'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Genetic variation at flowering time loci in wild and cultivated barley

The worldwide spread of barley cultivation required adaptation to agricultural environments far distant from those found in its centre of domestication. An important component of this adaptation is the timing of flowering, achieved predominantly in response to day length and temperature. Here, we use a collection of cultivars, landraces and wild barley accessions to investigate the origins and distribution of allelic diversity at four major flowering time loci, mutations at which have been under selection during the spread of barley cultivation into Europe. Our findings suggest that while mutant alleles at the PPD-H1 and PPD-H2 photoperiod loci occurred pre-domestication, the mutant vernalization non-responsive alleles utilized in landraces and cultivars at the VRN-H1 and VRN-H2 loci occurred post-domestication. The transition from wild to cultivated barley is associated with a doubling in the number of observed multi-locus flowering-time haplotypes, suggesting that the resulting phenotypic variation has aided adaptation to cultivation in the diverse ecogeographic locations encountered. Despite the importance of early-flowering alleles during the domestication of barley in Europe, we show that novel VRN alleles associated with early flowering in wild barley have been lost in domesticates, highlighting the potential of wild germplasm as a source of novel allelic variation for agronomic traits.

High resolution simulation of recent Arctic and Antarctic stratospheric chemical ozone loss compared to observations

Simulations of polar ozone losses were performed using the three-dimensional high-resolution (1∘ × 1∘) chemical transport model MIMOSA-CHIM. Three Arctic winters 1999–2000, 2001–2002, 2002–2003 and three Antarctic winters 2001, 2002, and 2003 were considered for the study. The cumulative ozone loss in the Arctic winter 2002–2003 reached around 35% at 475 K inside the vortex, as compared to more than 60% in 1999–2000. During 1999–2000, denitrification induces a maximum of about 23% extra ozone loss at 475 K as compared to 17% in 2002–2003. Unlike these two colder Arctic winters, the 2001–2002 Arctic was warmer and did not experience much ozone loss. Sensitivity tests showed that the chosen resolution of 1∘ × 1∘ provides a better evaluation of ozone loss at the edge of the polar vortex in high solar zenith angle conditions. The simulation results for ozone, ClO, HNO3, N2O, and NO y for winters 1999–2000 and 2002–2003 were compared with measurements on board ER-2 and Geophysica aircraft respectively. Sensitivity tests showed that increasing heating rates calculated by the model by 50% and doubling the PSC (Polar Stratospheric Clouds) particle density (from 5 × 10−3 to 10−2 cm−3) refines the agreement with in situ ozone, N2O and NO y levels. In this configuration, simulated ClO levels are increased and are in better agreement with observations in January but are overestimated by about 20% in March. The use of the Burkholder et al. (1990) Cl2O2 absorption cross-sections slightly increases further ClO levels especially in high solar zenith angle conditions. Comparisons of the modelled ozone values with ozonesonde measurement in the Antarctic winter 2003 and with Polar Ozone and Aerosol Measurement III (POAM III) measurements in the Antarctic winters 2001 and 2002, shows that the simulations underestimate the ozone loss rate at the end of the ozone destruction period. A slightly better agreement is obtained with the use of Burkholder et al. (1990) Cl2O2 absorption cross-sections.

Identifying uncertainties in Arctic climate change projections

Wide ranging climate changes are expected in the Arctic by the end of the 21st century, but projections of the size of these changes vary widely across current global climate models. This variation represents a large source of uncertainty in our understanding of the evolution of Arctic climate. Here we systematically quantify and assess the model uncertainty in Arctic climate changes in two CO2 doubling experiments: a multimodel ensemble (CMIP3) and an ensemble constructed using a single model (HadCM3) with multiple parameter perturbations (THC-QUMP). These two ensembles allow us to assess the contribution that both structural and parameter variations across models make to the total uncertainty and to begin to attribute sources of uncertainty in projected changes. We find that parameter uncertainty is an major source of uncertainty in certain aspects of Arctic climate. But also that uncertainties in the mean climate state in the 20th century, most notably in the northward Atlantic ocean heat transport and Arctic sea ice volume, are a significant source of uncertainty for projections of future Arctic change. We suggest that better observational constraints on these quantities will lead to significant improvements in the precision of projections of future Arctic climate change.

