Birationally rigid complete intersections of high codimension

We prove that a Fano complete intersection of codimension $k$ and index 1 in the complex projective space ${\mathbb P}^{M+k}$ for $k\geqslant 20$ and $M\geqslant 8k\log k$ with at most multi-quadratic singularities is birationally superrigid. The codimension of the complement to the set of birationally superrigid complete intersections in the natural parameter space is shown to be at least $\frac12 (M-5k)(M-6k)$. The proof is based on the techniques of hypertangent divisors combined with the recently discovered $4n^2$-inequality for complete intersection singularities.Comment: 29 page

Coupled measurements of δ¹⁸O and δD of hydration water and salinity of fluid inclusions in gypsum from the Messinian Yesares Member, Sorbas Basin (SE Spain)

We studied one cycle (Cycle 6) of gypsum-marl deposition from the Messinian Yesares Member in Sorbas Basin, Spain. The objective was to reconstruct the changing environment of deposition and its relation to astronomically-forced climate change. The δ1818O and δD of gypsum hydration water (CaSO4•2H2O) and salinity of fluid inclusions were measured in the same samples to test if they record the composition of the mother fluid from which gypsum was precipitated. Water isotopes are highly correlated with fluid inclusion salinity suggesting the hydration water has not exchanged after formation. The relatively low water isotope values and fluid inclusion salinities indicate a significant influence of meteoric water, whereas δ34S, δ18OSO4 26 and 87Sr/86Sr support a dominant marine origin for the gypsum deposits. The discrepancy between water and elemental isotope signatures can be reconciled if meteoric water dissolved previously deposited marine sulfates supplying calcium and sulfate ions to the basin which maintained gypsum saturation. This recycling process accounts for the marine δ34S, δ18OSO4 and 87Sr/86Sr signatures, whereas the low δ18O and δD values of gypsum hydration water and fluid inclusion salinities reflect the influence of freshwater. The cyclic deposition of gypsum and marl in the Yesares Member has previously been interpreted to reflect changing climate related to Earth’s precession cycle. We demonstrate that the δ18O, δD and salinity of the parent brine increased from low values at the base of Cycle 6 to a maximum in the massive gypsum palisade, and decreased again to lower values in the supercones at the top of the cycle. This pattern, together with changes in mineralogy (calcite-dolomite-gypsum), is consistent with a precession-driven change in climate with wettest conditions (summer insolation maxima) associated with the base of the calcium carbonate marls and driest conditions (summer insolation minima) during formation of the gypsum palisade.The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 339694 (Water Isotopes of Hydrated Minerals) to D. A. Hodell.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.epsl.2015.07.07

Spectrum of Clinical Signs and Genetic Characterization of Gelatinous Drop-Like Corneal Dystrophy in a Colombian Family

PURPOSE: To describe the clinical signs of gelatinous drop-like corneal dystrophy (GDLD) in a consanguineous Colombian family and determine the underlying genetic cause. METHODS: We performed ocular examination of available family members and bidirectionally Sanger sequenced the GDLD-associated gene, TACSTD2. In one individual, the presence of subepithelial amyloid was confirmed with biopsy. RESULTS: The parents were consanguineous and 5 of their 10 children had GDLD. Typical mulberry subepithelial deposits with subepithelial vascularization were present in 3 individuals; 2 individuals only had mild polymorphic anterior stromal opacity. We identified a homozygous TACSTD2 missense mutation, c.551A>G, p.(Tyr184Cys), in the affected family members. Both parents were heterozygous for the mutation, and unaffected siblings were either heterozygous or homozygous wild-type for this allele. In the Colombian population, this mutation has a minor allele frequency of 0.53%. CONCLUSION: The clinical presentation of GDLD in this family was variable and does not solely support an age-dependent progression of the phenotype, suggesting that environmental or other genetic factors can modify phenotypic expression. The relatively high prevalence of this mutation in the Colombian population suggests that other individuals may have undiagnosed subclinical disease

