Schwarzschild Geometry Emerging from Matrix Models

We demonstrate how various geometries can emerge from Yang-Mills type matrix models with branes, and consider the examples of Schwarzschild and Reissner-Nordstroem geometry. We provide an explicit embedding of these branes in R^{2,5} and R^{4,6}, as well as an appropriate Poisson resp. symplectic structure which determines the non-commutativity of space-time. The embedding is asymptotically flat with asymptotically constant \theta^{\mu\nu} for large r, and therefore suitable for a generalization to many-body configurations. This is an illustration of our previous work arXiv:1003.4132, where we have shown how the Einstein-Hilbert action can be realized within such matrix models.Comment: 21 pages, 1 figur

On Quantum Lie Algebras and Quantum Root Systems

As a natural generalization of ordinary Lie algebras we introduce the concept of quantum Lie algebras ${\cal L}_q(g)$. We define these in terms of certain adjoint submodules of quantized enveloping algebras $U_q(g)$ endowed with a quantum Lie bracket given by the quantum adjoint action. The structure constants of these algebras depend on the quantum deformation parameter $q$ and they go over into the usual Lie algebras when $q=1$. The notions of q-conjugation and q-linearity are introduced. q-linear analogues of the classical antipode and Cartan involution are defined and a generalised Killing form, q-linear in the first entry and linear in the second, is obtained. These structures allow the derivation of symmetries between the structure constants of quantum Lie algebras. The explicitly worked out examples of $g=sl_3$ and $so_5$ illustrate the results.Comment: 22 pages, latex, version to appear in J. Phys. A. see http://www.mth.kcl.ac.uk/~delius/q-lie.html for calculations and further informatio

Incorporating Redispersal Microsites into Myrmecochory in Eastern North American Forests

Studies addressing the benefits of “directed dispersal” in ant seed dispersal systems have highlighted the beneficial soil properties of the nests of ants that disperse their seeds. No studies, however, have explored the properties of soils nearby exemplary seed-dispersing ant nests, where recent work indicates that seeds are quickly “redispersed” in eastern North America. To address this, we focused on a forested ecosystem in eastern United States where a keystone seed-dispersing ant, Aphaenogaster rudis, commonly disperses the seeds of numerous understory herbs, including Jeffersonia diphylla. We collected soil cores beneath J. diphylla, around A. rudis nests where seeds are dispersed, and from other forest locations. We analyzed the collected soils for microbial activity using potential soil enzyme activity as a proxy, as well as a number of environmental parameters. We followed this with a glasshouse experiment testing whether the soils collected from near nests, beneath J. diphylla, and from other forested areas altered seedling emergence. We found that microbial activities were higher in near-nest microsites than elsewhere. Specifically, the potential enzyme activities of a carbon-degrading enzyme (β-glucosidase), a phosphorus-acquiring enzyme (phosphatase), and a sulfur-acquiring enzyme (sulfatase) were all significantly higher in areas near ant nests than elsewhere; this same pattern, although not significant, was found for the nitrogen-acquiring enzyme NAGase. No differences were found in other environmental variables we investigated (e.g., soil temperature, soil moisture, soil pH). Our field results indicate that soil biological processes are significantly different in near-nest soils, where the seeds are ultimately dispersed. However, our glasshouse germination trials revealed no enhanced germination in near-nest soils, thereby refuting any near-term advantages of directed dispersal to near-nest locations. Future work should be directed toward addressing whether areas near ant nests provide biologically meaningful escape from seed predation and enhanced establishment, and further characterization of soil microbial communities in such settings

Covariant differential complexes on quantum linear groups

We consider the possible covariant external algebra structures for Cartan's 1-forms on GL_q(N) and SL_q(N). We base upon the following natural postulates: 1. the invariant 1-forms realize an adjoint representation of quantum group; 2. all monomials of these forms possess the unique ordering. For the obtained external algebras we define the exterior derivative possessing the usual nilpotence condition, and the generally deformed version of Leibniz rules. The status of the known examples of GL_q(N)-differential calculi in the proposed classification scheme, and the problems of SL_q(N)-reduction are discussed.Comment: 23 page

Imaging cortical activity following affective stimulation with a high temporal and spatial resolution

