Submodularity in Batch Active Learning and Survey Problems on Gaussian Random Fields

Many real-world datasets can be represented in the form of a graph whose edge weights designate similarities between instances. A discrete Gaussian random field (GRF) model is a finite-dimensional Gaussian process (GP) whose prior covariance is the inverse of a graph Laplacian. Minimizing the trace of the predictive covariance Sigma (V-optimality) on GRFs has proven successful in batch active learning classification problems with budget constraints. However, its worst-case bound has been missing. We show that the V-optimality on GRFs as a function of the batch query set is submodular and hence its greedy selection algorithm guarantees an (1-1/e) approximation ratio. Moreover, GRF models have the absence-of-suppressor (AofS) condition. For active survey problems, we propose a similar survey criterion which minimizes 1'(Sigma)1. In practice, V-optimality criterion performs better than GPs with mutual information gain criteria and allows nonuniform costs for different nodes

Optical tristability and ultrafast Fano switching in nonlinear magneto-plasmonic nanoparticles

We consider light scattering by a coated magneto-plasmonic nanoparticle (MPNP) with a Kerr-type nonlinear plasmonic shell and a magneto-optic core. Such structure features two plasmon dipole modes, associated with electronic oscillations on the inner and outer surfaces of the shell. Driven in a nonlinear regime, each mode exhibits a bistable response. Bistability of an inner plasmon leads to switching between this state and a Fano resonance (Fano switching). Once the external light intensity exceeds the critical value, the bistability zones of both eigen modes overlap yielding optical tristability characterized by three stable steady states for a given wavelength and light intensity. We develop a dynamic theory of transitions between nonlinear steady states and estimate the characteristic switching time as short as 0.5 ps. We also show that the magneto-optical (MO) effect allows red- and blue- spectral shift of the Fano profile for right- and left- circular polarizations of the external light, rendering Fano switching sensitive to the light polarization. Specifically, one can reach Fano switching for the right circular polarization while cancelling it for the left circular polarization. Our results point to a novel class of ultrafast Fano switchers tunable by magnetic field for applications in nanophotonics.Comment: 13 pages, 6 figure

Portfolio optimisation using risky assets with options as derivative insurance

We introduce options on FTSE100 index in portfolio optimisation with shares in which conditional value at risk (CVaR) is minimised. The option considered here is the one that follows FTSE100 Index Option standards. Price of options are calculated under the risk neutral valuation. The efficient portfolio composed under this addition of options shows that put option will be selected as part of the investment for every level of targeted returns. Main finding shows that the use of options does indeed decrease downside risk, and leads to better in-sample portfolio performance. Out-of-sample and back-testing also shows better performance of CVaR efficient portfolios in which index options are included. All models are coded using AMPL and the results are analysed using Microsoft Excel. Data used in this study are obtained from Datastream. We conclude that adding a put index option in addition to stocks, in order to actively create a portfolio, can substantially reduce the risk at a relatively low cost. Further research work will consider the case when short positions are considered, including writing call options.This work was partially supported by the Department of Mathematics, Brunel University

The M33 Globular Cluster System with PAndAS Data: The Last Outer Halo Cluster?

We use CFHT/MegaCam data to search for outer halo star clusters in M33 as part of the Pan-Andromeda Archaeological Survey (PAndAS). This work extends previous studies out to a projected radius of 50 kpc and covers over 40 square degrees. We find only one new unambiguous star cluster in addition to the five previously known in the M33 outer halo (10 kpc <= r <= 50 kpc). Although we identify 2440 cluster candidates of various degrees of confidence from our objective image search procedure, almost all of these are likely background contaminants, mostly faint unresolved galaxies. We measure the luminosity, color and structural parameters of the new cluster in addition to the five previously-known outer halo clusters. At a projected radius of 22 kpc, the new cluster is slightly smaller, fainter and redder than all but one of the other outer halo clusters, and has g' ~ 19.9, (g'-i') ~ 0.6, concentration parameter c ~ 1.0, a core radius r_c ~ 3.5 pc, and a half-light radius r_h ~ 5.5 pc. For M33 to have so few outer halo clusters compared to M31 suggests either tidal stripping of M33's outer halo clusters by M31, or a very different, much calmer accretion history of M33.Comment: 37 pages, 9 figures. Accepted by the Astrophysical Journa

Age and mass studies for young star clusters in M31 from SEDs-fit

In this paper, we present photometry for young star clusters in M31, which are selected from Caldwell et al. These star clusters have been observed as part of the Beijing--Arizona--Taiwan--Connecticut (BATC) Multicolor Sky Survey from 1995 February to 2008 March. The BATC images including these star clusters are taken with 15 intermediate-band filters covering 3000--10000 \AA. Combined with photometry in the {\sl GALEX} far- and near-ultraviolet, broad-band $UBVRI$, SDSS $ugriz$, and infrared $JHK_{\rm s}$ of Two Micron All Sky Survey, we obtain their accurate spectral energy distributions (SEDs) from 1538-20000 \AA. We derive these star clusters' ages and masses by comparing their SEDs with stellar population synthesis models. Our results are in good agreement with previous determinations. The mean value of age and mass of young clusters ($<2$ Gyr) is about 385 Myr and $2\times 10^4 {M_\odot}$, respectively. There are two distinct peaks in the age distribution, a highest peak at age $\sim$ 60 Myr and a secondary peak around 250 Myr, while the mass distribution shows a single peak around $10^4 {M_\odot}$. A few young star clusters have two-body relaxation times greater than their ages, indicating that those clusters have not been well dynamically relaxed and therefore have not established the thermal equilibrium. There are several regions showing aggregations of young star clusters around the 10 kpc ring and the outer ring, indicating that the distribution of the young star clusters is well correlated with M31's star-forming regions. The young massive star clusters (age $\leq 100$ Myr and mass $\geq 10^4 {M_\odot}$) show apparent concentration around the ring splitting region, suggesting a recent passage of a satellite galaxy (M32) through M31 disk.Comment: Accepted for Publication in AJ, 15 pages, 14 figures and 4 table