About the maximal rank of 3-tensors over the real and the complex number field

High dimensional array data, tensor data, is becoming important in recent days. Then maximal rank of tensors is important in theory and applications. In this paper we consider the maximal rank of 3 tensors. It can be attacked from various viewpoints, however, we trace the method of Atkinson-Stephens(1979) and Atkinson-Lloyd(1980). They treated the problem in the complex field, and we will present various bounds over the real field by proving several lemmas and propositions, which is real counterparts of their results.Comment: 13 pages, no figure v2: correction and improvemen

Coloured peak algebras and Hopf algebras

For $G$ a finite abelian group, we study the properties of general equivalence relations on G_n=G^n\rtimes \SG_n, the wreath product of $G$ with the symmetric group \SG_n, also known as the $G$-coloured symmetric group. We show that under certain conditions, some equivalence relations give rise to subalgebras of \k G_n as well as graded connected Hopf subalgebras of \bigoplus_{n\ge o} \k G_n. In particular we construct a $G$-coloured peak subalgebra of the Mantaci-Reutenauer algebra (or $G$-coloured descent algebra). We show that the direct sum of the $G$-coloured peak algebras is a Hopf algebra. We also have similar results for a $G$-colouring of the Loday-Ronco Hopf algebras of planar binary trees. For many of the equivalence relations under study, we obtain a functor from the category of finite abelian groups to the category of graded connected Hopf algebras. We end our investigation by describing a Hopf endomorphism of the $G$-coloured descent Hopf algebra whose image is the $G$-coloured peak Hopf algebra. We outline a theory of combinatorial $G$-coloured Hopf algebra for which the $G$-coloured quasi-symmetric Hopf algebra and the graded dual to the $G$-coloured peak Hopf algebra are central objects.Comment: 26 pages latex2

Fast computation of Bernoulli, Tangent and Secant numbers

We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations. We also give very short in-place algorithms for computing the first n Tangent or Secant numbers in O(n^2) integer operations. These algorithms are extremely simple, and fast for moderate values of n. They are faster and use less space than the algorithms of Atkinson (for Tangent and Secant numbers) and Akiyama and Tanigawa (for Bernoulli numbers).Comment: 16 pages. To appear in Computational and Analytical Mathematics (associated with the May 2011 workshop in honour of Jonathan Borwein's 60th birthday). For further information, see http://maths.anu.edu.au/~brent/pub/pub242.htm

Evidence for a persistent, major excess in all cause admissions to hospital in children with type-1 diabetes: results from a large Welsh national matched community cohort study

OBJECTIVES: To estimate the excess in admissions associated with type1 diabetes in childhood. DESIGN: Matched-cohort study using anonymously linked hospital admission data. SETTING: Brecon Group Register of new cases of childhood diabetes in Wales linked to hospital admissions data within the Secure Anonymised Information Linkage Databank. POPULATION: 1577 Welsh children (aged between 0 and 15 years) from the Brecon Group Register with newly-diagnosed type-1 diabetes between 1999–2009 and 7800 population controls matched on age, sex, county, and deprivation, randomly selected from the local population. MAIN OUTCOME MEASURES: Difference in all-cause hospital admission rates, 30-days post-diagnosis until 31 May 2012, between participants and controls. RESULTS: Children with type-1 diabetes were followed up for a total of 12 102 person years and were at 480% (incidence rate ratios, IRR 5.789, (95% CI 5.34 to 6.723), p<0.0001) increased risk of hospital admission in comparison to matched controls. The highest absolute excess of admission was in the age group of 0–5 years, with a 15.4% (IRR 0.846, (95% CI 0.744 to 0.965), p=0.0061) reduction in hospital admissions for every 5-year increase in age at diagnosis. A trend of increasing admission rates in lower socioeconomic status groups was also observed, but there was no evidence of a differential rate of admissions between men and women when adjusted for background risk. Those receiving outpatient care at large centres had a 16.1% (IRR 0.839, (95% CI 0.709 to 0.990), p=0.0189) reduction in hospital admissions compared with those treated at small centres. CONCLUSIONS: There is a large excess of hospital admissions in paediatric patients with type-1 diabetes. Rates are highest in the youngest children with low socioeconomic status. Factors influencing higher admission rates in smaller centres (eg, “out of hours resources”) need to be explored with the aim of targeting modifiable influences on admission rates

A mental number line in human newborns

Humans represent numbers on a mental number line with smaller numbers on the left and larger numbers on the right side. A left\u2010to\u2010right oriented spatial\u2013numerical association, (SNA), has been demonstrated in animals and infants. However, the possibility that SNA is learnt by early exposure to caregivers\u2019 directional biases is still open. We conducted two experiments: in Experiment 1, we tested whether SNA is present at birth and in Experiment 2, we studied whether it depends on the relative rather than the absolute magnitude of numerousness. Fifty\u2010five\u2010hour\u2010old newborns, once habituated to a number (12), spontaneously associated a smaller number (4) with the left and a larger number (36) with the right side (Experiment 1). SNA in neonates is not absolute but relative. The same number (12) was associated with the left side rather than the right side whenever the previously experienced number was larger (36) rather than smaller (4) (Experiment 2). Control on continuous physical variables showed that the effect is specific of discrete magnitudes. These results constitute strong evidence that in our species SNA originates from pre\u2010linguistic and biological precursors in the brain

