Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.

High circulating levels of the dengue virus nonstructural protein NS1 early in dengue illness correlate with the development of dengue hemorrhagic fever

Infection with any 1 of 4 dengue viruses produces a spectrum of clinical illness ranging from a mild undifferentiated febrile illness to dengue fever (DF) to dengue hemorrhagic fever (DHF), a potentially life-threatening disease. The morbidity and mortality of DHF can be reduced by early hospitalization and careful supportive care. To determine its usefulness as a predictor of DHF, plasma levels of the secreted dengue virus nonstructural protein NS1 (sNS1) were measured daily in 32 children with dengue-2 virus infections participating in a prospective, hospital-based study. Free sNS1 levels in plasma correlated with viremia levels and were higher in patients with DHF than in those with DF. An elevated free sNS1 level (greater than or equal to600 ng/mL) within 72 h of illness onset identified patients at risk for developing DHF.

Early intervention: Narratives of learning, discipline and enculturation

Current understandings about literacy have moved away from the belief that literacy is simply a process that individuals do in their heads. These understandings do not negate the importance of the individual aspects of literacy learning, but they emphasize understandings of literacy as a social practice. In many cases, responses to early literacy intervention seem to be grounded in theories that appear out of step with current literacy research and consequent evidence that literacy is socially and culturally constructed. One such response is the Reading Recovery programme based on Clay’s theory of literacy acquisition. Clay (1992) describes the programme as a second chance to learn. However, others have suggested that programmes like Reading Recovery may in fact work toward the marginalization of particular groups, thereby helping to maintain the status quo along class, gender and ethnic lines. This article allows two professionals to bring their insider’s knowledge of Reading Recovery to an analysis of the construction of the programme. The article interweaves this analysis with the personal narratives of the researchers as they negotiated the borders between different understandings and beliefs about literacy and literacy pedagogy.

Application of spatial analysis techniques to adjust for fertility trends and identify interplot competition in early stage sugarcane selection trials

Most sugarcane breeding programs in Australia use large unreplicated trials to evaluate clones in the early stages of selection. Commercial varieties that are replicated provide a method of local control of soil fertility. Although such methods may be useful in detecting broad trends in the field, variation often occurs on a much smaller scale. Methods such as spatial analysis adjust a plot for variability by using information from immediate neighbours. These techniques are routinely used to analyse cereal data in Australia and have resulted in increased accuracy and precision in the estimates of variety effects. In this paper, spatial analyses in which the variability is decomposed into local, natural, and extraneous components are applied to early selection trials in sugarcane. Interplot competition in cane yield and trend in sugar content were substantial in many of the trials and there were often large differences in the selections between the spatial and current method used by the Bureau of Sugar Experiment Stations. A joint modelling approach for tonnes sugar per hectare in response to fertility trends and interplot competition is recommended.

The Phox Homology (PX) domain-dependent, 3-phosphoinositide-mediated association of sorting nexin-1 with an early sorting endosomal compartment is required for its ability to regulate epidermal growth factor receptor degradation

Recent studies have shown that phox homology (PX) domains act as phosphoinositide-binding motifs. The majority of PX domains studied show binding to phosphatidylinositol 3-monophosphate (Ptdlns(3)P), an association that allows the host protein to localize to membranes of the endocytic pathway. One issue, however, is whether PX domains may have alternative phosphoinositide binding specificities that could target their host protein to distinct subcellular compartments or allow their allosteric regulation by phosphoinositides other than PtdIns(3)P. It has been reported that the PX domain of sorting nexin 1 (SNX1) specifically binds phosphatidylinositol 3,4,5-trisphosphate (PtdIns(3,4,5)P-3) (Zhong, Q., Lazar, C. S., Tronchere, H., Sato, T., Meerloo, T., Yeo, M., Songyang, Z., Emr, S. D., and Gill, G. N. (2002) Proc. Natl. Acad. Sci. U. S. A. 99,6767-6772). In the present study, we have shown that whereas SNX1 binds PtdIns(3,4,5)P-3 in protein:lipid overlay assays, in liposomes-based assays, binding is observed to PtdIns(3)P and phosphatidylinositol 3,5-bisphosphate (PtdIns(3,5)P-2) but not to PtdIns(3,4,5)P-3. To address the significance of PtdIns(3,4,5)P-3 binding, we examined the subcellular localization of SNX1 under conditions in which plasma membrane PtdIns(3,4,5)P-3 levels were significantly elevated. Under these conditions, we failed to observe association of SNX1 with this membrane. However, consistent with the binding to PtdIns(3)P and PtdIns(3,5)P-2 being of more physiological significance was the observation that the association of SNX1 with an early endosomal compartment was dependent on a 3-phosphoinositide-binding PX domain and the presence of PtdIns(3)P on this compartment. Finally, we somal association of SNX1 is important for its ability to regulate the targeting of internalized epidermal growth factor receptor for lysosomal degradation.