Rossby number expansions, slaving principles, and balance dynamics

We consider the problem of constructing balance dynamics for rapidly rotating fluid systems. It is argued that the conventional Rossby number expansion—namely expanding all variables in a series in Rossby number—is secular for all but the simplest flows. In particular, the higher-order terms in the expansion grow exponentially on average, and for moderate values of the Rossby number the expansion is, at best, useful only for times of the order of the doubling times of the instabilities of the underlying quasi-geostrophic dynamics. Similar arguments apply in a wide class of problems involving a small parameter and sufficiently complex zeroth-order dynamics. A modified procedure is proposed which involves expanding only the fast modes of the system; this is equivalent to an asymptotic approximation of the slaving relation that relates the fast modes to the slow modes. The procedure is systematic and thus capable, at least in principle, of being carried to any order—unlike procedures based on truncations. We apply the procedure to construct higher-order balance approximations of the shallow-water equations. At the lowest order quasi-geostrophy emerges. At the next order the system incorporates gradient-wind balance, although the balance relations themselves involve only linear inversions and hence are easily applied. There is a large class of reduced systems associated with various choices for the slow variables, but the simplest ones appear to be those based on potential vorticity.

Subject-to-subject raising and the syntax of tense in L2 Spanish: a full access approach

This paper investigates the acquisition of syntax in L2 grammars. We tested adult L2 speakers of Spanish (English L1) on the feature specification of T(ense), which is different in English and Spanish in so-called subject-to-subject raising structures. We present experimental results with the verb parecer “to seem/to appear” in different tenses, with and without experiencers, and with Tense Phrase (TP), verb phrase (vP) and Adjectival Phrase (AP) complements. The results show that advanced L2 learners can perform just like native Spanish speakers regarding grammatical knowledge in this domain, although the subtle differences between both languages are not explicitly taught. We argue that these results support Full Access approaches to Universal Grammar (UG) in L2 acquisition, by providing evidence that uninterpretable syntactic features can be learned in adult L2, even when such features are not directly instantiated in the same grammatical domain in the L1 grammar.

Future changes in atmospheric rivers and their implications for winter flooding in Britain

Within the warm conveyor belt of extra-tropical cyclones, atmospheric rivers (ARs) are the key synoptic features which deliver the majority of poleward water vapour transport, and are associated with episodes of heavy and prolonged rainfall. ARs are responsible for many of the largest winter floods in the mid-latitudes resulting in major socioeconomic losses; for example, the loss from United Kingdom (UK) flooding in summer/winter 2012 is estimated to be about $1.6 billion in damages. Given the well-established link between ARs and peak river flows for the present day, assessing how ARs could respond under future climate projections is of importance in gauging future impacts from flooding. We show that North Atlantic ARs are projected to become stronger and more numerous in the future scenarios of multiple simulations from five state-of-the-art global climate models (GCMs) in the fifth Climate Model Intercomparison Project (CMIP5). The increased water vapour transport in projected ARs implies a greater risk of higher rainfall totals and therefore larger winter floods in Britain, with increased AR frequency leading to more flood episodes. In the high emissions scenario (RCP8.5) for 2074–2099 there is an approximate doubling of AR frequency in the five GCMs. Our results suggest that the projected change in ARs is predominantly a thermodynamic response to warming resulting from anthropogenic radiative forcing.

Tackling regional climate change by leaf albedo bio-geoengineering

The likelihood that continuing greenhouse-gas emissions will lead to an unmanageable degree of climate change [1] has stimulated the search for planetary-scale technological solutions for reducing global warming [2] (“geoengineering”), typically characterized by the necessity for costly new infrastructures and industries [3]. We suggest that the existing global infrastructure associated with arable agriculture can help, given that crop plants exert an important influence over the climatic energy budget 4 and 5 because of differences in their albedo (solar reflectivity) compared to soils and to natural vegetation [6]. Specifically, we propose a “bio-geoengineering” approach to mitigate surface warming, in which crop varieties having specific leaf glossiness and/or canopy morphological traits are specifically chosen to maximize solar reflectivity. We quantify this by modifying the canopy albedo of vegetation in prescribed cropland areas in a global-climate model, and thereby estimate the near-term potential for bio-geoengineering to be a summertime cooling of more than 1°C throughout much of central North America and midlatitude Eurasia, equivalent to seasonally offsetting approximately one-fifth of regional warming due to doubling of atmospheric CO2[7]. Ultimately, genetic modification of plant leaf waxes or canopy structure could achieve greater temperature reductions, although better characterization of existing intraspecies variability is needed first.

