Efficient computation of the Shapley value for game-theoretic network centrality

The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo

General method for extracting the quantum efficiency of dispersive qubit readout in circuit QED

We present and demonstrate a general three-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of the non-steady-state homodyne measurement. We derive analytically and demonstrate experimentally that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. We use the proven method to optimally bias a Josephson traveling-wave parametric amplifier and to quantify different noise contributions in the readout amplification chain.Comment: 10 pages, 6 figure

Carbon Deficiency in Externally-Polluted White Dwarfs: Evidence for Accretion of Asteroids

Existing determinations show that n(C)/n(Fe) is more than a factor of 10 below solar in the atmospheres of three white dwarfs that appear to be externally-polluted. These results are not easily explained if the stars have accreted interstellar matter, and we re-interpret these measurements as evidence that these stars have accreted asteroids of a chrondritic composition.Comment: 23 pages, 6 figures, accepted for Ap

Evidence for mTOR pathway activation in a spectrum of epilepsy-associated pathologies

Introduction Activation of the mTOR pathway has been linked to the cytopathology and epileptogenicity of malformations, specifically Focal Cortical Dysplasia (FCD) and Tuberous Sclerosis (TSC). Experimental and clinical trials have shown than mTOR inhibitors have anti-epileptogenic effects in TS. Dysmorphic neurones and balloon cells are hallmarks of FCDIIb and TSC, but similar cells are also occasionally observed in other acquired epileptogenic pathologies, including hippocampal sclerosis (HS) and Rasmussen’s encephalitis (RE). Our aim was to explore mTOR pathway activation in a range of epilepsy-associated pathologies and in lesion-negative cases. Results 50 epilepsy surgical pathologies were selected including HS ILAE type 1 with (5) and without dysmorphic neurones (4), FCDIIa (1), FCDIIb (5), FCDIIIa (5), FCDIIIb (3), FCDIIId (3), RE (5) and cortex adjacent to cavernoma (1). We also included pathology-negative epilepsy cases; temporal cortex (7), frontal cortex (2), paired frontal cortical samples with different ictal activity according to intracranial EEG recordings (4), cortex with acute injuries from electrode tracks (5) and additionally non-epilepsy surgical controls (3). Immunohistochemistry for phospho-S6 (pS6) ser240/244 and ser235/236 and double-labelling for Iba1, neurofilament, GFAP, GFAPdelta, doublecortin, and nestin were performed. Predominant neuronal labelling was observed with pS6 ser240/244 and glial labelling with pS6 ser235/236 in all pathology types but with evidence for co-expression in a proportion of cells in all pathologies. Intense labelling of dysmorphic neurones and balloon cells was observed in FCDIIb, but dysmorphic neurones were also labelled in RE and HS. There was no difference in pS6 labelling in paired samples according to ictal activity. Double-labelling immunofluorescent studies further demonstrated the co-localisation of pS6 with nestin, doublecortin, GFAPdelta in populations of small, immature neuroglial cells in a range of epilepsy pathologies. Conclusions Although mTOR activation has been more studied in the FCDIIb and TSC, our observations suggest this pathway is activated in a variety of epilepsy-associated pathologies, and in varied cell types including dysmorphic neurones, microglia and immature cell types. There was no definite evidence from our studies to suggest that pS6 expression is directly related to disease activity

String Method for the Study of Rare Events

We present a new and efficient method for computing the transition pathways, free energy barriers, and transition rates in complex systems with relatively smooth energy landscapes. The method proceeds by evolving strings, i.e. smooth curves with intrinsic parametrization whose dynamics takes them to the most probable transition path between two metastable regions in the configuration space. Free energy barriers and transition rates can then be determined by standard umbrella sampling technique around the string. Applications to Lennard-Jones cluster rearrangement and thermally induced switching of a magnetic film are presented.Comment: 4 pages, 4 figure