Abstract:
Let F be an infinite field. We prove that the right zero divisors of a three-dimensional associative F-algebra A must form the union of at most finitely many linear subspaces of A. The proof is elementary and written with students as the intended audience.

Abstract:
Graph canonization is the problem of computing a unique representative, a canon, from the isomorphism class of a given graph. This implies that two graphs are isomorphic exactly if their canons are equal. We show that graphs of bounded tree width can be canonized by logarithmic-space (logspace) algorithms. This implies that the isomorphism problem for graphs of bounded tree width can be decided in logspace. In the light of isomorphism for trees being hard for the complexity class logspace, this makes the ubiquitous class of graphs of bounded tree width one of the few classes of graphs for which the complexity of the isomorphism problem has been exactly determined.

Abstract:
Every open manifold L of dimension greater than one has complete Riemannian metrics g with bounded geometry such that (L,g) is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the local geometry of (L,g) suffice to make it quasi-isometric to a leaf of such a foliation. We introduce the `bounded homology property', a semi-local property of (L,g) that is necessary for it to be a leaf in a compact manifold in codimension one, up to quasi-isometry. An essential step involves a partial generalization of the Novikov closed leaf theorem to higher dimensions.

Abstract:
Forty-five severely obese adults (36 women) without certain comorbidities/medications underwent anthropometric measurements, polysomnography, and blood tests. We measured fasting serum glucose, insulin, selected cytokines, and calculated homeostasis model assessment estimates of insulin sensitivity (HOMA-IS) and pancreatic beta-cell function (HOMA-B).Both increases in apnea-hypopnea index (AHI) and the presence of prediabetes/diabetes were associated with reductions in HOMA-IS in the entire cohort even after adjustment for sex, race, age, and BMI (P = 0.003). In subjects with NGM (n = 30), OSA severity was associated with significantly increased HOMA-B (a trend towards decreased HOMA-IS) independent of sex and adiposity. OSA-related oxyhemoglobin desaturations correlated with TNF-α (r=-0.76; P = 0.001) in women with NGM and with IL-6 (rho=-0.55; P = 0.035) in women with IGM (n = 15) matched individually for age, adiposity, and AHI.OSA is independently associated with altered glucose homeostasis and increased basal beta-cell function in severely obese adults with NGM. The findings suggest that moderate to severe OSA imposes an excessive functional demand on pancreatic beta-cells, which may lead to their exhaustion and impaired secretory capacity over time. The two distinct biomarker profiles linking sleep apnea with NGM and IGM via TNF-α and IL-6 have been discerned in our study to suggest that sleep apnea and particularly nocturnal oxyhemoglobin desaturations are associated with chronic metabolic fluxes and specific cytokine stressors that reflect links between sleep apnea and glucose metabolism. The study may help illuminate potential mechanisms for glucose dysregulation in OSA, and resolve some controversy over the associations of OSA with TNF-α and IL-6 in previous studies.Obstructive sleep apnea (OSA) and impaired glucose metabolism (IGM) are closely linked to an epidemic of obesity in Western society, and both are associated with a significantly increased cardi

Abstract:
The following article presents an unusual case of atrial tachycardia, initially misdiagnosed due to a lack of clear P waves. The diagnosis was eventually confirmed using the atrial electrogram from the patient s pacemaker.

Abstract:
This article describes an interesting case of automated implantable cardioverter defibrillator (AICD) extrusion fifteen months after implantation. The case report is followed by a discussion of the causes and treatment of skin erosion following pacemaker/AICD insertion.

Abstract:
We develop a new framework for modeling innovation networks which evolve over time. The nodes in the network represent firms, whereas the directed links represent unilateral interactions between the firms. Both nodes and links evolve according to their own dynamics and on different time scales. The model assumes that firms produce knowledge based on the knowledge exchange with other firms, which involves both costs and benefits for the participating firms. In order to increase their knowledge production, firms follow different strategies to create and/or to delete links with other firms. Dependent on the information firms take into account for their decision, we find the emergence of different network structures. We analyze the conditions for the existence of these structures within a mathematical approach and underpin our findings by extensive computer simulations which show the evolution of the networks and their equilibrium state. In the discussion of the results, particular attention is given to the emergence of direct and indirect reciprocity in knowledge exchange, which refers to the emergence of cycles in the network structure. In order to motivate our modeling framework, in the first part of the chapter we give a broad overview of existing literature from economics and physics. This shows that our framework bridges and extends two different lines of research, namely the study of equilibrium networks with simple topologies and the dynamic approach of hypercycle models.

Abstract:
The frequency dependent transport is investigated for a two-dimensional disordered system under QHE conditions. The real and imaginary parts of the conductivity are calculated numerically in linear response using a recursive Green function technique. The energy dependence of $\sigma_{xx}(E,\omega)$ is obtained within the lowest Landau band. When the width of the system exceeds the characteristic length, $L_{\omega}=(\hbar\omega \rho(E))^{-1/2}$, the maximum of the real part of $\sigma_{xx}(E,\omega)$ decays with frequency almost linearly which is different from the classical Drude behaviour.

Abstract:
Frequency dependent electronic transport is investigated for a two-dimensional disordered system in the presence of a strong perpendicular static magnetic field. The ac-conductivity is calculated numerically from Kubo's linear response theory using a recursive Green's function technique. In the tail of the lowest Landau band, we find a linear frequency dependence for the imaginary part of $\sigma_{xx}(\omega)$ which agrees well with earlier analytical calculations. On the other hand, the frequency dependence of the real part can not be expressed by a simple power law. The broadening of the $\sigma_{xx}$-peak with frequency in the lowest Landau band is found to exhibit a scaling relation from which the critical exponent can be extracted.

Abstract:
We determine all the normal subgroups of the group of C^r diffeomorphisms of R^n, r = 1,2,...,infinity, except when r=n+1 or n=4, and also of the group of homeomorphisms of R^n (r=0). We also study the group A_0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with nonempty boundary, then the quotient of A_0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.