Bio-fortification of potato tubers using foliar zinc-fertiliser

Worldwide, many people are zinc (Zn)-deficient. Dietary Zn intake can be increased by producing crops with higher concentrations of Zn in their edible portions. This can be achieved by applying Zn-fertilisers to varieties with an increased ability to acquire Zn and to accumulate Zn in their edible portions. Potato (Solanum tuberosum L.) is an important food crop and is, therefore, a target for bio-fortification with Zn. Field trials incorporating a core collection of 23 potato genotypes, performed over 4 years (2006 – 2009), indicated significant genotypic effects on tuber Zn concentration and suggested that tuber Zn concentration was influenced by environmental effects, but also found that genotype environment (G E) interactions were not significant. Tuber Zn concentrations averaged 10.8 mg kg–1 dry matter (DM), and the ratio between the lowest and the highest varietal tuber Zn-concentration averaged 1.76. Tuber Zn concentrations could be increased by foliar Zn-fertilisation. Tuber yields of ‘Maris Piper’ were unaffected by foliar applications of < 1.08 g Zn plant–1. The relationship between tuber Zn concentration and foliar Zn application followed a saturation curve, reaching a maximum at approx. 30 mg Zn kg–1 DM at a foliar Zn application rate of 1.08 g plant–1. Despite a 40-fold increase in shoot Zn concentration compared to the unfertilised controls following foliar Zn fertilisation with 2.16 g Zn plant–1, only a doubling in tuber Zn concentration was observed. This suggests that the biofortification of tubers with Zn was restricted by the limited mobility of Zn in the phloem. A significant positive linear relationship between tuber Zn concentration and tuber N concentration supported the hypothesis of co-transport of Zn and N-compounds in the phloem.

Simulation of late-twenty-first-century changes in wintertime atmospheric circulation over Europe due to anthropogenic causes

Evidence is presented, based on an ensemble of climate change scenarios performed with a global general circulation model of the atmosphere with high horizontal resolution over Europe, to suggest that the end-of-century anthropogenic climate change over the North Atlantic--European region strongly projects onto the positive phase of the North Atlantic Oscillation during wintertime. It is reflected in a doubling of the residence frequency of the climate system in the associated circulation regime, in agreement with the nonlinear climate perspective. The strong increase in the amplitude of the response, compared to coarse-resolution coupled model studies, suggests that improved model representation of regional climate is needed to achieve more reliable projections of anthropogenic climate change on European climate.

General circulation model estimates of aerosol transport and radiative forcing during the Indian Ocean Experiment

Aerosol sources, transport, and sinks are simulated, and aerosol direct radiative effects are assessed over the Indian Ocean for the Indian Ocean Experiment (INDOEX) Intensive Field Phase during January to March 1999 using the Laboratoire de Me´te´orologie Dynamique (LMDZT) general circulation model. The model reproduces the latitudinal gradient in aerosol mass concentration and optical depth (AOD). The model-predicted aerosol concentrations and AODs agree reasonably well with measurements but are systematically underestimated during high-pollution episodes, especially in the month of March. The largest aerosol loads are found over southwestern China, the Bay of Bengal, and the Indian subcontinent. Aerosol emissions from the Indian subcontinent are transported into the Indian Ocean through either the west coast or the east coast of India. Over the INDOEX region, carbonaceous aerosols are the largest contributor to the estimated AOD, followed by sulfate, dust, sea salt, and fly ash. During the northeast winter monsoon, natural and anthropogenic aerosols reduce the solar flux reaching the surface by 25 W m�2, leading to 10–15% less insolation at the surface. A doubling of black carbon (BC) emissions from Asia results in an aerosol single-scattering albedo that is much smaller than in situ measurements, reflecting the fact that BC emissions are not underestimated in proportion to other (mostly scattering) aerosol types. South Asia is the dominant contributor to sulfate aerosols over the INDOEX region and accounts for 60–70% of the AOD by sulfate. It is also an important but not the dominant contributor to carbonaceous aerosols over the INDOEX region with a contribution of less than 40% to the AOD by this aerosol species. The presence of elevated plumes brings significant quantities of aerosols to the Indian Ocean that are generated over Africa and Southeast and east Asia.

Individual differences and the role of the L1 in L2 processing: an ERP investigation

This study used ERP (event-related potentials) to examine both the role of the L1 and the role of individual differences in the processing of agreement violations. Theories of L2 acquisition differ with regard to whether or not native-like acquisition of L2 features is possible (Schwartz and Sprouse, 1994, 1996; Tsimpli and Mastropavlou, 2007), and the results of previous ERP studies are inconsistent when it comes to whether or not native-like processing is observed in response to L2 agreement violations (e.g., Sabourin, 2003; Tokowicz and MacWhinney, 2005). Furthermore, studies of learners in early stages of L2 acquisition have found variability in the emergence of native-like responses (e.g., McLaughlin et al., 2010; Tanner et al., 2009), but sources of variability have not been investigated. The current study examines responses to gender and number agreement violations in English-speaking learners of Spanish (n=24). Stimuli targeted agreement in three conditions: subject-verb agreement (el barco flota/*flotan), which is similar in Spanish and English; number agreement on adjectival predicates (la isla rocosa/*rocosas), a context in which agreement is not instantiated in English; and gender agreement on adjectival predicates (la isla rocosa/*rocoso), which is unique to Spanish. Grammaticality judgments and ERP responses were also tested for correlations with aptitude scores on the Modern Languages Aptitude Test (MLAT; Carroll and Sapon, 1959) and the Raven Advanced Progressive Matrices (Raven, 1965). Results are in line with theories that claim native-like processing is acquirable, since learners demonstrated similar ERP responses to a control group of native Spanish-speakers (n=8) with regard to all three agreement types. Additionally, the MLAT (but not the Raven) was significantly correlated with sensitivity to number violations, both in terms of grammaticality judgments and ERP amplitudes, indicating a role for verbal but not nonverbal aptitude in L2 processing.

