camargo | Cord-blood 25-hydroxyvitamin D levels and risk of respiratory infection, wheezing, and asthma[END_REF]), P = 0.58 1.10 (0.70-0.95), P = 0.50 0.67 (0.54-0.81), P = 0.0002 0.86 (0.67 -1.11), P = 0.24 1.15 (0.79 -1.691), P = 0.46 Atopic dermatitis By the age of 1 By the age of 2 By the age of 3 By the age of 5 Early-onset Late-onset 0.88 (0.76-1.00), P = 0.08 0.86 (0.77-1.00), P = 0.05 0.87 (0.76-1.00), P = 0.05 0.82 (0.71-0.91), P = 0.003 0.82 (0.70-0.95), P = 0.01 0.82 (0.68-0.98), P = 0.03 0.84 (0.71-1.00), P = 0.05 0.82 (0.70-0.95), P = 0.02 0.82 (0.68-0.97), P = 0.02 0.75 (0.63-0.88), P = 0.0005 0.73 (0.62-0.90), P = 0.002 0.75 (0.60-0.94), P = 0.01 Asthma at 5 1.09 (0.87-1.38), P = 0.42 1.07 (0.78-1.45), P = 0.69 Allergic rhinitis at 5 1.06 (0.84-1.34), P = 0.62 0.99 (0.72-1.38), P = 0.98 *OR (95 % CI): odd ratio and 95% confidence interval. † Adjusted for city, mother's age, maternal history of allergy, pre-pregnancy body mass index, any smoking during pregnancy, any passive smoke exposure during the first 3 years of life, number of siblings, household income, newborn's sex and weight, season of birth, and exclusive breastfeeding for ≥ 4 months. ‡P = P-value.

Figure legends FIG 1 .

 legends1 Figure legends

FIG 2 .

 2 FIG 2. Adjusted associations between cord serum 25(OH)D levels and predicted probabilities

TABLE I .

 I Comparison of basic characteristics of mother-newborn pairs with (n = 239) and without (n = 901) measurement of cord serum 25(OH)D

		Study sample with	Sample without
		measurement	measurement	P-value
		(n = 239)	(n = 901)
	City, %
	Poitiers	47.7	57.3
	Nancy	52.3	42.7	0.008
	Maternal age, Mean ± SD* (years)	30.8 ± 4.6	30.5 ± 4.7	0.6
	< 25, %	9.2	11.6
	25-34, %	69.5	71.1
	> 34, %	21.3	17.4	0. 3
	BMI, Mean ± SD (kg/m 2 )	26.4 ± 4.4	26.3 ± 4.5	0.6
	Normal, %	46.8	45.9
	Overweight, %	36.7	37.1
	Moderate obesity, %	11.4	11.6
	Severe obesity, %	5.1	5.4	0.9
	Maternal allergies, %	31.4	31.0	0.9
	Paternal allergies, %	23.0	22.3	0.8
	Maternal educational level, %
	Primary school or less	3.3	4.9
	Secondary school	56.2	59.3
	University degree or higher	40.5	35.9	0.1
	Paternal educational level, %
	Primary school or less	8.2	7.2
	Secondary school	64.3	65.0
	University degree or higher	27.5	27.8	0.7
	Smoking during pregnancy (active, passive), %	31.9	31.8	0.5
	Environmental tobacco smoke exposure of the	44.8	48.5	0.3
	child (0-3 years),%
	Dampness in housing (0-3 years), %	5.9	7.8	0.3
	Attending daycare (0-1 years), %	15.9	12.0	0.1
	Household income (Euros), %
	≤ 2300	36.0	43.0
	> 2300	64.0	57.0	0.06
	Older siblings, %
	0	45.6	49.0
	1-2	48.1	47.5
	≥3	6.3	3.6	0.1
	Birth weight, Mean (kg) ± SD	3.4 ± 0.5	3.3 ± 0.5	0.06

Gestational age at birth, Mean (weeks) ± SD

		39.5 ± 1.5	39.2 ± 1.8	0.3
	Sex of the newborn, %
	Female	41.8	48.0
	Male	58.2	52.1	0.1
	Season of birth, %
	Summer	23.4	26.9
	Autumn	20.5	23.1
	Winter	16.7	23.8
	Spring	39.3	23.3	0.0008
	Exclusively breastfed for ≥ 4 months, %	16.3	14.8	0.6

* SD = standard deviation

TABLE II .

