Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Phenotypic consequences of copy number variation: insights from Smith-Magenis and Potocki-Lupski syndrome mouse models.

A large fraction of genome variation between individuals is comprised of submicroscopic copy number variation of genomic DNA segments. We assessed the relative contribution of structural changes and gene dosage alterations on phenotypic outcomes with mouse models of Smith-Magenis and Potocki-Lupski syndromes. We phenotyped mice with 1n (Deletion/+), 2n (+/+), 3n (Duplication/+), and balanced 2n compound heterozygous (Deletion/Duplication) copies of the same region. Parallel to the observations made in humans, such variation in gene copy number was sufficient to generate phenotypic consequences: in a number of cases diametrically opposing phenotypes were associated with gain versus loss of gene content. Surprisingly, some neurobehavioral traits were not rescued by restoration of the normal gene copy number. Transcriptome profiling showed that a highly significant propensity of transcriptional changes map to the engineered interval in the five assessed tissues. A statistically significant overrepresentation of the genes mapping to the entire length of the engineered chromosome was also found in the top-ranked differentially expressed genes in the mice containing rearranged chromosomes, regardless of the nature of the rearrangement, an observation robust across different cell lineages of the central nervous system. Our data indicate that a structural change at a given position of the human genome may affect not only locus and adjacent gene expression but also "genome regulation." Furthermore, structural change can cause the same perturbation in particular pathways regardless of gene dosage. Thus, the presence of a genomic structural change, as well as gene dosage imbalance, contributes to the ultimate phenotype.

Perinatal choline supplementation reveals a dissociation between two types of spatial strategies.

Choline supplementation improving memory functions in rodents is assumed to increase the synthesis and release of acetylcholine in the brain. We have found that a combined pre- and postnatal supplementation results in long-lasting facilitation of spatial memory in juvenile rats when training was conducted in presence of a local salient cue. The present work was aimed at analysing the effects of peri- and postnatal choline supplementation on spatial abilities of naive adult rats. Rats given a perinatal choline supplementation were trained in various cued procedures of the Morris navigation task when aged 5 months. The treatment had a specific effect of reducing the escape latency of the rats when the platform was at a fixed position in space and surrounded by a suspended cue. This effect was associated with an increased spatial bias when the cue and platform were removed. In this condition, the control rats showed impaired spatial discrimination following the removal of the target cue, most likely due to an overshadowing of the distant environmental cues. This impairment was not observed in the treated rats. Further training with the suspended cue at unpredictable places in the pool revealed longer escape latencies in the control than in the treated rats suggesting that this procedure induced a selective perturbation of the normal but not of the treated rats. A special probe trial with the cue at an irrelevant position and no escape platform revealed a significant bias of the control rats toward the cue and of the treated rats toward the uncued spatial escape position. This behavioural dissociation suggests that a salient cue associated with the target induces an alternative "non spatial" guidance strategy in normal rats, with the risk of overshadowing of the more distant spatial cues. In this condition, the choline supplementation facilities a spatial reliance on the cue, that is an overall facilitation of learning a set of spatial relations between several visual cues. As a consequence, the improved escape in presence of the cue is associated with a stronger memory of the spatial position following disappearance of the cue. This and previous observations suggest that a specific spatial attention process relies on the buffering of highly salient visual cues.to facilitate integration of their relative position in the environment.

Gestió forestal de masses d'arboç (Arbutus unedo) en regeneració després de foc al terme municipal d'Esparreguera