Cognitive Control of Escape Behaviour

When faced with potential predators, animals instinctively decide whether there is a threat they should escape from, and also when, how, and where to take evasive action. While escape is often viewed in classical ethology as an action that is released upon presentation of specific stimuli, successful and adaptive escape behaviour relies on integrating information from sensory systems, stored knowledge, and internal states. From a neuroscience perspective, escape is an incredibly rich model that provides opportunities for investigating processes such as perceptual and value-based decision-making, or action selection, in an ethological setting. We review recent research from laboratory and field studies that explore, at the behavioural and mechanistic levels, how elements from multiple information streams are integrated to generate flexible escape behaviour

The first maps of κd - the dust mass absorption coefficient - in nearby galaxies, with DustPedia

The dust mass absorption coefficient, κd is the conversion function used to infer physical dust masses from observations of dust emission. However, it is notoriously poorly constrained, and it is highly uncertain how it varies, either between or within galaxies. Here we present the results of a proof-of-concept study, using the DustPedia data for two nearby face-on spiral galaxies M 74 (NGC 628) and M 83 (NGC 5236), to create the first ever maps of κd in galaxies. We determine κd using an empirical method that exploits the fact that the dust-to-metals ratio of the interstellar medium is constrained by direct measurements of the depletion of gas-phase metals. We apply this method pixel-by-pixel within M 74 and M 83, to create maps of κd. We also demonstrate a novel method of producing metallicity maps for galaxies with irregularly sampled measurements, using the machine learning technique of Gaussian process regression. We find strong evidence for significant variation in κd. We find values of κd at 500 μm spanning the range 0.11-0.25 m^{2 kg^{-1}} in M 74, and 0.15-0.80 m^{2 kg^{-1}} in M 83. Surprisingly, we find that κd shows a distinct inverse correlation with the local density of the interstellar medium. This inverse correlation is the opposite of what is predicted by standard dust models. However, we find this relationship to be robust against a large range of changes to our method - only the adoption of unphysical or highly unusual assumptions would be able to suppress it

Misinterpreting carbon accumulation rates in records from near-surface peat

Peatlands are globally important stores of carbon (C) that contain a record of how their rates of C accumulation have changed over time. Recently, near-surface peat has been used to assess the effect of current land use practices on C accumulation rates in peatlands. However, the notion that accumulation rates in recently formed peat can be compared to those from older, deeper, peat is mistaken – continued decomposition means that the majority of newly added material will not become part of the long-term C store. Palaeoecologists have known for some time that high apparent C accumulation rates in recently formed peat are an artefact and take steps to account for it. Here we show, using a model, how the artefact arises. We also demonstrate that increased C accumulation rates in near-surface peat cannot be used to infer that a peatland as a whole is accumulating more C – in fact the reverse can be true because deep peat can be modified by events hundreds of years after it was formed. Our findings highlight that care is needed when evaluating recent C addition to peatlands especially because these interpretations could be wrongly used to inform land use policy and decisions

Coupling models of cattle and farms with models of badgers for predicting the dynamics of bovine tuberculosis (TB)

Bovine TB is a major problem for the agricultural industry in several countries. TB can be contracted and spread by species other than cattle and this can cause a problem for disease control. In the UK and Ireland, badgers are a recognised reservoir of infection and there has been substantial discussion about potential control strategies. We present a coupling of individual based models of bovine TB in badgers and cattle, which aims to capture the key details of the natural history of the disease and of both species at approximately county scale. The model is spatially explicit it follows a very large number of cattle and badgers on a different grid size for each species and includes also winter housing. We show that the model can replicate the reported dynamics of both cattle and badger populations as well as the increasing prevalence of the disease in cattle. Parameter space used as input in simulations was swept out using Latin hypercube sampling and sensitivity analysis to model outputs was conducted using mixed effect models. By exploring a large and computationally intensive parameter space we show that of the available control strategies it is the frequency of TB testing and whether or not winter housing is practised that have the most significant effects on the number of infected cattle, with the effect of winter housing becoming stronger as farm size increases. Whether badgers were culled or not explained about 5%, while the accuracy of the test employed to detect infected cattle explained less than 3% of the variance in the number of infected cattle

Physical weathering of carbonate host-rock by precipitation of soluble salts in caves: A case study in El Orón-Arco Cave (Region of Murcia, SE Spain)

