On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Estimation of hydraulic conductivity and its uncertainty from grain-size data using GLUE and artificial neural networks

peer reviewedaudience: researcher, professionalVarious approaches exist to relate saturated hydraulic conductivity (Ks) to grain-size data. Most methods use a single grain-size parameter and hence omit the information encompassed by the entire grain-size distribution. This study compares two data-driven modelling methods, i.e.multiple linear regression and artificial neural networks, that use the entire grain-size distribution data as input for Ks prediction. Besides the predictive capacity of the methods, the uncertainty associated with the model predictions is also evaluated, since such information is important for stochastic groundwater flow and contaminant transport modelling. Artificial neural networks (ANNs) are combined with a generalized likelihood uncertainty estimation (GLUE) approach to predict Ks from grain-size data. The resulting GLUE-ANN hydraulic conductivity predictions and associated uncertainty estimates are compared with those obtained from the multiple linear regression models by a leave-one-out cross-validation. The GLUE-ANN ensemble prediction proved to be slightly better than multiple linear regression. The prediction uncertainty, however, was reduced by half an order of magnitude on average, and decreased at most by an order of magnitude. This demonstrates that the proposed method outperforms classical data-driven modelling techniques. Moreover, a comparison with methods from literature demonstrates the importance of site specific calibration. The dataset used for this purpose originates mainly from unconsolidated sandy sediments of the Neogene aquifer, northern Belgium. The proposed predictive models are developed for 173 grain-size -Ks pairs. Finally, an application with the optimized models is presented for a borehole lacking Ks data

Configuration-interaction calculations of positron binding to group-II elements

The configuration-interaction (CI) method is applied to the study of positronic magnesium (e+Mg), positronic calcium (e+Ca), and positronic strontium (e+Sr). The CI expansion was seen to converge slowly with respect to Lmax, the maximum angular momentum of any orbital used to construct the CI basis. Despite doing explicit calculations with Lmax=10, extrapolation corrections to the binding energies for the Lmax→∞ limit were substantial in the case of e+Ca (25%) and e+Sr (50%). The extrapolated binding energies were 0.0162 hartree for e+Mg, 0.0165 hartree for e+Ca, and 0.0101 hartree for e+Sr. The static-dipole polarizabilities for the neutral parent atoms were computed as a by-product, giving 71.7a03, 162a03, and 204a03 for Mg, Ca, and Sr, respectively

SEDLIN Forms Homodimers: Characterisation of SEDLIN Mutations and Their Interactions with Transcription Factors MBP1, PITX1 and SF1

BACKGROUND: SEDLIN, a 140 amino acid subunit of the Transport Protein Particle (TRAPP) complex, is ubiquitously expressed and interacts with the transcription factors c-myc promoter-binding protein 1 (MBP1), pituitary homeobox 1 (PITX1) and steroidogenic factor 1 (SF1). SEDLIN mutations cause X-linked spondyloepiphyseal dysplasia tarda (SEDT). METHODOLOGY/PRINCIPAL FINDINGS: We investigated the effects of 4 missense (Asp47Tyr, Ser73Leu, Phe83Ser and Val130Asp) and the most C-terminal nonsense (Gln131Stop) SEDT-associated mutations on interactions with MBP1, PITX1 and SF1 by expression in COS7 cells. Wild-type SEDLIN was present in the cytoplasm and nucleus and interacted with MBP1, PITX1 and SF1; the SEDLIN mutations did not alter these subcellular localizations or the interactions. However, SEDLIN was found to homodimerize, and the formation of dimers between wild-type and mutant SEDLIN would mask a loss in these interactions. A mammalian SEDLIN null cell-line is not available, and the interactions between SEDLIN and the transcription factors were therefore investigated in yeast, which does not endogenously express SEDLIN. This revealed that all the SEDT mutations, except Asp47Tyr, lead to a loss of interaction with MBP1, PITX1 and SF1. Three-dimensional modelling studies of SEDLIN revealed that Asp47 resides on the surface whereas all the other mutant residues lie within the hydrophobic core of the protein, and hence are likely to affect the correct folding of SEDLIN and thereby disrupt protein-protein interactions. CONCLUSIONS/SIGNIFICANCE: Our studies demonstrate that SEDLIN is present in the nucleus, forms homodimers and that SEDT-associated mutations cause a loss of interaction with the transcription factors MBP1, PITX1 and SF1

The Adaptor Function of TRAPPC2 in Mammalian TRAPPs Explains TRAPPC2-Associated SEDT and TRAPPC9-Associated Congenital Intellectual Disability

