Curvature in Noncommutative Geometry
masoud khalkhali Western University
9661 - 9672 of 18370 Results
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Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
Jennifer Cano University of California System
On the role of the extra kinetic term coupling ƛ in classical Hořava-Lifshitz gravity
Luis Pires Radboud Universiteit Nijmegen
Black holes without Lorentz symmetry
Thomas Sotiriou University of Nottingham
Behind the Scenes of the Universe: From the Higgs to Dark Matter
Gianfranco Bertone University of Padova - Department of Mathematics
PIRSA:14050022Towards Scaling Relations in Relativistic Hydrodynamics and Gravity
Ryan Westernacher-Schneider Westgate Research
PIRSA:14050054Modeling of RNA Nanotube using Molecular Dynamics Simulation
Shyam Badu Wilfrid Laurier University
PIRSA:14050058Holographic Path to the Turbulent Side of Gravity
Stephen Green University of Nottingham
PIRSA:14050038
Curvature in Noncommutative Geometry
masoud khalkhali Western University
After the seminal work of Connes and Tretkoff on the Gauss-Bonnet theorem for the noncommutative 2-torus and its extension by Fathizadeh and myself, there have been significant developments in understanding the local differential geometry of these noncommutative spaces equipped with curved metrics. In this talk, I will review a series of joint works with Farzad Fathizadeh in which we compute the scalar curvature for curved noncommutative tori and prove the analogue of Weyl's law and Connes' trace theorem. Our final formula for the curvature matches precisely with the one computed independently by A. Connes and H. Moscovici. I will then report on our recent work on the computation of scalar curvature for noncommutative 4-tori (which involves intricacies due to violation of the Kähler condition). We show that metrics with constant curvature are extrema of the analogue of the Einstein–Hilbert action. A purely noncommutative feature in these works is the appearance of the modular automorphism from Tomita–Takesaki theory of KMS states in the final formulas for the curvature.Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
Jennifer Cano University of California System
The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall states at fillings 8 and 12 with experimentally-testable consequences. We also show examples for Abelian fractional quantum Hall states, the simplest examples being at filling fractions 8/7, 12/11, 8/15, 16/5. For all examples, we propose experiments that can distinguish distinct edge phases. Our results are summarized by the observation that edge phases correspond to lattices while bulk phases correspond to genera of lattices. Since there are typically multiple lattices in a genus, there are usually many stable fully chiral edge phases corresponding to the same bulk. We show that fermionic systems can have edge phases with only bosonic low-energy excitations and discuss a fermionic generalization of the relation between bulk topological spins and the central charge. The latter follows from our demonstration that every fermionic topological phase can be represented as a bosonic topological phase, together with some number of filled Landau levels. Our analysis also leads to a simple demonstration that all Abelian topological phases can be represented by a Chern-Simons theory parameterized by a K-matrix.On the role of the extra kinetic term coupling ƛ in classical Hořava-Lifshitz gravity
Luis Pires Radboud Universiteit Nijmegen
We study the classical constraint algebra of Hořava-Lifshitz gravity, where due to the breaking of 4d diffeomorphism symmetry, there is a new dimensionless coupling absent in GR and whose role is not yet clear. Starting from two apparently contradictory results, we show how the role of the extra coupling differs between the projectable and non-projectable versions of the theory. In particular, we see how in the latter, it gives rise to a non-trivial constraint algebra, akin to the conditions seen in the CMC gauge of GR.Black holes without Lorentz symmetry
Thomas Sotiriou University of Nottingham
Our current definition of what a black hole is relies heavily on the assumption that there exists a finite maximum speed of propagation for any signal. Indeed, one is tempted to think that the notion of a black hole has no place in a world with infinitely fast signal propagation. I will use concrete examples from Lorentz-violating gravity theories to demonstrate that this naive expectation is not necessarily true.Behind the Scenes of the Universe: From the Higgs to Dark Matter
Gianfranco Bertone University of Padova - Department of Mathematics
PIRSA:14050022Towards Scaling Relations in Relativistic Hydrodynamics and Gravity
Ryan Westernacher-Schneider Westgate Research
PIRSA:14050054Turbulence is ubiquitous in hydrodynamics and its study is dominated by statistical methods and dimensional arguments. Even so analytic results tend to rely heavily on statistical symmetries. I will discuss some such results in non-relativistic turbulence and possible extensions to the relativistic case. The 2+1 dimensionality of our numerical setup allows for gaining insight about 3+1 gravity through the fluid/gravity duality. This work aims to further our understanding of the fluid side in its own right. This partly entails determining the robustness of some recently derived relativistic hydrodynamic scaling relations which may have holographic applications.Critical Behavior of the Classical XY-model on Fractal Structures
PIRSA:14050060There has been considerable interest in determining whether the universality hypothesis extends to systems which are of non-integer dimension or to systems which are scale invariant (fractals). Specifically research into these types of systems is concerned with determining the relevance of topological properties to their critical phenomena. We have performed Monte Carlo simulations for the XY model on three fractal lattices with different topological properties: the Sierpinski pyramid Menger sponge and Sierpinski carpet. We will give an overview of our results and show that while some properties such as the order of ramification are important in determining the critical behavior of these structures the fractal dimension is not.Validation of predicted mRNA splicing mutations using high-throughput transcriptome data