The dissolution of carbonate host-rock by freshwater in phreatic or vadose conditions is the most common mechanism for the formation of caves; however, circulation of saline solutions through carbonate materials and precipitation of soluble salts may also play an important role. We studied the stable isotope composition (δ18O and δ34S of sulfate, δ18O and δD of structurally-bound gypsum hydration water and 87Sr/86Sr) and salinity of fluid inclusions in gypsum speleothems found in El Orón-Arco Cave (Cartagena, SE Spain). We suggest that physical weathering of carbonate host-rock was driven by precipitation of soluble sea-salts (mostly gypsum and halite), and this process controlled the recent geomorphological evolution of the cave. The Triassic carbonate host-rock shows clear evidence for salt weathering, including gypsum/halite infillings in cracks of the bedrock, mechanical spalling of the carbonate, and detachment of rock fragments that lead to the formation cave voids and in-situ accumulations of piles of unsorted rubble. Sulfur and oxygen isotopes of gypsum sulfate (3.0‰ < δ18O < 11.6‰ and 16.7‰ < δ34S < 20.7‰) are generally lower than modern seawater sulfate and suggest contributions from a 34S-depleted source (i.e. oxidation of pyrite). The δ18O and δD of gypsum hydration water are relatively low compared to expected values for the evaporation of pure seawater to gypsum saturation, suggesting that gypsum precipitation involved a secondary calcium-sulfate source or recycling of gypsum from previous stages, along with mixing of seawater and meteoric water seepage to the cave. The 87Sr/86Sr in gypsum shows intermediate values between modern seawater and Triassic carbonate values because of interaction between the solution and the bedrock. The salinities of the speleothem-forming solutions are relatively high (13.2 ± 3.2 wt% eq. NaCl) compared to gypsum formed from evaporated brackish solutions (i.e. ~4–8 wt% eq. NaCl) and indicate dissolution of earlier evaporites before secondary gypsum precipitation. This cave-forming mechanism, which is related to saline water circulation and precipitation of evaporitic minerals, may be common in other coastal caves

Noncommutative generalizations of theorems of Cohen and Kaplansky

This paper investigates situations where a property of a ring can be tested on a set of "prime right ideals." Generalizing theorems of Cohen and Kaplansky, we show that every right ideal of a ring is finitely generated (resp. principal) iff every "prime right ideal" is finitely generated (resp. principal), where the phrase "prime right ideal" can be interpreted in one of many different ways. We also use our methods to show that other properties can be tested on special sets of right ideals, such as the right artinian property and various homological properties. Applying these methods, we prove the following noncommutative generalization of a result of Kaplansky: a (left and right) noetherian ring is a principal right ideal ring iff all of its maximal right ideals are principal. A counterexample shows that the left noetherian hypothesis cannot be dropped. Finally, we compare our results to earlier generalizations of Cohen's and Kaplansky's theorems in the literature.Comment: 41 pages. To appear in Algebras and Representation Theory. Minor changes were made to the numbering system, in order to remain consistent with the published versio

Fluctuations in granular gases

A driven granular material, e.g. a vibrated box full of sand, is a stationary system which may be very far from equilibrium. The standard equilibrium statistical mechanics is therefore inadequate to describe fluctuations in such a system. Here we present numerical and analytical results concerning energy and injected power fluctuations. In the first part we explain how the study of the probability density function (pdf) of the fluctuations of total energy is related to the characterization of velocity correlations. Two different regimes are addressed: the gas driven at the boundaries and the homogeneously driven gas. In a granular gas, due to non-Gaussianity of the velocity pdf or lack of homogeneity in hydrodynamics profiles, even in the absence of velocity correlations, the fluctuations of total energy are non-trivial and may lead to erroneous conclusions about the role of correlations. In the second part of the chapter we take into consideration the fluctuations of injected power in driven granular gas models. Recently, real and numerical experiments have been interpreted as evidence that the fluctuations of power injection seem to satisfy the Gallavotti-Cohen Fluctuation Relation. We will discuss an alternative interpretation of such results which invalidates the Gallavotti-Cohen symmetry. Moreover, starting from the Liouville equation and using techniques from large deviation theory, the general validity of a Fluctuation Relation for power injection in driven granular gases is questioned. Finally a functional is defined using the Lebowitz-Spohn approach for Markov processes applied to the linear inelastic Boltzmann equation relevant to describe the motion of a tracer particle. Such a functional results to be different from injected power and to satisfy a Fluctuation Relation.Comment: 40 pages, 18 figure