L1-norm Regularized L1-norm Best-fit line problem

Background Conventional Principal Component Analysis (PCA) is a widely used technique to reduce data dimension. PCA finds linear combinations of the original features capturing maximal variance of data via Singular Value Decomposition (SVD). However, SVD is sensitive to outliers, and often leads to high dimensional results. To address the issues, we propose a new method to estimate best-fit one-dimensional subspace, called l1-norm Regularized l1-norm. Methods In this article, we describe a method to fit a lower-dimensional subspace by approximate a non-linear, non-convex, non-smooth optimization problem called l1 regularized l1-norm Best- Fit Line problem; minimize a combination of the l1 error and of the l1 regularization. The procedure can be simply performed using ratios and sorting. Also ,we present applications in the area of video surveillance, where our methodology allows for background subtraction with jitters, illumination changes, and clutters. Results We compared our performance with SVD on synthetic data. The numerical results showed our algorithm successfully found a better principal component from a grossly corrupted data than SVD in terms of discordance. Moreover, our algorithm provided a sparser principal component than SVD. However, we expect it to be faster on multi-node environment. Conclusions This paper proposes a new algorithm able to generate a sparse best-fit subspace robust to outliers. The projected subspaces sought on non-contaminated data, differ little from that of traditional PCA. When subspaces are projected from contaminated data, it attain arguably significant both smaller discordance and lower dimension than that of traditional PCA.https://scholarscompass.vcu.edu/gradposters/1074/thumbnail.jp

Advance Contracts for the Sale of Wool in Medieval England; An Undeveloped and Inefficient Market?

While it is commonly believed that derivative instruments are a recent invention, we document the existence of forward contracts for the sale of wool in medieval England around 700 years ago. The contracts were generally entered into by English monasteries, who frequently sold their wool for up to twenty years in advance to mostly foreign and particularly Italian merchants. Employing a unique source of data collected by hand from the historical records, we determine the interest rates implied in these transactions and we also examine the efficiency of the forward and spot markets. The calculated interest rates average around 20%, in accordance with available information concerning the interest rates used in other types of transactions at that time. Perhaps surprisingly, we also find little evidence of informational inefficiencies in these markets.Wood market, forward contracts, market efficinecy, Medieval England, Interest rates

Leger est aprendre mes fort est arendre;: Wool, Debt and the Dispersal of Pipewell Abbey (1280 - 1330)

has long been known that English Cistercian monasteries often sold their wool in advance to foreign merchants in the late thirteenth century. The abbey of Pipewell in Northamptonshire features in a number of such contracts with Cahorsin merchants. This paper looks again at these contracts in the context of over 200 other such agreements found in the governmental records. Why did Pipewell descend into penury over this fifty year period? This case study demonstrates that the promise of ready cash for their most valuable commodity led such abbots to make ambitious agreements – taking on yet more debt to service existing creditors - that would lead to their eventual bankruptcy.

Topsat – High Resolution Imaging from a Small Satellite

The Topsat mission is designed to demonstrate the capabilities of small satellites for classically high value remote sensing missions. Conceived by the UK’s Defence Evaluation and Research Agency (DERA), it will produce 2.5 m resolution panchromatic imagery and 5 m resolution multispectral imagery in three visible wavebands and allow direct transmission of the image data to a local mobile ground station. The Topsat programme is jointly funded by the UK Ministry of Defence (MoD) and by the British National Space Centre’s Mosaic small satellite initiative and includes provision for the spacecraft, ground segment, commercial launch and one year of planned operations. The mission will meet the national needs of the UK in two areas. The UK MoD will use Topsat to investigate the utility and issues of providing data acquisition and tasking resources to local command levels. BNSC are supporting the programme as a demonstration of an enhanced capability for UK small satellites leading to sales of similar systems and to allow the development of lower cost markets for remote sensing products producible from such systems. The Topsat mission is a collaboration between four UK partners. DERA are leading the mission and providing the data handling unit, high rate downlink, mobile ground station and operations. Surrey Satellites (SSTL) are providing the spacecraft bus and command and telemetry links. Rutherford Appleton Laboratory (RAL) are developing a near diffraction limited wide field of view camera which, when combined with a pitch compensation manoeuvre, allows the highly demanding optical performance characteristics to be achieved. Infoterra are responsible for developing potential markets for Topsat and future derivatives

Synthesis and Characterization of Novel Copolymers using Monomer Sequence Controlled Living Anionic Polymerization

1,1-Diphenylethylene (DPE) and functional derivatives of DPE have been used to prepare a variety of novel copolymers by living anionic polymerization. This research focuses on exploiting reactivity ratios to prepare copolymers with a variety of structures including alternating, tapered, statistical and telechelic copolymers. The copolymers were analysed by a variety of techniques including 1D and 2D NMR spectroscopy, MALDI-ToF mass spectrometry, differential scanning calorimetry and transmission electron microscopy

Infrared behaviour and renormalization scheme invariance of QCD observables

In this thesis we study the infrared (IR) behaviour of QCD observables, and solutions to the problem of renormalization scheme dependence. We investigate the IR behaviour of all-orders leading-b renormalon resummations for certain Euclidean observables (the Adler-D function and the GLS and Björken sum rules) in the Borei representation. We find that these resummations are finite at the Landau pole (Q(^2) =Λ(^2)) and also 'freeze’ to zero in the Q(^2)→ 0 limit. We find this finite Landau pole behaviour has its origin in curious relations between IR and UV renormalons, which correspond to deeper conformal symmetries in QCD Green's functions. We consider these Borei resumed results in a skeleton expansion representation. This representation leads naturally to the standard Borei representation in the UV(Q(^2) ˃Λ(^2)) region and to a modified Borei representation in the IR (Q(^2) ˂Λ(^2)) region. We also consider the ambiguous part of the perturbative expansion in these representations. By demanding that such ambiguities cancel with similar ambiguities generated by the non-perturbative OPE, we are led to a new model for power corrections. We apply the complete renormalization group improved (CORGI) approach to all-orders renormalon resummations of the above-mentioned sum rules and compare the resultant predictions with experimental data. We also test our model for power corrections on these observables and find that the data favours power corrections of reasonably small magnitude. We also apply the CORGI approach, together with the physical scale and the effective charge approaches, to moments of F^^ and Բշ^. We use the Bernstein averages method in which any dependence of the analysis on regions of X and Q2 inaccessible to experiment is reduced