3,239 research outputs found
Time-Evolution of the Power Spectrum of the Black Hole X-ray Nova XTE J1550-564
We have studied the time evolution of the power spectrum of XTE J1550-564,
using X-ray luminosity time series data obtained by the Rossi X-Ray Timing
Explorer satellite. A number of important practical fundamental issues arise in
the analysis of these data, including dealing with time-tagged event data,
removal of noise from a highly non-stationary signal, and comparison of
different time-frequency distributions. We present two new methods to
understand the time frequency variations, and compare them to the dynamic power
spectrum of Homan et al. All of the approaches provide evidence that the QPO
frequency varies in a systematic way during the time evolution of the signal.Comment: 4 pages, 3 figures; 2001 IEEE - EURASIP Workshop on Nonlinear Signal
and Image Processing (June 3-6, 2001), and to appear in the proceeding
Nonlinear Transformation of Differential Equations into Phase Space
Time-frequency representations transform a one-dimensional function into a two-dimensional function in the phase-space of time and frequency. The transformation to accomplish is a nonlinear transformation and there are an infinite number of such transformations. We obtain the governing differential equation for any two-dimensional bilinear phase-space function for the case when the governing equation for the time function is an ordinary differential equation with constant coefficients. This connects the dynamical features of the problem directly to the phase-space function and it has a number of advantages
Approximation of the Wigner Distribution for Dynamical Systems Governed by Differential Equations
A conceptually new approximation method to study the time-frequency properties of dynamical systems characterized by linear ordinary differential equations is presented. We bypass solving the differential equation governing the motion by writing the exact Wigner distribution corresponding to the solution of the differential equation. The resulting equation is a partial differential equation in time and frequency. We then show how it lends itself to effective approximation methods because in the time frequency plane there is a high degree of localization of the signal. Numerical examples are given and compared to exact solutions
Music-based interventions in palliative cancer care: a review of quantitative studies and neurobiological literature
PURPOSE: This study aimed to review quantitative literature pertaining to studies of music-based interventions in palliative cancer care and to review the neurobiological literature that may bare relevance to the findings from these studies. METHODS: A narrative review was performed, with particular emphasis on RCTs, meta-analyses, and systematic reviews. The Cochrane Library, Ovid, PubMed, CINAHL Plus, PsycINFO, and ProQuest were searched for the subject headings music, music therapy, cancer, oncology, palliative care, pain, anxiety, depression, mood, quality of life, prevalence, neuroscience, functional imaging, endogenous opioids, GABA, 5HT, dopamine, and permutations of these same search terms. Data for the review were comprised of articles published between 1970 and 2012. References of all the cited articles were also reviewed. RESULTS: Available evidence suggests that music-based interventions may have a positive impact on pain, anxiety, mood disturbance, and quality of life in cancer patients. Advances in neurobiology may provide insight into the potential mechanisms by which music impacts these outcomes. CONCLUSIONS: More research is needed to determine what subpopulation of cancer patients is most likely to respond to music-based interventions, what interventions are most effective for individual outcomes, and what measurement parameters best gauge their effectiveness
On acceleration with noise-corrupted gradients
Accelerated algorithms have broad applications
in large-scale optimization, due to their generality
and fast convergence. However, their stability in
the practical setting of noise-corrupted gradient
oracles is not well-understood. This paper provides two main technical contributions: (i) a new
accelerated method AGD+ that generalizes Nesterov’s AGD and improves on the recent method
AXGD (Diakonikolas & Orecchia, 2018), and (ii)
a theoretical study of accelerated algorithms under noisy and inexact gradient oracles, which is
supported by numerical experiments. This study
leverages the simplicity of AGD+ and its analysis to clarify the interaction between noise and
acceleration and to suggest modifications to the
algorithm that reduce the mean and variance of
the error incurred due to the gradient noise.Published versio
Multi-Swap -Means++
The -means++ algorithm of Arthur and Vassilvitskii (SODA 2007) is often
the practitioners' choice algorithm for optimizing the popular -means
clustering objective and is known to give an -approximation in
expectation. To obtain higher quality solutions, Lattanzi and Sohler (ICML
2019) proposed augmenting -means++ with local search
steps obtained through the -means++ sampling distribution to yield a
-approximation to the -means clustering problem, where is a large
absolute constant. Here we generalize and extend their local search algorithm
by considering larger and more sophisticated local search neighborhoods hence
allowing to swap multiple centers at the same time. Our algorithm achieves a approximation ratio, which is the best possible for local
search. Importantly we show that our approach yields substantial practical
improvements, we show significant quality improvements over the approach of
Lattanzi and Sohler (ICML 2019) on several datasets.Comment: NeurIPS 202
Instantaneous spectrum estimation of event-based densities
We present a method for obtaining a time-varying spectrum that is particularly suited when the data are in event-based form. This form arises in many areas of science and engineering, and especially in astronomy, where one has photon counting detectors. The method presented consists of three procedures. First, estimating the density using the kernel method; second, highpass filtering the manifestly positive density; finally, obtaining the time-frequency distribution with a modified Welch′s method. For the sake of validation event-based data are generated from a given distribution and the proposed method is used to construct the time-frequency spectrum and is compared to the original density. The results demonstrate the effectiveness of the method
Notes on Hierarchical Splines, DCLNs and i-theory
We define an extension of classical additive splines for multivariate function approximation that we call hierarchical splines. We show that the case of hierarchical, additive, piece-wise linear splines includes present-day Deep Convolutional Learning Networks (DCLNs) with linear rectifiers and pooling (sum or max). We discuss how these observations together with i-theory may provide a framework for a general theory of deep networks.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF - 1231216
On the dimension of max-min convex sets
We introduce a notion of dimension of max-min convex sets, following the
approach of tropical convexity. We introduce a max-min analogue of the tropical
rank of a matrix and show that it is equal to the dimension of the associated
polytope. We describe the relation between this rank and the notion of strong
regularity in max-min algebra, which is traditionally defined in terms of
unique solvability of linear systems and trapezoidal property.Comment: 19 pages, v2: many corrections in the proof
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