PIRSA:14050059This work has been published:Viner C Dorman SN Shirley BC and Rogan PK (2014)Validation of predicted mRNA splicing mutations using high-throughput transcriptome data [v1; ref status: indexedhttp://f1000r.es/2no]F1000Research20143:8 (doi:10.12688/f1000research.3-8.v1)Additionally this work has been accepted for a highlights presentation at the upcoming Great Lakes Bioinformatics Conference (GLBIO) in Cincinnati Ohio and it was recently presented as a poster at London Health Research Day (LHRD).Abstract:Interpretation of variants present in complete genomes or exomes reveals numerous sequence changes only a fraction of which are likely to be pathogenic. Variants predicted to alter mRNA splicing in particular can be validated by manual inspection of transcriptome sequencing data however this approach is intractable for large datasets. We show that abnormal mRNA splicing patterns are characterized by reads demonstrating either exon skipping cryptic splice site use and high levels of intron inclusion or combinations of these properties. This paper presents Veridical an in silico method for the automatic validation of DNA sequencing variants that alter mRNA splicing. Veridical leverages large numbers of control samples (that lack a putative mutation) applying z-tests to Yeo-Johnson transformed data to normalize read counts of abnormal RNA species in mutant versus non-mutant tissues. With the transformed data the null hypothesis based mainly on either counts of intronic or junctional reads can be rejected for true splicing mutations using conventional parametric statistical methods.Simulations of Binary Neutron Star Mergers
Marcelo Ponce University of Toronto
PIRSA:14050053By numerically solving Einstein equations we are able to study the strong regime of gravity. In many astrophysical scenarios strong gravity plays a fundamental role such as compact binary systems: e.g. Black Hole binaries binary Neutron Stars and Black Hole-Neutron Star systems. In this talk I will discuss the simulations our group has been conducting in binary Neutron Star system where we can study the dynamics and gravitational radiation of the systems but also establish important connections with electromagnetic counterparts and even testing alternatives theories of gravity (i.e. Scalar-Tensor theories).Modeling of RNA Nanotube using Molecular Dynamics Simulation
Shyam Badu Wilfrid Laurier University
PIRSA:14050058We construct the novel RNA nanpclusters- the RNAnanotubes made of several nanorings. We study the struc-tural properties (i.e. the Root Mean Square Deviation (RMSD)the radius of gyration and radial distribution function) ofRNA nanotube up to the size of about 20nm in physilogicalsolution that can be used for drug delivery into human body.We model RNA nanotube by utilizing molecular dynamicssimulation method implemented in NAMD and VMD. Thepatterns of energy and temperature variations of the systemsare also discussed. Furthermore we study the number of ionsaround the tube as a function of time at a particular temper-ature. We find that if the temperature increases the numberof ions increases within certain distance of the tube. We re-port that the number of ions within a certain distance aroundthe tubes decrease in quenched run. This indicates that someions evaporate with decrease in temperature aHolographic Path to the Turbulent Side of Gravity
Stephen Green University of Nottingham
PIRSA:14050038We study the dynamics of a 2 1-dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals under the gravity/fluid correspondence to 3 1-dimensional asymptotically antide Sitter (AAdS) black-brane solutions to the Einstein equation. We examine stability properties of shear flows which correspond to hydrodynamic quasinormal modes of the black brane. We find that for sufficiently high Reynolds number the solution undergoes an inverse turbulent cascade to long-wavelength modes. We then map this fluid solution via the gravity/fluid duality into a bulk metric. This suggests a new and interesting feature of the behavior of perturbed AAdS black holes and black branes which is not readily captured by a standard quasinormal mode analysis. Namely for sufficiently large perturbed black objects (with long-lived quasinormal modes) nonlinear effects transfer energy from short- to long-wavelength modes via a turbulent cascade within the metric perturbation. As long-wavelength modes have slower decay this transfer of energy lengthens the overall lifetime of the perturbation. We also discuss various implications of this behavior including expectations for higher dimensions and the possibility of predicting turbulence in more general gravitational scenarios.Tree-Based Cosmological Radiative Transfer
PIRSA:14050052One of the most challenging problems in computational galaxy formation is modeling distant heating and ionization by locally produced radiation. Most Radiative Transfer (RT) techniques are very computationally expensive and limit users to poor resolution or post-processing thus decoupling the radiation from the dynamics of the simulation. We present a new efficient method for RT implemented in the SPH code GASOLINE aimed at full cosmological simulations. The method is tree-based (similar to a gravity solver) scaling as N$_sinklogN_source$ in the optically thin case and as N$_sinklogN_sourcelogN_tot$ in the optically thick case. Applications range from the reionization of the Universe to H$_2$ formation and destruction. First applications focus on FUV and EUV emission from Milky Way-type galaxies and how these affect satellites galaxies.