Els incendis forestals són una pertorbació amb un paper decisiu en l’estructura i dinàmica dels ecosistemes mediterranis. La majoria de les seves espècies vegetals presenten mecanismes de resposta al foc, com la germinació de llavors i la rebrotada d’individus cremats. Les masses forestals regenerades a partir de rebrots assoleixen densitats massa altes i una baixa producció, i, per tant, és fonamental dur a terme una gestió mitjançant tractaments silvícoles. El principal objectiu d’aquest projecte és quantificar l’efecte de la selecció de rebrots i la selecció de rebrots més la desbrossada sobre el creixement de l’Arbutus unedo. S’han estudiat 12 parcel—les en regeneració després dels incendis de 1985, 1986 i 1994 al terme municipal d’Esparreguera. Els resultats mostren que els dos tractaments afavoreixen de la mateixa manera el creixement dels peus d’Arbutus unedo, a causa de la disminució de la competència intraespecífica i interespecífica. La desbrossada (a nivell de parcel—la, no d’individu), no obstant, provoca un increment probablement perjudicial de l’alçada dels rebrots, per la major disponibilitat de llum. Per tal de proposar un model de gestió forestal, s’ha realitzat una anàlisi multicriterial dels diferents escenaris, on s’han considerat altres criteris, com són el model de combustible, la possibilitat de pastura i el cost econòmic. L’alternativa preferida en els boscos d’Arbutus unedo és la selecció de rebrots i la desbrossada.

Real time GPS precise positioning of LEO satellites

Report for the scientific sojourn at the German Aerospace Center (DLR) , Germany, during June and July 2006. The main objective of the two months stay has been to apply the techniques of LEO (Low Earth Orbiters) satellites GPS navigation which DLR currently uses in real time navigation. These techniques comprise the use of a dynamical model which takes into account the precise earth gravity field and models to account for the effects which perturb the LEO’s motion (such as drag forces due to earth’s atmosphere, solar pressure, due to the solar radiation impacting on the spacecraft, luni-solar gravity, due to the perturbation of the gravity field for the sun and moon attraction, and tidal forces, due to the ocean and solid tides). A high parameterized software was produced in the first part of work, which has been used to asses which accuracy could be reached exploring different models and complexities. The objective was to study the accuracy vs complexity, taking into account that LEOs at different heights have different behaviors. In this frame, several LEOs have been selected in a wide range of altitudes, and several approaches with different complexity have been chosen. Complexity is a very important issue, because processors onboard spacecrafts have very limited computing and memory resources, so it is mandatory to keep the algorithms simple enough to let the satellite process it by itself.

