Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices (The Extended Version)

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These densities are encoded in the form of the so called M-transforms, for which polynomial equations are found. We exploit the methods of planar diagrammatics, enhanced to the non-Hermitian case, and free random variables, respectively; both are described in the appendices. As particular results of these two main equations, we find the singular behavior of the spectral densities near zero. Moreover, we propose a finite-size form of the spectral density of the product close to the border of its eigenvalues' domain. Also, led by the striking similarity between the two main equations, we put forward a conjecture about a simple relationship between the eigenvalues and singular values of any non-Hermitian random matrix whose spectrum exhibits rotational symmetry around zero.Comment: 50 pages, 8 figures, to appear in the Proceedings of the 23rd Marian Smoluchowski Symposium on Statistical Physics: "Random Matrices, Statistical Physics and Information Theory," September 26-30, 2010, Krakow, Polan

Facilitating the Decentralised Exchange of Cryptocurrencies in an Order-Driven Market

This article discusses a protocol to facilitate decentralised exchanges on an order-driven market through a consortium of market services operators. We discuss whether this hybrid protocol combining a centralised initiation phase with a decentralised execution phase outperforms fully centralised exchanges with regards to efficiency and security. Here, a fully efficient and fully secure protocol is defined as one where traders incur no trading costs or opportunity costs and counterparty risk is absent. We devise a protocol addressing the main downsides in the decentralised exchange process that uses a facilitating distributed ledger, maintains an order book and monitors the order status in real-time to provide accurate exchange rate information and performance scoring of participants. We show how performance ratings can lower opportunity costs and how a rolling benchmark rate of verifiable trades can be used to establish a trustworthy exchange rate between cryptocurrencies. The formal validation of the proposed technical mechanisms is the subject of future work

Judgments in the Sharing Economy: The Effect of User-Generated Trust and Reputation Information on Decision-Making Accuracy and Bias

The growing ecosystem of peer-to-peer enterprise – the Sharing Economy (SE) – has brought with it a substantial change in how we access and provide goods and services. Within the SE, individuals make decisions based mainly on user-generated trust and reputation information (TRI). Recent research indicates that the use of such information tends to produce a positivity bias in the perceived trustworthiness of fellow users. Across two experimental studies performed on an artificial SE accommodation platform, we test whether users’ judgments can be accurate when presented with diagnostic information relating to the quality of the profiles they see or if these overly positive perceptions persist. In study 1, we find that users are quite accurate overall (70%) at determining the quality of a profile, both when presented with full profiles or with profiles where they selected three TRI elements they considered useful for their decisionmaking. However, users tended to exhibit an “upward quality bias” when making errors. In study 2, we leveraged patterns of frequently vs. infrequently selected TRI elements to understand whether users have insights into which are more diagnostic and find that presenting frequently selected TRI elements improved users’ accuracy. Overall, our studies demonstrate that – positivity bias notwithstanding – users can be remarkably accurate in their online SE judgments

Asymmetric correlation matrices: an analysis of financial data

We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrices to distinguish between noise and non trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non symmetric correlation matrix. We find several non trivial results, also when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.Comment: Revised version; 11 pages, 13 figure

Accounting for risk of non linear portfolios: a novel Fourier approach

The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power law tails. We show how the knowledge of the model characteristic function leads to Fourier representations for two standard risk measures, the Value at Risk and the Expected Shortfall, and for their sensitivities with respect to the model parameters. We detail the numerical implementation of our formulae and we emphasizes the reliability and efficiency of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur. Phys. J.

Evidence for light-by-light scattering in heavy-ion collisions with the ATLAS detector at the LHC

Light-by-light scattering (gamma gamma -> gamma gamma) is a quantum-mechanical process that is forbidden in the classical theory of electrodynamics. This reaction is accessible at the Large Hadron Collider thanks to the large electromagnetic field strengths generated by ultra-relativistic colliding lead ions. Using 480 mu b(-1) of lead-lead collision data recorded at a centre-of-mass energy per nucleon pair of 5.02 TeV by the ATLAS detector, here we report evidence for light-by-light scattering. A total of 13 candidate events were observed with an expected background of 2.6 +/- 0.7 events. After background subtraction and analysis corrections, the fiducial cross-section of the process Pb + Pb (gamma gamma) -> Pb-(center dot) + Pb-(center dot) gamma gamma, for photon transverse energy E-T > 3 GeV, photon absolute pseudorapidity vertical bar eta vertical bar < 2.4, diphoton invariant mass greater than 6 GeV, diphoton transverse momentum lower than 2 GeV and diphoton acoplanarity below 0.01, is measured to be 70 +/- 24 (stat.) +/- 17 (syst.) nb, which is in agreement with the standard model predictions

Lipofundin-Induced Hyperlipidemia Promotes Oxidative Stress and Atherosclerotic Lesions in New Zealand White Rabbits

Atherosclerosis represents a major cause of death in the world. It is known that Lipofundin 20% induces atherosclerotic lesions in rabbits, but its effects on serum lipids behaviour and redox environment have not been addressed. In this study, New Zealand rabbits were treated with 2 mL/kg of Lipofundin for 8 days. Then, redox biomarkers and serum lipids were determined spectrophotometrically. On the other hand, the development of atherosclerotic lesions was confirmed by eosin/hematoxylin staining and electron microscopy. At the end of the experiment, total cholesterol, triglycerides, cholesterol-LDL, and cholesterol-HDL levels were significantly increased. Also, a high index of biomolecules damage, a disruption of both enzymatic and nonenzymatic defenses, and a reduction of nitric oxide were observed. Our data demonstrated that Lipofundin 20% induces hyperlipidemia, which promotes an oxidative stress state. Due to the importance of these phenomena as risk factors for atherogenesis, we suggest that Lipofundin induces atherosclerosis mainly through these mechanisms

System Test of the ATLAS Muon Spectrometer in the H8 Beam at the CERN SPS

An extensive system test of the ATLAS muon spectrometer has been performed in the H8 beam line at the CERN SPS during the last four years. This spectrometer will use pressurized Monitored Drift Tube (MDT) chambers and Cathode Strip Chambers (CSC) for precision tracking, Resistive Plate Chambers (RPCs) for triggering in the barrel and Thin Gap Chambers (TGCs) for triggering in the end-cap region. The test set-up emulates one projective tower of the barrel (six MDT chambers and six RPCs) and one end-cap octant (six MDT chambers, A CSC and three TGCs). The barrel and end-cap stands have also been equipped with optical alignment systems, aiming at a relative positioning of the precision chambers in each tower to 30-40 micrometers. In addition to the performance of the detectors and the alignment scheme, many other systems aspects of the ATLAS muon spectrometer have been tested and validated with this setup, such as the mechanical detector integration and installation, the detector control system, the data acquisition, high level trigger software and off-line event reconstruction. Measurements with muon energies ranging from 20 to 300 GeV have allowed measuring the trigger and tracking performance of this set-up, in a configuration very similar to the final spectrometer. A special bunched muon beam with 25 ns bunch spacing, emulating the LHC bunch structure, has been used to study the timing resolution and bunch identification performance of the trigger chambers. The ATLAS first-level trigger chain has been operated with muon trigger signals for the first time