Morse Theory and the Topology of Configuration Space

The first and second homology groups are computed for configuration spaces of framed three-dimensional point particles with annihilation included, when up to two particles and an antiparticle are present

Cartan-Preserving Automorphisms and the Weyl Group of Kac-Moody Algebras

The group Ñ defined as the normalizer of the Cartan subalgebra in the group of all (inner and outer) automorphisms of affine Kac-Moody (KM) algebras is shown to play a fundamental role in the structure of these algebras. It is a (discrete) Galilean group which incorporates the affine and Weyl group structure of the KM algebra and the space-time structure of the bosonic string. It links the Virasoro and KM algebras in a non-trivial way and it plays a key role in the ‘vertex’ construction

Possible alternative mechanism to SUSY: conservative extensions of the Poincar\'e group

A group theoretical mechanism is outlined, which can indecomposably extend the Poincar\'e group by the compact internal (gauge) symmetries at the price of allowing some nilpotent (or, more precisely: solvable) internal symmetries in addition. Due to the presence of this nilpotent part, the prohibitive argument of the well known Coleman-Mandula and McGlinn no-go theorems do not go through. In contrast to SUSY or extended SUSY, in our construction the symmetries extending the Poincar\'e group will be all internal, i.e. they do not act on the spacetime, merely on some internal degrees of freedom -- hence the name: conservative extensions of the Poincar\'e group. Using the Levi decomposition and O'Raifeartaigh theorem, the general structure of all possible conservative extensions of the Poincar\'e group is outlined, and a concrete example group is presented with U(1) being the compact gauge group component. It is argued that such nilpotent internal symmetries may be inapparent symmetries of some more fundamental field variables, and therefore do not carry an ab initio contradiction with the present experimental understanding in particle physics. The construction is compared to (extended) SUSY, since SUSY is somewhat analogous to the proposed mechanism. It is pointed out, however, that the proposed mechanism is less irregular in comparison to SUSY, in certain aspects. The only exoticity needed in comparison to a traditional gauge theory setting is that the full group of internal symmetries is not purely compact, but is a semi-direct product of a nilpotent and of a compact part.Comment: 10 pages, contribution to Proceedings of X. International Symposium on Quantum Theory and Symmetries, Springer (2018

Autopodial development is selectively impaired by misexpression of chordin-like 1 in the chick limb

AbstractChordin-like 1 (CHRDL1) is a secreted bone morphogenetic protein (BMP) antagonist expressed in mesenchymal tissues whose function in development of the skeleton has not been examined in detail. Here we show Chrdl1 is dynamically expressed in the early distal limb bud mesenchyme, with expression becoming downregulated as development proceeds. Chrdl1 expression is largely excluded from the critical signaling center of the posterior limb bud, the Zone of Polarizing Activity (ZPA), as has been described for the BMP antagonist Gremlin (GREM1) (Scherz et al., 2004, Science, 305, 396–399). Unlike Grem1, Chrdl1 is expressed in the hindlimb by a small subset of ZPA cells and their descendants suggesting divergent regulation and function between the various BMP antagonists. Ectopic expression of Chrdl1 throughout the avian limb bud using viral misexpression resulted in an oligodactyly phenotype with loss of digits from the anterior limb, although the development of more proximal elements of the zeugopod and stylopod were unaffected. Overgrowths of soft tissue and syndactyly were also observed, resulting from impaired apoptosis and failure of the anterior mesenchyme to undergo SOX9-dependent chondrogenesis, instead persisting as an interdigital-like soft tissue phenotype. Sonic hedgehog (SHH) and fibroblast growth factor (FGF) signaling were upregulated and persisted later in development, however these changes were only detected late in limb development at timepoints when endogenous Grem1 would normally be downregulated and increasing BMP signaling would cause termination of Shh and Fgf expression. Our results suggest that the early stages of the GREM1–SHH–FGF signaling network are resistant to Chrdl1-overexpression, leading to normal formation of proximal limb structures, but that later Bmp expression, impaired by ectopic CHRDL1, is essential for formation of the correct complement of digits

The Spin-Statistics Connection from Homology Groups of Configuration Space and an Anyon Wess-Zumino Term

The first and second homology groups H_i for configuration spaces of framed two-dimensional particles and antiparticles, with annihilation included, are computed when up to two particles and an antiparticle are present. The set of ‘frames’ considered are S^2, SO(2) and SO(3). It is found that the H_1 groups are those of the ‘frames’ and are generated by a cycle corresponding to a 2π frame rotation. This same cycle is homologous to the exchange path -the spin -statistics theorem. Furthermore for the frame space SO(2), H_2 contains a Z subgroup which implies the existence of a nontrivial Wess-Zumino term. A rotationally and translationally invariant, topologically nontrivial Wess-Zumino term for a pair of anyons and an antianyon is exhibited for this case

