Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos corrected; improvements on the statements and comments suggested by a referee. Keywords: singular flows, singular-hyperbolic attractor, exponential decay of correlations, exact dimensionality, logarithm la

Glycaemia as a sign of the viability of the foetuses in the last days of gestation in dairy goats with pregnancy toxaemia

Pregnancy toxaemia is one of the most common diseases affecting small ruminants in the last month of gestation. Nearly 80% of the foetal growth occurs in the last 6 weeks of gestation. Fat goats and goats carrying twins and triplets are at greater risk. Pregnancy toxaemia is characterized by metabolic acidosis, hypoglycaemia and ketonaemia and a very high mortality rate. In our study five does with pregnancy toxaemia showed a marked hyperglycaemia (12.4 ± 5.4 mmol/L). Although our findings are based on a small population sample (10 goats), we nonetheless postulate that hyperglycaemia could be explained by the death of the foetuses. Caesarian surgery was performed on four of the five does with hyperglycaemia (HG does). In the fifth, kidding was induced. In this group, two does had two dead foetuses, two had three dead foetuses and one does had four foetuses, only one of which was alive. Caesarian surgery was performed on all five does with hypoglycaemia (LG does). Four does of the LG group had three foetuses and one had two foetuses, all alive. The HG doe had lower rectal temperatures, lower sodium and higher urea nitrogen (BUN) in the blood when compared with the LG does. As the condition of affected does may deteriorate quickly, the results of the present study suggest that in the last days of pregnancy goats with pregnancy toxaemia and concurrent hypoglycaemia should be considered for caesarian surgery

Chemotactic response and adaptation dynamics in Escherichia coli

Adaptation of the chemotaxis sensory pathway of the bacterium Escherichia coli is integral for detecting chemicals over a wide range of background concentrations, ultimately allowing cells to swim towards sources of attractant and away from repellents. Its biochemical mechanism based on methylation and demethylation of chemoreceptors has long been known. Despite the importance of adaptation for cell memory and behavior, the dynamics of adaptation are difficult to reconcile with current models of precise adaptation. Here, we follow time courses of signaling in response to concentration step changes of attractant using in vivo fluorescence resonance energy transfer measurements. Specifically, we use a condensed representation of adaptation time courses for efficient evaluation of different adaptation models. To quantitatively explain the data, we finally develop a dynamic model for signaling and adaptation based on the attractant flow in the experiment, signaling by cooperative receptor complexes, and multiple layers of feedback regulation for adaptation. We experimentally confirm the predicted effects of changing the enzyme-expression level and bypassing the negative feedback for demethylation. Our data analysis suggests significant imprecision in adaptation for large additions. Furthermore, our model predicts highly regulated, ultrafast adaptation in response to removal of attractant, which may be useful for fast reorientation of the cell and noise reduction in adaptation.Comment: accepted for publication in PLoS Computational Biology; manuscript (19 pages, 5 figures) and supplementary information; added additional clarification on alternative adaptation models in supplementary informatio

A Component of Retinal Light Adaptation Mediated by the Thyroid Hormone Cascade

Analysis with DNA-microrrays and real time PCR show that several genes involved in the thyroid hormone cascade, such as deiodinase 2 and 3 (Dio2 and Dio3) are differentially regulated by the circadian clock and by changes of the ambient light. The expression level of Dio2 in adult rats (2–3 months of age) kept continuously in darkness is modulated by the circadian clock and is up-regulated by 2 fold at midday. When the diurnal ambient light was on, the expression level of Dio2 increased by 4–8 fold and a consequent increase of the related protein was detected around the nuclei of retinal photoreceptors and of neurons in inner and outer nuclear layers. The expression level of Dio3 had a different temporal pattern and was down-regulated by diurnal light. Our results suggest that DIO2 and DIO3 have a role not only in the developing retina but also in the adult retina and are powerfully regulated by light. As the thyroid hormone is a ligand-inducible transcription factor controlling the expression of several target genes, the transcriptional activation of Dio2 could be a novel genomic component of light adaptation

A through-life costing methodology for use in product-service-systems

Availability-based contracts which provide customers with the use of assets such as machines, ships, aircraft platforms or subsystems like engines and avionics are increasingly offered as an alternative to the purchase of an asset and separate support contracts. The cost of servicing a durable product can be addressed by Through-life Costing (TLC). Providers of advanced services are now concerned with the cost of delivering outcomes that meet customer requirements using combinations of assets and activities via a Product Service System (PSS). This paper addresses the question: To what extent are the current approaches to TLC methodologically appropriate for costing the provision of advanced services, particularly availability, through a PSS? A novel methodology for TLC is outlined addressing the challenges of PSS cost assessment with regard to 'what?' (cost object), 'why/to what extent?' (scope and boundaries), and 'how?' (computations). The research provides clarity for those seeking to cost availability in a performance-orientated contractual setting and provides insight to the measures that may be associated with it. In particular, a reductionist approach that focuses on one cost object at a time is not appropriate for a PSS. Costing an advanced service delivered through a PSS is a problem of attributing the value of means to the economic activities carried out for specific ends to be achieved. Cost results from the interplay between monetary and non-monetary metrics, and uncertainties thereof. Whilst seeking to ensure generality of the findings, the application of TLC examined here is limited to a military aircraft platform and subsystems. © 2014 Elsevier B.V. All rights reserved

