Multilateral inversion of A_r, C_r and D_r basic hypergeometric series

In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and involves two infinite matrices which are not lower-triangular. The present paper features three different multivariable generalizations of the above result. These are extracted from Gustafson's A_r and C_r extensions and of the author's recent A_r extension of Bailey's 6-psi-6 summation formula. By combining these new multidimensional matrix inverses with A_r and D_r extensions of Jackson's 8-phi-7 summation theorem three balanced very-well-poised 8-psi-8 summation theorems associated with the root systems A_r and C_r are derived.Comment: 24 page

Automated Problem Decomposition for the Boolean Domain with Genetic Programming

Researchers have been interested in exploring the regularities and modularity of the problem space in genetic programming (GP) with the aim of decomposing the original problem into several smaller subproblems. The main motivation is to allow GP to deal with more complex problems. Most previous works on modularity in GP emphasise the structure of modules used to encapsulate code and/or promote code reuse, instead of in the decomposition of the original problem. In this paper we propose a problem decomposition strategy that allows the use of a GP search to find solutions for subproblems and combine the individual solutions into the complete solution to the problem

A new multivariable 6-psi-6 summation formula

By multidimensional matrix inversion, combined with an A_r extension of Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7 summation is derived. By a polynomial argument this 8-phi-7 summation is transformed to another multivariable 8-phi-7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6-phi-5 summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey's very-well-poised 6-psi-6 summation formula.Comment: 16 page

Production and quality evaluation of cake from wheat and red banana flour blends

Cakes are convenient food products prepared from flour basically wheat and other principal ingredients and often baked. This study investigated the quality of cake produced from flour blends of wheat and red banana. Cakes were produced from eight formulations of flour blends of wheat and red banana at 10-80% ratios. Cakes from 100% wheat flour served as the control. The flour blends were analysed for functional properties while the cakes were subjected to proximate, physical and sensory evaluation. Results of the functional properties of the flour blends significantly (p<0.05) increased with increased proportion of banana flour in all the parameters evaluated. The same trend was observed in the proximate composition of the cakes in the ash, fibre and carbohydrate contents. Amongst the physical properties (weight, height, volume) of the cakes evaluated the weights were significantly (p<0.05) higher in the flour blends than the control sample (100% wheat flour). The sensory evaluation showed high scores of preference and acceptance in cakes containing up to 30% banana flour and were comparable to the control (100% wheat) in all the parameters analysed. The study revealed that cake produced from wheat/banana flour blends possesses good nutrient quality comparable to the control (100% wheat flour)

African American English speaking 2nd graders, verbal-s, and educational achievement: Event related potential and math study findings

A number of influential linguistic analyses hold that African American English (AAE) has no verbal-s, the-s that, for example, turns drink into drinks in more mainstream English varieties.On such accounts, sentences like Mary drinks coffee are ungrammatical in AAE. Previous behavioral studies suggest that in addition to being ungrammatical, AAE speaking children find these sentences cognitively demanding, and that their presence in mathematical reasoning tests can depress scores. Until now, however, no online sentence processing study nor investigation of neurophysiological markers has been done to support these findings. Aimed at addressing this gap in the literature, the auditory ERP experiment described herein revealed two different processes associated with AAE speaking 2nd graders listening to this type of sentence: a morphosyntactic structure building problem, reflected in a bilateral early anterior-central negativity; and an increase in working memory load, indicated by a bilateral late long-lasting anterior-central negativity. Study participants also took an orally administered test of math word problems. Consistent with previous findings, results showed they answered fewer questions correctly when those questions contained verbal-s than when they did not

UK monitoring and deposition of tephra from the May 2011 eruption of Grímsvötn, Iceland

Mapping the transport and deposition of tephra is important for the assessment of an eruption’s impact on health, transport, vegetation and infrastructure, but it is challenging at large distances from a volcano (> 1000 km), where it may not be visible to the naked eye. Here we describe a range of methods used to quantify tephra deposition and impact on air quality during the 21–28 May 2011 explosive basaltic eruption of Grímsvötn volcano, Iceland. Tephra was detected in the UK with tape-on-paper samples, rainwater samples, rainwater chemistry analysis, pollen slides and air quality measurements. Combined results show that deposition was mainly in Scotland, on 23–25 May. Deposition was patchy, with adjacent locations recording different results. Tape-on-paper samples, collected by volunteer citizen scientists, and giving excellent coverage across the UK, showed deposition at latitudes >55°N, mainly on 24 May. Rainwater samples contained ash grains mostly 20–30 μm long (maximum recorded grainsize 80 μm) with loadings of up to 116 grainscm-2. Analysis of rainwater chemistry showed high concentrations of dissolved Fe and Al in samples from N Scotland on 24–27 May. Pollen slides recorded small glass shards (3–4 μm long) deposited during rainfall on 24–25 May and again on 27 May. Air quality monitoring detected increased particulate matter concentrations in many parts of the country. An hourly concentration of particles  53°N) on 24 May but no negative effects on health were reported. Although the eruption column reached altitudes of 20 km above sea level, air mass trajectories suggest that only tephra from the lowest 4 km above sea level of the eruption plume was transported to the UK. This demonstrates that even low plumes could deliver tephra to the UK and suggests that the relative lack of basaltic tephra in the tephrochronological record is not due to transport processes