 II Association between cord blood 25(OH)D levels (per 5 ng/mL increase) and risk of wheeze and atopic dermatitis outcomes, and asthma and allergic rhinitis(n = 239)

		OR (95% CI) *
	Outcome	Unadjusted	Adjusted †
	Wheeze
	Early transient
	Late-onset
	Persistent


Hrachya Astsatryan

Vladimir Sahakyan

Yuri Shoukouryan

Michel Daydé
email: michel.dayde@enseeiht.fr

Aurélie Hurault

Ronan Guivarch
email: ronan.guivarch@enseeiht.fr

Harutyun Terzyan
email: hterzian@seua.am

Levon Hovhannisyan

Aurelie Hurault
email: aurelie.hurault@enseeiht.fr

A Hurault

On the Easy Use of Scientific Computing Services for Large Scale Linear Algebra and Parallel Decision Making with the P-Grade Portal

Keywords: Scientific computing (Petitet Advanced trading, Sparse linear algebra solvers, P-grade portal, Parallel decision making

come   L'archive ouverte pluridisciplinaire

et al. 1999) aims at constructing mathematical models and numerical solution techniques for solving problems arising in science and engineering. In this paper, we describe the services of an integrated portal based on the P-Grade (Parallel Grid Run-time and Application Development Environment) portal (http://www.p-grade.hu) that enables the solution of large-scale linear systems of equations using direct solvers, makes easier the use of parallel block iterative algorithm and provides an interface for parallel decision making algorithms. The ultimate goal is to develop a single sign on integrated multi-service environment providing an easy access to different kind of mathematical calculations and algorithms to be performed on hybrid distributed computing infrastructures combining the benefits of large clusters, Grid or cloud, when needed.

Introduction

Scientific computing aims at constructing mathematical models and numerical solution techniques for solving problems arising in science (including life and social sciences) and engineering. The solution of linear system of equations lies at the heart of most calculations in scientific computing. For the past twenty years, there has been a great deal of activity in the area of algorithms and software for solving linear algebra problems. It is often difficult for non expert users to take advantage of nowadays computational infrastructures (Grids, clusters, GPU, ...) or even to use the available advanced libraries, because they often require to be familiar with middleware and tools, parallel programming techniques and packages (MPI, OpenMP, CUDA, etc.) and numerical libraries (ScaLAPACK, LAPACK, BLAS, etc.).

The purpose of this article is to describe the scientific computing services that are deployed within our Portal and how their access has been made straightforward. One of the main components is an environment enabling the solution of large-scale linear systems of equations and algorithms on hybrid HPC infrastructures (heterogeneous Grids composed of clusters with and without GPUs), which is the extension of the previous work [START_REF] Astsatryan | Introduction of a Grid-aware portlet for numerical calculations[END_REF][START_REF] Astsatryan | A Gridaware web interface with advanced service trading for linear algebra calculations[END_REF]. The environment is responsible of scheduling the computing jobs to remote GPU and Grid computing facilities (workload management service) by matching the complexity of the user-submitted expression, the parameters of algorithms and the resource status information collected from information services. The computational resources of the Armenian National Grid (ArmGrid) infrastructure [START_REF] Astsatryan | Grid activities in Armenia[END_REF] has been used that unifies different architectures (multicore processors, GPUs) and network topologies (Myrinet, Infiniband, Gigabit). Currently ArmGrid consists of seven Grid sites located in the leading research and educational organizations of Armenia [START_REF]Armenian National Grid Infrastructure[END_REF].

Related Work

Several projects that can be related to the Problem Solving Environments introduced in the 90's provide advanced functionalities but are typically restricted to a certain application area. They provide all the computational facilities needed to express and solve a target class of problems i.e. advanced solution methods enriched sometimes with an easy selection mechanism between alter-natives. They often attempt to use the common language of the class of problems to simplify users life. Some examples are of course MATLAB, OC-TAVE, NETSOLVE/GRIDSOLVE [START_REF] Hardt | Interactive Grid-access using Gridsolve and giggle[END_REF], CAC-TUS [START_REF] Gabrielle | Cactus tools for Grid applications[END_REF], DECIDE [START_REF] Ardizzone | The DECIDE science gateway[END_REF], NEOS [START_REF] Czyzyk | The NEOS server[END_REF], GRID-TLSE [START_REF] Daydé | On deploying scientific software within the GRID-TLSE project[END_REF], PETSc, etc.