Differential Calcium Signaling by Cone Specific Guanylate Cyclase-Activating Proteins from the Zebrafish Retina

Zebrafish express in their retina a higher number of guanylate cyclase-activating proteins (zGCAPs) than mammalians pointing to more complex guanylate cyclase signaling systems. All six zGCAP isoforms show distinct and partial overlapping expression profiles in rods and cones. We determined critical Ca2+-dependent parameters of their functional properties using purified zGCAPs after heterologous expression in E.coli. Isoforms 1–4 were strong, 5 and 7 were weak activators of membrane bound guanylate cyclase. They further displayed different Ca2+-sensitivities of guanylate cyclase activation, which is half maximal either at a free Ca2+ around 30 nM (zGCAP1, 2 and 3) or around 400 nM (zGCAP4, 5 and 7). Zebrafish GCAP isoforms showed also differences in their Ca2+/Mg2+-dependent conformational changes and in the Ca2+-dependent monomer-dimer equilibrium. Direct Ca2+-binding revealed that all zGCAPs bound at least three Ca2+. The corresponding apparent affinity constants reflect binding of Ca2+ with high (≤100 nM), medium (0.1–5 µM) and/or low (≥5 µM) affinity, but were unique for each zGCAP isoform. Our data indicate a Ca2+-sensor system in zebrafish rod and cone cells supporting a Ca2+-relay model of differential zGCAP operation in these cells

A Computational Study on the Role of Gap Junctions and Rod Ih Conductance in the Enhancement of the Dynamic Range of the Retina

Recent works suggest that one of the roles of gap junctions in sensory systems is to enhance their dynamic range by avoiding early saturation in the first processing stages. In this work, we use a minimal conductance-based model of the ON rod pathways in the vertebrate retina to study the effects of electrical synaptic coupling via gap junctions among rods and among AII amacrine cells on the dynamic range of the retina. The model is also used to study the effects of the maximum conductance of rod hyperpolarization activated current Ih on the dynamic range of the retina, allowing a study of the interrelations between this intrinsic membrane parameter with those two retina connectivity characteristics. Our results show that for realistic values of Ih conductance the dynamic range is enhanced by rod-rod coupling, and that AII-AII coupling is less relevant to dynamic range amplification in comparison with receptor coupling. Furthermore, a plot of the retina output response versus input intensity for the optimal parameter configuration is well fitted by a power law with exponent . The results are consistent with predictions of more theoretical works and suggest that the earliest expression of gap junctions along the rod pathways, together with appropriate values of rod Ih conductance, has the highest impact on vertebrate retina dynamic range enhancement

Stress corrosion cracking: Characteristics, Mechanisms and Experimental study

Stress corrosion cracking (SCC) is a phenomenon in which the cracking of a metal alloy usually results from the combined action of a corrodent and tensile stress. Stresses that cause cracking can be residual or may be applied during service. A degree of mechanistic understanding of SCC will enable most metallic engineering materials to operate safely though stress corrosion cracking failures still continue to occur unexpectedly in industry. In this paper, the characteristics, mechanisms and methods of SCC prevention are reviewed. The results of experimental studies on alpha brass are also reported of which the failure mode conformed with the film-rupture and anodic dissolution mechanism

Metarhodopsin control by arrestin, light-filtering screening pigments, and visual pigment turnover in invertebrate microvillar photoreceptors

The visual pigments of most invertebrate photoreceptors have two thermostable photo-interconvertible states, the ground state rhodopsin and photo-activated metarhodopsin, which triggers the phototransduction cascade until it binds arrestin. The ratio of the two states in photoequilibrium is determined by their absorbance spectra and the effective spectral distribution of illumination. Calculations indicate that metarhodopsin levels in fly photoreceptors are maintained below ~35% in normal diurnal environments, due to the combination of a blue-green rhodopsin, an orange-absorbing metarhodopsin and red transparent screening pigments. Slow metarhodopsin degradation and rhodopsin regeneration processes further subserve visual pigment maintenance. In most insect eyes, where the majority of photoreceptors have green-absorbing rhodopsins and blue-absorbing metarhodopsins, natural illuminants are predicted to create metarhodopsin levels greater than 60% at high intensities. However, fast metarhodopsin decay and rhodopsin regeneration also play an important role in controlling metarhodopsin in green receptors, resulting in a high rhodopsin content at low light intensities and a reduced overall visual pigment content in bright light. A simple model for the visual pigment–arrestin cycle is used to illustrate the dependence of the visual pigment population states on light intensity, arrestin levels and pigment turnover