On a conjecture regarding the upper graph box dimension of bounded subsets of the real line

Let X \subset R be a bounded set; we introduce a formula that calculates the upper graph box dimension of X (i.e.the supremum of the upper box dimension of the graph over all uniformly continuous functions defined on X). We demonstrate the strength of the formula by calculating the upper graph box dimension for some sets and by giving an "one line" proof, alternative to the one given in [1], of the fact that if X has finitely many isolated points then its upper graph box dimension is equal to the upper box dimension plus one. Furthermore we construct a collection of sets X with infinitely many isolated points, having upper box dimension a taking values from zero to one while their graph box dimension takes any value in [max{2a,1},a + 1], answering this way, negatively to a conjecture posed in [1]

Pupil mobility, attainment and progress in secondary school

This paper is the second of two articles arising from a study of the association between pupil mobility and attainment in national tests and examinations in an inner London borough. The first article (Strand & Demie, 2006) examined the association of pupil mobility with attainment and progress during primary school. It concluded that pupil mobility had little impact on performance in national tests at age 11, once pupils’ prior attainment at age 7 and other pupil background factors such as age, sex, special educational needs, stage of fluency in English and socio-economic disadvantage were taken into account. The present article reports the results for secondary schools (age 11-16). The results indicate that pupil mobility continues to have a significant negative association with performance in public examinations at age 16, even after including statistical controls for prior attainment at age 11 and other pupil background factors. Possible reasons for the contrasting results across school phases are explored. The implications for policy and further research are discussed

Two ideals connected with strong right upper porosity at a point

Let $SP$ be the set of upper strongly porous at $0$ subsets of $\mathbb R^{+}$ and let $\hat I(SP)$ be the intersection of maximal ideals $I \subseteq SP$. Some characteristic properties of sets $E\in\hat I(SP)$ are obtained. It is shown that the ideal generated by the so-called completely strongly porous at $0$ subsets of $\mathbb R^{+}$ is a proper subideal of $\hat I(SP).$Comment: 18 page

Arithmetic progressions in sets of fractional dimension

Let E\subset\rr be a closed set of Hausdorff dimension $\alpha$. We prove that if $\alpha$ is sufficiently close to 1, and if $E$ supports a probabilistic measure obeying appropriate dimensionality and Fourier decay conditions, then $E$ contains non-trivial 3-term arithmetic progressions.Comment: 42 page

Coordinated Translocation of Mammalian Gli Proteins and Suppressor of Fused to the Primary Cilium

Intracellular transduction of Hedgehog (Hh) signals in mammals requires functional primary cilia. The Hh signaling effectors, the Gli family of transcription factors, and their negative regulator, Suppressor of Fused (Sufu), accumulate at the tips of cilia; however, the molecular mechanism regulating this localization remains elusive. In the current study, we show that the ciliary localization of mammalian Gli proteins depends on both their N-terminal domains and a central region lying C-terminal to the zinc-finger DNA-binding domains. Invertebrate Gli homologs Ci and Tra1, when over-expressed in ciliated mouse fibroblasts, fail to localize to the cilia, suggesting the lack of a vertebrate-specific structural feature required for ciliary localization. We further show that activation of protein kinase A (PKA) efficiently inhibits ciliary localization of Gli2 and Gli3, but only moderately affects the ciliary localization of Gli1. Interestingly, variants of Gli2 mimicking the phosphorylated or non-phosphorylated states of Gli2 are both localized to the cilia, and their ciliary localizations are subjected to the inhibitory effect of PKA activation, suggesting a likely indirect mechanism underlying the roles of PKA in Gli ciliary localization. Finally, we show that ciliary localization of Sufu is dependent on ciliary-localized Gli proteins, and is inhibited by PKA activation, suggesting a coordinated mechanism for the ciliary translocation of Sufu and Gli proteins

NOD2-C2 - a novel NOD2 isoform activating NF-κB in a muramyl dipeptide-independent manner

<p>Abstract</p> <p>Background</p> <p>The innate immune system employs several receptor families that form the basis of sensing pathogen-associated molecular patterns. NOD (nucleotide-binding and oligomerization domain) like receptors (NLRs) comprise a group of cytosolic proteins that trigger protective responses upon recognition of intracellular danger signals. NOD2 displays a tandem caspase recruitment domain (CARD) architecture, which is unique within the NLR family.</p> <p>Findings</p> <p>Here, we report a novel alternative transcript of the <it>NOD2 </it>gene, which codes for a truncated tandem CARD only protein, called NOD2-C2. The transcript isoform is highest expressed in leucocytes, a natural barrier against pathogen invasion, and is strictly linked to promoter usage as well as predominantly to one allele of the single nucleotide polymorphism rs2067085. Contrary to a previously identified truncated single CARD NOD2 isoform, NOD2-S, NOD2-C2 is able to activate NF-κB in a dose dependent manner independently of muramyl dipeptide (MDP). On the other hand NOD2-C2 competes with MDPs ability to activate the NOD2-driven NF-κB signaling cascade.</p> <p>Conclusion</p> <p>NOD2 transcripts having included an alternative exon downstream of exon 3 (exon 3a) are the endogenous equivalents of a previously described <it>in vitro </it>construct with the putative protein composed of only the two N-terminal CARDs. This protein form (NOD2-C2) activates NF-κB independent of an MDP stimulus and is a potential regulator of NOD2 signaling.</p

Molecular basis of caspase-1 polymerization and its inhibition by a new capping mechanism

Inflammasomes are cytosolic caspase-1-activation complexes that sense intrinsic and extrinsic danger signals, and trigger inflammatory responses and pyroptotic cell death. Homotypic interactions among Pyrin domains and caspase recruitment domains (CARDs) in inflammasome-complex components mediate oligomerization into filamentous assemblies. Several cytosolic proteins consisting of only interaction domains exert inhibitory effects on inflammasome assembly. In this study, we determined the structure of the human caspase-1 CARD domain (caspase-1[superscript CARD]) filament by cryo-electron microscopy and investigated the biophysical properties of two caspase-1-like CARD-only proteins: human inhibitor of CARD (INCA or CARD17) and ICEBERG (CARD18). Our results reveal that INCA caps caspase-1 filaments, thereby exerting potent inhibition with low-nanomolar K[subscript i] on caspase-1[superscript CARD] polymerization in vitro and inflammasome activation in cells. Whereas caspase-1[superscript CARD] uses six complementary surfaces of three types for filament assembly, INCA is defective in two of the six interfaces and thus terminates the caspase-1 filament

Planning community-wide special events / 1123

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