Magnetization relaxation in (Ga,Mn)As ferromagnetic semiconductors

We describe a theory of Mn local-moment magnetization relaxation due to p-d kinetic-exchange coupling with the itinerant-spin subsystem in the ferromagnetic semiconductor (Ga,Mn)As alloy. The theoretical Gilbert damping coefficient implied by this mechanism is calculated as a function of Mn moment density, hole concentration, and quasiparticle lifetime. Comparison with experimental ferromagnetic resonance data suggests that in annealed strongly metallic samples, p-d coupling contributes significantly to the damping rate of the magnetization precession at low temperatures. By combining the theoretical Gilbert coefficient with the values of the magnetic anisotropy energy, we estimate that the typical critical current for spin-transfer magnetization switching in all-semiconductor trilayer devices can be as low as $\sim 10^{5} {\rm A cm}^{-2}$.Comment: 4 pages, 2 figures, submitted to Rapid Communication

The relationship between central Indian terrestrial vegetation and monsoon rainfall distributions in different hydroclimatic extreme years using time-series satellite data

The study explored the dependence of the spatio-temporal pattern of rainfall and its variability on the spatial distribution of forests in the central Indian landscape, which covers ~1 million km2, includes five states, and supports a population of 329 million people. The monsoon rainfall is, thus, a crucial source of freshwater for these population. We analyzed the relationship between rainfall and satellite-derived vegetation vigor, vegetation fraction, and elevation across 22 experimental zones across central India (i.e., forested, non-forested, and agricultural regions; buffer zones within and outside forests). Around 87% of annual rainfall is received during the monsoon, with maximum rainfall (~1600 mm) in Odisha and minimum (~900 mm) in Maharashtra. The average rainfall was greater (~1500 mm) inside forests than in non-forested regions (~1000 mm). Moreover, 245 mm km−2 year−1 of rainfall was observed over forests during monsoon, but only 215 mm km−2 year−1 in non-forested areas. Overall, rainfall increases from the forest edge towards the forest core logarithmically at a rate of ~10 mm km−1 year−1, and it decreases exponentially when moving away from the forest edge at an average rate of −20 mm km−1 year−1 over 0-to-50 km range, and at a rate of −7.5 mm km−1 year−1 over the 50-to-100 km range. This rate of decrease was maximum in Madhya Pradesh and Jharkhand and minimum in Chhattisgarh. The results confirmed the crucial role of forests in the distribution of monsoon rainfall, but in the elevated and Western Ghats regions, the orographic effect is dominant. These findings are of great concern to forest policymakers to conserve and protect the central Indian forests

The β3-integrin endothelial adhesome regulates microtubule-dependent cell migration

Integrin β3 is seen as a key anti-angiogenic target for cancer treatment due to its expression on neovasculature, but the role it plays in the process is complex; whether it is pro- or anti-angiogenic depends on the context in which it is expressed. To understand precisely β3's role in regulating integrin adhesion complexes in endothelial cells, we characterised, by mass spectrometry, the β3-dependent adhesome. We show that depletion of β3-integrin in this cell type leads to changes in microtubule behaviour that control cell migration. β3-integrin regulates microtubule stability in endothelial cells through Rcc2/Anxa2-driven control of active Rac1 localisation. Our findings reveal that angiogenic processes, both in vitro and in vivo, are more sensitive to microtubule targeting agents when β3-integrin levels are reduced

A basin- to channel-scale unstructured grid hurricane storm surge model applied to southern Louisiana

Southern Louisiana is characterized by low-lying topography and an extensive network of sounds, bays, marshes, lakes, rivers, and inlets that permit widespread inundation during hurricanes. A basin- to channel-scale implementation of the Advanced Circulation (ADCIRC) unstructured grid hydrodynamic model has been developed that accurately simulates hurricane storm surge, tides, and river flow in this complex region. This is accomplished by defining a domain and computational resolution appropriate for the relevant processes, specifying realistic boundary conditions, and implementing accurate, robust, and highly parallel unstructured grid numerical algorithms. The model domain incorporates the western North Atlantic, the Gulf of Mexico, and the Caribbean Sea so that interactions between basins and the shelf are explicitly modeled and the boundary condition specification of tidal and hurricane processes can be readily defined at the deep water open boundary. The unstructured grid enables highly refined resolution of the complex overland region for modeling localized scales of flow while minimizing computational cost. Kinematic data assimilative or validated dynamic-modeled wind fields provide the hurricane wind and pressure field forcing. Wind fields are modified to incorporate directional boundary layer changes due to overland increases in surface roughness, reduction in effective land roughness due to inundation, and sheltering due to forested canopies. Validation of the model is achieved through hindcasts of Hurricanes Betsy and Andrew. A model skill assessment indicates that the computed peak storm surge height has a mean absolute error of 0.30 m

Dirichlet fundamental domains and complex-projective varieties

We prove that for every finitely-presented group G there exists a 2-dimensional irreducible complex-projective variety W with the fundamental group G, so that all singularities of W are normal crossings and Whitney umbrellas.Comment: 1 figur