Several projects based on web portals are providing advanced features (workflow manager, easy deployment of services, authentication and authorization procedures, information services, etc.) for building problem solving environments or deploying software and tools for scientific communities, such as P-GRADE [START_REF] Farkas | P-GRADE portal: a generic workflow system to support user communities[END_REF][START_REF] Kacsuk | P-GRADE portal family for Grid infrastructures[END_REF][START_REF] Kacsuk | WS-PGRADE/gUSE generic DCI gateway framework for a large variety of user communities[END_REF] and DIET [START_REF] Caron | DIET: a scalable toolbox to build network enabled servers on the Grid[END_REF]. Both P-GRADE and DIET are providing a workflow manager that allows an easy composition of services. They also supply facilities for deploying new services and provide APIs for generating web portals.

NetSolve/GridSolve aims at aggregating heterogeneous computational resources inteconnected by a network. It is a RPC based system that provides a seamless bridge between the standard programming interfaces and the use of the Grid. The library software deployed over the servers involved in the Grid is easily accessed from Fortran, MatLab, . . . . The NEOS server provides a large range of optimization software with a minimum input from users. Cactus is an open source problem solving environment designed for scientists and engineers that runs on many architectures. The Cactus user community has created and is maintaining toolkits for several research fields for example the Einstein Toolkit in computational relativistic astrophysics. GRID-TLSE is an expert site available through a web portal located at http://Gridtlse.org that provides an easy access to a large variety of direct solvers for sparse linear systems to enable comparative analysis on usersubmitted problems, as well as on matrices from collections also available on the site. The site provides user assistance in choosing the right solver for a given problem and in setting the appropriate values for the control parameters of the solver. It is also intended to be a testbed for experts in sparse linear algebra which provides tools to create working groups, and a bibliography database on sparse matrices.

Our work makes use of P-GRADE for developing the web portal that allows users to enter their requests and recover the subsequent results.

Central to the work we describe in this paper, is the advanced trader we are using [START_REF] Hurault | Advanced service trading for scientific computing over the Grid[END_REF] and to our knowledge there is no generic approach capable of handling complex expression such as this tool available in a scientific computing environment. Our web portal mainly aims at simplifying the use of scientific libraries deployed as a set of computational services (i.e. each procedure of the library is seen as a service).

The globalization of resources (hardware and software) on large scale distributed computing infrastructures requires advanced trading mechanisms to identify the service or the composition of services able to fulfill a user request. Our advanced trader is using a sophisticated semanticbased service description similar to algebraic data type. The services (typically procedures of a library) are described in terms of their algebraic and semantic properties. This is quite similar to proceed to a description of algorithms in a certain application area, in other words it is based on the ontology of an application area covered by a scientific library (including description of the solution techniques). It is then possible with such a description to automatically compute the service or the combination of services that satisfy a user request expressed and then generate the list of library calls to be performed. The corresponding workflow with call to the local or remote procedures involved (depending on the amount of data or calculations) is then built automatically without the need of the user assistance. As a major benefit, users are not required to explicit call Grid-services but instead manipulate high-level domain-specific expressions similar to MATLAB to describe their calculations.

Similar issues are available within MATLAB or SciLab where user requests may occasionally be translated into a sequence of calls to a libray (e.g. x = A \ b in MATLAB generates a workflow involving calls to LAPACK LU factorization followed by forward-backward substitutions for a dense square matrix).

Our approach is fully generic and can be used in almost all application areas. An experimental version of this approach has been implemented within GridSolve [START_REF] Hurault | Intelligent service trading and brokering for distributed network services in Grid-Solve[END_REF].

Grid Software Pool

Our software is structured into three main layers:

• User interface: it allows users to manipulate their data (initialization, uploading, suppression, . . . .) and to enter their computational requests using a MATLAB type of syntax. • Analyzer/converter and advanced trader: the analyzer / converter is in charge of analyzing and converting the user expression into a XML format used as an input by the advanced trader in charge of computing the service or the list of services that fulfill the user request • Job preparation modules: it converts the workflow generated by the advanced trader into a list of local or remote calls (depending on the location of services and on the size of the computations if services are available on several computers of different capacities), launches the calculations and recovers the results to be sent back to the user interface.

