The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic

To what extent is behaviour a problem in English schools?:Exploring the scale and prevalence of deficits in classroom climate

The working atmosphere in the classroom is an important variable in the process of education in schools, with several studies suggesting that classroom climate is an important influence on pupil attainment. There are wide differences in the extent to which classroom climate is considered to be a problem in English schools. Some ‘official’ reports suggest that behaviour in schools is ‘satisfactory or better’ in the vast majority of schools; other sources have pointed to behaviour being a serious and widespread problem. The paper details four studies conducted over the past decade which aimed to explore these disparities. The aim of the research was to gain a more accurate insight into the extent to which deficits in classroom climate limit educational attainment and equality of educational opportunity in English schools. The findings question the suggestion that behaviour is satisfactory or better in 99.7% of English schools and the concluding section suggests ways in which deficits in classroom climate might be addressed. Although the study is limited to classrooms in England, OECD studies suggest that deficits in the working atmosphere in classrooms occur in many countries. The study therefore has potential relevance for education systems in other countries

Ectodomains of the LDL receptor-related proteins LRP1b and LRP4 have anchorage independent functions in vivo.

BACKGROUND: The low-density lipoprotein (LDL) receptor gene family is a highly conserved group of membrane receptors with diverse functions in developmental processes, lipoprotein trafficking, and cell signaling. The low-density lipoprotein (LDL) receptor-related protein 1b (LRP1B) was reported to be deleted in several types of human malignancies, including non-small cell lung cancer. Our group has previously reported that a distal extracellular truncation of murine Lrp1b that is predicted to secrete the entire intact extracellular domain (ECD) is fully viable with no apparent phenotype. METHODS AND PRINCIPAL FINDINGS: Here, we have used a gene targeting approach to create two mouse lines carrying internally rearranged exons of Lrp1b that are predicted to truncate the protein closer to the N-terminus and to prevent normal trafficking through the secretary pathway. Both mutations result in early embryonic lethality, but, as expected from the restricted expression pattern of LRP1b in vivo, loss of Lrp1b does not cause cellular lethality as homozygous Lrp1b-deficient blastocysts can be propagated normally in culture. This is similar to findings for another LDL receptor family member, Lrp4. We provide in vitro evidence that Lrp4 undergoes regulated intramembraneous processing through metalloproteases and gamma-secretase cleavage. We further demonstrate negative regulation of the Wnt signaling pathway by the soluble extracellular domain. CONCLUSIONS AND SIGNIFICANCE: Our results underline a crucial role for Lrp1b in development. The expression in mice of truncated alleles of Lrp1b and Lrp4 with deletions of the transmembrane and intracellular domains leads to release of the extracellular domain into the extracellular space, which is sufficient to confer viability. In contrast, null mutations are embryonically (Lrp1b) or perinatally (Lrp4) lethal. These findings suggest that the extracellular domains of both proteins may function as a scavenger for signaling ligands or signal modulators in the extracellular space, thereby preserving signaling thresholds that are critical for embryonic development, as well as for the clear, but poorly understood role of LRP1b in cancer

Finite type approximations of Gibbs measures on sofic subshifts

Consider a H\"older continuous potential $\phi$ defined on the full shift A^\nn, where $A$ is a finite alphabet. Let X\subset A^\nn be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$ associated to $\phi$. Besides, there is a natural nested sequence of subshifts of finite type $(X_m)$ converging to the sofic subshift $X$. To this sequence we can associate a sequence of Gibbs measures $(\mu_{\phi}^m)$. In this paper, we prove that these measures weakly converge at exponential speed to $\mu_\phi$ (in the classical distance metrizing weak topology). We also establish a strong mixing property (ensuring weak Bernoullicity) of $\mu_\phi$. Finally, we prove that the measure-theoretic entropy of $\mu_\phi^m$ converges to the one of $\mu_\phi$ exponentially fast. We indicate how to extend our results to more general subshifts and potentials. We stress that we use basic algebraic tools (contractive properties of iterated matrices) and symbolic dynamics.Comment: 18 pages, no figure

The effectiveness of pollutant removal from municipal wastewater in vertical flow constructed wetlands

