Phases of unimodular complex valued maps: optimal estimates, the factorization method, and the sum-intersection property of Sobolev spaces

International audienceWe establish optimal lifting estimates for unimodular complex valued maps in the Sobolev spaces $W^{s,p}$. This extends previous results of Bourgain, Dávila-Ignat and Merlet, and relies on new techniques (factorization, duality). We obtain a characterization, based on average martingale estimates, of fractional Sobolev spaces

Contributions à la théorie des espaces de fonctions : singularités et relèvements

In this thesis we study some aspects of certain functional spaces. On the one hand we focus on the singularities of maps W^{1, n} with values ​​in the unit sphere S^n, and secondly, on liftings of maps W^{s, p} with values ​​in the circle S^1.The first part concerns the minimization problem of a weighted Dirichlet energy. Admissible maps are functions which are continuous functions outside a given singular set prescribed by the boundary of a rectifiable current. We obtain the exact formula, which improves the result of Alberto, Baldi and Orlando (2003). In the same time, we generalize some results previously obtained by Brezis, Coron, Lieb (1986), Almgren, Browder, Lieb (1988).The second part focuses on the best control of unimodular maps and it is based on the work of Bourgain, Brezis, Mironescu (2000, 2002). Using some known methods and some new ones, we study optimal estimates of seminorms W^{s, p} of liftings, for different values ​​of s and p. We also obtain a new characterization of the space W^{s, p} for s<1 in terms of dyadic seminorm.Dans cette thèse nous étudions quelques aspects des certains espaces de fonctions. D’une part nous nous intéressons aux singularités des applications W^{1,n} à valeurs dans la sphère unité S^n, et d’autre part, aux relèvements des applications W^{s,p} à valeurs dans le cercle S^1.La première partie concerne le problème de minimisation d’une énergie de type Dirichlet à poids. Les fonctions admissibles sont les fonctions continues hors d’un ensemble singulier donné prescrit par le bord d’un courant rectifiable. Nous obtenons la formule exacte, résultat qui améliore celui d’Alberto, Baldi et Orlando (2003). Il s’agit aussi d’une généralisation des résultats obtenus précédemment par Brezis, Coron, Lieb (1986), Almgren, Browder, Lieb (1988).La deuxième partie porte sur le meilleur contrôle des phases des applications uni-modulaires et elle se repose sur les travaux de Bourgain, Brezis, Mironescu (2000, 2002). A l’aide de quelques méthodes connues et des méthodes nouvelles, nous étudions des estimations optimales des semi-normes W^{s,p} des relèvements selon les différentes valeurs de s et de p. Nous obtenons aussi une nouvelle caractérisation de W^{s,p} pour s<1 en termes de semi-norme dyadique

The Spread of Nezara viridula (Hemiptera:Pentatomidae) Species from its First Occurrence in Romania

Lately in horticultural agroecosystems from Romania joined several insect species autochthonous. Among these is a species of bugs known as southern green stink bugs or Nezara viridula L. (Insecta: Hemiptera: Pentatomidae). Unlike other new entrants this bug species has a diversified polifagism being present in many plants but obvious damage produce only tomato fruit. The causes are unknown. Can be found in gardens, green spaces and parks. Often is observed in vegetable gardens where populations comprise all stages (egg, larva/nymph, adult). Although it has African origins of a warm area is interesting installation and survival in temperate zones like those in Europe. Presence in Europe appears to be more random which excludes primarily spread through the neighborhood. By observations made in west of Romania, during 2010-2015 we wanted to watch the evolution of the insect from the first point of occurrence (Timișoara, 2010). Also, were monitored tomato crops and ornamentals in gardens and green spaces from 5 counties. Only in four monitored counties it was observed this species. Most adults and larvae were registered in Timis county (5-6 adults or 7-8 larvae/tomato plant and 10 -11 adults or 15-20 larvae/ornamental shrub). In our country the insect has proven to be capable of a rapid spread in a relatively short time interval including surrounding counties

Is Diabrotica virgifera virgifera still considered a dangerous pest from crops of Romania?

