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

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

Leverage Effect In Chinese And American Index Returns

A lot of changes have happened in the Chinese economy in the last three decades. To study whether these changes affect the symmetric or asymmetric behavior of the volatility in Chinese Stock Market, in this paper we analyze, first, the main stylized facts in similar Chinese and American index returns and, second, we compare the leverage effect of volatility in three different periods for these indexes.The estimated results with GJR-GARCH and TA-ARSV models have shown that the behaviour of Chinese index returns was different depending on whether China was part of the Trade World Trade Organization (WTO)

An updated catalog of M33 clusters and candidates: UBVRIUBVRI photometry, and some statistical results

We present $UBVRI$ photometry for 392 star clusters and candidates in the field of M33, which are selected from the most recent star cluster catalog. In this catalog, the authors listed star clusters' parameters such as cluster positions, magnitudes and colors in the $UBVRIJHK_s$ filters, and so on. However, a large fraction of objects in this catalog do not have previously published photometry. Photometry is performed using archival images from the Local Group Galaxies Survey, which covers 0.8 deg$^2$ along the major axis of M33. Detailed comparisons show that, in general, our photometry is consistent with previous measurements. Positions (right ascension and declination) for some clusters are corrected here. Combined with previous literature, we constitute a large sample of M33 star clusters. Based on this cluster sample, we present some statistical results: none of the M33 youngest clusters ($\sim 10^7$ yr) have masses approaching $10^5$ $M_{\odot}$; roughly half the star clusters are consistent with the $10^4$ to $10^5$ $M_{\odot}$ mass models; the continuous distribution of star clusters along the model line indicates that M33 star clusters have been formed continuously from the epoch of the first star cluster formation until recent times; there are $\sim 50$ star clusters which being overlapped with the Galactic globular clusters on the color-color diagram, and these clusters are old globular clusters candidates in M33.Comment: Accepted for Publication in AJ, 22 pages, 12 figures and 9 table

Rankings In The Euro Zone Based On Macroeconomic Information

One consequence of the Great Recession that began in 2008 has been the sovereign debt crisis within the European Monetary Union (EMU) and the increasing risk premium associated with government debt of "peripheral" countries (primarily, Greece, Ireland, Portugal and Spain). Firstly, this paper analyses what macroeconomic variables are more related with the evolution of the risk premium, using panel data estimation. Secondly, we also try to sort the countries belonging to the monetary union in terms of their likelihood of experiencing an increase in the risk premium. To this purpose, we use discrete multicriteria decision aid methods

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

Quantum expander for gravitational-wave observatories

Quantum uncertainty of laser light limits the sensitivity of gravitational-wave observatories. In the past 30 years, techniques for squeezing the quantum uncertainty as well as for enhancing the gravitational-wave signal with optical resonators were invented. Resonators, however, have finite linewidths; and the high signal frequencies that are produced during the scientifically highly interesting ring-down of astrophysical compact-binary mergers cannot be resolved today. Here, we propose an optical approach for expanding the detection bandwidth. It uses quantum uncertainty squeezing inside one of the optical resonators, compensating for finite resonators' linewidths while maintaining the low-frequency sensitivity unchanged. Introducing the quantum expander for boosting the sensitivity of future gravitational-wave detectors, we envision it to become a new tool in other cavity-enhanced metrological experiments