Graded extension of SO(2,1) Lie algebra and the search for exact solutions of Dirac equation by point canonical transformations

SO(2,1) is the symmetry algebra for a class of three-parameter problems that includes the oscillator, Coulomb and Morse potentials as well as other problems at zero energy. All of the potentials in this class can be mapped into the oscillator potential by point canonical transformations. We call this class the "oscillator class". A nontrivial graded extension of SO(2,1) is defined and its realization by two-dimensional matrices of differential operators acting in spinor space is given. It turns out that this graded algebra is the supersymmetry algebra for a class of relativistic potentials that includes the Dirac-Oscillator, Dirac-Coulomb and Dirac-Morse potentials. This class is, in fact, the relativistic extension of the oscillator class. A new point canonical transformation, which is compatible with the relativistic problem, is formulated. It maps all of these relativistic potentials into the Dirac-Oscillator potential.Comment: Replaced with a more potrable PDF versio

Terrestrial temperature evolution of southern Africa during the late Pleistocene and Holocene:Evidence from the Mfabeni Peatland

The scarcity of suitable high-resolution archives, such as ancient natural lakes, that span beyond the Holocene, hinders long-term late Quaternary temperature reconstructions in southern Africa. Here we target two cores from Mfabeni Peatland, one of the few long continuous terrestrial archives in South Africa that reaches into the Pleistocene, to generate a composite temperature record spanning the last ∼43 kyr. The Mfabeni Peatland has previously been proven suitable for temperature and hydrological reconstructions based on pollen and geochemical proxies. Here we use branched glycerol dialkyl glycerol tetraethers (brGDGTs) preserved in the Mfabeni peatland to derive a new quantitative air temperature record for south-east Africa. Our temperature record generally follows global trends in temperature and atmospheric CO2 concentrations, but is decoupled at times. Annual air temperatures during Marine Isotope Stage (MIS) 3 were moderately high (c. 20.5 °C), but dropped by c. 5 °C during the Last Glacial Maximum, reaching a minimum at c.16–15 ka. Asynchronous with local insolation, this cooling may have resulted from reduced sea surface temperatures linked to a northward shift in the Southern Hemisphere westerly winds. Concurrent with the southward retreat of the westerlies, and increasing sea surface temperatures offshore, warming from minimum temperatures (c. 15.0 °C) to average Holocene temperatures (c. 20.0 °C) occurred across the deglaciation. This warming was briefly but prominently interrupted by a millennial-scale cooling event of c. 3 °C at c. 2.4 ka, concurrent with a sudden change in hydrological conditions. The average Holocene temperatures of c. 20.0 °C were similar to those reconstructed for MIS 3, but after the 2.4 ka cooling period, air temperatures in the Mfabeni peat recovered and steadily increased towards the present. In summary, our record demonstrates that land temperature in eastern South Africa is highly sensitive to global drivers as well as nearby sea surface temperatures

Absence of photophysiological response to iron addition in autumn phytoplankton in the Antarctic sea-ice zone

he high nutrient–low chlorophyll condition of the Southern Ocean is generally thought to be caused by the low bioavailability of micronutrients, particularly iron, which plays an integral role in phytoplankton photosynthesis. Nevertheless, the Southern Ocean experiences seasonal blooms that generally initiate in austral spring, peak in summer, and extend into autumn. This seasonal increase in primary productivity is typically linked to the seasonal characteristics of nutrient and light supply. To better understand the potential limitations on productivity in the Antarctic sea-ice zone (SIZ), the photophysiological response of phytoplankton to iron addition (2.0 nM FeCl3) was investigated during autumn along the Antarctic coast off Dronning Maud Land. Five short-term (24 h) incubation experiments were conducted around Astrid Ridge (68∘ S) and along a 6∘ E transect, where an autumn bloom was identified in the region of the western SIZ. Surface iron concentrations ranged from 0.27 to 1.39 nM around Astrid Ridge, and 0.56 to 0.63 nM along the 6∘ E transect. Contrary to expectation, the photophysiological response of phytoplankton to iron addition, measured through the photosynthetic efficiency and the absorption cross-section for photosystem II, showed no significant responses. It is thus proposed that since the autumn phytoplankton in the SIZ exhibited a lack of an iron limitation at the time of sampling, the ambient iron concentrations may have been sufficient to fulfil the cellular requirements. This provides new insights into extended iron replete post-bloom conditions in the typically assumed iron deficient high nutrient–low chlorophyll Southern Ocea