Morphosyntactic processing in advanced second language (L2) learners: An event-related potential investigation of the effects of L1-L2 similarity and structural distance

Different theoretical accounts of second language (L2) acquisition differ with respect to whether or not advanced learners are predicted to show native like processing for features not instantiated in the native language (L1). We examined how native speakers of English, a language with number but not gender agreement, process number and gender agreement in Spanish. We compare agreement within a determiner phrase (órgano muy complejo “[DP organ-MASC-SG very complex-MASC-SG]”) and across a verb phrase (cuadro es auténtico “painting-MASC-SG [VP is authentic-MASC-SG]”) in order to investigate whether native like processing is limited to local domains (e.g. within the phrase), in line with Clahsen and Felser (2006). We also examine whether morphological differences in how the L1 and L2 realize a shared feature impact processing by comparing number agreement between nouns and adjectives, where only Spanish instantiates agreement, and between demonstratives and nouns, where English also instantiates agreement. Similar to Spanish natives, advanced learners showed a P600 for both number and gender violations overall, in line with the Full Transfer/Full Access Hypothesis (Schwartz and Sprouse, 1996), which predicts that learners can show native-like processing for novel features. Results also show that learners can establish syntactic dependencies outside of local domains, as suggested by the presence of a P600 for both within and across phrase violations. Moreover, similar to native speakers, learners were impacted by the structural distance (number of intervening phrases) between the agreeing elements, as suggested by the more positive waveforms for within than across-phrase agreement overall. These results are consistent with the proposal that learners are sensitive to hierarchical structure.

Using the past to constrain the future: how the palaeorecord can improve estimates of global warming

Climate sensitivity is defined as the change in global mean equilibrium temperature after a doubling of atmospheric CO2 concentration and provides a simple measure of global warming. An early estimate of climate sensitivity, 1.5—4.5°C, has changed little subsequently, including the latest assessment by the Intergovernmental Panel on Climate Change. The persistence of such large uncertainties in this simple measure casts doubt on our understanding of the mechanisms of climate change and our ability to predict the response of the climate system to future perturbations. This has motivated continued attempts to constrain the range with climate data, alone or in conjunction with models. The majority of studies use data from the instrumental period (post-1850), but recent work has made use of information about the large climate changes experienced in the geological past. In this review, we first outline approaches that estimate climate sensitivity using instrumental climate observations and then summarize attempts to use the record of climate change on geological timescales. We examine the limitations of these studies and suggest ways in which the power of the palaeoclimate record could be better used to reduce uncertainties in our predictions of climate sensitivity.

Writing in French in secondary schools in England and Germany: are the British really 'bad language learners’?

It is widely assumed that the British are poorer modern foreign language (MFL) learners than their fellow Europeans. Motivation has often been seen as the main cause of this perceived disparity in language learning success. However, there have also been suggestions that curricular and pedagogical factors may play a part. This article reports a research project investigating how German and English 14- to 16-year-old learners of French as a first foreign language compare to one another in their vocabulary knowledge and in the lexical diversity, accuracy and syntactic complexity of their writing. Students from comparable schools in Germany and England were set two writing tasks which were marked by three French native speakers using standardised criteria aligned to the Common European Framework of Reference (CEF). Receptive vocabulary size and lexical diversity were established by the X_lex test and a verb types measure respectively. Syntactic complexity and formal accuracy were respectively assessed using the mean length of T-units (MLTU) and words/error metrics. Students' and teachers' questionnaires and semi-structured interviews were used to provide information and participants' views on classroom practices, while typical textbooks and feedback samples were analysed to establish differences in materials-related input and feedback in the two countries. The German groups were found to be superior in vocabulary size, and in the accuracy, lexical diversity and overall quality – but not the syntactic complexity – of their writing. The differences in performance outcomes are analysed and discussed with regard to variables related to the educational contexts (e.g. curriculum design and methodology).