Commutator Leavitt path algebras

For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras L_K(E) that satisfy L_K(E)=[L_K(E),L_K(E)]. We also show that these Leavitt path algebras have the additional (unusual) property that all their Lie ideals are (ring-theoretic) ideals, and construct examples of such rings with various ideal structures.Comment: 24 page

Gauge Theory Wilson Loops and Conformal Toda Field Theory

The partition function of a family of four dimensional N=2 gauge theories has been recently related to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory is A_1 conformal Toda field theory, i.e. Liouville theory. For this case the relation has been extended showing that the expectation value of gauge theory loop operators can be reproduced in Liouville theory inserting in the correlators the monodromy of chiral degenerate fields. In this paper we study Wilson loops in SU(N) gauge theories in the fundamental and anti-fundamental representation of the gauge group and show that they are associated to monodromies of a certain chiral degenerate operator of A_{N-1} Toda field theory. The orientation of the curve along which the monodromy is evaluated selects between fundamental and anti-fundamental representation. The analysis is performed using properties of the monodromy group of the generalized hypergeometric equation, the differential equation satisfied by a class of four point functions relevant for our computation.Comment: 17 pages, 3 figures; references added

Semiclassical Analysis of M2-brane in AdS_4 x S^7 / Z_k

We start from the classical action describing a single M2-brane on AdS_4 x S^7/ Z_k and consider semiclassical fluctuaitions around a static, 1/2 BPS configuration whose shape is AdS_2 x S^1. The internal manifold S^7/ Z_k is described as a U(1) fibration over CP^3 and the static configuration is wrapped on the U(1) fiber. Then the configuration is reduced to an AdS_2 world-sheet of type IIA string on AdS_4 x CP^3 through the Kaluza-Klein reduction on the S^1. It is shown that the fluctuations form an infinite set of N=1 supermultiplets on AdS_2, for k=1,2. The set is invariant under SO(8) which may be consistent with N=8 supersymmetry on AdS_2. We discuss the behavior of the fluctuations around the boundary of AdS_2 and its relation to deformations of Wilson loop operator.Comment: 27 pages, v2: references added, v3: major revision including the clarification of k=2 case, references added, version to appear in JHE

Summing Up All Genus Free Energy of ABJM Matrix Model

The localization technique allows us to compute the free energy of the U(N)_k x U(N)_{-k} Chern-Simons-matter theory dual to type IIA strings on AdS_4 x CP^3 from weak to strong 't Hooft coupling \lambda = N / k at finite N, as demonstrated by Drukker, Marino, and Putrov. In this note we study further the free energy at large 't Hooft coupling with the aim of testing AdS/CFT at the quantum gravity level and, in particular, sum up all the 1/N corrections, apart from the worldsheet instanton contributions. The all genus partition function takes a remarkably simple form -- the Airy function, Ai (k^{4/3} \lambda_r), with the renormalized 't Hooft coupling \lambda_r.Comment: 18 pages, no figures, v2: typos corrected and references adde

Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS

We study correlation functions of Wilson loops and local operators in a subsector of N=4 SYM which preserves two supercharges. Localization arguments allow to map the problem to a calculation in bosonic two-dimensional Yang-Mills theory. In turn, this can be reduced to computing correlators in certain Gaussian multi-matrix models. We focus on the correlation function of a Wilson loop and two local operators, and solve the corresponding three-matrix model exactly in the planar limit. We compare the strong coupling behavior to string theory in AdS_5xS^5, finding precise agreement. We pay particular attention to the case in which the local operators have large R-charge J \sim sqrt{lambda} at strong coupling.Comment: 50 pages, 9 figures. v2: minor changes, references adde

Dynamics of Barred Galaxies

Some 30% of disc galaxies have a pronounced central bar feature in the disc plane and many more have weaker features of a similar kind. Kinematic data indicate that the bar constitutes a major non-axisymmetric component of the mass distribution and that the bar pattern tumbles rapidly about the axis normal to the disc plane. The observed motions are consistent with material within the bar streaming along highly elongated orbits aligned with the rotating major axis. A barred galaxy may also contain a spheroidal bulge at its centre, spirals in the outer disc and, less commonly, other features such as a ring or lens. Mild asymmetries in both the light and kinematics are quite common. We review the main problems presented by these complicated dynamical systems and summarize the effort so far made towards their solution, emphasizing results which appear secure. (Truncated)Comment: This old review appeared in 1993. Plain tex with macro file. 82 pages 18 figures. A pdf version with figures at full resolution (3.24MB) is available at http://www.physics.rutgers.edu/~sellwood/bar_review.pd