Self-gravitating clouds of generalized Chaplygin and modified anti-Chaplygin Gases

The Chaplygin gas has been proposed as a possible dark energy, dark matter candidate. As a working fluid in a Friedmann-Robertson-Walker universe, it exhibits early behavior reminiscent of dark matter, but at later times is more akin to a cosmological constant. In any such universe, however, one can expect local perturbations to form. Here we obtain the general equations for a self-gravitating relativistic Chaplygin gas. We solve these equations and obtain the mass-radius relationship for such structures, showing that only in the phantom regime is the mass-radius relationship large enough to be a serious candidate for highly compact massive objects at the galaxy core. In addition, we study the cosmology of a modified anti-Chaplygin gas. A self-gravitating cloud of this matter is an exact solution to Einstein's equations.Comment: 16 page

Si3AlP: A new promising material for solar cell absorber

First-principles calculations are performed to study the structural and optoelectronic properties of the newly synthesized nonisovalent and lattice-matched (Si2)0.6(AlP)0.4 alloy [T. Watkins et al., J. Am. Chem. Soc. 2011, 133, 16212.] We find that the ordered CC-Si3AlP with a basic unit of one P atom surrounded by three Si atoms and one Al atom is the most stable one within the experimentally observed unit cell.1 Si3AlP has a larger fundamental band gap and a smaller direct band gap than Si, thus it has much higher absorption in the visible light region. The calculated properties of Si3AlP suggest that it is a promising candidate for improving the performance of the existing Si-based solar cells. The understanding on the stability and band structure engineering obtained in this study is general and can be applied for future study of other nonisovalent and lattice-matched semiconductor alloys

β-diversity scaling patterns are consistent across metrics and taxa

We thank the University of St Andrews Bioinformatics Unit (Wellcome Trust ISSF grant 105621/Z/14/Z). L.H.A.was supported by Fundação para a Ciência e Tecnologia, Portugal (POPH/FSE SFRH/BD/90469/2012), A.E.M. by the ERC BioTIME (250189) and BioCHANGE (727440), and B.J.M. by USDA Hatch grant to MAFES #1011538 and NSF ABI grant #1660000. The BioTIME database was funded by ERC AdG BioTIME (250189) and ERC PoC BioCHANGE (727440).β‐diversity (variation in community composition) is a fundamental component of biodiversity, with implications for macroecology, community ecology and conservation. However, its scaling properties are poorly understood. Here, we systematically assessed the spatial scaling of β‐diversity using 12 empirical large‐scale datasets including different taxonomic groups, by examining two conceptual types of β‐diversity and explicitly considering the turnover and nestedness components. We found highly consistent patterns across datasets. Multiple‐site β‐diversity (i.e. variation across multiple sites) scaling curves were remarkably consistent, with β‐diversity decreasing with sampled area according to a power law. For pairwise dissimilarities, the rates of increase of dissimilarity with geographic distance remained largely constant across scales, while grain size (or scale level) had a stronger effect on overall dissimilarity. In both analyses, turnover was the main contributor to β‐diversity, following total β‐diversity patterns closely, while the nestedness component was largely insensitive to scale changes. Our results highlight the importance of integrating both inter‐ and intraspecific aggregation patterns across spatial scales, which underpin substantial differences in community structure from local to regional scales.PostprintPeer reviewe

Biological and geophysical feedbacks with fire in the Earth system

Roughly 3% of the Earth's land surface burns annually, representing a critical exchange of energy and matter between the land and atmosphere via combustion. Fires range from slow smouldering peat fires, to low-intensity surface fires, to intense crown fires, depending on vegetation structure, fuel moisture, prevailing climate, and weather conditions. While the links between biogeochemistry, climate and fire are widely studied within Earth system science, these relationships are also mediated by fuels—namely plants and their litter—that are the product of evolutionary and ecological processes. Fire is a powerful selective force and, over their evolutionary history, plants have evolved traits that both tolerate and promote fire numerous times and across diverse clades. Here we outline a conceptual framework of how plant traits determine the flammability of ecosystems and interact with climate and weather to influence fire regimes. We explore how these evolutionary and ecological processes scale to impact biogeochemical and Earth system processes. Finally, we outline several research challenges that, when resolved, will improve our understanding of the role of plant evolution in mediating the fire feedbacks driving Earth system processes. Understanding current patterns of fire and vegetation, as well as patterns of fire over geological time, requires research that incorporates evolutionary biology, ecology, biogeography, and the biogeosciences

Functional distinctiveness of major plant lineages

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106060/1/jec12208.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/106060/2/jec12208-sup-0001-Supp_Info.pd