Covering dimension and differential inclusions

summary:In this paper we shall establish a result concerning the covering dimension of a set of the type $\{x\in X:\Phi (x)\cap \Psi (x)\neq \emptyset \}$, where $\Phi$, $\Psi$ are two multifunctions from $X$ into $Y$ and $X$, $Y$ are real Banach spaces. Moreover, some applications to the differential inclusions will be given

Existence and multiplicity of solutions for Dirichlet problems involving nonlinearities with arbitrary growth.

In this article we study the existence and multiplicity of solutions for the Dirichlet problem \displaylines{ -\Delta_p u=\lambda f(x,u)+ \mu g(x,u)\quad\hbox{in }\Omega,\cr u=0\quad\hbox{on } \partial \Omega} where $\Omega$ is a bounded domain in $\mathbb{R}^N$, $f,g:\Omega \times \mathbb{R}\to \mathbb{R}$ are Caratheodory functions, and $\lambda,\mu$ are nonnegative parameters. We impose no growth condition at $\infty$ on the nonlinearities f,g. A corollary to our main result improves an existence result recently obtained by Bonanno via a critical point theorem for $C^1$ functionals which do not satisfy the usual sequential weak lower semicontinuity property

Existence of General Competitive Equilibria: A Variational Approach

We study the existence of general competitive equilibria in economies with agents and goods in a finite number. We show that there exists a Walras competitive equilibrium in all ownership private economies such that, for all consumers, initial endowments do not contain free goods and utility functions are locally Lipschitz quasiconcave. The proof of the existence of competitive equilibria is based on variational methods by applying a theoretical existence result for Generalized Quasi Variational Inequalities

A long-term time series of global and diffuse photosynthetically active radiation in the Mediterranean: interannual variability and cloud effects

Abstract. Measurements of global and diffuse photosynthetically active radiation (PAR) have been carried out on the island of Lampedusa, in the central Mediterranean Sea, since 2002. PAR is derived from observations made with multi-filter rotating shadowband radiometers (MFRSRs) by comparison with a freshly calibrated PAR sensor and by relying on the on-site Langley plots. In this way, a long-term calibrated record covering the period 2002–2016 is obtained and is presented in this work. The monthly mean global PAR peaks in June, with about 160 W m−2, while the diffuse PAR reaches 60 W m−2 in spring or summer. The global PAR displays a clear annual cycle with a semi amplitude of about 52 W m−2. The diffuse PAR annual cycle has a semi amplitude of about 12 W m−2. A simple method to retrieve the cloud-free PAR global and diffuse irradiances in days characterized by partly cloudy conditions has been implemented and applied to the dataset. This method allows retrieval of the cloud-free evolution of PAR and calculation of the cloud radiative effect, CRE, for downwelling PAR. The cloud-free monthly mean global PAR reaches 175 W m−2 in summer, while the diffuse PAR peaks at about 40 W m−2. The cloud radiative effect, CRE, on global and diffuse PAR is calculated as the difference between all-sky and cloud-free measurements. The annual average CRE is about −14.7 W m−2 for the global PAR and +8.1 W m−2 for the diffuse PAR. The smallest CRE is observed in July, due to the high cloud-free condition frequency. Maxima (negative for the global, and positive for the diffuse component) occur in March–April and in October, due to the combination of elevated PAR irradiances and high occurrence of cloudy conditions. Summer clouds appear to be characterized by a low frequency of occurrence, low altitude, and low optical thickness, possibly linked to the peculiar marine boundary layer structure. These properties also contribute to produce small radiative effects on PAR in summer. The cloud radiative effect has been deseasonalized to remove the influence of annual irradiance variations. The monthly mean normalized CRE for global PAR can be well represented by a multi-linear regression with respect to monthly cloud fraction, cloud top pressure, and cloud optical thickness, as determined from satellite MODIS observations. The behaviour of the normalized CRE for diffuse PAR can not be satisfactorily described by a simple multi-linear model with respect to the cloud properties, due to its non-linear dependency, in particular on the cloud optical depth. The analysis suggests that about 77 % of the global PAR interannual variability may be ascribed to cloud variability in winter