3D geoelectrical monitoring to follow hydric soil behaviour during rainfall

RESUME Durant les dernières années, les méthodes électriques ont souvent été utilisées pour l'investigation des structures de subsurface. L'imagerie électrique (Electrical Resistivity Tomography, ERT) est une technique de prospection non-invasive et spatialement intégrée. La méthode ERT a subi des améliorations significatives avec le développement de nouveaux algorithmes d'inversion et le perfectionnement des techniques d'acquisition. La technologie multicanale et les ordinateurs de dernière génération permettent la collecte et le traitement de données en quelques heures. Les domaines d'application sont nombreux et divers: géologie et hydrogéologie, génie civil et géotechnique, archéologie et études environnementales. En particulier, les méthodes électriques sont souvent employées dans l'étude hydrologique de la zone vadose. Le but de ce travail est le développement d'un système de monitorage 3D automatique, non- invasif, fiable, peu coûteux, basé sur une technique multicanale et approprié pour suivre les variations de résistivité électrique dans le sous-sol lors d'événements pluvieux. En raison des limitations techniques et afin d'éviter toute perturbation physique dans la subsurface, ce dispositif de mesure emploie une installation non-conventionnelle, où toutes les électrodes de courant sont placées au bord de la zone d'étude. Le dispositif le plus approprié pour suivre les variations verticales et latérales de la résistivité électrique à partir d'une installation permanente a été choisi à l'aide de modélisations numériques. Les résultats démontrent que le dispositif pôle-dipôle offre une meilleure résolution que le dispositif pôle-pôle et plus apte à détecter les variations latérales et verticales de la résistivité électrique, et cela malgré la configuration non-conventionnelle des électrodes. Pour tester l'efficacité du système proposé, des données de terrain ont été collectées sur un site d'étude expérimental. La technique de monitorage utilisée permet de suivre le processus d'infiltration 3D pendant des événements pluvieux. Une bonne corrélation est observée entre les résultats de modélisation numérique et les données de terrain, confirmant par ailleurs que le dispositif pôle-dipôle offre une meilleure résolution que le dispositif pôle-pôle. La nouvelle technique de monitorage 3D de résistivité électrique permet de caractériser les zones d'écoulement préférentiel et de caractériser le rôle de la lithologie et de la pédologie de manière quantitative dans les processus hydrologiques responsables d'écoulement de crue. ABSTRACT During the last years, electrical methods were often used for the investigation of subsurface structures. Electrical resistivity tomography (ERT) has been reported to be a useful non-invasive and spatially integrative prospecting technique. The ERT method provides significant improvements, with the developments of new inversion algorithms, and the increasing efficiency of data collection techniques. Multichannel technology and powerful computers allow collecting and processing resistivity data within few hours. Application domains are numerous and varied: geology and hydrogeology, civil engineering and geotechnics, archaeology and environmental studies. In particular, electrical methods are commonly used in hydrological studies of the vadose zone. The aim of this study was to develop a multichannel, automatic, non-invasive, reliable and inexpensive 3D monitoring system designed to follow electrical resistivity variations in soil during rainfall. Because of technical limitations and in order to not disturb the subsurface, the proposed measurement device uses a non-conventional electrode set-up, where all the current electrodes are located near the edges of the survey grid. Using numerical modelling, the most appropriate arrays were selected to detect vertical and lateral variations of the electrical resistivity in the framework of a permanent surveying installation system. The results show that a pole-dipole array has a better resolution than a pole-pole array and can successfully follow vertical and lateral resistivity variations despite the non-conventional electrode configuration used. Field data are then collected at a test site to assess the efficiency of the proposed monitoring technique. The system allows following the 3D infiltration processes during a rainfall event. A good correlation between the results of numerical modelling and field data results can be observed since the field pole-dipole data give a better resolution image than the pole-pole data. The new device and technique makes it possible to better characterize the zones of preferential flow and to quantify the role of lithology and pedology in flood- generating hydrological processes.

Valproic acid related idiosyncratic drug induced hepatotoxicity in a glioblastoma patient treated with temozolomide.

Glioblastoma patients undergoing treatment with surgery followed by radiation and temozolomide chemotherapy often develop a state of immunosuppression and are at risk for opportunistic infections and reactivation of hepatitis and herpes viruses. We report the case of a 48-year-old glioblastoma patient who developed acute cholestatic hepatitis with hepatic failure during adjuvant treatment with temozolomide and the integrin inhibitor cilengitide. A viral hepatitis was excluded and valproic acid treatment was stopped. Upon normalisation of the liver tests, temozolomide treatment was resumed without perturbation of the liver tests. Valproic acid related idiosyncratic drug induced hepatotoxicity should be considered as a differential diagnosis in glioblastoma patients undergoing adjuvant therapy.

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.

Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer.

Red blood cell (RBC) parameters such as morphology, volume, refractive index, and hemoglobin content are of great importance for diagnostic purposes. Existing approaches require complicated calibration procedures and robust cell perturbation. As a result, reference values for normal RBC differ depending on the method used. We present a way for measuring parameters of intact individual RBCs by using digital holographic microscopy (DHM), a new interferometric and label-free technique with nanometric axial sensitivity. The results are compared with values achieved by conventional techniques for RBC of the same donor and previously published figures. A DHM equipped with a laser diode (lambda = 663 nm) was used to record holograms in an off-axis geometry. Measurements of both RBC refractive indices and volumes were achieved via monitoring the quantitative phase map of RBC by means of a sequential perfusion of two isotonic solutions with different refractive indices obtained by the use of Nycodenz (decoupling procedure). Volume of RBCs labeled by membrane dye Dil was analyzed by confocal microscopy. The mean cell volume (MCV), red blood cell distribution width (RDW), and mean cell hemoglobin concentration (MCHC) were also measured with an impedance volume analyzer. DHM yielded RBC refractive index n = 1.418 +/- 0.012, volume 83 +/- 14 fl, MCH = 29.9 pg, and MCHC 362 +/- 40 g/l. Erythrocyte MCV, MCH, and MCHC achieved by an impedance volume analyzer were 82 fl, 28.6 pg, and 349 g/l, respectively. Confocal microscopy yielded 91 +/- 17 fl for RBC volume. In conclusion, DHM in combination with a decoupling procedure allows measuring noninvasively volume, refractive index, and hemoglobin content of single-living RBCs with a high accuracy.