Tungsten isotope evidence from similar to 3.8-Gyr metamorphosed sediments for early meteorite bombardment of the Earth

The 'Late Heavy Bombardment' was a phase in the impact history of the Moon that occurred 3.8-4.0 Gyr ago, when the lunar basins with known dates were formed(1,2). But no record of this event has yet been reported from the few surviving rocks of this age on the Earth. Here we report tungsten isotope anomalies, based on the Hf-182-W-182 system (half-life of 9 Myr), in metamorphosed sedimentary rocks from the 3.7-3.8-Gyr-old Isua greenstone belt of West Greenland and closely related rocks from northern Labrador, Canada. As it is difficult to conceive of a mechanism by which tungsten isotope heterogeneities could have been preserved in the Earth's dynamic crust-mantle environment from a time when short-lived Hf-182 was still present, we conclude that the metamorphosed sediments contain a component derived from meteorites.

New W-isotope evidence for rapid terrestrial accretion and very early core formation

The short-lived Hf-182-W-182-isotope system is an ideal clock to trace core formation and accretion processes of planets. Planetary accretion and metal/silicate fractionation chronologies are calculated relative to the chondritic Hf-182-W-182-isotope evolution. Here, we report new high-precision W-isotope data for the carbonaceous chondrite Allende that are much less radiogenic than previously reported and are in good agreement with published internal Hf-W chronometry of enstatite chondrites. If the W-isotope composition of terrestrial rocks, representing the bulk silicate Earth, is homogeneous and 2.24 epsilon(182W) units more radiogenic than that of the bulk Earth, metal/silicate differentiation of the Earth occurred very early. The new W-isotope data constrain the mean time of terrestrial core formation to 34 million years after the start of solar system accretion. Early terrestrial core formation implies rapid terrestrial accretion, thus permitting formation of the Moon by giant impact while Hf-182 was still alive. This could explain why lunar W-isotopes are more radiogenic than the terrestrial value. Copyright (C) 2002 Elsevier Science Ltd.

A cassette ligation strategy with thioether replacement of three Gly-Gly peptide bonds: Total chemical synthesis of the 101 residue protein early pregnancy factor [psi(CH2S)(28-29,56-57,76-77)]

The 101 residue protein early pregnancy factor (EPF), also known as human chaperonin 10, was synthesized from four functionalized, but unprotected, peptide segments by a sequential thioether ligation strategy. The approach exploits the differential reactivity of a peptide-NHCH2CH2SH thiolate with XCH2CO-peptides, where X = Cl or I/Br. Initial model studies with short functionalized (but unprotected) peptides showed a significantly faster reaction of a peptide-NHCH2CH2SH thiolate with a BrCH2CO-peptide than with a CICH2CO-peptide, where thiolate displacement of the halide leads to chemoselective formation of a thioether surrogate for the Gly-Gly peptide bond. This rate difference was used as the basis of a novel sequential ligation approach to the synthesis of large polypeptide chains. Thus, ligation of a model bifunctional N-alpha-chloroacetyl, C-terminal thiolated peptide with a second N-alpha-bromoacetyl peptide demonstrated chemoselective bromide displacement by the thiol group. Further investigations showed that the relatively unreactive N-alpha-chloroacetyl peptides could be activated by halide exchange using saturated KI solutions to yield the highly reactive No-iodoacetyl peptides. These findings were used to formulate a sequential thioether ligation strategy for the synthesis of EPF, a 101 amino acid protein containing three Gly-Gly sites approximately equidistantly spaced within the peptide chain. Four peptide segments or cassettes comprising the EPF protein sequence (BrAc-[EPF 78-101] 12, ClAc-[EPF 58-75]-[NHCH2CH2SH] 13, ClAc-[EPF 30-55]-[NHCH2CH2SH] 14, and Ac-[EPF 1-27]-[NHCH2CH2SH] 15) of EPF were synthesized in high yield and purity using Boc SPPS chemistry. In the stepwise sequential ligation strategy, reaction of peptides 12 and 13 was followed by conversion of the N-terminal chloroacetyl functional group to an iodoacetyl, thus activating the product peptide for further ligation with peptide 14. The process of ligation followed by iodoacetyl activation was repeated to yield an analogue of EPF (EPF psi(CH2S)(28-29,56-57,76-77)) 19 in 19% overall yield.