Vortex Rings in two Component Bose-Einstein Condensates

We study the structure of the vortex core in two-component Bose-Einstein condensates. We demonstrate that the order parameter may not vanish and the symmetry may not be restored in the core of the vortex. In this case such vortices can form vortex rings known as vortons in particle physics literature. In contrast with well-studied superfluid $^4He$, where similar vortex rings can be stable due to Magnus force only if they move, the vortex rings in two-component BECs can be stable even if they are at rest. This beautiful effect was first discussed by Witten in the cosmic string context, where it was shown that the stabilization occurs due to condensation of the second component of the field in the vortex core. This second condensate trapped in the core may carry a current along the vortex ring counteracting the effect of string tension that causes the loop to shrink. We speculate that such vortons may have been already observed in the laboratory. We also speculate that the experimental study of topological structures in BECs can provide a unique opportunity to study cosmology and astrophysics by doing laboratory experiments.Comment: 21 pages, 2 figure

Cosmic distance-duality as probe of exotic physics and acceleration

In cosmology, distances based on standard candles (e.g. supernovae) and standard rulers (e.g. baryon oscillations) agree as long as three conditions are met: (1) photon number is conserved, (2) gravity is described by a metric theory with (3) photons travelling on unique null geodesics. This is the content of distance-duality (the reciprocity relation) which can be violated by exotic physics. Here we analyse the implications of the latest cosmological data sets for distance-duality. While broadly in agreement and confirming acceleration we find a 2-sigma violation caused by excess brightening of SN-Ia at z > 0.5, perhaps due to lensing magnification bias. This brightening has been interpreted as evidence for a late-time transition in the dark energy but because it is not seen in the d_A data we argue against such an interpretation. Our results do, however, rule out significant SN-Ia evolution and extinction: the "replenishing" grey-dust model with no cosmic acceleration is excluded at more than 4-sigma despite this being the best-fit to SN-Ia data alone, thereby illustrating the power of distance-duality even with current data sets.Comment: 6 pages, 4 colour figures. Version accepted as a Rapid Communication in PR

Assembly of functional photosystem complexes in Rhodobacter sphaeroides incorporating carotenoids from the spirilloxanthin pathway

Carotenoids protect the photosynthetic apparatus against harmful radicals arising from the presence of both light and oxygen. They also act as accessory pigments for harvesting solar energy, and are required for stable assembly of many light-harvesting complexes. In the phototrophic bacterium Rhodobacter (Rba.) sphaeroides phytoene desaturase (CrtI) catalyses three sequential desaturations of the colourless carotenoid phytoene, extending the number of conjugated carbon–carbon double bonds, N, from three to nine and producing the yellow carotenoid neurosporene; subsequent modifications produce the yellow/red carotenoids spheroidene/spheroidenone (N = 10/11). Genomic crtI replacements were used to swap the native three-step Rba. sphaeroides CrtI for the four-step Pantoea agglomerans enzyme, which re-routed carotenoid biosynthesis and culminated in the production of 2,2′-diketo-spirilloxanthin under semi-aerobic conditions. The new carotenoid pathway was elucidated using a combination of HPLC and mass spectrometry. Premature termination of this new pathway by inactivating crtC or crtD produced strains with lycopene or rhodopin as major carotenoids. All of the spirilloxanthin series carotenoids are accepted by the assembly pathways for LH2 and RC–LH1–PufX complexes. The efficiency of carotenoid-to-bacteriochlorophyll energy transfer for 2,2′-diketo-spirilloxanthin (15 conjugated Cdouble bond; length as m-dashC bonds; N = 15) in LH2 complexes is low, at 35%. High energy transfer efficiencies were obtained for neurosporene (N = 9; 94%), spheroidene (N = 10; 96%) and spheroidenone (N = 11; 95%), whereas intermediate values were measured for lycopene (N = 11; 64%), rhodopin (N = 11; 62%) and spirilloxanthin (N = 13; 39%). The variety and stability of these novel Rba. sphaeroides antenna complexes make them useful experimental models for investigating the energy transfer dynamics of carotenoids in bacterial photosynthesis

Light scattering from disordered overlayers of metallic nanoparticles

We develop a theory for light scattering from a disordered layer of metal nanoparticles resting on a sample. Averaging over different disorder realizations is done by a coherent potential approximation. The calculational scheme takes into account effects of retardation, multipole excitations, and interactions with the sample. We apply the theory to a system similar to the one studied experimentally by Stuart and Hall [Phys. Rev. Lett. {\bf 80}, 5663 (1998)] who used a layered Si/SiO$_2$/Si sample. The calculated results agree rather well with the experimental ones. In particular we find conspicuous maxima in the scattering intensity at long wavelengths (much longer than those corresponding to plasmon resonances in the particles). We show that these maxima have their origin in interference phenomena in the layered sample.Comment: 19 pages, 12 figure