Introduction to quantum groups

We give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz). In particular, we recall the basic facts from Hopf (*-) algebra theory, theory of compact (matrix) quantum groups and the theory of their actions on compact quantum spaces. We also provide the most important examples, including the classification of quantum SL(2)-groups, their real forms and quantum spheres. We also consider quantum SL_q(N)-groups and quantum Lorentz groups.Comment: very small changes, will appear in Rev. Math. Phys., 46 pages, use commands: csh intro.uu, tex intro (twice

The Origin of Large-scale HI structures in the Magellanic Bridge

We investigate the formation of a number of key large-scale HI features in the ISM of the Magellanic Bridge using dissipationless numerical simulation techniques. This study comprises the first direct comparison between detailed HI maps of the Bridge and numerical simulations. We confirm that the SMC forms two tidal filaments: a near arm, which forms the connection between the SMC and LMC, and a counterarm. We show that the HI of the most dense part of the Bridge can become arranged into a bimodal configuration, and that the formation of a "loop" of HI, located off the North-Eastern edge of the SMC can be reproduced simply as a projection of the counter-arm, and without invoking localised energy-deposition processes such as SNe or stellar winds.Comment: 5 Pages, 4 Figures, Accepted - MNRAS let

Gamma-Ray Light Curves and Spectra of Models for Type-Ia Supernovae

Based on detailed Monte Carlo calculations, we present gamma-ray energy deposition functions, gamma-ray light curves, and gamma-ray spectra for a large set of theoretical models of Type Ia supernovae including ''classical'' detonation and deflagration, delayed detonation, explosions of low mass white dwarfs, and tamped detonation scenarios. Our computations show that models for Type Ia supernovae can be discriminated and the absolute amount of Ni-56 synthesized in the event can be determined on the basis of the gamma-ray light curves and spectra if gamma-ray measurements are combined with observations at other wavelengths, e.g., in the optical band. We discuss at which times gamma-ray observations are most suitable and needed from the theoretical point of view. The implication of the upper limit in the gamma-ray flux by CGRO experiment for our understanding of SN 1991 T is discussed. We find that this limit is consistent with both the optical light curve and the implied distance (12.5 Mpc), i.e., several models can be ruled out by the gamma-ray observations.Astronom

Sequential Sparsening by Successive Adaptation in Neural Populations

In the principal cells of the insect mushroom body, the Kenyon cells (KC), olfactory information is represented by a spatially and temporally sparse code. Each odor stimulus will activate only a small portion of neurons and each stimulus leads to only a short phasic response following stimulus onset irrespective of the actual duration of a constant stimulus. The mechanisms responsible for the sparse code in the KCs are yet unresolved. Here, we explore the role of the neuron-intrinsic mechanism of spike-frequency adaptation (SFA) in producing temporally sparse responses to sensory stimulation in higher processing stages. Our single neuron model is defined through a conductance-based integrate-and-fire neuron with spike-frequency adaptation [1]. We study a fully connected feed-forward network architecture in coarse analogy to the insect olfactory pathway. A first layer of ten neurons represents the projection neurons (PNs) of the antenna lobe. All PNs receive a step-like input from the olfactory receptor neurons, which was realized by independent Poisson processes. The second layer represents 100 KCs which converge onto ten neurons in the output layer which represents the population of mushroom body extrinsic neurons (ENs). Our simulation result matches with the experimental observations. In particular, intracellular recordings of PNs show a clear phasic-tonic response that outlasts the stimulus [2] while extracellular recordings from KCs in the locust express sharp transient responses [3]. We conclude that the neuron-intrinsic mechanism is can explain a progressive temporal response sparsening in the insect olfactory system. Further experimental work is needed to test this hypothesis empirically. [1] Muller et. al., Neural Comput, 19(11):2958-3010, 2007. [2] Assisi et. al., Nat Neurosci, 10(9):1176-1184, 2007. [3] Krofczik et. al. Front. Comput. Neurosci., 2(9), 2009.Comment: 5 pages, 2 figures, This manuscript was submitted for review to the Eighteenth Annual Computational Neuroscience Meeting CNS*2009 in Berlin and accepted for oral presentation at the meetin