Lately, Diabrotica virgifera virgifera Le Conte adults (western corn rootworm) (Coleoptera: Chrysomelidae) extended the range of host plants and also the spreading area in Romania. Though, until recently it was associatedonly with corn plant (it highlighted the research in Europe) today we can say that this invasive insect, in adult stage,became oligophagous. The current state of research in the field, somewhat restrained, outlines the monitoringaspects of morphology, biology, control and less at plant atractivity. This is the main reason in addressing currenttopics. Also, if we want to answer the question is Diabrotica virgifera virgifera still considered a dangerous pest fromcrops of Romania? the answer is definitely positive. The research took place over the course of tho years of study 2011 and 2012. In our studies we used observation cages type I and II (small cages and high cages). Thus for theevaluation of trophic preferences were achieved through the determination of frequency and intensity of attackson various plants. In the experimental covered setting is obvious attraction towards other than corn comparativewith uncovered setting. By far, the preferred were plants from Cucurbitaceae and Leguminosae. According to theobservations made on the leaves with the highest average attack occurred at the plants of melon, soybean andbeans. The damage done by insects on flowers have highlighted orientation towards plants of sunflower, cucumberand melon. Between variants down to the various plant species in relation to the total number of leaves, flowers, leaves and flowers attacked. Actually, this species invaded the corn crops in western, southern counties, the Nordicand central Romania and damaged few crops. But we supposed that in follow soon will be present throughout thecountry and the attractiveness of the new plants will grow

Non-invasive intracranial pressure monitoring for high-grade gliomas patients treated with radiotherapy: results of the GMaPIC trial

IntroductionPatients with high-grade gliomas are at risk of developing increased intracranial hypertension (ICHT) in relation to the increase in volume of their tumor. ICP change cannot be measured by invasive method but can be estimated by using routine clinical signs, in combination with a standard imaging method, magnetic resonance imaging (MRI). A non-invasive monitoring of ICP could be of interest in high-grade glioma, in particular after radiotherapy treatment with as major side effect a cerebral oedema.Patients and MethodsThis prospective clinical study aimed to compare the ICP changes (estimated by a non-invasive method based upon distortion product otoacoustic emissions (DPOAE) monitoring) with volume changes observed on MRI in patients with high-grade gliomas treated with radiotherapy. DPOAE measurements were performed one month after the end of radiotherapy and then every 3 months for one year. At each visit, the patient also underwent MRI as well as an evaluation of clinical signs.ResultsThe variation in the estimate of intracranial pressure readout measured at each follow-up visit (in absolute value with respect to the baseline measurements) was significantly associated with the variation of T2/FLAIR volume (n=125; p&lt;0.001) with a cut off value of change ICP readout of 40.2 degrees (e.i. an estimated change of 16 mm Hg).DiscussionThe GMaPIC trial confirm the hypothesis that the ICP change estimated by DPOAEs measurement using a non-invasive medical device is correlated with the change of the tumor or edema in high grade glioma after radiotherapy. The device could thus become an easy-to-use and non-invasive intracranial pressure monitoring tool for these patients.Clinical Trial RegistrationClinicaltrials.gov, identifier (NCT02520492

Outcomes among oropharyngeal and oral cavity cancer patients treated with postoperative volumetric modulated arctherapy

BackgroundPresently, there are few published reports on postoperative radiation therapy for oropharyngeal and oral cavity cancers treated with IMRT/VMAT technique. This study aimed to assess the oncological outcomes of this population treated with postoperative VMAT in our institution, with a focus on loco-regional patterns of failure.Material and methodsBetween 2011 and 2019, 167 patients were included (40% of oropharyngeal cancers, and 60% of oral cavity cancers). The median age was 60 years. There was 64.2% of stage IV cancers. All patients had both T and N surgery. 34% had a R1 margin, 42% had perineural invasion. 72% had a positive neck dissection and 42% extranodal extension (ENE). All patients were treated with VMAT with simultaneous integrated boost with three dose levels: 66Gy in case of R1 margin and/or ENE, 59.4-60Gy on the tumor bed, and 54Gy on the prophylactic areas. Concomittant cisplatin was administrated concomitantly when feasible in case of R1 and/or ENE.ResultsThe 1- and 2-year loco-regional control rates were 88.6% and 85.6% respectively. Higher tumor stage (T3/T4), the presence of PNI, and time from surgery &gt;45 days were significant predictive factors of worse loco-regional control in multivariate analysis (p=0.02, p=0.04, and p=0.02). There were 17 local recurrences: 11 (64%) were considered as infield, 4 (24%) as marginal, and 2 (12%) as outfield. There were 9 regional recurrences only, 8 (89%) were considered as infield, and 1 (11%) as outfield. The 1- and 2-year disease-free survival (DFS) rates were 78.9% and 71.8% respectively. The 1- and 2-year overall survival (OS) rates were 88.6% and 80% respectively. Higher tumor stage (T3/T4) and the presence of ENE were the two prognostic factors significantly associated with worse DFS and OS in multivariate analysis.ConclusionOur outcomes for postoperative VMAT for oral cavity and oropharyngeal cancers are encouraging, with high rates of loco-regional control. However, the management of ENE still seems challenging