Robust And Optimal Opportunistic Scheduling For Downlink 2-Flow Network Coding With Varying Channel Quality and Rate Adaptation

This paper considers the downlink traffic from a base station to two different clients. When assuming infinite backlog, it is known that inter-session network coding (INC) can significantly increase the throughput of each flow. However, the corresponding scheduling solution (when assuming dynamic arrivals instead and requiring bounded delay) is still nascent. For the 2-flow downlink scenario, we propose the first opportunistic INC + scheduling solution that is provably optimal for time-varying channels, i.e., the corresponding stability region matches the optimal Shannon capacity. Specifically, we first introduce a new binary INC operation, which is distinctly different from the traditional wisdom of XORing two overheard packets. We then develop a queue-length-based scheduling scheme, which, with the help of the new INC operation, can robustly and optimally adapt to time-varying channel quality. We then show that the proposed algorithm can be easily extended for rate adaptation and it again robustly achieves the optimal throughput. A byproduct of our results is a scheduling scheme for stochastic processing networks (SPNs) with random departure, which relaxes the assumption of deterministic departure in the existing results. The new SPN scheduler could thus further broaden the applications of SPN scheduling to other real-world scenarios

Dynamics of Order Parameter in Photoexcited Peierls Chain

The photoexcited dynamics of order parameter in Peierls chain is investigated by using a microscopic quantum theory in the limit where the hot electrons may establish themselves into a quasi-equilibrium state described by an effective temperature. The optical phonon mode responsible for the Peierls instability is coupled to the electron subsystem, and its dynamic equation is derived in terms of the density matrix technique. Recovery dynamics of the order parameter is obtained, which reveals a number of interesting features including the change of oscillation frequency and amplitude at phase transition temperature and the photo-induced switching of order parameter.Comment: 5 pages, 3 figure

Essays on Information Asymmetry and Price Impact in Market Microstructure

Essays on Information Asymmetry and Price Impact in Market Microstructure This thesis comprises of topics on information asymmetry and price impact in market microstructure. Our first paper introduces a new estimation method for the probability of informed trading - PIN (Easley, Kiefer, O’Hara and Paperman, 1996; Easley, Hvidkjaer and O’Hara, 2002; Easley, Hvidkjaer and O’Hara, 2010; Lin and Ke, 2011; and Yan and Zhang, 2012). PIN is an information asymmetry measure in market microstructure, and estimates the percentage of informed trading in the market. It is based on a structural model assuming Poisson arrival rates for informed and uninformed traders and daily Bernoulli probabilities on the occurrence of news, and type of news (e.g., good or bad news). We create a new method for estimating PIN using a hierarchical agglomerative clustering algorithm which we call Cluster PIN (CPIN). We show that it is superior to the most recent methods (Easley, Hvidkjaer and O’Hara, 2010; Lin and Ke, 2011; Yan and Zhang, 2012) in terms of accuracy, robustness and speed (approximately 300 times faster) and bypasses some of the problems faced with maximum likelihood estimation, such as the floating point exception. We show that CPIN is also able to explicitly classify trading days into ’good’, ’bad’ and ’no news’ days which is not possible with existing approaches. This allows us to check the reliability of CPIN via an ex-post analysis of trading statistics (buy/sell volume, returns, volatility and spreads) under these three classification groups. This thesis also examines price impact, which is used to measure the information content of trades. Hasbrouck (1991) states that trades convey information and the magnitude of price impact for a given trade size is in proportion to the level of informed traders in the population. The price impact of a trade is estimated as cumulative quote revisions (or mid-price changes) due to incoming trades, i.e., signed log volume (Hasbrouck, 1991; Dufour and Engle, 2000). Hasbrouck (1991) use a bivariate VAR to model the interactions between quote revisions and trades, and show that lagged trades can impact quote revisions. Then the cumulative impulse response function (CIRF) of the VAR model is used to estimate the price impact of trades. Dufour and Engle (2000) show that both incoming trade duration and size can influence price impact as they reflect the level of informativeness of the trades. Our second paper examines the drivers of quote revisions. We extend upon Dufour and Engle (2000) by also considering quoted spreads and depth as variables in the VAR model. From this, we show that quote revisions are not only affected by incoming trades, but also driven by order book illiquidity factors, such as quoted spreads and depth. Given the large number of parameters in our VAR model, we use adaptive lasso (Tibshirani, 1996; Zou, 2006; Hsu, Hung and Chang, 2008; and Ren and Zhang, 2010), to conduct robust variable selection and parameter estimation simultaneously; and show order book variables remain significant after variable selection. We construct time-varying price impact by estimating our VAR model at weekly intervals from January 2007 to December 2012. To the best of our knowledge, our research is the first to analyze time-varying price impact. Our third paper examines the relationship between time-varying price impact and volatility. Our fourth paper studies the relationship between time-varying price impact and volume synchronized probability of informed trading - VPIN (see Easley, Lopez de Prado and O’Hara, 2012). Both measures relate to information asymmetry and risk aversion costs. However contrary to expectations, we find that there is a negative relationship between price impact and VPIN. We provide a heterogeneous rational expectation equilibrium model to explain our empirical findings. We show the seemingly counterintuitive result can be explained if one allowed for heterogeneity of beliefs amongst informed traders in processing news events

Condensate wave function and elementary excitations of bosonic polar molecules: beyond the first Born approximation

We investigate the condensate wave function and elementary excitations of strongly interacting bosonic polar molecules in a harmonic trap, treating the scattering amplitude beyond the standard first Born approximation (FBA). By using an appropriate trial wave function in the variational method, effects of the leading order correction beyond the FBA have been investigated and shown to be significantly enhanced when the system is close to the phase boundary of collapse. How such leading order effect of going beyond the FBA can be observed in a realistic experiment is also discussed.Comment: 7 pages, 4 figure