Condensation of polyhedric structures onto soap films

We study the existence of solutions to general measure-minimization problems over topological classes that are stable under localized Lipschitz homotopy, including the standard Plateau problem without the need for restrictive assumptions such as orientability or even rectifiability of surfaces. In case of problems over an open and bounded domain we establish the existence of a “minimal candidate”, obtained as the limit for the local Hausdorff convergence of a minimizing sequence for which the measure is lower-semicontinuous. Although we do not give a way to control the topological constraint when taking limit yet— except for some examples of topological classes preserving local separation or for periodic two-dimensional sets — we prove that this candidate is an Almgren-minimal set. Thus, using regularity results such as Jean Taylor’s theorem, this could be a way to find solutions to the above minimization problems under a generic setup in arbitrary dimension and codimension.

Molecular mechanisms of drug resistance in clinical Candida species isolated from tunisian hospitals.

Antifungal resistance of Candida species is a clinical problem in the management of diseases caused by these pathogens. In this study we identified from a collection of 423 clinical samples taken from Tunisian hospitals two clinical Candida species (Candida albicans JEY355 and Candida tropicalis JEY162) with decreased susceptibility to azoles and polyenes. For JEY355, the fluconazole (FLC) MIC was 8 μg/ml. Azole resistance in C. albicans JEY355 was mainly caused by overexpression of a multidrug efflux pump of the major facilitator superfamily, Mdr1. The regulator of Mdr1, MRR1, contained a yet-unknown gain-of-function mutation (V877F) causing MDR1 overexpression. The C. tropicalis JEY162 isolate demonstrated cross-resistance between FLC (MIC > 128 μg/ml), voriconazole (MIC > 16 μg/ml), and amphotericin B (MIC > 32 μg/ml). Sterol analysis using gas chromatography-mass spectrometry revealed that ergosterol was undetectable in JEY162 and that it accumulated 14α-methyl fecosterol, thus indicating a perturbation in the function of at least two main ergosterol biosynthesis proteins (Erg11 and Erg3). Sequence analyses of C. tropicalis ERG11 (CtERG11) and CtERG3 from JEY162 revealed a deletion of 132 nucleotides and a single amino acid substitution (S258F), respectively. These two alleles were demonstrated to be nonfunctional and thus are consistent with previous studies showing that ERG11 mutants can only survive in combination with other ERG3 mutations. CtERG3 and CtERG11 wild-type alleles were replaced by the defective genes in a wild-type C. tropicalis strain, resulting in a drug resistance phenotype identical to that of JEY162. This genetic evidence demonstrated that CtERG3 and CtERG11 mutations participated in drug resistance. During reconstitution of the drug resistance in C. tropicalis, a strain was obtained harboring only defective Cterg11 allele and containing as a major sterol the toxic metabolite 14α-methyl-ergosta-8,24(28)-dien-3α,6β-diol, suggesting that ERG3 was still functional. This strain therefore challenged the current belief that ERG11 mutations cannot be viable unless accompanied by compensatory mutations. In conclusion, this study, in addition to identifying a novel MRR1 mutation in C. albicans, constitutes the first report on a clinical C. tropicalis with defective activity of sterol 14α-demethylase and sterol Δ(5,6)-desaturase leading to azole-polyene cross-resistance.