Resolving the backbone tilt of crystalline poly(3-hexylthiophene) with resonant tender X-ray diffraction

The way in which conjugated polymers pack in the solid state strongly affects the performance of polymer-based optoelectronic devices. However, even for the most crystalline conjugated polymers the precise packing of chains within the unit cell is not well established. Here we show that by performing resonant X-ray diffraction experiments at the sulfur K-edge we are able to resolve the tilting of the planar backbones of crystalline poly(3-hexylthiophene) (P3HT) within the unit cell. This approach exploits the anisotropic nature of the X-ray optical properties of conjugated polymers, enabling us to discern between different proposed crystal structures. By comparing our data with simulations based on different orientations, a tilting of the planar conjugated backbone with respect to the side chain stacking direction of 30 ± 5° is determined

Fundamental genomic unity of ethnic India is revealed by analysis of mitochondrial DNA

Mitochondrial DNA (mtDNA) profiles of 23 ethnic populations of India drawn from diverse cultural, linguistic and geographical backgrounds are presented. There is extensive sharing of a small number of mtDNA haplotypes, reconstructed on the basis of restriction fragment length polymorphisms, among the populations. This indicates that Indian populations were founded by a small number of females, possibly arriving on one of the early waves of out-of-Africa migration of modern humans; ethnic differentiation occurred subsequently through demographic expansions and geographic dispersal. The Asian-specific haplogroup M is in high frequency in most populations, especially tribal populations and Dravidian populations of southern India. Populations in which the frequencies of haplogroup M are relatively lower show higher frequencies of haplogroup U; such populations are primarily caste populations of northern India. This finding is indicative of a higher Caucasoid admixture in northern Indian populations. By examining the sharing of haplotypes between Indian and south-east Asian populations, we have provided evidence that south-east Asia was peopled by two waves of migration, one originating in India and the other originating in southern China. These findings have been examined and interpreted in the light of inferences derived from previous genomic and historical studies

L2 series solutions of the Dirac equation for power-law potentials at rest mass energy

We obtain solutions of the three dimensional Dirac equation for radial power-law potentials at rest mass energy as an infinite series of square integrable functions. These are written in terms of the confluent hypergeometric function and chosen such that the matrix representation of the Dirac operator is tridiagonal. The "wave equation" results in a three-term recursion relation for the expansion coefficients of the spinor wavefunction which is solved in terms of orthogonal polynomials. These are modified versions of the Meixner-Pollaczek polynomials and of the continuous dual Hahn polynomials. The choice depends on the values of the angular momentum and the power of the potential.Comment: 13 pages, 1 Tabl

Inference of population splits and mixtures from genome-wide allele frequency data

Many aspects of the historical relationships between populations in a species are reflected in genetic data. Inferring these relationships from genetic data, however, remains a challenging task. In this paper, we present a statistical model for inferring the patterns of population splits and mixtures in multiple populations. In this model, the sampled populations in a species are related to their common ancestor through a graph of ancestral populations. Using genome-wide allele frequency data and a Gaussian approximation to genetic drift, we infer the structure of this graph. We applied this method to a set of 55 human populations and a set of 82 dog breeds and wild canids. In both species, we show that a simple bifurcating tree does not fully describe the data; in contrast, we infer many migration events. While some of the migration events that we find have been detected previously, many have not. For example, in the human data we infer that Cambodians trace approximately 16% of their ancestry to a population ancestral to other extant East Asian populations. In the dog data, we infer that both the boxer and basenji trace a considerable fraction of their ancestry (9% and 25%, respectively) to wolves subsequent to domestication, and that East Asian toy breeds (the Shih Tzu and the Pekingese) result from admixture between modern toy breeds and "ancient" Asian breeds. Software implementing the model described here, called TreeMix, is available at http://treemix.googlecode.comComment: 28 pages, 6 figures in main text. Attached supplement is 22 pages, 15 figures. This is an updated version of the preprint available at http://precedings.nature.com/documents/6956/version/