Keil J, Adenauer H, Catani C, Neuner F. Imaging cortical activity following affective stimulation with a high temporal and spatial resolution. BMC Neuroscience. 2009;10(1):83.Background:The affective and motivational relevance of a stimulus has a distinct impact on cortical processing, particularly in sensory areas. However, the spatial and temporal dynamics of this affective modulation of brain activities remains unclear. The purpose of the present study was the development of a paradigm to investigate the affective modulation of cortical networks with a high temporal and spatial resolution. We assessed cortical activity with MEG using a visual steady-state paradigm with affective pictures. A combination of a complex demodulation procedure with a minimum norm estimation was applied to assess the temporal variation of the topography of cortical activity. Results: Statistical permutation analyses of the results of the complex demodulation procedure revealed increased steady-state visual evoked field amplitudes over occipital areas following presentation of affective pictures compared to neutral pictures. This differentiation shifted in the time course from occipital regions to parietal and temporal regions. Conclusion: It can be shown that stimulation with affective pictures leads to an enhanced activity in occipital region as compared to neutral pictures. However, the focus of differentiation is not stable over time but shifts into temporal and parietal regions within four seconds of stimulation. Thus, it can be crucial to carefully choose regions of interests and time intervals when analyzing the affective modulation of cortical activity

Effects of dopaminergic modulation on electrophysiological brain response to affective stimuli

Introduction: Several theoretical accounts of the role of dopamine suggest that dopamine has an influence on the processing of affective stimuli. There is some indirect evidence for this from studies showing an association between the treatment with dopaminergic agents and self-reported affect. Materials and methods: We addressed this issue directly by examining the electrophysiological correlates of affective picture processing during a single-dose treatment with a dopamine D2 agonist (bromocriptine), a dopamine D2 antagonist (haloperidol), and a placebo. We compared early and late event-related brain potentials (ERPs) that have been associated with affective processing in the three medication treatment conditions in a randomized double-blind crossover design amongst healthy males. In each treatment condition, subjects attentively watched neutral, pleasant, and unpleasant pictures while ERPs were recorded. Results: Results indicate that neither bromocriptine nor haloperidol has a selective effect on electrophysiological indices of affective processing. In concordance with this, no effects of dopaminergic modulation on self-reported positive or negative affect was observed. In contrast, bromocriptine decreased overall processing of all stimulus categories regardless of their affective content. Discussion: The results indicate that dopaminergic D2 receptors do not seem to play a crucial role in the selective processing of affective visual stimuli

Bicovariant Differential Geometry of the Quantum Group SLh(2)SL_h(2)

There are only two quantum group structures on the space of two by two unimodular matrices, these are the $SL_q(2)$ and the $SL_h(2)$ [9-13] quantum groups. One can not construct a differential geometry on $SL_q(2)$, which at the same time is bicovariant, has three generators, and satisfies the Liebnitz rule. We show that such a differential geometry exists for the quantum group $SL_h(2)$ and derive all of its properties

On the Renormalizability of Noncommutative U(1) Gauge Theory - an Algebraic Approach

We investigate the quantum effects of the nonlocal gauge invariant operator $\frac{1}{{}{D}^{2}}{F}_{\mu \nu}\ast \frac{1}{{}{D}^{2}}{F}^{\mu \nu}$ in the noncommutative U(1) action and its consequences to the infrared sector of the theory. Nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the Lorentz invariance. More recently, a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field, and the first loop analysis was carried out $(Eur.Phys.J.\textbf{C62}:433-443,2009)$. We will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only BRST doublets. This will allow us to make a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT.Comment: standard Latex no figures, version2 accepted in J. Phys A: Math Theo

Tensor calculus on noncommutative spaces

It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an infinite number of degrees of freedom per point of the base manifold). We show that on a symplectic manifold this freedom may be almost completely eliminated if one extends the star product to all tensor fields in a covariant way and impose some natural conditions on the tensor algebra. The remaining ambiguity either correspond to constant renormalizations to the symplectic structure, or to maps between classically equivalent field theory actions. We also discuss how one can introduce the Riemannian metric in this approach and the consequences of our results for noncommutative gravity theories.Comment: 17p; v2: extended version, to appear in CQ

Weyl approach to representation theory of reflection equation algebra

The present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum groups). We suggest a universal method of constructing finite dimensional irreducible non-commutative representations in the framework of the Weyl approach well known in the representation theory of classical Lie groups and algebras. With this method a series of irreducible modules is constructed which are parametrized by Young diagrams. The spectrum of central elements s(k)=Tr_q(L^k) is calculated in the single-row and single-column representations. A rule for the decomposition of the tensor product of modules into the direct sum of irreducible components is also suggested.Comment: LaTeX2e file, 27 pages, no figure