A general wavelet-based profile decomposition in the critical embedding of function spaces

We characterize the lack of compactness in the critical embedding of functions spaces $X\subset Y$ having similar scaling properties in the following terms : a sequence $(u_n)_{n\geq 0}$ bounded in $X$ has a subsequence that can be expressed as a finite sum of translations and dilations of functions $(\phi_l)_{l>0}$ such that the remainder converges to zero in $Y$ as the number of functions in the sum and $n$ tend to $+\infty$. Such a decomposition was established by G\'erard for the embedding of the homogeneous Sobolev space $X=\dot H^s$ into the $Y=L^p$ in $d$ dimensions with $0<s=d/2-d/p$, and then generalized by Jaffard to the case where $X$ is a Riesz potential space, using wavelet expansions. In this paper, we revisit the wavelet-based profile decomposition, in order to treat a larger range of examples of critical embedding in a hopefully simplified way. In particular we identify two generic properties on the spaces $X$ and $Y$ that are of key use in building the profile decomposition. These properties may then easily be checked for typical choices of $X$ and $Y$ satisfying critical embedding properties. These includes Sobolev, Besov, Triebel-Lizorkin, Lorentz, H\"older and BMO spaces.Comment: 24 page

Concentration analysis and cocompactness

Loss of compactness that occurs in may significant PDE settings can be expressed in a well-structured form of profile decomposition for sequences. Profile decompositions are formulated in relation to a triplet $(X,Y,D)$, where $X$ and $Y$ are Banach spaces, $X\hookrightarrow Y$, and $D$ is, typically, a set of surjective isometries on both $X$ and $Y$. A profile decomposition is a representation of a bounded sequence in $X$ as a sum of elementary concentrations of the form $g_kw$, $g_k\in D$, $w\in X$, and a remainder that vanishes in $Y$. A necessary requirement for $Y$ is, therefore, that any sequence in $X$ that develops no $D$-concentrations has a subsequence convergent in the norm of $Y$. An imbedding $X\hookrightarrow Y$ with this property is called $D$-cocompact, a property weaker than, but related to, compactness. We survey known cocompact imbeddings and their role in profile decompositions

Sentiment analysis tools should take account of the number of exclamation marks!!!

There are various factors that affect the sentiment level expressed in textual comments. Capitalization of letters tends to mark something for attention and repeating of letters tends to strengthen the emotion. Emoticons are used to help visualize facial expressions which can affect understanding of text. In this paper, we show the effect of the number of exclamation marks used, via testing with twelve online sentiment tools. We present opinions gathered from 500 respondents towards “like” and “dislike” values, with a varying number of exclamation marks. Results show that only 20% of the online sentiment tools tested considered the number of exclamation marks in their returned scores. However, results from our human raters show that the more exclamation marks used for positive comments, the more they have higher “like” values than the same comments with fewer exclamations marks. Similarly, adding more exclamation marks for negative comments, results in a higher “dislike”

Pseudomonas rhizophila S211, a New Plant Growth-Promoting Rhizobacterium with Potential in Pesticide-Bioremediation

A number of Pseudomonas strains function as inoculants for biocontrol, biofertilization, and phytostimulation, avoiding the use of pesticides and chemical fertilizers. Here, we present a new metabolically versatile plant growth-promoting rhizobacterium, Pseudomonas rhizophila S211, isolated from a pesticide contaminated artichoke field that shows biofertilization, biocontrol and bioremediation potentialities. The S211 genome was sequenced, annotated and key genomic elements related to plant growth promotion and biosurfactant (BS) synthesis were elucidated. S211 genome comprises 5,948,515 bp with 60.4% G+C content, 5306 coding genes and 215 RNA genes. The genome sequence analysis confirmed the presence of genes involved in plant-growth promoting and remediation activities such as the synthesis of ACC deaminase, putative dioxygenases, auxin, pyroverdin, exopolysaccharide levan and rhamnolipid BS. BS production by P. rhizophila S211 grown on olive mill wastewater based media was effectively optimized using a central-composite experimental design and response surface methodology (RSM). The optimum conditions for maximum BS production yield (720.80 ± 55.90 mg/L) were: 0.5% (v/v) inoculum size, 15% (v/v) olive oil mill wastewater (OMWW) and 40◦C incubation temperature at pH 6.0 for 8 days incubation period. Biochemical and structural characterization of S211 BS by chromatography and spectroscopy studies suggested the glycolipid nature of the BS. P. rhizophila rhamnolipid was stable over a wide range of temperature (40–90◦C), pH (6–10), and salt concentration (up to 300mM NaCl). Due to its low-cost production, emulsification activities and high performance in solubilization enhancement of chemical pesticides, the indigenous BS-producing PGPR S211 could be used as a promising agent for environmental bioremediation of pesticide-contaminated agricultural soils

