The local convexity of solving systems of quadratic equations

This paper considers the recovery of a rank $r$ positive semidefinite matrix $X X^T\in\mathbb{R}^{n\times n}$ from $m$ scalar measurements of the form $y_i := a_i^T X X^T a_i$ (i.e., quadratic measurements of $X$). Such problems arise in a variety of applications, including covariance sketching of high-dimensional data streams, quadratic regression, quantum state tomography, among others. A natural approach to this problem is to minimize the loss function $f(U) = \sum_i (y_i - a_i^TUU^Ta_i)^2$ which has an entire manifold of solutions given by $\{XO\}_{O\in\mathcal{O}_r}$ where $\mathcal{O}_r$ is the orthogonal group of $r\times r$ orthogonal matrices; this is {\it non-convex} in the $n\times r$ matrix $U$, but methods like gradient descent are simple and easy to implement (as compared to semidefinite relaxation approaches). In this paper we show that once we have $m \geq C nr \log^2(n)$ samples from isotropic gaussian $a_i$, with high probability {\em (a)} this function admits a dimension-independent region of {\em local strong convexity} on lines perpendicular to the solution manifold, and {\em (b)} with an additional polynomial factor of $r$ samples, a simple spectral initialization will land within the region of convexity with high probability. Together, this implies that gradient descent with initialization (but no re-sampling) will converge linearly to the correct $X$, up to an orthogonal transformation. We believe that this general technique (local convexity reachable by spectral initialization) should prove applicable to a broader class of nonconvex optimization problems.Comment: 36 pages, 3 figure

A Long XMM-Newton Observation of An Extreme Narrow Line Seyfert 1: PG 1244+026

We explore the origin of the strong soft X-ray excess in Narrow Line Seyfert 1 galaxies using spectral-timing information from a 120ks {\it XMM-Newton} observation of PG 1244+026. Spectral fitting alone cannot distinguish between a true additional soft X-ray continuum component and strongly relativistically smeared reflection, but both models also require a separate soft blackbody component. This is most likely intrinsic emission from the disc extending into the lowest energy X-ray bandpass. The {\it RMS} spectra on short timescales (200-5000s) contain both (non-disk) soft excess and power law emission. However, the spectrum of the variability on these timescales correlated with the 4-10 keV lightcurve contains only the power law. Together these show that there is fast variability of the soft excess which is independent of the 4-10 keV variability. This is inconsistent with a single reflection component making the soft X-ray excess as this necessarily produces correlated variability in the 4-10 keV bandpass. Instead, the {\it RMS} and covariance spectra are consistent with an additional cool Comptonisation component which does not contribute to the spectrum above 2 keV.Comment: 15 pages, 12 figures, 5 tables, accepted by MNRA

Chinese agriculture technology demonstration centres in Southern Africa: The new business of development

Chinese aid in the African agriculture sector is one of the enduring forms of involvement on the continent. The launching of Agriculture Technology Demonstration Centres (ATDCs) in 2006 marked a new intensive phase in agricultural aid, which seeks to find sustainability through public-private partnerships and to promote Chinese commercial pursuits. Based on in-depth fieldwork in Mozambique and South Africa, this paper provides a critical analysis of ATDCs practices. As per the three key objectives of the ATDC - technology transfer, business development, and sustainability -, the authors find three major results. First, the agro-technology transfer proves to be beneficial but at a very localized level. Second, Chinese agribusiness companies have been introduced to the host countries through the platform of the ATDC, and are partially fulfilling the commercial aim of the project. Third, the long-standing problem of aid unsustainability remains a major concern with the newly launched ATDC project. The deficiency of policy design and lack of effective bilateral interactions are identified as the main reasons for the problems experienced. (Résumé d'auteur

The S&P 500 Index Effect in Continuous Time: Evidence from Overnight, Intraday and Tick-by-Tick Stock Price Performance

The advent of index tracking early in the 1970s and the continuous growth of assets tied to the S&P 500 index have enforced perceptions of the importance of becoming an index-member, due to increased demand by index fund participants for the stocks involved in index composition changes. This study focuses on S&P 500 inclusions and examines the impact of potential overnight price adjustment after the announcement of an S&P 500 index change. We find evidence of a significant overnight price change that diminishes the profits available to speculators although there are still profits available from the first day after announcement until a few days after the actual event. More importantly observing the tick-by-tick stock price performance of the key days of the event window for the first time, we find evidence of consistent trading patterns during trading hours over inclusion event. A separate analysis of two different sub-periods as well as of NASDAQ and NYSE listed stocks allows for a detailed examination of the price and volume effect in continuous time.Index effect, S&P 500, market efficiency, price pressure

Stratigraphy and chronology of a 15ka sequence of multi-sourced silicic tephras in a montane peat bog, eastern North Island, New Zealand.

We document the stratigraphy, composition, and chronology of a succession of 16 distal, silicic tephra layers interbedded with lateglacial and Holocene peats and muds up to c. 15 000 radiocarbon years (c. 18 000 calendar years) old at a montane site (Kaipo Bog) in eastern North Island, New Zealand. Aged from 665 +/- 15 to 14 700 +/- 95 14C yr BP, the tephras are derived from six volcanic centres in North Island, three of which are rhyolitic (Okataina, Taupo, Maroa), one peralkaline (Tuhua), and two andesitic (Tongariro, Egmont). Correlations are based on multiple criteria: field properties and stratigraphic interrelationships, ferromagnesian silicate mineral assemblages, glass-shard major element composition (from electron microprobe analysis), and radiocarbon dating. We extend the known distribution of tephras in eastern North Island and provide compositional data that add to their potential usefulness as isochronous markers. The chronostratigraphic framework established for the Kaipo sequence, based on both site-specific and independently derived tephra-based radiocarbon ages, provides the basis for fine-resolution paleoenvironmental studies at a climatically sensitive terrestrial site from the mid latitudes of the Southern Hemisphere. Tephras identified as especially useful paleoenvironmental markers include Rerewhakaaitu and Waiohau (lateglacial), Konini (lateglacial-early Holocene), Tuhua (middle Holocene), and Taupo and Kaharoa (late Holocene)

Gambling on the S&P 500's Gold Seal: New Evidence on the Index Effect

This study examines the abnormal returns, trading activity and long term performance of stocks that were added to the S&P 500 Index during the period 1990 to 2002. By using a three-factor pricing model that allows for firm size and value characteristics as well as market risk, we are able to shed new light on the widely observed ‘index effect’. We argue that for the years 1990-1997 in particular, firm size mattered in the long-run and firm size effects cannot be captured by a single factor model for abnormal returns. We also find a transitory increase in trading volume between the announcement and a few days after the effective date. The “seal” of S&P 500 Index membership has very long term effects and inclusion is not an information-free event.Index effect, S&P 500, market efficiency, price pressure, three-factor model

Precision Electro-Weak and Hadronic Luminosity Calculations

We have used YFS Monte Carlo techniques to obtain per-mil level accuracy for the Bhabha scattering cross section used in the luminosity monitor in electro-weak scattering experiments. We will describe techniques for extending these methods for use in the W production luminosity cross section for hadron colliders.Comment: 8 pages (LaTex) with 5 figures (EPS). Presented by S.A. Yost at the Third International Symposium on Quantum Theory and Symmetries, Cincinnati, Sept. 10 - 14, 200