The foreign exchange market: return distributions, multifractality, anomalous multifractality and Epps effect

We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all the pairs considered are well described by the nonextensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the nonextensivity q-parameter values for different exchange rates and this can be related to the importance of a given exchange rate in the world's currency trade. Temporal correlations organize the series of returns such that they develop the multifractal characteristics for all the exchange rates with a varying degree of symmetry of the singularity spectrum f(alpha) however. The most symmetric spectrum is identified for the GBP/USD. We also form time series of triangular residual returns and find that the distributions of their fluctuations develop disproportionately heavier tails as compared to small fluctuations which excludes description in terms of q-Gaussians. The multifractal characteristics for these residual returns reveal such anomalous properties like negative singularity exponents and even negative singularity spectra. Such anomalous multifractal measures have so far been considered in the literature in connection with the diffusion limited aggregation and with turbulence. We find that market inefficiency on short time scales leads to the occurrence of the Epps effect on much longer time scales. Although the currency market is much more liquid than the stock markets and it has much larger transaction frequency, the building-up of correlations takes up to several hours - time that does not differ much from what is observed in the stock markets. This may suggest that non-synchronicity of transactions is not the unique source of the observed effect

Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation

We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. We construct flows on the moduli space of algebraic Riemann surfaces that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities.Comment: 15 page

Ergodic Jacobi matrices and conformal maps

We study structural properties of the Lyapunov exponent $\gamma$ and the density of states $k$ for ergodic (or just invariant) Jacobi matrices in a general framework. In this analysis, a central role is played by the function $w=-\gamma+i\pi k$ as a conformal map between certain domains. This idea goes back to Marchenko and Ostrovskii, who used this device in their analysis of the periodic problem

Detection and imaging in strongly backscattering randomly layered media

Abstract. Echoes from small reflectors buried in heavy clutter are weak and difficult to distinguish from the medium backscatter. Detection and imaging with sensor arrays in such media requires filtering out the unwanted backscatter and enhancing the echoes from the reflectors that we wish to locate. We consider a filtering and detection approach based on the singular value decomposition of the local cosine transform of the array response matrix. The algorithm is general and can be used for detection and imaging in heavy clutter, but its analysis depends on the model of the cluttered medium. This paper is concerned with the analysis of the algorithm in finely layered random media. We obtain a detailed characterization of the singular values of the transformed array response matrix and justify the systematic approach of the filtering algorithm for detecting and refining the time windows that contain the echoes that are useful in imaging

Modelling of the effect of ELMs on fuel retention at the bulk W divertor of JET

Effect of ELMs on fuel retention at the bulk W target of JET ITER-Like Wall was studied with multi-scale calculations. Plasma input parameters were taken from ELMy H-mode plasma experiment. The energetic intra-ELM fuel particles get implanted and create near-surface defects up to depths of few tens of nm, which act as the main fuel trapping sites during ELMs. Clustering of implantation-induced vacancies were found to take place. The incoming flux of inter-ELM plasma particles increases the different filling levels of trapped fuel in defects. The temperature increase of the W target during the pulse increases the fuel detrapping rate. The inter-ELM fuel particle flux refills the partially emptied trapping sites and fills new sites. This leads to a competing effect on the retention and release rates of the implanted particles. At high temperatures the main retention appeared in larger vacancy clusters due to increased clustering rate

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices

We present a simple Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this probability is computed explicitly for Wishart and Gaussian ensembles. The method is quite general and applies to other related problems, e.g. the joint large deviation function for large fluctuations of top eigenvalues. Our results are relevant to widely employed data compression techniques, namely the principal components analysis. Analytical predictions are verified by extensive numerical simulations.Comment: 4 pages, 3 .eps figures include

Proceedings of the CSE 2017 Annual PGR Symposium (CSE-PGSym17)

Welcome to the Proceedings of the second Annual Postgraduate Research Symposium of the School of Computing, Science and Engineering (CSE-PGSym 2017). After the success of the first symposium, the school is delighted to run its second symposium which is being held in The Old Fire Station on 17th March 2017. The symposium is organised by the Salford Innovation Research Centre (SIRC) to provide a forum for the PGR community in the school to share their research work, engage with their peers and staff and stimulate new ideas. In line with SIRC’s strategy, the symposium aims to bring together researchers from the six groups that make up the centre to engage in multidisciplinary discussions and collaborations. It also aims to contribute to the creation of a collaborative environment within the Research Centre and the Groups and share information and explore new ideas. This is also aligned with the University’s ICZ (Industrial Collaboration Zone) programme for creating cultural, physical and virtual environments for collaboration, innovation and learning

Impact of ICRF on the scrape-off layer and on plasma wall interactions: From present experiments to fusion reactor

Recent achievements in studies of the effects of ICRF (Ion Cyclotron Range of Frequencies) power on the SOL (Scrape-Off Layer) and PWI (Plasma Wall Interactions) in ASDEX Upgrade (AUG), Alcator C-Mod, and JET-ILW are reviewed. Capabilities to diagnose and model the effect of DC biasing and associated impurity production at active antennas and on magnetic field connections to antennas are described. The experiments show that ICRF near-fields can lead not only to E×B convection, but also to modifications of the SOL density, which for Alcator C-Mod are limited to a narrow region near antenna. On the other hand, the SOL density distribution along with impurity sources can be tailored using local gas injection in AUG and JET-ILW with a positive effect on reduction of impurity sources. The technique of RF image current cancellation at antenna limiters was successfully applied in AUG using the 3-strap AUG antenna and extended to the 4-strap Alcator C-Mod field-aligned antenna. Multiple observations confirmed the reduction of the impact of ICRF on the SOL and on total impurity production when the ratio of the power of the central straps to the total antenna power is in the range 0.6<P$_{cen}$/P$_{total}$<0.8. Near-field calculations indicate that this fairly robust technique can be applied to the ITER ICRF antenna, enabling the mode of operation with reduced PWI. On the contrary, for the A2 antenna in JET-ILW the technique is hindered by RF sheaths excited at the antenna septum. Thus, in order to reduce the effect of ICRF power on PWI in a future fusion reactor, the antenna design has to be optimized along with design of plasmafacing components