The efficiency of pollution removal from municipal sewage in two vertical flow constructed wetlands consisting of gravel filters with surface area 4 x 5 m, depth 60 cm, covered by reedwas evaluated over a period of two years. The flow of wastewater was about 50 mm per day.Wastewater underwent only mechanical treatment before reed bed B, but reed bed A wassupplied with wastewater after biological treatment with activated sludge. Sewage wassampled before and after filtration every IO days. Measurements were made of sewage supplyand discharge, precipitation and wastewater temperatures. The main indicator of efficiencywas the elimination of suspended solids, carbon, nitrogen and phosphorus from thewastewater during filtration. The elimination of the pollution load was 2-25 g per squaremeter per day for the BOD5 and 0--3.5 g per square meter per day for total nitrogen. Rates ofpollution removal were between 2 and 4 times as high in bed Bas in bed A. The rate ofBOD5 removal and the coefficient k for BOD5 were strongly dependent on temperature for reed bedB; less so far for bed A. The difference between summer and winter indicates that the surfacearea of constructed wetland B should be 3 times bigger during winter to obtain the summerrate ofBOD5 pollution removal in the climatic conditions ofNorth Poland (54a° N)

Application of LANDSAT data and digital image processing

There are no author-identified significant results in this report

Can willow roots oxygenate leachate in vegetation filter beds?¬ a mass spectrometer investigation in Wales

Membrane inlet mass spectrometry (MIMS) was used to monitor dissolved gas concentrations in-situ in laboratory microcosms and in a constructed willow vegetation filter bed in Walesused to treat leachate. A mini-rhizotron digital camera system was developed for use incombination with MIMS studies of gas dynamics. The major results of the studies are:-• Diurnal cycles in the concentrations of 02, CO2 and C� were shown to occur with arooted willow cutting in a stirred microcosm.• Willow beds show considerable sub-surface spatial diversity. Generally, oxygen decreaseswith depth whereas methane and carbon dioxide increase with depth. Small pockets ofgases were seen. Oxygen occurred throughout the profile.• Microbial processes follow diurnal cycles. Oxygen is released from willow roots duringdaylight. Methane and carbon dioxide accumulate during the dark.• The high degree of mixing distributes oxygenated water throughout the bed. Stopping theflow of leachate allowed conditions to become anaerobic, except in local micro-sites.These techniques appear to offer considerable potential for direct measurement of sub-surfaceenvironments in constructed wetlands, particularly in respect of the microbial processesoccurring in the bed, and the oxygenation capacity of willow vegetation filters

Ultrasonic Sensors to Measure Internal Temperature Distribution

The in-process measurement of the internal temperature distribution is an important step toward improved processing of steels. A promising approach is the measurement of ultrasonic velocity, combined with a priori information on heat flow. Reference data on ultrasonic velocity versus temperature have been obtained for austenitic 304 stainless steel and for ferritic AISI 1018 steel. For stainless steel the longitudinal-wave velocity is nearly linear with temperature, with a proportionality constant of about -0.7 meters per second per degree Kelvin. In this paper we review the technical approach being used to ultrasonically determine internal temperature distribution. For this we (1) map the average velocity (hence average temperature) within hot steel samples (using a pulsed-laser driver and an electromagnetic acoustic transducer (EMAT) receiver) and (2) apply a reconstruction model that is based on ultrasonic tomography and utilizes the equations of heat flow

Correlation decay and recurrence estimates for some robust nonuniformly hyperbolic maps

We study decay of correlations, the asymptotic distribution of hitting times and fluctuations of the return times for a robust class of multidimensional non-uniformly hyperbolic transformations. Oliveira and Viana [15] proved that there is a unique equilibrium state for a large class of non- uniformly expanding transformations and Holder continuous potentials with small variation. For an open class of potentials with small variation, we prove quasi-compactness of the Ruelle-Perron-Frobenius operator in a space $V_\theta$ of functions with essential bounded variation that strictly contain Holder continuous observables. We deduce that the equilibrium states have exponential decay of correlations. Furthermore, we prove exponential asymptotic distribu- tion of hitting times and log-normal fluctuations of the return times around the average given by the metric entropy.Comment: 24 page

Protecting Half the Planet and Transforming Human Systems Are Complementary Goals

The unfolding crises of mass extinction and climate change call for urgent action in response. To limit biodiversity losses and avert the worst effects of climate disruption, we must greatly expand nature protection while simultaneously downsizing and transforming human systems. The conservation initiative Nature Needs Half (or Half Earth), calling for the conservation of half the Earth's land and seas, is commensurate with the enormous challenges we face. Critics have objected to this initiative as harboring hardship for people near protected areas and for failing to confront the growth economy as the main engine of global ecological destruction. In response to the first criticism, we affirm that conservation policies must be designed and implemented in collaboration with Indigenous and local communities. In response to the second criticism, we argue that protecting half the Earth needs to be complemented by downscaling and reforming economic life, humanely and gradually reducing the global population, and changing food production and consumption. By protecting nature generously, and simultaneously contracting and transforming the human enterprise, we can create the conditions for achieving justice and well-being for both people and other species. If we fail to do so, we instead accept a chaotic and impoverished world that will be dangerous for us all