Predicting Axonal Response to Molecular Gradients with a Computational Model of Filopodial Dynamics

Axons are often guided to their targets in the developing nervous system by attractive or repulsive molecular concentration gradients. We propose a computational model for gradient sensing and directed movement of the growth cone mediated by filopodia. We show that relatively simple mechanisms are sufficient to generate realistic rajectories for both the short-term response of axons to steep gradients and the long-term response of axons to shallow gradients. The model makes testable predictions for axonal response to attractive and repulsive gradients of different concentrations and steepness, the size of the intracellular amplification of the gradient signal, and the differences in intracellular signaling required for repulsive versus attractive turning

Search on a Hypercubic Lattice through a Quantum Random Walk: II. d=2

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretised according to the staggered lattice fermion formalism. $d=2$ is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behaviour. As a result, the construction used in our accompanying article \cite{dgt2search} provides an $O(\sqrt{N}\log N)$ algorithm, which is not optimal. The scaling behaviour can be improved to $O(\sqrt{N\log N})$ by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi \cite{tulsi}. We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimise the proportionality constants of the scaling behaviour of the algorithm by numerically tuning the parameters.Comment: Revtex4, 5 pages (v2) Introduction and references expanded. Published versio

Search on a Hypercubic Lattice using a Quantum Random Walk: I. d>2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, i.e. finding a marked vertex on a $d$-dimensional hypercubic lattice. The restriction on movement hardly matters for $d>2$, and scaling behaviour close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimise the proportionality constants of the scaling behaviour, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean field theory or the $d\to\infty$ limit). In particular, the scaling behaviour for $d=3$ is only about 25% higher than the optimal $d\to\infty$ value.Comment: 11 pages, Revtex (v2) Introduction and references expanded. Published versio

String-Dust Distributions with the Kerr-NUT symmetry

We attempt to solve the Einstein equations for string dust and null flowing radiation for the general axially symmetric metric, which we believe is being done for the first time. We obtain the string-dust and radiating generalizations of the Kerr and the NUT solutions. There also occurs an interesting case of radiating string-dust which arises from string-dust generalization of Vaidya's solution of a radiating star.Comment: 15 pages, TeX version. tex error correcte

Effect of Process Parameters on Surface Quality and MRR in EDM of SS 440 C Using ANN

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Submillimeter-wave emission of three Galactic red novae: cool molecular outflows produced by stellar mergers

Red novae are optical transients erupting at luminosities typically higher than those of classical novae. Their outbursts are believed to be caused by stellar mergers. We present millimeter/submillimeter-wave observations with ALMA and SMA of the three best known Galactic red novae, V4332 Sgr, V1309 Sco, and V838 Mon. The observations were taken 22, 8, and 14 yr after their respective eruptions and reveal the presence of molecular gas at excitation temperatures of 35-200 K. The gas displays molecular emission in rotational transitions with very broad lines (full width $\sim$400 km\s). We found emission of CO, SiO, SO, SO$_2$ (in all three red novae), H$_2$S (covered only in V838 Mon) and AlO (present in V4332 Sgr and V1309 Sco). No anomalies were found in the isotopic composition of the molecular material and the chemical (molecular) compositions of the three red novae appear similar to those of oxygen-rich envelopes of classical evolved stars (RSGs, AGBs, post-AGBs). The minimum masses of the molecular material that most likely was dispersed in the red-nova eruptions are 0.1, 0.01, and 10$^{-4}$ M$_{\odot}$ for V838 Mon, V4332 Sgr, and V1309 Sco, respectively. The molecular outflows in V4332 Sgr and V1309 Sco are spatially resolved and appear bipolar. The kinematic distances to V1309 Sco and V4332 Sgr are 2.1 and 4.2 kpc, respectively. The kinetic energy stored in the ejecta of the two older red-nova remnants of V838 Mon and V4332 Sgr is of order $10^{46}$ erg, similar to values found for some post-AGB (pre-PN) objects whose bipolar ejecta were also formed in a short-duration eruption. Our observations strengthen the link between these post-AGB objects and red novae and support the hypothesis that some of the post-AGB objects were formed in a common-envelope ejection event or its most catastrophic outcome, a merger.Comment: 19 pages, 13 figures, accepted to A&