Extension of formal conjugations between diffeomorphisms

We study the formal conjugacy properties of germs of complex analytic diffeomorphisms defined in the neighborhood of the origin of ${\mathbb C}^{n}$. More precisely, we are interested on the nature of formal conjugations along the fixed points set. We prove that there are formally conjugated local diffeomorphisms $\phi, \eta$ such that every formal conjugation $\hat{\sigma}$ (i.e. $\eta \circ \hat{\sigma} = \hat{\sigma} \circ \phi$) does not extend to the fixed points set $Fix (\phi)$ of $\phi$, meaning that it is not transversally formal (or semi-convergent) along $Fix (\phi)$. We focus on unfoldings of 1-dimensional tangent to the identity diffeomorphisms. We identify the geometrical configurations preventing formal conjugations to extend to the fixed points set: roughly speaking, either the unperturbed fiber is singular or generic fibers contain multiple fixed points.Comment: 34 page

Cybersecurity and medical devices: A practical guide for cardiac electrophysiologists

Medical devices increasingly depend on software. While this expands the ability of devices to perform key therapeutic and diagnostic functions, reliance on software inevitably causes exposure to hazards of security vulnerabilities. This article uses a recent high‐profile case example to outline a proactive approach to security awareness that incorporates a scientific, risk‐based analysis of security concerns that supports ongoing discussions with patients about their medical devices.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138357/1/pace13102_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138357/2/pace13102.pd

Ergodic Jacobi matrices and conformal maps

We study structural properties of the Lyapunov exponent $\gamma$ and the density of states $k$ for ergodic (or just invariant) Jacobi matrices in a general framework. In this analysis, a central role is played by the function $w=-\gamma+i\pi k$ as a conformal map between certain domains. This idea goes back to Marchenko and Ostrovskii, who used this device in their analysis of the periodic problem

Anaesthetic considerations of adults with Morquio's syndrome - a case report

<p>Abstract</p> <p>Background</p> <p>The anaesthetic management of patients with Morquio syndrome is complicated by a number of factors including odontoid hypoplasia, atlantoaxial instability, thoracic kyphosis, and deposition of mucopolysaccharides in the soft tissue of the oropharnyx.</p> <p>Case presentation</p> <p>Herein we describe the anaesthetic considerations and management of a 26 year old adult with Morquio syndrome, who presented for an elective hip replacement.</p> <p>Conclusion</p> <p>This report details an awake fiberoptic intubation in an adult with Morquio syndrome. We recommend that this approach be considered in patients with Morquio syndrome undergoing general anaesthesia.</p

Meromorphic Approximants to Complex Cauchy Transforms with Polar Singularities

We study AAK-type meromorphic approximants to functions $F$, where $F$ is a sum of a rational function $R$ and a Cauchy transform of a complex measure $\lambda$ with compact regular support included in $(-1,1)$, whose argument has bounded variation on the support. The approximation is understood in $L^p$-norm of the unit circle, $p\geq2$. We obtain that the counting measures of poles of the approximants converge to the Green equilibrium distribution on the support of $\lambda$ relative to the unit disk, that the approximants themselves converge in capacity to $F$, and that the poles of $R$ attract at least as many poles of the approximants as their multiplicity and not much more.Comment: 39 pages, 4 figure

Neuroglial ATP release through innexin channels controls microglial cell movement to a nerve injury

Microglia, the immune cells of the central nervous system, are attracted to sites of injury. The injury releases adenosine triphosphate (ATP) into the extracellular space, activating the microglia, but the full mechanism of release is not known. In glial cells, a family of physiologically regulated unpaired gap junction channels called innexons (invertebrates) or pannexons (vertebrates) located in the cell membrane is permeable to ATP. Innexons, but not pannexons, also pair to make gap junctions. Glial calcium waves, triggered by injury or mechanical stimulation, open pannexon/innexon channels and cause the release of ATP. It has been hypothesized that a glial calcium wave that triggers the release of ATP causes rapid microglial migration to distant lesions. In the present study in the leech, in which a single giant glial cell ensheathes each connective, hydrolysis of ATP with 10 U/ml apyrase or block of innexons with 10 µM carbenoxolone (CBX), which decreased injury-induced ATP release, reduced both movement of microglia and their accumulation at lesions. Directed movement and accumulation were restored in CBX by adding ATP, consistent with separate actions of ATP and nitric oxide, which is required for directed movement but does not activate glia. Injection of glia with innexin2 (Hminx2) RNAi inhibited release of carboxyfluorescein dye and microglial migration, whereas injection of innexin1 (Hminx1) RNAi did not when measured 2 days after injection, indicating that glial cells’ ATP release through innexons was required for microglial migration after nerve injury. Focal stimulation either mechanically or with ATP generated a calcium wave in the glial cell; injury caused a large, persistent intracellular calcium response. Neither the calcium wave nor the persistent response required ATP or its release. Thus, in the leech, innexin membrane channels releasing ATP from glia are required for migration and accumulation of microglia after nerve injury