Clinical variability at the mild end of BRAT1-related spectrum: Evidence from two families with genotype–phenotype discordance

Biallelic mutations in the BRAT1 gene, encoding BRCA1-associated ATM activator 1, result in variable phenotypes, from rigidity and multifocal seizure syndrome, lethal neonatal to neurodevelopmental disorder, and cerebellar atrophy with or without seizures, without obvious genotype-phenotype associations. We describe two families at the mildest end of the spectrum, differing in clinical presentation despite a common genotype at the BRAT1 locus. Two siblings displayed nonprogressive congenital ataxia and shrunken cerebellum on magnetic resonance imaging. A third unrelated patient showed normal neurodevelopment, adolescence-onset seizures, and ataxia, shrunken cerebellum, and ultrastructural abnormalities on skin biopsy, representing the mildest form of NEDCAS hitherto described. Exome sequencing identified the c.638dup and the novel c.1395G>A BRAT1 variants, the latter causing exon 10 skippings. The p53-MCL test revealed normal ATM kinase activity. Our findings broaden the allelic and clinical spectrum of BRAT1-related disease, which should be suspected in presence of nonprogressive cerebellar signs, even without a neurodevelopmental disorder

Characterization of PM10 sources in the central Mediterranean

The Mediterranean Basin atmosphere is influenced by both strong natural and anthropogenic aerosol emissions and is also subject to important climatic forcings. Several programs have addressed the study of the Mediterranean basin; nevertheless important pieces of information are still missing. In this framework, PM10 samples were collected on a daily basis on the island of Lampedusa (35.5° N, 12.6° E; 45 m a.s.l.), which is far from continental pollution sources (the nearest coast, in Tunisia, is more than 100 km away). After mass gravimetric measurements, different portions of the samples were analyzed to determine the ionic content by ion chromatography (IC), the soluble metals by inductively coupled plasma atomic emission spectrometry (ICP-AES), and the total (soluble + insoluble) elemental composition by particle-induced x-ray emission (PIXE). Data from 2007 and 2008 are used in this study. The Positive Matrix Factorization (PMF) model was applied to the 2-year long data set of PM10 mass concentration and chemical composition to assess the aerosol sources affecting the central Mediterranean basin. Seven sources were resolved: sea salt, mineral dust, biogenic emissions, primary particulate ship emissions, secondary sulfate, secondary nitrate, and combustion emissions. Source contributions to the total PM10 mass were estimated to be about 40 % for sea salt, around 25 % for mineral dust, 10 % each for secondary nitrate and secondary sulfate, and 5 % each for primary particulate ship emissions, biogenic emissions, and combustion emissions. Large variations in absolute and relative contributions are found and appear to depend on the season and on transport episodes. In addition, the secondary sulfate due to ship emissions was estimated and found to contribute by about one-third to the total sulfate mass. Results for the sea-salt and mineral dust sources were compared with estimates of the same contributions obtained from independent approaches, leading to an estimate of the water content bound to the sea salt in the marine source

Agenesis of the putamen and globus pallidus caused by recessive mutations in the homeobox gene GSX2

