New Results on Quantum Property Testing

We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$. Here the probability \PP_f(j) of an outcome $j\in[m]$ is the fraction of its domain that $f$ maps to $j$. We give quantum algorithms for testing whether two such distributions are identical or $\epsilon$-far in $L_1$-norm. Recently, Bravyi, Hassidim, and Harrow \cite{BHH10} showed that if \PP_f and \PP_g are both unknown (i.e., given by oracles $f$ and $g$), then this testing can be done in roughly $\sqrt{m}$ quantum queries to the functions. We consider the case where the second distribution is known, and show that testing can be done with roughly $m^{1/3}$ quantum queries, which we prove to be essentially optimal. In contrast, it is known that classical testing algorithms need about $m^{2/3}$ queries in the unknown-unknown case and about $\sqrt{m}$ queries in the known-unknown case. Based on this result, we also reduce the query complexity of graph isomorphism testers with quantum oracle access. While those examples provide polynomial quantum speed-ups, our third example gives a much larger improvement (constant quantum queries vs polynomial classical queries) for the problem of testing periodicity, based on Shor's algorithm and a modification of a classical lower bound by Lachish and Newman \cite{lachish&newman:periodicity}. This provides an alternative to a recent constant-vs-polynomial speed-up due to Aaronson \cite{aaronson:bqpph}.Comment: 2nd version: updated some references, in particular to Aaronson's Fourier checking proble

Peridocity, Change Detection and Prediction in Microarrays

Three topics in the analysis of microarray genomic data are discussed and improved statistical methods are developed in each case. A statistical test with higher power is developed for detecting periodicity in microarray time series data. Periodicity in short series, with non-Fourier frequencies, is detected through a Pearson curve calibrated to the null distribution obtained by computer simulation. Unlike other traditional methods, this approach is applicable even in the presence of missing values or unequal time intervals. The usefulness of the new method is demonstrated on simulated series as well as actual microarray time series. The second topic develops a new method for detection of changes in DNA or gene copy number. Regions for DNA copy number aberrations in chromosomal material are detected using maximum overlapping discrete wavelet transform (MODWT). It is shown how repeated application of MODWT to a series can be used to confirm the presence of change points. Application to simulated as well as array CGH (Comparative Genomic Hybridization) data confirms the excellent performance of this method. In the third topic, it is shown that an improved class predictor for tissue samples in microarray experiments is developed by incorporating nearest neighbour covariates (NNC). It is demonstrated that this method reduces the mis-classification errors in both simulated and actual microarray data

The Political Economy of Car Sales in Athens, Greece

Greece is widely hailed to be among the most prominent victims of the recent global recession since the downfall of its economic activity, caused by local and international factors, has reached levels that are directly comparable to the Great Recession. In this context, we attempt to shed light on a prominent victim of this situation, i.e. the car sales industry in Athens, Greece over the time period 2000-2012 using monthly data. To this end, an appropriate econometric model, that incorporates a large number of potential determinants which account for the relevant factors, is used and several econometric techniques are employed such as stationarity testing; filtering; white noise testing; periodicity analysis; correlation analysis and causality testing. Our empirical investigation determines the macroeconomic and other variables that act either as pro- or countercyclical factors in business cycles fluctuations of the car sales industry in Athens

The Political Economy of Car Sales in Athens, Greece

Greece is widely hailed to be among the most prominent victims of the recent global recession since the downfall of its economic activity, caused by local and international factors, has reached levels that are directly comparable to the Great Recession. In this context, we attempt to shed light on a prominent victim of this situation, i.e. the car sales industry in Athens, Greece over the time period 2000-2012 using monthly data. To this end, an appropriate econometric model, that incorporates a large number of potential determinants which account for the relevant factors, is used and several econometric techniques are employed such as stationarity testing; filtering; white noise testing; periodicity analysis; correlation analysis and causality testing. Our empirical investigation determines the macroeconomic and other variables that act either as pro- or countercyclical factors in business cycles fluctuations of the car sales industry in Athens

Hereditary properties of permutations are strongly testable

We show that for every hereditary permutation property and every ∊0 > 0, there exists an integer M such that if a permutation π is ∊o-far from in the Kendall's tau distance, then a random subpermutation of π of order M has the property P with probability at most ∊0. This settles an open problem whether hereditary permutation properties are strongly testable, i.e., testable with respect to the Kendall's tau distance, which is considered to be the edit distance for permutations. Our method also yields a proof of a conjecture of Hoppen, Kohayakawa, Moreira and Sampaio on the relation of the rectangular distance and the Kendall's tau distance of a permutation from a hereditary property

The effects of seasonally adjusting a periodic autoregressive process

Traditional methods for the analysis of seasonal and nonstationary time series assume that seasonality and a stochastic trend can be separated in some way. However, several macroeconomic time series display patterns which i