As a consequence, all the difficulties inherent to the use of the gLite middleware, MPI programming or construction of the library calls are then totally hidden to the user which is the main goal of our generic approach.

Overall Organization of the Grid Portal

The Web portal of our scientific computing environment is based on the P-GRADE Grid Portal. It is a web based, service rich environment for the development, execution and monitoring of workflows and workflow based parameter studies on various Grid platforms. It hides low-level Grid access mechanisms by high-level graphical interfaces; making even non Grid expert users capable of defining and executing distributed applications on multi-institutional computing infrastructures.

The P-GRADE Portal can access multiple Grids simultaneously, which enables the easy distribution of complex applications on several platforms. Our scientific computing environment aims at providing a seamless bridge between the linear algebra calculations/algorithms and middlewares, tools, parallel programming techniques, linear algebra libraries, etc. The Web portal is based on a module for managing the numerical objects, an analyzer and a converter, an advanced trader and the job preparation modules. It provides services for solving large-scale linear systems (including a range of dense and sparse direct solvers and a parallel iterative methods) and services for parallel decisionmaking.

The essential software components of the Grid Software pool include the portal, the gLite [START_REF]gLite[END_REF] middleware, an advanced trader, compilers, the MPI communication library and basic linear algebra libraries implemented on CPU and GPU. The deployment and the efficient use of the software components over a heterogeneous distributed computing infrastructure are quite challenging. In this context, our main option is to set up the environment only on the base of open-source technologies and software components that simplify the use of new computational resources and infrastructures.

gLite is a well spread middleware for Grid computing that provides a framework for building applications executed over distributed computing and storage resources across the Internet. The LFC (LCG File Catalog) data management of gLite is used, where the Grid Unique IDentifier represents a given file. The data are stored on the storage element of the target Grid site, which has a fast interconnection with the worker nodes. The interconnection between target architectures, numerical objects types and libraries is given in Fig. 1.

Services and High-Level User Interface

One of the main challenges in our work is to provide non-expert users a seamless access to the scientific computing services that are deployed within our Web portal. This is achieved by allowing users to express their requests using mathematical expressions similar to MatLab or SciLab The analyzer module (PHP code) carried out syntactic and semantic analysis of the expression entered by the user by checking the main parameters and analyzing the expressions and the numerical objects involved. If the expression is correct, the converter converts the expression into the corresponding XML format (required as an input for the advanced trader module) that fully defines the given expression including the parameters and their properties.

The advanced service trading module (based on the work described in [START_REF] Hurault | Advanced service trading for scientific computing over the Grid[END_REF]) computes the services required to perform the user request i.e. converts the mathematical expressions given by the user into a list of procedures calls (functions of libraries) that answer to its request.

Our service trading approach consists in adding additional semantic information to the services in order to allow finding the service or combination of services that provide relevant answers to a user request using equational unification to identify all the possible choices. This approach allows to significantly reduce the ambiguities of the current trading technologies for domain specific use. The user does not need to know the exact name of the service he is looking for, he just has to describe the mathematical operation he wants to compute in a given applicative area (here linear algebra) and to provide the data that the operation will use. The service trader finds an appropriate service or combination of services. It could also be possible to provide the user (through the portal) a list of possible choices and asks him to choose the best one according to his needs (this is not currently implemented). Depending on the problem size (typically if the order of the matrices involved into a matrix-matrix operation is over a certain size), we switch from BLAS to PBLAS in order to use the resources of Grid infrastructures. Practically, we switch to the Grid if the operation exceeds the memory of the server of the portal Depending on the problem size, we switch from BLAS to PBLAS (if the operation does not fit into the memory of the server of the portal which is 8 GB) using the resources of Grid infrastructures. Practically for a matrix-matrix multiplication on the Armcluster we switch when the matrix size exceeds 8,192 (assuming they are all matrices are square of same size) [START_REF] Astsatryan | Enabling large-scale linear systems of equations on Hybrid HPC infrastructures[END_REF].

