Cluster-based network modeling: From snapshots to complex dynamical systems

We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM describes short- and long-term behavior and is fully automatable, as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict, and control complex systems in all scientific fields

Metric for attractor overlap

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised comparison of flow data sets. The starting point is two or more attractors, i.e., ensembles of states representing different operating conditions. The proposed metric generalizes the standard Hilbert-space distance between two snapshots to snapshot ensembles of two attractors. A reduced-order analysis for big data and many attractors is enabled by coarse-graining the snapshots into representative clusters with corresponding centroids and population probabilities. For a large number of attractors, MAO is augmented by proximity maps for the snapshots, the centroids, and the attractors, giving scientifically interpretable visual access to the closeness of the states. The coherent structures belonging to the overlap and disjoint states between these attractors are distilled by few representative centroids. We employ MAO for two quite different actuated flow configurations: (1) a two-dimensional wake of the fluidic pinball with vortices in a narrow frequency range and (2) three-dimensional wall turbulence with broadband frequency spectrum manipulated by spanwise traveling transversal surface waves. MAO compares and classifies these actuated flows in agreement with physical intuition. For instance, the first feature coordinate of the attractor proximity map correlates with drag for the fluidic pinball and for the turbulent boundary layer. MAO has a large spectrum of potential applications ranging from a quantitative comparison between numerical simulations and experimental particle-image velocimetry data to the analysis of simulations representing a myriad of different operating conditions.Comment: 33 pages, 20 figure

xROM: A Toolkit for Reduced-Order Modeling of Fluid Flows

This book initiates the new Series `Machine Learning Tools in Fluid Mechanics' published by the Technische Universität Braunschweig. The series focuses on machine learning tools for fluid mechanics tasks, like analysis, dynamic modeling, response modeling, control and closures. The tools comprise documentations of publicly available software packages, of good practices and of application studies. Our book introduces the software platform xROM, which is a freely available package for spectral analysis and reduced-order modeling. Initially, xROM was developed as a tool to quickly derive dynamic POD models from snapshot data and Galerkin projection using the Navier-Stokes equations. This purpose has since expanded, and xROM has become a platform that allows easy modular expansions and collaborations with partners worldwide. In this book, however, we focus on POD-based Galerkin modeling for reasons of simplicity

Strong HI Lyman-α\alpha variations from the 11 Gyr-old host star Kepler-444: a planetary origin ?

Kepler-444 provides a unique opportunity to probe the atmospheric composition and evolution of a compact system of exoplanets smaller than the Earth. Five planets transit this bright K star at close orbital distances, but they are too small for their putative lower atmosphere to be probed at optical/infrared wavelengths. We used the Space Telescope Imaging Spectrograph instrument onboard the Hubble Space Telescope to search for the signature of the planet's upper atmospheres at six independent epochs in the Ly-$\alpha$ line. We detect significant flux variations during the transits of both Kepler-444e and f (~20%), and also at a time when none of the known planets was transiting (~40%). Variability in the transition region and corona of the host star might be the source of these variations. Yet, their amplitude over short time scales (~2-3 hours) is surprisingly strong for this old (11.2+-1.0Gyr) and apparently quiet main-sequence star. Alternatively, we show that the in-transits variations could be explained by absorption from neutral hydrogen exospheres trailing the two outer planets (Kepler-444e and f). They would have to contain substantial amounts of water to replenish such hydrogen exospheres, which would reveal them as the first confirmed ocean-planets. The out-of-transit variations, however, would require the presence of a yet-undetected Kepler-444g at larger orbital distance, casting doubt on the planetary origin scenario. Using HARPS-N observations in the sodium doublet, we derived the properties of two Interstellar Medium clouds along the line-of-sight toward Kepler-444. This allowed us to reconstruct the stellar Ly-$\alpha$ line profile and to estimate the XUV irradiation from the star, which would still allow for a moderate mass loss from the outer planets after 11.2Gyr. Follow-up of the system at XUV wavelengths will be required to assess this tantalizing possibility.Comment: Accepted for publication in A&A Name of the system added to the title in most recent versio

Investigating Cepheid ℓ\ell Carinae's Cycle-to-cycle Variations via Contemporaneous Velocimetry and Interferometry

Baade-Wesselink-type (BW) techniques enable geometric distance measurements of Cepheid variable stars in the Galaxy and the Magellanic clouds. The leading uncertainties involved concern projection factors required to translate observed radial velocities (RVs) to pulsational velocities and recently discovered modulated variability. We carried out an unprecedented observational campaign involving long-baseline interferometry (VLTI/PIONIER) and spectroscopy (Euler/Coralie) to search for modulated variability in the long-period (P $\sim$ 35.5 d) Cepheid Carinae. We determine highly precise angular diameters from squared visibilities and investigate possible differences between two consecutive maximal diameters, $\Delta_{\rm{max}} \Theta$. We characterize the modulated variability along the line-of-sight using 360 high-precision RVs. Here we report tentative evidence for modulated angular variability and confirm cycle-to-cycle differences of $\ell$ Carinae's RV variability. Two successive maxima yield $\Delta_{\rm{max}} \Theta$ = 13.1 $\pm$ 0.7 (stat.) {\mu}as for uniform disk models and 22.5 $\pm$ 1.4 (stat.) {\mu}as (4% of the total angular variation) for limb-darkened models. By comparing new RVs with 2014 RVs we show modulation to vary in strength. Barring confirmation, our results suggest the optical continuum (traced by interferometry) to be differently affected by modulation than gas motions (traced by spectroscopy). This implies a previously unknown time-dependence of projection factors, which can vary by 5% between consecutive cycles of expansion and contraction. Additional interferometric data are required to confirm modulated angular diameter variations. By understanding the origin of modulated variability and monitoring its long-term behavior, we aim to improve the accuracy of BW distances and further the understanding of stellar pulsations.Comment: Accepted for publication in MNRAS. 19 pages, 13 figures, 10 table

