Phase Retrieval by Linear Algebra

The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement matrices, a non-asymptotic error bound is derived, yielding an asymptotic regime of accurate approximation comparable to that for the spectral vector method

Forecasting Value-at-Risk with Time-Varying Variance, Skewness and Kurtosis in an Exponential Weighted Moving Average Framework

This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over time using a modified form of the Gram-Charlier density in which skewness and kurtosis appear directly in the functional form of this density. In this setting VaR can be described as a function of the time-varying higher moments by applying the Cornish-Fisher expansion series of the first four moments. An evaluation of the predictive performance of the proposed model in the estimation of 1-day and 10-day VaR forecasts is performed in comparison with the historical simulation, filtered historical simulation and GARCH model. The adequacy of the VaR forecasts is evaluated under the unconditional, independence and conditional likelihood ratio tests as well as Basel II regulatory tests. The results presented have significant implications for risk management, trading and hedging activities as well as in the pricing of equity derivatives

The Impact of User Effects on the Performance of Dual Receive Antenna Diversity Systems in Flat Rayleigh Fading Channels

In this paper we study the impact of user effects on the performance of receive antenna diversity systems in flat Rayleigh fading channels. Three diversity combining techniques are compared: maximal ratio combining (MRC), equal gain combining (EGC), and selection combining (SC). User effects are considered in two scenarios: 1) body loss (the reduction of effective antenna gain due to user effects) on a single antenna, and 2) equal body loss on both antennas. The system performance is assessed in terms of mean SNR, link reliability, bit error rate of BPSK, diversity order and ergodic capacity. Our results show that body loss on a single antenna has limited (bounded) impact on system performance. In comparison, body loss on both antennas has unlimited (unbounded) impact and can severely degrade system performance. Our results also show that with increasing body loss on a single antenna the performance of EGC drops faster than that of MRC and SC. When body loss on a single antenna is larger than a certain level, EGC is not a “sub-optimal” method anymore and has worse performance than SC

TT-adic exponential sums of polynomials in one variable

The $T$-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the T-adic exponential sum. This bound gives lower bounds for the Newton polygon of the $L$-function of exponential sums of $p$-power order

Virtual Compton Scattering from the Proton and the Properties of Nucleon Excited States

We calculate the $N^*$ contributions to the generalized polarizabilities of the proton in virtual Compton scattering. The following nucleon excitations are included: $N^*(1535)$, $N^*(1650)$, $N^*(1520)$, $N^*(1700)$, $\Delta(1232)$, $\Delta^*(1620)$ and $\Delta^*(1700)$. The relationship between nucleon structure parameters, $N^*$ properties and the generalized polarizabilities of the proton is illustrated.Comment: 13 pages of text (Latex) plus 4 figures (as uuencoded Z-compressed .tar file created by csh script uufiles

The robust selection of predictive genes via a simple classifier

Identifying genes that direct the mechanism of a disease from expression data is extremely useful in understanding how that mechanism works. This in turn may lead to better diagnoses and potentially can lead to a cure for that disease. This task becomes extremely challenging when the data are characterised by only a small number of samples and a high number of dimensions, as it is often the case with gene expression data. Motivated by this challenge, we present a general framework that focuses on simplicity and data perturbation. These are the keys for the robust identification of the most predictive features in such data. Within this framework, we propose a simple selective na¨ıve Bayes classifier discovered using a global search technique, and combine it with data perturbation to increase its robustness to small sample sizes. An extensive validation of the method was carried out using two applied datasets from the field of microarrays and a simulated dataset, all confounded by small sample sizes and high dimensionality. The method has been shown capable of identifying genes previously confirmed or associated with prostate cancer and viral infections