The localization of single pulse in VLBI observation

In our previous work, we propose a cross spectrum based method to extract single pulse signals from RFI contaminated data, which is originated from geodetic VLBI postprocessing. This method fully utilizes fringe phase information of the cross spectrum and hence maximizes signal power, however the localization was not discussed in that work yet. As the continuation of that work, in this paper, we further study how to localize single pulses using astrometric solving method. Assuming that the burst is a point source, we derive the burst position by solving a set of linear equations given the relation between residual delay and offset to a priori position. We find that the single pulse localization results given by both astrometric solving and radio imaging are consistent within 3 sigma level. Therefore we claim that it is possible to derive the position of a single pulse with reasonable precision based on only 3 or even 2 baselines with 4 milliseconds integration. The combination of cross spectrum based detection and the localization proposed in this work then provide a thorough solution for searching single pulse in VLBI observation. According to our calculation, our pipeline gives comparable accuracy as radio imaging pipeline. Moreover, the computational cost of our pipeline is much smaller, which makes it more practical for FRB search in regular VLBI observation. The pipeline is now publicly available and we name it as "VOLKS", which is the acronym of "VLBI Observation for frb Localization Keen Searcher".Comment: 11 pages, 4 figures, 3 tables, accepted for publication in A

Pairs Trading: An Optimal Selling Rule with Constraints

The focus of this paper is on identifying the most effective selling strategy for pairs trading of stocks. In pairs trading, a long position is held in one stock while a short position is held in another. The goal is to determine the optimal time to sell the long position and repurchase the short position in order to close the pairs position. The paper presents an optimal pairs-trading selling rule with trading constraints. In particular, the underlying stock prices evolve according to a two dimensional geometric Brownian motion and the trading permission process is given in terms of a two-state {trading allowed, trading not allowed} Markov chain. It is shown that the optimal policy can be determined by a threshold curve which is obtained by solving the associated HJB equations (quasi-variational inequalities). A closed form solution is obtained. A verification theorem is provided. Numerical experiments are also reported to demonstrate the optimal policies and value functions