Statistical Analysis of the Main Ionospheric Trough Using Swarm in Situ Measurements

A statistical analysis of the topside main ionospheric trough is implemented by using the Swarm constellation in situ plasma density measurements from December 2013 to November 2019. The key features of the main trough, such as the occurrence rate, minimum position, width, and depth, are characterized and quantified. The distribution patterns of these parameters are investigated with respect to magnetic local time, season, longitude, solar activity, and geomagnetic activity levels, respectively. The main results are as follows: (1) The diurnal variation of the trough occurrence rate usually exhibits a primary peak in the early morning, a subsidiary peak in the late evening, and a slight reduction around midnight especially in the Northern Hemisphere. (2) The seasonal variation of the nighttime trough has maximum occurrence rates around equinoxes, higher than those in local winter. (3) The trough distribution has an evident hemispherical asymmetry. It is more pronounced in the Northern Hemisphere during the winter and equinoctial seasons, with its average nighttime occurrence rate being 20â 30% higher than that in the Southern Hemisphere. The trough minimum position and the trough width also exhibit more significant fluctuation in the Northern Hemisphere. (4) The longitudinal pattern of the trough shows clear eastâ west preferences, which has a higher occurrence rate in eastern (western) longitudes around the December (June) solstice. (5) Conditions for the trough occurrence are more favored in low solar activity and high geomagnetic activity periods.Key PointsThe occurrence rate of the main ionospheric trough at 450â 550 km exhibits a slight midnight reduction comparing with evening/morning peaksThe trough has a longitudinal preference with higher occurrence rate in the eastern (western) longitudes around the December (June) solsticeConditions for the trough occurrence are more favored in equinoxes than local winter and in Northern Hemisphere than Southern HemispherePeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154408/1/jgra55592.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154408/2/jgra55592_am.pd

The involvement of tau in nucleolar transcription and the stress response

Tau is known for its pathological role in neurodegenerative diseases, including Alzheimer’s disease (AD) and other tauopathies. Tau is found in many subcellular compartments such as the cytosol and the nucleus. Although its normal role in microtubule binding is well established, its nuclear role is still unclear. Here, we reveal that tau localises to the nucleolus in undifferentiated and differentiated neuroblastoma cells (SHSY5Y), where it associates with TIP5, a key player in heterochromatin stability and ribosomal DNA (rDNA) transcriptional repression. Immunogold labelling on human brain sample confirms the physiological relevance of this finding by showing tau within the nucleolus colocalises with TIP5. Depletion of tau results in an increase in rDNA transcription with an associated decrease in heterochromatin and DNA methylation, suggesting that under normal conditions tau is involved in silencing of the rDNA. Cellular stress induced by glutamate causes nucleolar stress associated with the redistribution of nucleolar non-phosphorylated tau, in a similar manner to fibrillarin, and nuclear upsurge of phosphorylated tau (Thr231) which doesn’t colocalise with fibrillarin or nucleolar tau. This suggests that stress may impact on different nuclear tau species. In addition to involvement in rDNA transcription, nucleolar non-phosphorylated tau also undergoes stress-induced redistribution similar to many nucleolar protein

Comparative 3D analyses and palaeoecology of giant early amphibians (Temnospondyli: Stereospondyli)

Macroevolutionary, palaeoecological and biomechanical analyses in deep time offer the possibility to decipher the structural constraints, ecomorphological patterns and evolutionary history of extinct groups. Here, 3D comparative biomechanical analyses of the extinct giant early amphibian group of stereospondyls together with living lissamphibians and crocodiles, shows that: i) stereospondyls had peculiar palaeoecological niches with proper bites and stress patterns very different than those of giant salamanders and crocodiles; ii) their extinction may be correlated with the appearance of neosuchians, which display morphofunctional innovations. Stereospondyls weathered the end-Permian mass extinction, re-radiated, acquired gigantic sizes and dominated (semi) aquatic ecosystems during the Triassic. Because these ecosystems are today occupied by crocodilians, and stereospondyls are extinct amphibians, their palaeobiology is a matter of an intensive debate: stereospondyls were a priori compared with putative living analogous such as giant salamanders and/or crocodilians and our new results try to close this debate.Peer ReviewedPostprint (published version

Flexible prey handling, preference and a novel capture technique in invasive, sub-adult Chinese mitten crabs

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