Attenuation of super-soft X-ray sources by circumstellar material

Recent studies have suggested the possibility of significantly obscuring super-soft X-ray sources in relatively modest amounts of local matter lost from the binaries themselves. If correct, then this would have explained the paucity of observed super-soft X-ray sources and would have significance for the search for single-degenerate type Ia supernova progenitors. We point out that earlier studies of circumbinary obscuration ignored photo-ionisations of the gas by the emission from the super-soft X-ray source. We revisit the problem using a full, self-consistent calculation of the ionisation state of the circumbinary material photo-ionised by the radiation of the central source. Our results show that the circumstellar mass-loss rates required for obcuration of super-soft X-ray sources is about an order of magnitude larger than those reported in earlier studies, for comparable model parameters. While this does not entrirely rule out the possibility of circumstellar material obscuring super-soft X-ray sources, it makes it unlikely that this effect alone can account for the majority of the missing super-soft X-ray sources. We discuss the observational appearance of hypothetical obscured nuclear burning white dwarfs and show that they have signatures making them distinct from photo-ionised nebulae around super-soft X-ray sources imbedded in the low density ISM.Comment: MNRAS, accepted; 11 pages, 10 figures, 1 tabl

Non-Commutative Open (p,q)-String Theories

In this paper we make an SL(2,Z)-covariant generalisation of the noncommutative theories, NCYM and NCOS on the D3-brane, and NCOS on the D5-brane in type IIB. Usually, the noncommutative theories are obtained by studying perturbative F-string theory, and the parameters governing the noncommutative theories are given by the open string data. The S-duality of NCYM and NCOS on the D3-brane has been seen by dualising the background, keeping the F-string under study fixed. We give an SL(2,Z)-covariant generalisation of the open string data relevant when one instead studies perturbative (p,q)-string theory. The S-duality of NCYM and NCOS on the D3-brane is reproduced by instead keeping the background fixed and studying different (p,q)-string theories. We also obtain new noncommutative open (p,q)-string theories on the D3-brane and the D5-brane which are S-dual to ordinary NCOS. The theories are studied using the supergravity duals of the D3-brane and the D5-brane, corresponding to a probe brane in the relevant background.Comment: AMSLaTeX. 23 pages. Minor clarifications added. To be published in JHE

Hardness of Bichromatic Closest Pair with Jaccard Similarity

Consider collections $\mathcal{A}$ and $\mathcal{B}$ of red and blue sets, respectively. Bichromatic Closest Pair is the problem of finding a pair from $\mathcal{A}\times \mathcal{B}$ that has similarity higher than a given threshold according to some similarity measure. Our focus here is the classic Jaccard similarity $|\textbf{a}\cap \textbf{b}|/|\textbf{a}\cup \textbf{b}|$ for $(\textbf{a},\textbf{b})\in \mathcal{A}\times \mathcal{B}$. We consider the approximate version of the problem where we are given thresholds $j_1>j_2$ and wish to return a pair from $\mathcal{A}\times \mathcal{B}$ that has Jaccard similarity higher than $j_2$ if there exists a pair in $\mathcal{A}\times \mathcal{B}$ with Jaccard similarity at least $j_1$. The classic locality sensitive hashing (LSH) algorithm of Indyk and Motwani (STOC '98), instantiated with the MinHash LSH function of Broder et al., solves this problem in $\tilde O(n^{2-\delta})$ time if $j_1\ge j_2^{1-\delta}$. In particular, for $\delta=\Omega(1)$, the approximation ratio $j_1/j_2=1/j_2^{\delta}$ increases polynomially in $1/j_2$. In this paper we give a corresponding hardness result. Assuming the Orthogonal Vectors Conjecture (OVC), we show that there cannot be a general solution that solves the Bichromatic Closest Pair problem in $O(n^{2-\Omega(1)})$ time for $j_1/j_2=1/j_2^{o(1)}$. Specifically, assuming OVC, we prove that for any $\delta>0$ there exists an $\varepsilon>0$ such that Bichromatic Closest Pair with Jaccard similarity requires time $\Omega(n^{2-\delta})$ for any choice of thresholds $j_2<j_1<1-\delta$, that satisfy $j_1\le j_2^{1-\varepsilon}$

Obscuring Supersoft X-ray Sources in Stellar Winds

We investigate the possibility of obscuring supersoft X-ray sources in the winds of companion stars. We derive limits on the amount of circumstellar material needed to fully obscure a 'canonical' supersoft X-ray source in the Large Magellanic Cloud, as observed with the Chandra X-ray Observatory.Comment: Conference proceedings for IAU Symposium no. 281 "Binary Paths to Type Ia Supernova Explosions", 5-10 July 2011, Padova, Ital

Architecture and noise analysis of continuous variable quantum gates using two-dimensional cluster states

Due to its unique scalability potential, continuous variable quantum optics is a promising platform for large scale quantum computing and quantum simulation. In particular, very large cluster states with a two-dimensional topology that are suitable for universal quantum computing and quantum simulation can be readily generated in a deterministic manner, and routes towards fault-tolerance via bosonic quantum error-correction are known. In this article we propose a complete measurement-based quantum computing architecture for the implementation of a universal set of gates on the recently generated two-dimensional cluster states [1,2]. We analyze the performance of the various quantum gates that are executed in these cluster states as well as in other two-dimensional cluster states (the bilayer-square lattice and quad-rail lattice cluster states [3,4]) by estimating and minimizing the associated stochastic noise addition as well as the resulting gate error probability. We compare the four different states and find that, although they all allow for universal computation, the quad-rail lattice cluster state performs better than the other three states which all exhibit similar performance