Identifying Finite-Time Coherent Sets from Limited Quantities of Lagrangian Data

A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into pairs of coherent sets, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by posing an optimization problem, which once solved, yields a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. As a result, given a fixed amount of data our approach, which can use sets of globally supported basis functions, has the potential to more accurately approximate the desired functions than other functions tailored to use compactly supported indicator functions. This difference enables our approach to produce effective approximations of pairs of coherent sets in problems with relatively limited quantities of Lagrangian data, which is usually the case with real geophysical data. We apply this method to three examples of increasing complexity: the first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.Comment: 14 pages, 7 figure

A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. In this manuscript, we present a data driven method for approximating the leading eigenvalues, eigenfunctions, and modes of the Koopman operator. The method requires a data set of snapshot pairs and a dictionary of scalar observables, but does not require explicit governing equations or interaction with a "black box" integrator. We will show that this approach is, in effect, an extension of Dynamic Mode Decomposition (DMD), which has been used to approximate the Koopman eigenvalues and modes. Furthermore, if the data provided to the method are generated by a Markov process instead of a deterministic dynamical system, the algorithm approximates the eigenfunctions of the Kolmogorov backward equation, which could be considered as the "stochastic Koopman operator" [1]. Finally, four illustrative examples are presented: two that highlight the quantitative performance of the method when presented with either deterministic or stochastic data, and two that show potential applications of the Koopman eigenfunctions

Mining Frequent Graph Patterns with Differential Privacy

Discovering frequent graph patterns in a graph database offers valuable information in a variety of applications. However, if the graph dataset contains sensitive data of individuals such as mobile phone-call graphs and web-click graphs, releasing discovered frequent patterns may present a threat to the privacy of individuals. {\em Differential privacy} has recently emerged as the {\em de facto} standard for private data analysis due to its provable privacy guarantee. In this paper we propose the first differentially private algorithm for mining frequent graph patterns. We first show that previous techniques on differentially private discovery of frequent {\em itemsets} cannot apply in mining frequent graph patterns due to the inherent complexity of handling structural information in graphs. We then address this challenge by proposing a Markov Chain Monte Carlo (MCMC) sampling based algorithm. Unlike previous work on frequent itemset mining, our techniques do not rely on the output of a non-private mining algorithm. Instead, we observe that both frequent graph pattern mining and the guarantee of differential privacy can be unified into an MCMC sampling framework. In addition, we establish the privacy and utility guarantee of our algorithm and propose an efficient neighboring pattern counting technique as well. Experimental results show that the proposed algorithm is able to output frequent patterns with good precision

Radiotelemetry Of Heart Rates From Free-Ranging Gulls

A lightweight radiotelemetry system with a range of 80 km was used to monitor heart rate from free-ranging Herring Gulls on flights of up to 20 km. Heart rate varied from 130 beats/min in a resting bird to 625 beats/min for sustained flight. Soaring birds showed rates similar to those of birds sitting quietly on the ground. Simultaneous records of telemetered heart rate and intraspecific conflict on the nesting island revealed that cardiac acceleration preceded overt visual communication. Intensely aggressive behavior was accompanied by heart rates approaching those of sustained flight. Heart rate as a measure of metabolic cost indicates that the gull\u27s behavioral adaptations for long-distance flight, food location and intraspecific communication result in major energy savings

COMPTEL Observations of the Gamma-Ray Blazar PKS 1622-297

We report results of observations and analyses on the gamma-ray blazar PKS 1622-297, with emphasis on the COMPTEL data (0.75 - 30 MeV) collected between April 1991 and November 1997. PKS 1622-297 was detected as a source of gamma-rays by the EGRET experiment aboard CGRO in 1995 during a gamma-ray outburst at energies above 100 MeV lasting for five weeks. In this time period the blazar was significantly (~ 5.9 sigma) detected by COMPTEL at 10-30 MeV. At lower COMPTEL energies the detection is marginal, resulting in a hard MeV spectrum. The combined COMPTEL/EGRET energy spectrum shows a break at MeV energies. The broad-band spectrum (radio - gamma-rays) shows that the gamma-ray emission dominates the overall power output. On top of the 5-week gamma-ray outburst, EGRET detected a huge flare lasting for > 1 day. Enhanced MeV emission (10 - 30 MeV) is found near the time of this flare, suggesting a possible time delay with respect to the emission above 100 MeV. Outside the 5-week flaring period in 1995, we do not detect MeV emission from PKS 1622-297.Comment: 10 pages including 9 figures, accepted for publication in A&

Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition

Dynamic mode decomposition (DMD) provides a practical means of extracting insightful dynamical information from fluids datasets. Like any data processing technique, DMD's usefulness is limited by its ability to extract real and accurate dynamical features from noise-corrupted data. Here we show analytically that DMD is biased to sensor noise, and quantify how this bias depends on the size and noise level of the data. We present three modifications to DMD that can be used to remove this bias: (i) a direct correction of the identified bias using known noise properties, (ii) combining the results of performing DMD forwards and backwards in time, and (iii) a total least-squares-inspired algorithm. We discuss the relative merits of each algorithm, and demonstrate the performance of these modifications on a range of synthetic, numerical, and experimental datasets. We further compare our modified DMD algorithms with other variants proposed in recent literature

COMPTEL observations of the Virgo blazars 3C 273 and 3C 279

We report the main MeV properties (detections, light curves, spectra) of the Virgo blazars 3C 273 and 3C 279 which were derived from a consistent analysis of all COMPTEL Virgo observations between 1991 and 1997