The Job preparation module recovers the list of services computed by the advanced trader and selects the target infrastructure where the job will be executed taking into account the type, the complexity of the given expression (list of services) and the generated amount of calculation. Currently, the complexity of the expression is defined only by the size of the matrix but there is obviously space for setting up better strategies. In the case of using the Grid infrastructure as a target resource, a JDL (Job Definition Language) [START_REF]Job Description Language HowTo[END_REF] file is automatically created by the Job preparation module to specify the resources that a job requires, then the file is submitted to the Grid infrastructure within the P-Grade Portal.

The main benefit of such an approach is that the user has only to type a mathematical expression and to provide the required data (matrices, vectors, and numbers) in order to get the results (see Fig. 2). All given expressions and results are saved into a centralized database. The real matrices are located in the storage element of the Grid infrastructure, which makes visible the data from the worker nodes of the Grid infrastructure. There is obviously space for further improvements in terms of scheduling considering issues such as machine load, energy saving, distributed storage of data, etc. As an illustration of the interface, we consider a simple example. Assume that a user wants to solve the following algebraic expression C = A * ( B * C ), where A, B and C are general type 100,000by-100,000 matrices. The user enters the mathematical expression to be evaluated that involves the numerical objects initialized as: A * ( B * C ) in the Web page for submitting user requests and then submits it for execution (see Fig. 3).

After the syntactic and semantic analyzes by the Analyzer, if the expression is correct, an XML file indicated below is created by the Converter that describes the expression.

The advanced trader module takes this XML file (fully defined expression) and computes the list of functions (or services) that can solve the requested expression. Since the matrices are quite large, the execution will be performed remotely using PBLAS (in case of smaller size matrixes it can be CPU or GPU realization of BLAS instead of PBLAS). The output of the service trader consists into two consecutive calls to PsGEMM (the PsGEMM ('N', 'N', 100000, 100000, 100000, 1., B, 1, 1, DESCB, C, 1, 1, DESCC, 0., p2, 1, 1,

DESCp2) \\ p2 = B * C PsGEMM ('N', 'N', 100000, 100000, 100000, 1 A, 1 1 DESCA, p2, 1, 1, DESCp2, 0., p1, 1, 1, DESCp1) \\ p1 = A * p2 p1
Considering the size of the matrices involved in the operation, the execution of these PBLAS procedures be performed over the Grid, the Job preparation module will then generated an execution script launched over the Grid in order to recover the result of the user request that are sent back to the Web interface.

Data Management in the Portal

The users define and insert the new numerical objects (see Fig. 4) that are required in their mathematical calculations. Both uploading and generation mechanisms are available for the creation of numerical objects by specifying their types and properties, such as triangular, identity, symmetric, . . . for matrices. The interface provides to users different options (download, delete or change parameters) for the uploaded numerical objects. The parameters (types, properties, names, etc.) of the numerical objects are stored on the local mysql database of the portal and then the numerical objects are transferred to the storage element of the Grid infrastructure. Currently the portal uses the storage element of the ArmGrid infrastructure with the capacity of 8 TB.

Mathematical Services

The computational services currently deployed within our scientific computing environment include libraries for dense and sparse linear algebra (including direct and iterative solvers) and a solver for decision making problems. These libraries cover the major types of architectures (serial and parallel computers using the OpenMP and MPI programming paradigms and GPUs) and allow to solve a wide range of problems.

The services deployed within our scientific environment are procedures of the various scientific libraries. The C or Fortran codes of these proce-Fig. 4 Scientific computing environment based on P-GRADE: data initialization dures are encapsulated within a shell script that allows to call them (input is the output of the trader module, output is the JDL file) from gLite when they are used remotely (which is not required when they are executed locally). Practically all ScaLAPACK procedures are encapsulated with that script and their functionalites, data input and output are described to the advanced trader.

Service for Large-Scale Linear Systems

Several libraries for dense linear algebra (ScaLA-PACK, MAGMA, PSBLAS) in addition to the MUMPS package that provides a range of sparse direct solvers are available:

• ScaLAPACK [START_REF] Blackford | ScaLAPACK: a linear algebra library for message-passing computers[END_REF] is a library of highperformance linear algebra routines for distributed memory message-passing MIMD (multiple instruction, multiple data) computers and networks of workstations supporting Parallel Virtual Machine and/or Message Passing Interface. With ScaLAPACK comes an additional library called the PBLAS, which can be seen as a parallel version of the BLAS (Basic Linear Algebra Subprograms) [START_REF] Blackford | An updated set of basic linear algebra subprograms[END_REF]. Using the PBLAS, simple matrix/vector and more complex operations can be performed in parallel.

