On the Assouad dimension of self-similar sets with overlaps

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the \emph{weak separation property} is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the \emph{weak separation property} is not satisfied, in which case the Assouad dimension is maximal (equal to one). In the first case we prove that the self-similar set is Ahlfors regular, and in the second case we use the fact that if the \emph{weak separation property} is not satisfied, one can approximate the identity arbitrarily well in the group generated by the similarity mappings, and this allows us to build a \emph{weak tangent} that contains an interval. We also obtain results in higher dimensions and provide illustrative examples showing that the `equality/maximal' dichotomy does not extend to this setting.Comment: 24 pages, 2 figure

Twist Is Required for Muscle Template Splitting during AdultDrosophilaMyogenesis

AbstractThe basic helix–loop–helix transcription factor Twist is required for normal development of larval and adult somatic muscles inDrosophila.Adult flies normally have six pairs of dorsal longitudinal indirect flight muscles (DLMs), whereas when Twist function is reduced, only three pairs of DLMs are formed. Althoughtwistis expressed in precursors of adult muscles throughout the larval and early pupal stages, we demonstrate that Twist function is required only during the late larval stage for DLM patterning. In wild-type flies, this is just prior to the time when three pairs of persistent larval muscle fibers split longitudinally to form templates for the six pairs of DLMs. By examining sections at various times during pupal development, we found that splitting of the larval muscles does not occur intwistmutants, indicating that Twist function is required to induce major changes in the larval templates prior to differentiation. The function of Twist in larval muscle splitting is likely mediated by myocyte enhancer factor-2 (MEF2) since inMef2hypomorphic mutants splitting is also reduced andMef2expression is dependent upon Twist. Our findings define specific roles for Twist and MEF2 during pupal myogenesis and demonstrate that these transcription factors function in adult muscle precursor cells to regulate downstream factors controlling muscle cell splitting and morphogenesis

Effects of Sequence Context on the Binding of Tryptophan-Containing Peptides by the Cucurbit[8]uril-Methyl Viologen Complex

This paper describes a novel assay for measuring the relative extent of peptide binding in a large parallel format and the use of this assay to explore the effects of sequence context on the binding of tryptophan (Trp)-containing peptides by the synthetic receptor comprising the noncovalent complex between cucurbit[8]uril and methyl viologen (i.e. Q8√MV). The extent of quenching of Trp fluorescence upon binding to Q8√MV was used to measure the relative extent of binding and thus the relative affinities of 104 Trp-containing peptides, in parallel, using a fluorescence plate reader. This study resulted in the remarkable observation that the identity of the amino acid residues at positions adjacent to the Trp-binding site has little if any influence on the binding affinity. This finding suggests that Q8√MV should be effective for the recognition of Trp residues within a broad range of peptide sequences

A reexamination of real stock returns, real interest rates, real activity, and inflation: Evidence from a large data set

Using the informational sufficiency procedure from Forni and Gambetti (2014) along with data from McCracken and Ng (2014), we update the results of Lee (1992) and find that his Vector Autoregression (VAR) is informationally deficient. To correct this problem, we estimate a Factor Augmented VAR (FAVAR) and analyze the differences once informational deficiency is corrected with an emphasis on the relationship between real stock returns and inflation. In particular, we examine Modigliani and Cohn’s (1979) inflation illusion hypothesis, Fama’s (1983) proxy hypothesis, and the “anticipated policy hypothesis.

Prospectus, January 31, 2007

https://spark.parkland.edu/prospectus_2007/1002/thumbnail.jp

Relationship of national institutes of health stroke scale to 30-day mortality in medicare beneficiaries with acute ischemic stroke.

BackgroundThe National Institutes of Health Stroke Scale (NIHSS), a well-validated tool for assessing initial stroke severity, has previously been shown to be associated with mortality in acute ischemic stroke. However, the relationship, optimal categorization, and risk discrimination with the NIHSS for predicting 30-day mortality among Medicare beneficiaries with acute ischemic stroke has not been well studied.Methods and resultsWe analyzed data from 33102 fee-for-service Medicare beneficiaries treated at 404 Get With The Guidelines-Stroke hospitals between April 2003 and December 2006 with NIHSS documented. The 30-day mortality rate by NIHSS as a continuous variable and by risk-tree determined or prespecified categories were analyzed, with discrimination of risk quantified by the c-statistic. In this cohort, mean age was 79.0 years and 58% were female. The median NIHSS score was 5 (25th to 75th percentile 2 to 12). There were 4496 deaths in the first 30 days (13.6%). There was a strong graded relation between increasing NIHSS score and higher 30-day mortality. The 30-day mortality rates for acute ischemic stroke by NIHSS categories were as follows: 0 to 7, 4.2%; 8 to 13, 13.9%; 14 to 21, 31.6%; 22 to 42, 53.5%. A model with NIHSS alone provided excellent discrimination whether included as a continuous variable (c-statistic 0.82 [0.81 to 0.83]), 4 categories (c-statistic 0.80 [0.79 to 0.80]), or 3 categories (c-statistic 0.79 [0.78 to 0.79]).ConclusionsThe NIHSS provides substantial prognostic information regarding 30-day mortality risk in Medicare beneficiaries with acute ischemic stroke. This index of stroke severity is a very strong discriminator of mortality risk, even in the absence of other clinical information, whether used as a continuous or categorical risk determinant. (J Am Heart Assoc. 2012;1:42-50.)