On the importance of nonlinear modeling in computer performance prediction

Computers are nonlinear dynamical systems that exhibit complex and sometimes even chaotic behavior. The models used in the computer systems community, however, are linear. This paper is an exploration of that disconnect: when linear models are adequate for predicting computer performance and when they are not. Specifically, we build linear and nonlinear models of the processor load of an Intel i7-based computer as it executes a range of different programs. We then use those models to predict the processor loads forward in time and compare those forecasts to the true continuations of the time seriesComment: Appeared in "Proceedings of the 12th International Symposium on Intelligent Data Analysis

Spatially resolved X-ray spectroscopy and modeling of the nonthermal emission of the PWN in G0.9+0.1

We performed a spatially resolved spectral X-ray study of the pulsar wind nebula (PWN) in the supernova remnant G0.9+0.1. Furthermore we modeled its nonthermal emission in the X-ray and very high energy (VHE, E > 100 GeV) gamma-ray regime. Using Chandra ACIS-S3 data, we investigated the east-west dependence of the spectral properties of G0.9+0.1 by calculating hardness ratios. We analyzed the EPIC-MOS and EPIC-pn data of two on-axis observations of the XMM-Newton telescope and extracted spectra of four annulus-shaped regions, centered on the region of brightest emission of the source. A radially symmetric leptonic model was applied in order to reproduce the observed X-ray emission of the inner part of the PWN. Using the optimized model parameter values obtained from the X-ray analysis, we then compared the modeled inverse Compton (IC) radiation with the published H.E.S.S. gamma-ray data. The spectral index within the four annuli increases with growing distance to the pulsar, whereas the surface brightness drops. With the adopted model we are able to reproduce the characteristics of the X-ray spectra. The model results for the VHE gamma radiation, however, strongly deviate from the H.E.S.S. data.Comment: 8 pages, 7 figures, accepted for publication in Astronomy & Astrophysic

Nonlinear dynamics of giant resonances in atomic nuclei

The dynamics of monopole giant resonances in nuclei is analyzed in the time-dependent relativistic mean-field model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the time-series of dynamical variables that characterize the proton and neutron density distributions. The analysis of the resulting recurrence plots and correlation dimensions indicate regular motion for the isoscalar mode, and chaotic dynamics for the isovector oscillations. Information-theoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum systems that have spatial as well as temporal structure.Comment: 24 pages, RevTeX, 15 PS figures, submitted Phys. Rev.

Spatially resolved XMM-Newton analysis and a model of the nonthermal emission of MSH 15-52

We present an X-ray analysis and a model of the nonthermal emission of the pulsar wind nebula (PWN) MSH15-52. We analyzed XMM-Newton data to obtain the spatially resolved spectral parameters around the pulsar PSRB1509-58. A steepening of the fitted power-law spectra and decrease in the surface brightness is observed with increasing distance from the pulsar. In the second part of this paper, we introduce a model for the nonthermal emission, based on assuming the ideal magnetohydrodynamic limit. This model is used to constrain the parameters of the termination shock and the bulk velocity of the leptons in the PWN. Our model is able to reproduce the spatial variation of the X-ray spectra. The parameter ranges that we found agree well with the parameter estimates found by other authors with different approaches. In the last part of this paper, we calculate the inverse Compton emission from our model and compare it to the emission detected with the H.E.S.S. telescope system. Our model is able to reproduce the flux level observed with H.E.S.S., but not the spectral shape of the observed TeV {\gamma}-ray emission.Comment: Accepted for publication in A&A, 9 pages, 15 figure

Estimating good discrete partitions from observed data: symbolic false nearest neighbors

A symbolic analysis of observed time series data requires making a discrete partition of a continuous state space containing observations of the dynamics. A particular kind of partition, called ``generating'', preserves all dynamical information of a deterministic map in the symbolic representation, but such partitions are not obvious beyond one dimension, and existing methods to find them require significant knowledge of the dynamical evolution operator or the spectrum of unstable periodic orbits. We introduce a statistic and algorithm to refine empirical partitions for symbolic state reconstruction. This method optimizes an essential property of a generating partition: avoiding topological degeneracies. It requires only the observed time series and is sensible even in the presence of noise when no truly generating partition is possible. Because of its resemblance to a geometrical statistic frequently used for reconstructing valid time-delay embeddings, we call the algorithm ``symbolic false nearest neighbors''