• MAGMA (Matrix Algebra on GPU and Multicore Architectures) [START_REF] Tomov | Towards dense linear algebra for hybrid GPU accelerated manycore systems[END_REF] is a collection of next generation linear algebra libraries for heterogeneous architectures. MAGMA allows applications to fully exploit the power of current heterogeneous systems of multi/manycore CPUs and multi-GPUs to deliver the fastest possible time to accurate solution within given energy constraints. • The PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms) [START_REF] Filippone | PSBLAS: a library for parallel linear algebra computation on sparse matrices[END_REF] provides a framework to enable easy, efficient and portable implementations of iterative solvers for linear systems on parallel computers. It implements parallel versions of most of the Sparse BLAS computational kernels (sparse matrix by dense matrix multiplication, sparse block diagonal system solution, sparse matrix norms, vector norms, etc.), sparse matrix man-agement functionalities and parallel implementations of preconditioned Krylov solvers. • The MUMPS (MUltifrontal Massively Parallel sparse direct Solver) library [START_REF]MUMPS: A MUltifrontal Massively Parallel Sparse Direct Solver[END_REF] is a package for solving systems of linear equations of the form Ax = b, where A is a sparse matrix that can be either unsymmetric, symmetric positive definite, or general symmetric.

The matrix-matrix multiplication is one of the most important computational service for largescale linear systems. Parallel matrix-matrix multiplication has been investigated and benchmarked using the computational resources of the Arm-Grid infrastructure. Particularly, a series of experiments have been done on the high-performance computing Armcluster system, which consists of 128 3.06 GHz Intel Xeon processors and uses Myrinet 2000 network topology.

The PDGEMM double precision routine from the PBLAS in ScaLAPACK is used for benchmarking, as it is the one of most widely used computational kernel. Figure 5 reports the performance and scalability of PDGEMM for square matrices: the matrices ranks range from 600 to 12,000. The figure only includes the execution of the service, because the total execution time and the latency of the portal depends of the scheduling of jobs in the Grid environment which introduces strong variations depending on the overall load of the server (other jobs are running) and explain the superlinear speedup with the matrices of size 8,000 and the absence of gain when moving from 64 to 96 processors. The limits of the portal depends Fig. 5 ScaLAPACK PDGEMM benchmarking on Armcluster (performance in GFlops vs number of processors) on the capacities of the storage and on the computational resources of the virtual organization supported the portal. In our case 128 cores and 8 TB of storage (the resources of Armcluster) are available for the portal. Currently the storage element of the ArmNGI is used for the experiments, which is interconnected with the Grid sites via 1 Gbps of dedicated bandwith.

Services for Parallel Iterative Methods to

Solve Large Sparse Linear Systems

Iterative methods are, with direct methods, the other family of methods for solving general, large sparse linear systems Ax = b [START_REF] Saad | Iterative methods for sparse linear systems[END_REF]. The principle is generally to construct a sequence of iterates converging towards the solution of the linear system. Among the large variety of iterative methods, we focus on Krylov methods [START_REF] Saad | Iterative methods for sparse linear systems[END_REF][START_REF] Van Der Vorst | Iterative Krylov Methods for Large Linear Systems[END_REF] and Cimmino methods [START_REF] Arioli | A block projection method for sparse matrices[END_REF][START_REF] Arioli | Block Lanczos techniques for accelerating the Block Cimmino method[END_REF]. In the future it is planned to benchmark these iterative methods, as well as to deploy other iterative methods.

Services for Krylov Methods

The Krylov methods are based on a projection processes onto Krylov subspaces, which are subspaces spanned by the vectors {b, Ab, A 2 b, ..., A i b}. In short, these techniques approximate A -1 b by p(A)b, where p is a polynomial. The solution is constructed by many approaches that give rise to different methods [START_REF] Arioli | A block projection method for sparse matrices[END_REF]:

• The Ritz-Galerkin approach: full orthogonalization method (FOM), conjugate gradient (CG) methods, • The minimum norm residual approach: GM-RES method and its variants, • The Petrov-Galerkin approach: Bi-CG and QMR methods, • The minimum norm error approach: SYMMLQ method, ... We focus on the following two methods: GMRES method for unsymmetric matrices and Conjugate Gradient for symmetric definite matrices. The services implemented in the platform are based on these two methods. These methods can be parallelized using some of the libraries we deployed over the platform such as PSBLAS.