A basis for variational calculations in d dimensions

In this paper we derive expressions for matrix elements (\phi_i,H\phi_j) for the Hamiltonian H=-\Delta+\sum_q a(q)r^q in d > 1 dimensions. The basis functions in each angular momentum subspace are of the form phi_i(r)=r^{i+1+(t-d)/2}e^{-r^p/2}, i >= 0, p > 0, t > 0. The matrix elements are given in terms of the Gamma function for all d. The significance of the parameters t and p and scale s are discussed. Applications to a variety of potentials are presented, including potentials with singular repulsive terms of the form b/r^a, a,b > 0, perturbed Coulomb potentials -D/r + B r + Ar^2, and potentials with weak repulsive terms, such as -g r^2 + r^4, g > 0.Comment: 22 page

A First Global Oceanic Compilation of Observational Dissolved Aluminum Data With Regional Statistical Data Treatment

Large national and international observational efforts over recent decades have provided extensive and invaluable datasets of a range of ocean variables. Compiled large datasets, structured, or unstructured, are a powerful tool that allow scientists to access and synthesize data collected over large spatial and temporal scales. The data treatment approaches for any element in the ocean could lead to new global perspectives of their distribution patterns and to a better understanding of large-scale oceanic processes and their impact on other biogeochemical cycles, which may not be evident otherwise. Ocean chemistry Big Data analysis may not just be limited to distribution patterns, but may be used to assess how sampling efforts and analytical methodologies can be improved. Furthermore, a systematic global scale assessment of data is important to evaluate the gaps in knowledge and to provide avenues for future research. In this context, here we provide an extensive compilation of oceanic aluminum (Al) concentration data from global ocean basins, including data available in the GEOTRACES Intermediate Data product (Schlitzer et al., 2018), but also thus far unpublished data

Nanoplankton : the dominant vector for carbon export across the Atlantic Southern Ocean in spring

DATA AND MATERIAL AVAILABILITY : The data used in this manuscript are available in the Zenodo data repository: 10.5281/zenodo.7820428. All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.SUPPLEMENTARY MATERIAL : Supplementary Text; Figs. S1 to S4; Tables S1 and S2.Across the Southern Ocean, large (≥20 μm) diatoms are generally assumed to be the primary vector for carbon export, although this assumption derives mainly from summertime observations. Here, we investigated carbon production and export potential during the Atlantic Southern Ocean’s spring bloom from size-fractionated measurements of net primary production (NPP), nitrogen (nitrate, ammonium, urea) and iron (labile inorganic iron, organically complexed iron) uptake, and a high-resolution characterization of phytoplankton community composition. The nanoplankton-sized (2.7 to 20 μm) diatom, Chaetoceros spp., dominated the biomass, NPP, and nitrate uptake across the basin (40°S to 56°S), which we attribute to their low iron requirement, rapid response to increased light, and ability to escape grazing when aggregated into chains. We estimate that the spring Chaetoceros bloom accounted for >25% of annual export production across the Atlantic Southern Ocean, a finding consistent with recent observations from other regions highlighting the central role of the phytoplankton “middle class” in carbon export.The South African National Research Foundation, South African National Antarctic Programme, University of Cape Town Science Faculty Fellowship, University of Cape Town Vice-Chancellor Doctoral Research Scholarship, University of Cape Town Vice-Chancellor Future Leaders 2030 Award, European Union’s Horizon 2020 Research and Innovation Programme No. 844733, Academy of Finland, and Funds from an Anonymous Charitable Donor Trust as part of Whales and Climate Change Program.https://www.science.org/journal/sciadvhj2024GeneticsSDG-14:Life below wate