Background: The TRAPP (Transport protein particle) complex is a conserved protein complex functioning at various steps in vesicle transport. Although yeast has three functionally and structurally distinct forms, TRAPPI, II and III, emerging evidence suggests that mammalian TRAPP complex may be different. Mutations in the TRAPP complex subunit 2 (TRAPPC2) cause X-linked spondyloepiphyseal dysplasia tarda, while mutations in the TRAPP complex subunit 9 (TRAPPC9) cause postnatal mental retardation with microcephaly. The structural interplay between these subunits found in mammalian equivalent of TRAPPI and those specific to TRAPPII and TRAPPIII remains largely unknown and we undertook the present study to examine the interaction between these subunits. Here, we reveal that the mammalian equivalent of the TRAPPII complex is structurally distinct from the yeast counterpart thus leading to insight into mechanism of disease. Principal Findings: We analyzed how TRAPPII- or TRAPPIII- specific subunits interact with the six-subunit core complex of TRAPP by co-immunoprecipitation in mammalian cells. TRAPPC2 binds to TRAPPII-specific subunit TRAPPC9, which in turn binds to TRAPPC10. Unexpectedly, TRAPPC2 can also bind to the putative TRAPPIII-specific subunit, TRAPPC8. Endogenous TRAPPC9-positive TRAPPII complex does not contain TRAPPC8, suggesting that TRAPPC2 binds to either TRAPPC9 or TRAPPC8 during the formation of the mammalian equivalents of TRAPPII or TRAPPIII, respectively. Therefore, TRAPPC2 serves as an adaptor for the formation of these complexes. A disease-causing mutation of TRAPPC2, D47Y, failed to interact with either TRAPPC9 or TRAPPC8, suggesting that aspartate 47 in TRAPPC2 is at or near the site of interaction with TRAPPC9 or TRAPPC8, mediating the formation of TRAPPII and/or TRAPPIII. Furthermore, disease-causing deletional mutants of TRAPPC9 all failed to interact with TRAPPC2 and TRAPPC10. Conclusions: TRAPPC2 serves as an adaptor for the formation of TRAPPII or TRAPPIII in mammalian cells. The mammalian equivalent of TRAPPII is likely different from the yeast TRAPPII structurally. © 2011 Zong et al.published_or_final_versio

Somitogenesis Clock-Wave Initiation Requires Differential Decay and Multiple Binding Sites for Clock Protein

Somitogenesis is a process common to all vertebrate embryos in which repeated blocks of cells arise from the presomitic mesoderm (PSM) to lay a foundational pattern for trunk and tail development. Somites form in the wake of passing waves of periodic gene expression that originate in the tailbud and sweep posteriorly across the PSM. Previous work has suggested that the waves result from a spatiotemporally graded control protein that affects the oscillation rate of clock-gene expression. With a minimally constructed mathematical model, we study the contribution of two control mechanisms to the initial formation of this gene-expression wave. We test four biologically motivated model scenarios with either one or two clock protein transcription binding sites, and with or without differential decay rates for clock protein monomers and dimers. We examine the sensitivity of wave formation with respect to multiple model parameters and robustness to heterogeneity in cell population. We find that only a model with both multiple binding sites and differential decay rates is able to reproduce experimentally observed waveforms. Our results show that the experimentally observed characteristics of somitogenesis wave initiation constrain the underlying genetic control mechanisms

Foxp3 expression in human cancer cells

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

Quantitative Characterization of the Filiform Mechanosensory Hair Array on the Cricket Cercus

Crickets and other orthopteran insects sense air currents with a pair of abdominal appendages resembling antennae, called cerci. Each cercus in the common house cricket Acheta domesticus is approximately 1 cm long, and is covered with 500 to 750 filiform mechanosensory hairs. The distribution of the hairs on the cerci, as well as the global patterns of their movement vectors, have been characterized semi-quantitatively in studies over the last 40 years, and have been shown to be very stereotypical across different animals in this species. Although the cercal sensory system has been the focus of many studies in the areas of neuroethology, development, biomechanics, sensory function and neural coding, there has not yet been a quantitative study of the functional morphology of the receptor array of this important model system.We present a quantitative characterization of the structural characteristics and functional morphology of the cercal filiform hair array. We demonstrate that the excitatory direction along each hair's movement plane can be identified by features of its socket that are visible at the light-microscopic level, and that the length of the hair associated with each socket can also be estimated accurately from a structural parameter of the socket. We characterize the length and directionality of all hairs on the basal half of a sample of three cerci, and present statistical analyses of the distributions.The inter-animal variation of several global organizational features is low, consistent with constraints imposed by functional effectiveness and/or developmental processes. Contrary to previous reports, however, we show that the filiform hairs are not re-identifiable in the strict sense