A Robust Method for Detecting Interdependences: Application to Intracranially Recorded EEG

We present a measure for characterizing statistical relationships between two time sequences. In contrast to commonly used measures like cross-correlations, coherence and mutual information, the proposed measure is non-symmetric and provides information about the direction of interdependence. It is closely related to recent attempts to detect generalized synchronization. However, we do not assume a strict functional relationship between the two time sequences and try to define the measure so as to be robust against noise, and to detect also weak interdependences. We apply our measure to intracranially recorded electroencephalograms of patients suffering from severe epilepsies.Comment: 29 pages, 5 figures, paper accepted for publication in Physica

Computational Topology Techniques for Characterizing Time-Series Data

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and holes - could be useful for real-world data, TDA lets us compare different systems, and even do membership testing or change-point detection. However, TDA is computationally expensive and involves a number of free parameters. This complexity can be obviated by coarse-graining, using a construct called the witness complex. The parametric dependence gives rise to the concept of persistent homology: how shape changes with scale. Its results allow us to distinguish time-series data from different systems - e.g., the same note played on different musical instruments.Comment: 12 pages, 6 Figures, 1 Table, The Sixteenth International Symposium on Intelligent Data Analysis (IDA 2017

The Vela Pulsar and its Synchrotron Nebula

(Abridged) We present high-resolution Chandra X-ray observations of PSR B0833-45, the 89 ms pulsar associated with the Vela supernova remnant. We have acquired two observations separated by one month to search for changes in the pulsar and its environment following an extreme glitch in its rotation frequency. We find a well-resolved nebula with a toroidal morphology remarkably similar to that observed in the Crab Nebula, along with an axial Crab-like jet. Between the two observations the flux from the pulsar is found to be steady to within 0.75%; the 3 sigma limit on the fractional increase in the pulsar's X-ray flux is < ~10^-5 of the inferred glitch energy. We use this limit to constrain parameters of glitch models and neutron star structure. We do find a significant increase in the flux of the nebula's outer arc; if associated with the glitch, the inferred propagation velocity is > 0.7c, similar to that seen in the brightening of the Crab Nebula wisps. We propose an explanation for the X-ray structure of the Vela synchrotron nebula based on a model originally developed for the Crab Nebula. In a departure from the Crab model, the magnetization parameter "sigma" of the Vela pulsar wind is allowed to be of order unity; this is consistent with the simplest MHD transport of magnetic field from the pulsar to the nebula, where B < 4 X 10^-4 G. We review effects that may enhance the probability of alignment between the spin axis and space velocity of a pulsar, and speculate that short-period, slowly moving pulsars are just the ones best-suited to producing synchrotron nebulae with such aligned structures.Comment: 16 pages with 8 figures, uses LaTex, emulateapj.sty. Refereed version. To appear in The Astrophysical Journa

Modulation of NTC frequencies by Pc5 ULF pulsations : experimental test of the generation mechanism and magnetoseismology of the emitting surface

Nonthermal continuum (NTC) radiation is believed to be emitted by the conversion of an electrostatic wave into an electromagnetic one, which takes place at the Earth's magnetic equator. It is generally accepted that the frequency of the electrostatic wave at the source meets a local characteristic frequency placed in between two multiples of the electron cyclotron frequency, fce, which results in emission of a narrow band frequency element. In an event on 14 August 2003, we compare oscillations of the central frequency of distinct NTC frequency elements observed from Cluster orbiting near perigee, with simultaneous Pc5 Ultra Low Frequency (ULF) pulsations in the magnetic field observed from the same platform. The latter magnetic perturbations are interpreted as magnetohydrodynamic poloidal waves, where fundamental and second harmonic modes coexist. The NTC oscillation and the fundamental wave have similar periods, but are phase shifted by a quarter of period. From the correlation between both signals, and the proximity of the NTC source (localized via triangulation) with Cluster, we infer that the poloidal perturbations are spatially uniform between the source and the satellites. From the phase shift between signals, we conclude that the electrostatic wave which converts into NTC is mainly governed by the plasma density, affected by movements of the magnetic field lines. Furthermore, we demonstrate that the observations can be used to perform a magnetoseismology of the emitting surface. The results show a steepening of the plasmapause density profile near the satellites, which can be responsible for the generation of NTC emission