Service for Block-Cimmino Method

The Cimmino method [START_REF] Arioli | A block projection method for sparse matrices[END_REF][START_REF] Arioli | Block Lanczos techniques for accelerating the Block Cimmino method[END_REF] is a row projection method in which the original linear system is divided into subsystems. At each iteration, it computes one projection per subsystem and uses these projections to construct an approximation to the solution of the linear system. The Block-Cimmino method, as all the block algorithms, can be efficiently parallelized, for example, by distributing the different blocks on the available processors. However, the IRIT Team develops another approach [START_REF] Balsa | An hybrid approach for the parallelization of a block iterative algorithm[END_REF] where the block distribution onto the processors is not explicitly performed within the code: the MUMPS multi-frontal sparse solver is in charge of handling the data distribution and parallelism.

Service for Parallel Decision Making

Searching algorithms for solving the non-linear multi-parametric experimental problems (optimization problems) contains series of control parameters, which defines the effectiveness of the extremum computational meanings that usually define the success of the search of extremum. Besides, the extremal problems usually contain gully situations, which make the extremum search process significantly complicated. In practice the passage of gully situations is implemented as a rule through the search from various start points. The service deployed (see Fig. 6) allows for not only the parallelization of the solution of extreme problem itself, but also to simultaneously solve the problem by using some set of values of control parameters and then select the best solution.

Fig. 6 Service for parallel decision making

As it will be shown, the development of mentioned approach solves the problem of adaptation in some manner and allows for a significantly increment of the speed and quality of the solution of optimization problems.

Let's consider a non-linear multi-parametric extreme problem [START_REF] Terzyan | Decision Making Algorithms in Electromechanics[END_REF][START_REF] Terzyan | Simulation of electromechanical systems[END_REF].

F (x) = F (x 1 , x 2 , . . . , x n ) → min x∈D ⇒ x *
With the non linear limitations of inequality type D : ϕ (x) = ϕ i (x 1 , x 2 . . . , x n ) ≥ 0, i = 1, 2, . . . , l, where F (x) is the goal function, xis the vector of variable variables, z is the dimension of the range of the extreme search, x * is the vector of optimal values of variables, D is the allowable range formed by technical requirements in the form of l limitations. The transfer to the acceptable range D will be implemented through minimization of the non-negative function.

Q (x) = ϕ i <0 |ϕ i | |ϕ i | + 1
The developed parallel algorithms have been benchmarked on the nonlinear problem of optimal projection of synchronic generator with obvious poles [START_REF] Terzyan | On solution of decision-making problem in distributed computing environment[END_REF] using the service of the portal. For example, in case of random-search algorithm the total number of experiments are 27 (3 3 ), because three values of the following control variables are used: x 0 -vector of the start point coordinates, k u -coefficient of the step division, µ-the count of maximum tries inside of hypersphere. In our benchmarks we have achieved a 8.64 speedup when simulations are run using 27 cores of the Grid site located in the State Engineering University of Armenia. The investigations of the developed system show that using the Web portal is essential, because big differences in the goal function optimal value occur depending on the best and worst set of control parameters.

The random search with the best selection, the classic genetic and gradient algorithms have also been implemented and tested. The experiments show that the discussed approach is also effective for the mentioned algorithms.

Conclusion

The full implementation of our environment for scientific computing over the Grid and GPUs will allow users, who are not familiar with the parallel programming technologies and software tools (Grid and cluster middlewares, parallel and GPU programming, queue system, linear algebra libraries), to use the services over the portal while hidding all the details of the underlying distributed computing infrastructure. The environment is a good tool for demonstrating how computations can be transparently performed over the Grid or GPU from the user point of view.

Fig. 1

 1 Fig. 1 Interconnection between the target architectures

Fig. 2

 2 Fig. 2 Interconnections of modules

Fig. 3

 3 Fig. 3 Algebraic equation request entered by the user

Acknowledgements This joint work has been done within the framework of the "Development of a Second Generation Scientific Computing Infrastructure Based on P-Grade Portal" (Centre National de la Recherche Scientifique, France and State Committee of Science of Armenia) Project.