Bayesian changepoint analysis for atomic force microscopy and soft material indentation

Material indentation studies, in which a probe is brought into controlled physical contact with an experimental sample, have long been a primary means by which scientists characterize the mechanical properties of materials. More recently, the advent of atomic force microscopy, which operates on the same fundamental principle, has in turn revolutionized the nanoscale analysis of soft biomaterials such as cells and tissues. This paper addresses the inferential problems associated with material indentation and atomic force microscopy, through a framework for the changepoint analysis of pre- and post-contact data that is applicable to experiments across a variety of physical scales. A hierarchical Bayesian model is proposed to account for experimentally observed changepoint smoothness constraints and measurement error variability, with efficient Monte Carlo methods developed and employed to realize inference via posterior sampling for parameters such as Young's modulus, a key quantifier of material stiffness. These results are the first to provide the materials science community with rigorous inference procedures and uncertainty quantification, via optimized and fully automated high-throughput algorithms, implemented as the publicly available software package BayesCP. To demonstrate the consistent accuracy and wide applicability of this approach, results are shown for a variety of data sets from both macro- and micro-materials experiments--including silicone, neurons, and red blood cells--conducted by the authors and others.Comment: 20 pages, 6 figures; submitted for publicatio

Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH4_4, CO and evidence for C2_2H6_6 absorption

We present an analysis of the VIMS solar occultations dataset, which allows us to extract vertically resolved information on the characteristics of Titan's atmosphere between 100-700 km with a characteristic vertical resolution of 10 km. After a series of data treatment procedures, 4 occultations out of 10 are retained. This sample covers different seasons and latitudes of Titan. The transmittances show clearly the evolution of the haze and detect the detached layer at 310 km in Sept. 2011 at mid-northern latitudes. Through the inversion of the transmission spectra with a line-by-line radiative transfer code we retrieve the vertical distribution of CH$_4$ and CO mixing ratio. The two methane bands at 1.4 and 1.7 {\mu}m are always in good agreement and yield an average stratospheric abundance of $1.28\pm0.08$%. This is significantly less than the value of 1.48% obtained by the GCMS/Huygens instrument. The analysis of the residual spectra after the inversion shows that there are additional absorptions which affect a great part of the VIMS wavelength range. We attribute many of these additional bands to gaseous ethane, whose near-infrared spectrum is not well modeled yet. Ethane contributes significantly to the strong absorption between 3.2-3.5 {\mu}m that was previously attributed only to C-H stretching bands from aerosols. Ethane bands may affect the surface windows too, especially at 2.7 {\mu}m. Other residual bands are generated by stretching modes of C-H, C-C and C-N bonds. In addition to the C-H stretch from aliphatic hydrocarbons at 3.4 {\mu}m, we detect a strong and narrow absorption at 3.28 {\mu}m which we tentatively attribute to the presence of PAHs in the stratosphere. C-C and C-N stretching bands are possibly present between 4.3-4.5 {\mu}m. Finally, we obtain the CO mixing ratio between 70-170 km. The average result of $46\pm16$ ppm is in good agreement with previous studies.Comment: 51 pages, 28 figure

A range unit root test

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analyse time series with strong serial dependence, the focus being placed in the detection of eventual unit roots in an autorregresive model fitted to the series. In this paper we propose a completely different method to test for the type of long-wave patterns observed not only in unit root time series but also in series following more complex data generating mechanisms. To this end, our testing device analyses the trend exhibit by the data, without imposing any constraint on the generating mechanism. We call our device the Range Unit Root (RUR) Test since it is constructed from running ranges of the series. These statistics allow a more general characterization of a strong serial dependence in the mean behavior, thus endowing our test with a number of desirable properties, among which its error-model-free asymptotic distribution, the invariance to nonlinear monotonic transformations of the series and the robustness to the presence of level shifts and additive outliers. In addition, the RUR test outperforms the power of standard unit root tests on near-unit-root stationary time series and is asymptotically immune to noise

A RANGE UNIT ROOT TEST

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analyse time series with strong serial dependence, the focus being placed in the detection of eventual unit roots in an autorregresive model fitted to the series. In this paper we propose a completely different method to test for the type of“long-wave” patterns observed not only in unit root time series but also in series following more complex data generating mechanisms. To this end, our testing device analyses the trend exhibit by the data, without imposing any constraint on the generating mechanism. We call our device the Range Unit Root (RUR) Test since it is constructed from running ranges of the series. These statistics allow a more general characterization of a strong serial dependence in the mean behavior, thus endowing our test with a number of desirable properties, among which its error-model-free asymptotic distribution, the invariance to nonlinear monotonic transformations of the series and the robustness to the presence of level shifts and additive outliers. In addition, the RUR test outperforms the power of standard unit root tests on near-unit-root stationary time series and is asymptotically immune to noise.

On the time lags of the LIGO signals

To date, the LIGO collaboration has detected three gravitational wave (GW) events appearing in both its Hanford and Livingston detectors. In this article we reexamine the LIGO data with regard to correlations between the two detectors. With special focus on GW150914, we report correlations in the detector noise which, at the time of the event, happen to be maximized for the same time lag as that found for the event itself. Specifically, we analyze correlations in the calibration lines in the vicinity of 35\,Hz as well as the residual noise in the data after subtraction of the best-fit theoretical templates. The residual noise for the other two events, GW151226 and GW170104, exhibits similar behavior. A clear distinction between signal and noise therefore remains to be established in order to determine the contribution of gravitational waves to the detected signals.Comment: The body of the current version is essentially identical to the previous one submitted to arxiv and JCAP. In order to meet the various suggestions of the referees, we have included an extended and detailed Appendix. This Appendix also contains significant new results that provide additional support for our conclusions. This version of our manuscript has been accepted for publication by JCA