Numerical Distribution Functions for Seasonal Unit Root Tests

When working with time series data observed at intervals smaller than a year, it is often necessary to test for the presence of seasonal unit roots. One of the most widely used methods for testing seasonal unit roots is that of HEGY, which provides test statistics with non-standard distributions. This paper describes a generalisation of this method for any periodicity and uses a response surface regressions approach to calculate the critical values and P values of the HEGY statistics whatever the periodicity and sample size of the data. The algorithms are prepared with the Gretl open source econometrics package and some new tables of critical values for daily, hourly and half-hourly data are presented.seasonality, unit roots, surface response analysis

Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach

We address in this article, how to calculate the restoring characteristic and the excitation of a nonlinear forced oscillating system. Under the assumption that the forced nonlinear oscillator has a periodic solution with period, we constructed a system of linear equations by introducing time-dependent multipliers. The periodicity assumption helps simplify the system of linear equations. The stability and uniqueness are also presented for the inverse problem. Numerical testing is conducted to show the effectiveness of our presented methodology.Peer ReviewedPostprint (author's final draft

Skylab SO71/SO72 circadian periodicity experiment

The circadian rhythm hardware activities from 1965 through 1973 are considered. A brief history of the programs leading to the development of the combined Skylab SO71/SO72 Circadian Periodicity Experiment (CPE) is given. SO71 is the Skylab experiment number designating the pocket mouse circadian experiment, and SO72 designates the vinegar gnat circadian experiment. Final design modifications and checkout of the CPE, integration testing with the Apollo service module CSM 117 and the launch preparation and support tasks at Kennedy Space Center are reported

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

Periodic Radio Variability in NRAO 530: Phase Dispersion Minimization Analysis

In this paper, a periodicity analysis of the radio light curves of the blazar NRAO 530 at 14.5, 8.0, and 4.8 GHz is presented employing an improved Phase Dispersion Minimization (PDM) technique. The result, which shows two persistent periodic components of $\sim 6$ and $\sim 10$ years at all three frequencies, is consistent with the results obtained with the Lomb-Scargle periodogram and weighted wavelet Z-transform algorithms. The reliability of the derived periodicities is confirmed by the Monte Carlo numerical simulations which show a high statistical confidence. (Quasi-)Periodic fluctuations of the radio luminosity of NRAO 530 might be associated with the oscillations of the accretion disk triggered by hydrodynamic instabilities of the accreted flow. \keywords{methods: statistical -- galaxies: active -- galaxies: quasar: individual: NRAO 530}Comment: 8 pages, 5 figures, accepted by RA

The evidence for and against astronomical impacts on climate change and mass extinctions: A review

Numerous studies over the past 30 years have suggested there is a causal connection between the motion of the Sun through the Galaxy and terrestrial mass extinctions or climate change. Proposed mechanisms include comet impacts (via perturbation of the Oort cloud), cosmic rays and supernovae, the effects of which are modulated by the passage of the Sun through the Galactic midplane or spiral arms. Supposed periodicities in the fossil record, impact cratering dates or climate proxies over the Phanerozoic (past 545 Myr) are frequently cited as evidence in support of these hypotheses. This remains a controversial subject, with many refutations and replies having been published. Here I review both the mechanisms and the evidence for and against the relevance of astronomical phenomena to climate change and evolution. This necessarily includes a critical assessment of time series analysis techniques and hypothesis testing. Some of the studies have suffered from flaws in methodology, in particular drawing incorrect conclusions based on ruling out a null hypothesis. I conclude that there is little evidence for intrinsic periodicities in biodiversity, impact cratering or climate on timescales of tens to hundreds of Myr. Furthermore, Galactic midplane and spiral arm crossings seem to have little or no impact on biological or climate variation above background level. (truncated)Comment: 51 pages, 7 figures, 140 references. To appear in the International Journal of Astrobiology. For hyperref version with full resolution figures see http://www.mpia-hd.mpg.de/homes/calj/astimpact_ija.pd