Selectivity in regeneration of the oculomotor nerve in the cichlid fish, Astronotus ocellatus

It has long been considered a general rule for nerve regeneration that the reinnervation of skeletal muscle is nonselective. Regenerating nerve fibers are supposed to reconnect with one skeletal muscle as readily as another according to studies covering a wide range of vertebrates (Weiss, 1937; Weiss & Taylor, 1944; Weiss & Hoag, 1946; Bernstein & Guth, 1961; Guth, 1961, 1962, 1963). Similarly, in embryogenesis proper functional connexions between nerve centers and particular muscles are supposedly attained, not by selective nerve outgrowth but rather through a process of ‘myotypic modulation’ (Weiss, 1955) that presupposes nonselective peripheral innervation. Doubt about the general validity of this rule and the concepts behind it has come from a series of studies on regeneration of the oculomotor nerve in teleosts, urodeles, and anurans and of spinal fin nerves in teleosts (Sperry, 1946, 1947, 1950, 1965; Sperry & Deupree, 1956; Arora & Sperry, 1957a, 1964)

Unusual echocardiographic finding leading to diagnosis of pulmonary sequestration

Pulmonary sequestration is an embryonic mass of non- functioning lung tissue that does not communicate with the tracheobronchial tree and has a reported incidence of 0.15%-6.4% of all the pulmonary malformations. This anomaly is classified as either intralobar or extralobar with the later variety lying outside the normal investment of visceral pleura. The arterial supply is predominantly by an anomalous artery usually arising from either abdominal or thoracic aorta, while the venous drainage occurs commonly via systemic rather than pulmonary veins. Identification of the anomalous arterial supply has therapeutic implication because the majority of infants clinically present large shunt lesions attributed to these channels in early infancy. The diagnosis in such cases is usually established by computed tomography (CT), angiography, magnetic resonance angiography and conventional angiography. This article reports a 28 day old neonate who presented with features of large shunt lesion, in which echocardiography was instrumental in the diagnosis of a large collateral supplying the sequestrated lung.peer-reviewe

Implementation of higher-order absorbing boundary conditions for the Einstein equations

We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated by rewriting the boundary conditions as a system of ODEs for a set of auxiliary variables intrinsic to the boundary. From these we construct boundary data for a set of well-posed constraint-preserving boundary conditions for the Einstein equations in a first-order generalized harmonic formulation. This construction has direct applications to outer boundary conditions in simulations of isolated systems (e.g., binary black holes) as well as to the problem of Cauchy-perturbative matching. As a test problem for our numerical implementation, we consider linearized multipolar gravitational waves in TT gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We demonstrate that the perfectly absorbing boundary condition B_L of order L=l yields no spurious reflections to linear order in perturbation theory. This is in contrast to the lower-order absorbing boundary conditions B_L with L<l, which include the widely used freezing-Psi_0 boundary condition that imposes the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in Class. Quantum Grav

Sum-of-squares lower bounds for planted clique

Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size k is planted in a random G(n, 1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for k ~ sqrt(n). In this paper we study the complexity of the planted clique problem under algorithms from the Sum-of-squares hierarchy. We prove the first average case lower bound for this model: for almost all graphs in G(n,1/2), r rounds of the SOS hierarchy cannot find a planted k-clique unless k > n^{1/2r} (up to logarithmic factors). Thus, for any constant number of rounds planted cliques of size n^{o(1)} cannot be found by this powerful class of algorithms. This is shown via an integrability gap for the natural formulation of maximum clique problem on random graphs for SOS and Lasserre hierarchies, which in turn follow from degree lower bounds for the Positivestellensatz proof system. We follow the usual recipe for such proofs. First, we introduce a natural "dual certificate" (also known as a "vector-solution" or "pseudo-expectation") for the given system of polynomial equations representing the problem for every fixed input graph. Then we show that the matrix associated with this dual certificate is PSD (positive semi-definite) with high probability over the choice of the input graph.This requires the use of certain tools. One is the theory of association schemes, and in particular the eigenspaces and eigenvalues of the Johnson scheme. Another is a combinatorial method we develop to compute (via traces) norm bounds for certain random matrices whose entries are highly dependent; we hope this method will be useful elsewhere

New Approximability Results for the Robust k-Median Problem

We consider a robust variant of the classical $k$-median problem, introduced by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust $k$-Median problem}, we are given an $n$-vertex metric space $(V,d)$ and $m$ client sets $\set{S_i \subseteq V}_{i=1}^m$. The objective is to open a set $F \subseteq V$ of $k$ facilities such that the worst case connection cost over all client sets is minimized; in other words, minimize $\max_{i} \sum_{v \in S_i} d(F,v)$. Anthony et al.\ showed an $O(\log m)$ approximation algorithm for any metric and APX-hardness even in the case of uniform metric. In this paper, we show that their algorithm is nearly tight by providing $\Omega(\log m/ \log \log m)$ approximation hardness, unless ${\sf NP} \subseteq \bigcap_{\delta >0} {\sf DTIME}(2^{n^{\delta}})$. This hardness result holds even for uniform and line metrics. To our knowledge, this is one of the rare cases in which a problem on a line metric is hard to approximate to within logarithmic factor. We complement the hardness result by an experimental evaluation of different heuristics that shows that very simple heuristics achieve good approximations for realistic classes of instances.Comment: 19 page

On Fitting a Surface

This article deals with the problem of fitting the surface f=g (x) h(y) to the set of points (x/sub i/,y/sub j/,f/j). Functions g(x) and h(y) are supposed to be expressible in terms of orthonormal sets of functions. The desired coefficients of these functions are determined as characteristic vectors corresponding to the largest characteristic root of two materials having common characteristic roots

Reliability of a Modular Standby Redundant System with Unrecoverable Failures

This paper considers a stand by redundant system consisting of two identical modules. Each module is compose of N distinct components in series. The failure of a module may be attributed due to the failure of any of its N components. The ith components of a module has an arbitrary repair time CDF, G./sub i/ (t). The stand by module has been assumed to have a nonzero hazard rate even when unpowered. The failure of an on-line module is identified through a sensing device which has a probability 'c' of successfully recovering a fault in the on-line module. Expressions for the distribution of the Time to First System Failure (TFSF), the expected TFSF, and the reliability of the system have been derived by using the theory of Markov renewal processes