Exponentially small splitting of separatrices in the perturbed McMillan map

The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantities related to the splitting, namely the Lazutkin invariant and the area of the lobe between two consecutive primary homoclinic points. Complex matching techniques are in the core of this work. The coefficients involved in the expansion have a resurgent origin, as shown in [MSS08].

Regulation of the akt signalling in human skeletal muscle atrophy

Abstract : The term "muscle disuse" is often used to refer collectively to reductions in neuromuscular activity as observed with sedentary lifestyles, reduced weight bearing, cancer, chronic obstructive pulmonary disease, chronic heart failure, spinal cord injury, sarcopenia or exposure to microgravity (spaceflight). Muscle disuse atrophy, caused by accelerated proteolysis, is predominantly due to the activation of the ATP-dependent ubiquitin (Ub) proteasome pathway. The current advances in understanding the molecular factors contributing to the Ub-dependent proteolysis process have been made mostly in rodent models of human disease and denervation with few investigations performed directly in humans. Recently, in mice, the genes Atrogin-1 and MuRF1 have been designated as primary candidates in the control of muscle atrophy. Additionally, the decreased activity of the Akt/GSK-3ß and Akt/mTOR pathways has been associated with a reduction in protein synthesis and contributing to skeletal muscle atrophy. Therefore, it is now commonly accepted that skeletal muscle atrophy is the result of a decreased protein synthesis concomitant with an increase in protein degradation (Glass 2003). Atrogin-1 and MuRF1 are genes expressed exclusively in muscle. In mice, their expression has been shown to be directly correlated with the severity of atrophy. KO-mice experiments showed a major protection against atrophy when either of these genes were deleted. Skeletal muscle hypertrophy is an important function in normal postnatal development and in the adaptive response to exercise. It has been shown, in vitro, that the activation of phosphatidylinositol 3-kinase (PI-3K), by insulin growth factor 1 (IGF-1), stimulates myotubes hypertrophy by activating the downstream pathways, Akt/GSK-3ß and Akt/mTOR. It has also been demonstrated in mice, in vivo, that activation of these signalling pathways causes muscle hypertrophy. Moreover, the latter were recently proposed to also reduce muscle atrophy by inhibiting the FKHR mediated transcription of several muscle atrophy genes; Atrogin-1 and MuRF1. Therefore, these targets present new avenues for developing further the understanding of the molecular mechanisms involved in both skeletal muscle atrophy and hypertrophy. The present study proposed to investigate the regulation of the Akt/GSK-3ß and Akt/mTOR signalling pathways, as well as the expression levels of the "atrogenes", Atrogin-1 and MuRF1, in four human models of skeletal muscle atrophy. In the first study, we measured the regulation of the Akt signalling pathway after 8 weeks of both hypertrophy stimulating resistance training and atrophy stimulation de-training. As expected following resistance training, muscle hypertrophy and an increase in the phosphorylation status of the different members of the Akt pathway was observed. This was paralleled by a concomitant decrease in FOXO1 nuclear protein content. Surprisingly, exercise training also induced an increase in the, expression of the atrophy genes and proteins involved in the ATP-dependant ubiquitin-proteasome system. On the opposite, following the de-training period a muscle atrophy, relative to the post-training muscle size, was measured. At the same time, the phosphorylation levels of Akt and GSK-3ß were reduced while the amount of FOXO1 in the nucleus increased. After the atrophy phase, there was also a reduction in Atrogin-1 and MuRF1 contents. In this study, we demonstrate for the first time in healthy human skeletal muscle, that the regulation of Akt and its downstream targets GSK-3ß, mTOR and FOXO1 are associated with both thé skeletal muscle hypertrophy and atrophy processes. Amyotrophic lateral sclerosis (ALS) is a progressive neurodegenerative disease characterized by the loss of both upper and lower motor