Critical study of the distribution of rotational velocities of Be stars; II: Differential rotation and some hidden effects interfering with the interpretation of the Vsin i parameter

We assume that stars may undergo surface differential rotation to study its impact on the interpretation of $V\!\sin i$ and on the observed distribution $\Phi(u)$ of ratios of true rotational velocities u=V/V_\rm c (V_\rm c is the equatorial critical velocity). We discuss some phenomena affecting the formation of spectral lines and their broadening, which can obliterate the information carried by $V\!\sin i$ concerning the actual stellar rotation. We studied the line broadening produced by several differential rotational laws, but adopted Maunder's expression $\Omega(\theta)=\Omega_o(1+\alpha\cos^2\theta)$ as an attempt to account for all of these laws with the lowest possible number of free parameters. We studied the effect of the differential rotation parameter $\alpha$ on the measured $V\!\sin i$ parameter and on the distribution $\Phi(u)$ of ratios u=V/V_\rm c. We conclude that the inferred $V\!\sin i$ is smaller than implied by the actual equatorial linear rotation velocity V_\rm eq if the stars rotate with $\alpha0$. For a given $|\alpha|$ the deviations of $V\!\sin i$ are larger when $\alpha<0$. If the studied Be stars have on average $\alpha<0$, the number of rotators with V_\rm eq\simeq0.9V_\rm c is larger than expected from the observed distribution $\Phi(u)$; if these stars have on average $\alpha>0$, this number is lower than expected. We discuss seven phenomena that contribute either to narrow or broaden spectral lines, which blur the information on the rotation carried by $V\!\sin i$ and, in particular, to decide whether the Be phenomenon mostly rely on the critical rotation. We show that two-dimensional radiation transfer calculations are needed in rapid rotators to diagnose the stellar rotation more reliably.Comment: To appear in A&

Prognostic impact of lymphadenectomy in clinically early stage malignant germ cell tumour of the ovary

Background:The aim of this study was to determine the impact of lymphadenectomy and nodal metastasis on survival in clinical stage I malignant ovarian germ cell tumour (OGCT).Methods:Data were obtained from the National Cancer Institute registry from 1988 to 2006. Analyses were performed using Student's t-test, Kaplan–Meier and Cox proportional hazard methods.Results:In all, 1083 patients with OGCT who have undergone surgical treatment and deemed at time of the surgery to have disease clinically confined to the ovary were included 590 (54.48%) had no lymphadenectomy (LND−1) and 493 (45.52%) had lymphadenectomy. Of the 493 patients who had lymphadenectomy, 441 (89.5%) were FIGO surgical stage I (LND+1) and 52 (10.5%) were upstaged to FIGO stage IIIC due to nodal metastasis (LND+3C). The 5-year survival was 96.9% for LND−1, 97.7% for LND+1 and 93.4% for LND+3C (P=0.5). On multivariate analysis, lymphadenectomy was not an independent predictor of survival when controlling for age, histology and race (HR: 1.26, 95% CI: 0.62–2.58, P=0.5). Moreover, the presence of lymph node metastasis had no significant effect on survival (HR: 2.7, 95% CI: 0.67–10.96, P=0.16).Conclusion:Neither lymphadenectomy nor lymph node metastasis was an independent predictor of survival in patients with OGCT confined to the ovary. This probably reflects the highly chemosensitive nature of these tumours

Respondent-Driven Sampling in a Study of Drug Users in New York City: Notes from the Field

Beth Israel Medical Center (BIMC), in collaboration with the Centers for Disease Control (CDC) and the New York State Department of Health (NYSDOH), used respondent-driven sampling (RDS) in a study of HIV seroprevalence among drug users in New York City in 2004. We report here on operational issues with RDS including recruitment, coupon distribution, storefront operations, police and community relations, and the overall lessons we learned. Project staff recruited eight seeds from a syringe exchange in Lower Manhattan to serve as the initial study participants. Upon completion of the interview that lasted approximately 1 h and a blood draw, each seed was given three coupons to recruit three drug users into the study. Each of the subsequent eligible participants was also given three coupons to recruit three of their drug-using acquaintances. Eligible participants had to have: injected, smoked or snorted an illicit drug in the last 6 months (other than marijuana), aged 18 or older, adequate English language knowledge to permit informed consent and complete questionnaire. From April to July 2004, 618 drug users were interviewed, including 263 (43%) current injectors, 119 (19%) former injectors, and 236 (38%) never injectors. Four hundred sixty nine (76%) participants were men, 147 (24%) were women, and two (<1%) were transgender. By race/ethnicity, 285 (46%) were black, 218 (35%) Hispanic, 88 (14%) white, 23 (4%) mixed/not specified, and four (<1%) native American. Interviews were initially done on a drop-in basis but this system changed to appointments 1 month into the study due to the large volume of subjects coming in for interviews. Data collection was originally proposed to last for 1 year with a target recruitment of 500 drug users. Utilizing RDS, we were able to recruit and interview 118 more drug users than originally proposed in one quarter of the time. RDS was efficient with respect to time and economics (we did not have to hire an outreach worker) and effective in recruiting a diverse sample of drug users