Basal ganglia are subcortical grey nuclei that play essential roles in controlling voluntary movements, cognition and emotion. While basal ganglia dysfunction is observed in many neurodegenerative or metabolic disorders, congenital malformations are rare. In particular, dysplastic basal ganglia are part of the malformative spectrum of tubulinopathies and X-linked lissencephaly with abnormal genitalia, but neurodevelopmental syndromes characterized by basal ganglia agenesis are not known to date. We ascertained two unrelated children (both female) presenting with spastic tetraparesis, severe generalized dystonia and intellectual impairment, sharing a unique brain malformation characterized by agenesis of putamina and globi pallidi, dysgenesis of the caudate nuclei, olfactory bulbs hypoplasia, and anomaly of the diencephalic-mesencephalic junction with abnormal corticospinal tract course. Whole-exome sequencing identified two novel homozygous variants, c.26C>A; p.(S9*) and c.752A>G; p.(Q251R) in the GSX2 gene, a member of the family of homeobox transcription factors, which are key regulators of embryonic development. GSX2 is highly expressed in neural progenitors of the lateral and median ganglionic eminences, two protrusions of the ventral telencephalon from which the basal ganglia and olfactory tubercles originate, where it promotes neurogenesis while negatively regulating oligodendrogenesis. The truncating variant resulted in complete loss of protein expression, while the missense variant affected a highly conserved residue of the homeobox domain, was consistently predicted as pathogenic by bioinformatic tools, resulted in reduced protein expression and caused impaired structural stability of the homeobox domain and weaker interaction with DNA according to molecular dynamic simulations. Moreover, the nuclear localization of the mutant protein in transfected cells was significantly reduced compared to the wild-type protein. Expression studies on both patients' fibroblasts demonstrated reduced expression of GSX2 itself, likely due to altered transcriptional self-regulation, as well as significant expression changes of related genes such as ASCL1 and PAX6. Whole transcriptome analysis revealed a global deregulation in genes implicated in apoptosis and immunity, two broad pathways known to be involved in brain development. This is the first report of the clinical phenotype and molecular basis associated to basal ganglia agenesis in humans

Cellular and molecular effects of protons: apoptosis induction and potential implications for cancer therapy.

Due to their ballistic precision, apoptosis induction by protons could be a strategy to specifically eliminate neoplastic cells. To characterize the cellular and molecular effects of these hadrons, we performed dose-response and time-course experiments by exposing different cell lines (PC3, Ca301D, MCF7) to increasing doses of protons and examining them with FACS, RT-PCR, and electron spin resonance (ESR). Irradiation with a dose of 10 Gy of a 26,7 Mev proton beam altered cell structures such as membranes, caused DNA double strand breaks, and significantly increased intracellular levels of hydroxyl ions, are active oxygen species (ROS). This modified the transcriptome of irradiated cells, activated the mitochondrial (intrinsic) pathway of apoptosis, and resulted in cycle arrest at the G2/M boundary. The number of necrotic cells within the irradiated cell population did not significantly increase with respect to the controls. The effects of irradiation with 20 Gy were qualitatively as well as quantitatively similar, but exposure to 40 Gy caused massive necrosis. Similar experiments with photons demonstrated that they induce apoptosis in a significantly lower number of cells and in a temporally delayed manner. These data advance our knowledge on the cellular and molecular effects of proton irradiation and could be useful for improving current hadrontherapy protocols

Visual attention and autistic behavior in infants with fragile X syndrome

Fragile X syndrome (FXS) is the leading known inherited cause of intellectual disability and the most common known biological cause of autism. Approximately 25% to 50% of males with FXS meet full diagnostic criteria for autism. Despite the high comorbidity between FXS and autism and the ability to diagnose FXS prenatally or at birth, no studies have examined indicators of autism in infants with FXS. The current study focused on indices of visual attention, one of the earliest and most robust behavioral indicators of autism in idiopathic (non-FXS) autism. Analyses revealed lower HR variability, shallower HR decelerations, and prolonged look durations in 12-month old infants with FXS that were correlated with severity of autistic behavior but not mental age

Chronic Antidiabetic Sulfonylureas In Vivo: Reversible Effects on Mouse Pancreatic β-Cells

In a mouse study aiming to understand why long-term treatment for type 2 diabetes with sulfonylureas eventually fails, Colin Nichols and Maria Remedi suggest that slow restoration of insulin secretion may be possible after a drug-resting period