A class of quadratic deformations of Lie superalgebras

We study certain Z_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. We derive the equivalent of the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate in detail one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.Comment: 26pp, LaTeX. Original title: "Finite dimensional quadratic Lie superalgebras"; abstract re-worded; text clarified; 3 references added; rearrangement of minor appendices into text; new subsection 4.

Unrelated Helpers in a Primitively Eusocial Wasp: Is Helping Tailored Towards Direct Fitness?

The paper wasp Polistes dominulus is unique among the social insects in that nearly one-third of co-foundresses are completely unrelated to the dominant individual whose offspring they help to rear and yet reproductive skew is high. These unrelated subordinates stand to gain direct fitness through nest inheritance, raising the question of whether their behaviour is adaptively tailored towards maximizing inheritance prospects. Unusually, in this species, a wealth of theory and empirical data allows us to predict how unrelated subordinates should behave. Based on these predictions, here we compare helping in subordinates that are unrelated or related to the dominant wasp across an extensive range of field-based behavioural contexts. We find no differences in foraging effort, defense behaviour, aggression or inheritance rank between unrelated helpers and their related counterparts. Our study provides no evidence, across a number of behavioural scenarios, that the behaviour of unrelated subordinates is adaptively modified to promote direct fitness interests

Three‐dimensional forward stratigraphic modelling of the sedimentary architecture of meandering‐river successions in evolving half‐graben rift basins

The spatial organisation of meandering‐river deposits varies greatly within the sedimentary fills of rift basins, depending on how differential rates of fault propagation and subsidence interplay with autogenic processes to drive changes in fluvial channel‐belt position and rate of migration, avulsion frequency and mechanisms of meander‐bend cut off. This set of processes fundamentally influences stacking patterns of the accumulated successions. Quantitative predictions of the spatio‐temporal evolution and internal architecture of meandering fluvial deposits in such tectonically active settings remain limited. A numerical forward stratigraphic model—the Point‐Bar Sedimentary Architecture Numerical Deduction (PB‐SAND)—is applied to examine relationships between differential rates of subsidence and resultant fluvial channel‐belt migration, reach avulsion and channel‐deposit stacking in active, fault‐bounded half‐grabens. The model is used to reconstruct and predict the complex morphodynamics of fluvial meanders, their generated channel belts, and the associated lithofacies distributions that accumulate as heterogeneous fluvial successions in rift settings, constrained by data from seismic images and outcrop successions. The 3D modelling outputs are used to explore sedimentary heterogeneity at various spatio‐temporal scales. Results show how the connectivity of sand‐prone geobodies can be quantified as a function of subsidence rate, which itself decreases both along and away from the basin‐bounding fault. In particular, results highlight the spatial variability in the size and connectedness of sand‐prone geobodies that is seen in directions perpendicular and parallel to the basin axis, and that arises as a function of the interaction between spatial and temporal variations in rates of accommodation generation and fault‐influenced changes in river morphodynamics. The results have applied significance, for example, to both hydrocarbon exploration and assessment of groundwater aquifers. The expected greatest connectivity of fluvial sandbody in a half‐graben is primarily determined by the complex interplay between the frequency and rate of subsidence, the style of basin propagation, the rates of migration of channel belts, the frequency of avulsion and the proportion and spatial distribution of variably sand‐prone channel and bar deposits

SLˉ(4,R)\bar{SL}(4,R) Embedding for a 3D World Spinor Equation

A generic-curved spacetime Dirac-like equation in 3D is constructed. It has, owing to the $\bar{SL}(n,R)$ group deunitarizing automorphism, a physically correct unitarity and flat spacetime particle properties. The construction is achieved by embedding $\bar{SL}(3,R)$ vector operator $X_{\mu}$, that plays a role of Dirac's $\gamma_{\mu}$ matrices, into $\bar{SL}(4,R)$. Decomposition of the unitary irreducible spinorial $\bar{SL}(4,R)$ representations gives rise to an explicit form of the infinite $X_{\mu}$ matrices