neurons, which leads to severe muscle weakness and atrophy. All measurements were performed in biopsies from 22 ALS patients and 16 healthy controls. ALS patients displayed an increase in Atrogin-1 mRNA and protein content which was associated with a decrease in Akt activity. However there was no difference in the mRNA and phospho-protein content of FOXO1, FOXO3a, p70S6K and GSK-3ß. The transcriptional regulation of human Atrogin-1 may be controlled by an Akt-mediated transcription factor other than FKHR or via an other signalling pathway. Chronic complete spinal cord injury (SCI) is associated with severe muscle atrophy which is linked to co-morbidity factors such as diabetes, obesity, lipid disorders and cardiovascular diseases. Molecular mechanisms associated with chronic complete SCI-related muscle atrophy are not well understood. The aim of the present study was to determine if there was an increase in catabolic signalling targets such as Atrogin-1, MuRF1, FOXO and myostatin, and decreases in anabolic signalling targets such as IGF, Akt, GSK-3ß, mTOR, 4E-BP1 and p-70S6K in chronic complete SCI patients. All measurements were performed in biopsies taken from 8 complete chronic SCI patients and 7 age matched healthy controls. In SCI patients when compared with controls, there was a significant reduction in mRNA levels of Atrogin1, MuRF1 and Myostatin. Protein levels for Atrogin-1, FOX01 and FOX03a were also reduced. IGF-1 and both phosphorylated GSK-3ß and 4E-BP1 were decreased; the latter two in an Akt and mTOR independent manner, respectively. Reductions in Atrogin-1, MuRF1, FOXO and myostatin suggest the existence of an internal mechanism aimed at reducing further loss of muscle proteins during chronic SCI. The downregulation of signalling proteins regulating anabolism such as IGF, GSK3ß and 4E-BP1 would reduce the ability to increase protein synthesis rates in this chronic state of muscle wasting. The molecular mechanisms controlling age-related skeletal muscle loss in humans are poorly understood. The present study aimed to investigate the regulation of several genes and proteins involved in the activation of key signalling pathways promoting muscle hypertrophy such as GH/STAT5/IGF, IGF/Akt/GSK-3ß/4E-BP1 and muscle atrophy such as TNFα/SOCS3 and Akt/FOXO/Atrogin-1 or MuRF1 in muscle biopsies from 13 young and 16 elderly men. In the older, as compared with the young subjects, TNFα and SOCS-3 were increased while growth hormone receptor protein (GHR) and IGF-1 mRNA were both decreased. Akt protein levels were increased however no change in phosphorylated Akt content was observed. GSK-3ß phosphorylation levels were increased while 4E-BP1 was not changed. Nuclear FKHR and FKHRL1 protein levels were decreased, with no changes in their atrophy target genes, Atrogin-1 and MuRF1. Myostatin mRNA and protein levels were significantly elevated. Human sarcopenia may be linked to a reduction in the activity or sensitivity of anabolic signalling proteins such as GHR, IGF and Akt. TNFα, SOCS-3 and myostatin are potential candidates influencing this anabolic perturbation. In conclusion our results support those obtained in rodent or ín vitro models, and demonstrate Akt plays a pivotal role in the control of muscle mass in humans. However, the Akt phosphorylation status was dependant upon the model of muscle atrophy as Akt phosphorylation was reduced in all atrophy models except for SCI. Additionally, the activity pattern of the downstream targets of Akt appears to be different upon the various human models. It seems that under particular conditions such as spinal cord injury or sarcopenia, .the regulation of GSK-3ß, 4eBP1 and p70S6K might be independent of Akt suggesting alternative signalling pathways in the control of these the anabolic response in human skeletal muscle. The regulation of Atrogin-1 and MuRF1 in some of our studies has been shown to be also independent of the well-described Akt/FOXO signalling pathway suggesting that other transcription factors may regulate human Atrogin-1 and MuRF1. These four different models of skeletal muscle atrophy and hypertrophy have brought a better understanding concerning the molecular mechanisms controlling skeletal muscle mass in humans.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).