Conversion of Uric Acid into Ammonium in Oil-Degrading Marine Microbial Communities: a Possible Role of Halomonads

Uric acid is a promising hydrophobic nitrogen source for biostimulation of microbial activities in oil-impacted marine environments. This study investigated metabolic processes and microbial community changes in a series of microcosms using sediment from the Mediterranean and the Red Sea amended with ammonium and uric acid. Respiration, emulsification, ammonium and protein concentration measurements suggested a rapid production of ammonium from uric acid accompanied by the development of microbial communities containing hydrocarbonoclastic bacteria after 3 weeks of incubation. About 80 % of uric acid was converted to ammonium within the first few days of the experiment. Microbial population dynamics were investigated by Ribosomal Intergenic Spacer Analysis and Illumina sequencing as well as by culture-based techniques. Resulting data indicated that strains related to Halomonas spp. converted uric acid into ammonium, which stimulated growth of microbial consortia dominated by Alcanivorax spp. and Pseudomonas spp. Several strains of Halomonas spp. were isolated on uric acid as the sole carbon source showed location specificity. These results point towards a possible role of halomonads in the conversion of uric acid to ammonium utilized by hydrocarbonoclastic bacteria.With exception of XH and JC, all authors were supported by the FP7 Project ULIXES (FP7-KBBE-2010-266473). This work was further funded by grant BIO2011-25012 from the Spanish Ministry of the Economy and Competitiveness. FM was supported by Università degli Studi di Milano, European Social Fund (FSE) and Regione Lombardia (contract BDote Ricerca^). DD acknowledges support of KAUST, King Abdullah University of Science and Technology. PG acknowledges the support of the European Commission through the project Kill-Spill (FP7, Contract Nr 312139).Peer Reviewe

Profiling of the BRCA1 transcriptome through microarray and ChIP-chip analysis

A role for BRCA1 in the direct and indirect regulation of transcription is well established. However, a comprehensive view of the degree to which BRCA1 impacts transcriptional regulation on a genome-wide level has not been defined. We performed genome-wide expression profiling and ChIP-chip analysis, comparison of which revealed that although BRCA1 depletion results in transcriptional changes in 1294 genes, only 44 of these are promoter bound by BRCA1. However, 27% of these transcripts were linked to transcriptional regulation possibly explaining the large number of indirect transcriptional changes observed by microarray analysis. We show that no specific consensus sequence exists for BRCA1 DNA binding but rather demonstrate the presence of a number of known and novel transcription factor (TF)- binding sites commonly found on BRCA1 bound promoters. Co-immunoprecipitations confirmed that BRCA1 interacts with a number of these TFs including AP2-α, PAX2 and ZF5. Finally, we show that BRCA1 is bound to a subset of promoters of genes that are not altered by BRCA1 loss, but are transcriptionally regulated in a BRCA1-dependent manner upon DNA damage. These data suggest a model, whereby BRCA1 is present on defined promoters as part of an inactive complex poised to respond to various genotoxic stimuli

Ensemble approach for generalized network dismantling

Finding a set of nodes in a network, whose removal fragments the network below some target size at minimal cost is called network dismantling problem and it belongs to the NP-hard computational class. In this paper, we explore the (generalized) network dismantling problem by exploring the spectral approximation with the variant of the power-iteration method. In particular, we explore the network dismantling solution landscape by creating the ensemble of possible solutions from different initial conditions and a different number of iterations of the spectral approximation.Comment: 11 Pages, 4 Figures, 4 Table

Mathematical Modeling of the Role of Mitochondrial Fusion and Fission in Mitochondrial DNA Maintenance

10.1371/journal.pone.0076230PLOS ONE8101-1