Clinical features that identify children with primary immunodeficiency diseases

BACKGROUND: The 10 warning signs of primary immunodeficiency diseases (PID) have been promoted by various organizations in Europe and the United States to predict PID. However, the ability of these warning signs to identify children with PID has not been rigorously tested. OBJECTIVE: The main goal of this study was to determine the effectiveness of these 10 warning signs in predicting defined PID among children who presented to 2 tertiary pediatric immunodeficiency centers in the north of England. METHODS: A retrospective survey of 563 children who presented to 2 pediatric immunodeficiency centers was undertaken. The clinical records of 430 patients with a defined PID and 133 patients for whom detailed investigations failed to establish a specific PID were reviewed. RESULTS: Overall, 96% of the children with PID were referred by hospital clinicians. The strongest identifiers of PID were a family history of immunodeficiency disease in addition to use of intravenous antibiotics for sepsis in children with neutrophil PID and failure to thrive in children with T-lymphocyte PID. With these 3 signs, 96% of patients with neutrophil and complement deficiencies and 89% of children with T-lymphocyte immunodeficiencies could be identified correctly. Family history was the only warning sign that identified children with B-lymphocyte PID. CONCLUSIONS: PID awareness initiatives should be targeted at hospital pediatricians and families with a history of PID rather than the general public. Our results provide the general pediatrician with a simple refinement of 10 warning signs for identifying children with underlying immunodeficiency diseases. </jats:sec

Switching the stereochemical outcome of 6-endo-trig cyclizations; Synthesis of 2,6-Cis-6-substituted 4-oxopipecolic acids

A base-mediated 6-endo-trig cyclization of readily accessible enone-derived α-amino acids has been developed for the direct synthesis of novel 2,6-cis-6- substituted-4-oxo-L-pipecolic acids. A range of aliphatic and aryl side chains were tolerated by this mild procedure to give the target compounds in good overall yields. Molecular modeling of the 6-endo-trig cyclization allowed some insight as to how these compounds were formed, with the enolate intermediate generated via an equilibrium process, followed by irreversible tautomerization/neutralization providing the driving force for product formation. Stereoselective reduction and deprotection of the resulting 2,6-cis-6-substituted 4-oxo-L-pipecolic acids to the corresponding 4-hydroxy-L-pipecolic acids was also performed

Telomere dynamics in wild banded mongooses: Evaluating longitudinal and quasi-longitudinal markers of senescence

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Telomere length and the rate of telomere shortening have been suggested as particularly useful physiological biomarkers of the processes involved in senescent decline of somatic and reproductive function. However, longitudinal data on changes in telomere length across the lifespan are difficult to obtain, particularly for long-lived animals. Quasi-longitudinal studies have been proposed as a method to gain insight into telomere dynamics in long-lived species. In this method, minimally replicative cells are used as the baseline telomere length against which telomere length in highly replicative cells (which represent the current state) can be compared. Here we test the assumptions and predictions of the quasi-longitudinal approach using longitudinal telomere data in a wild cooperative mammal, the banded mongoose, Mungos mungo. Contrary to our prediction, telomere length (TL) was longer in leukocytes than in ear cartilage. Longitudinally, the TL of ear cartilage shortened with age, but there was no change in the TL of leukocytes, and we also observed many individuals in which TL increased rather than decreased with age. Leukocyte TL but not cartilage TL was a predictor of total lifespan, while neither predicted post-sampling survival. Our data do not support the hypothesis that cross-tissue comparison in TL can act as a quasi-longitudinal marker of senescence. Rather, our results suggest that telomere dynamics in banded mongooses are more complex than is typically assumed, and that longitudinal studies across whole life spans are required to elucidate the link between telomere dynamics and senescence in natural populations.The research was funded by a European Research Council Consolidator’s Grant (no. 309249) to MAC and a Natural Environment Research Council (UK) Standard Grant (NE/G019657/1) to MAC and JDB

Associations between feed efficiency and aspects of lactation curves in primiparous Holstein dairy cattle.

Genetic selection for improved feed efficiency in dairy cattle has received renewed attention over the last decade to address the needs of a growing global population. As milk yield is a critical component of feed efficiency metrics in dairy animals, our objective was to evaluate the associations between feed efficiency in primiparous Holstein cattle and parameters of a mathematical model describing individual lactation curves. The Dijkstra lactation curve model was fit to individual lactation records from 34 Holstein heifers with previously estimated measures of feed efficiency. We found that the optimal fit of the Dijkstra model was achieved using daily milk yield records up to 21 d in milk to capture the rise to peak milk yield and using monthly dairy herd improvement records for the remainder of lactation to accurately characterize lactation persistency. In the period of lactation before peak milk yield, improved feed efficiency was associated with a faster increase in daily milk yield over a shorter period of time at the expense of increased mobilization of body reserves; this serves to reinforce the concept that dairy cattle are primarily capital breeders versus income breeders. Feed efficiency in the period following peak lactation, as measured by gross feed efficiency, return over feed costs, and net energy efficiency of lactation, was positively associated with higher peak milk yield. The findings in early lactation suggest that estimates of feed efficiency could be improved by evaluating feed efficiency relative to conception, rather than parturition and lactation, to better account for the energy stored and released from body reserves in capital breeding