Stable Distribution

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Ariel Amir - One of the best experts on this subject based on the ideXlab platform.

  • stochastic modeling of cell growth with symmetric or asymmetric division
    Physical Review E, 2016
    Co-Authors: Andrew Marantan, Ariel Amir
    Abstract:

    We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the "master equation" describing how the resource Distribution evolves over subsequent generations and use it to study the properties of Stable resource Distributions. We find conditions under which a unique Stable resource Distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the Stable Distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the Stable Distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendix, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.

  • stochastic modeling of cell growth with symmetric or asymmetric division
    Physical Review E, 2016
    Co-Authors: Andrew Marantan, Ariel Amir
    Abstract:

    We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource Distribution over subsequent generations and use it to study the properties of Stable resource Distributions. We find conditions under which a unique Stable resource Distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the Stable Distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the Stable Distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.

Changcheng Wang - One of the best experts on this subject based on the ideXlab platform.

  • using sar images to detect ships from sea clutter
    IEEE Geoscience and Remote Sensing Letters, 2008
    Co-Authors: Mingsheng Liao, Changcheng Wang, Yong Wang, Liming Jiang
    Abstract:

    An innovative constant false alarm rate (CFAR) algorithm was studied for ship detection using synthetic aperture radar (SAR) images of the sea. Two advances were achieved. An alpha-Stable Distribution rather than a traditional Weibull or -Distribution was used to model the Distribution of sea clutter. The Distribution of sea clutter in a SAR image was typically heterogeneous, caused mainly by variable wind and current conditions. Image segmentation was carried out to improve the homogeneity of the Distribution in each subimage or region. In comparison with ship detection using the CFAR algorithms based on the Weibull or K -Distribution, our algorithm detected the most number of ships with the smallest number of false alarms.

  • Ship detection in SAR image based on the Alpha-Stable Distribution
    Sensors, 2008
    Co-Authors: Changcheng Wang, Mingsheng Liao, Xiaofeng Li
    Abstract:

    This paper describes an improved Constant False Alarm Rate (CFAR) ship detection algorithm in spaceborne synthetic aperture radar (SAR) image based on AlphaStable Distribution model. Typically, the CFAR algorithm uses the Gaussian Distribution model to describe statistical characteristics of a SAR image background clutter. However, the Gaussian Distribution is only valid for multilook SAR images when several radar looks are averaged. As sea clutter in SAR images shows spiky or heavy-tailed characteristics, the Gaussian Distribution often fails to describe background sea clutter. In this study, we replace the Gaussian Distribution with the Alpha-Stable Distribution, which is widely used in impulsive or spiky signal processing, to describe the background sea clutter in SAR images. In our proposed algorithm, an initial step for detecting possible ship targets is employed. Then, similar to the typical two-parameter CFAR algorithm, a local process is applied to the pixel identified as possible target. A RADARSAT-1 image is used to validate this Alpha-Stable Distribution based algorithm. Meanwhile, known ship location data during the time of RADARSAT-1 SAR image acquisition is used to validate ship detection results. Validation results show improvements of the new CFAR algorithm based on the Alpha-Stable Distribution over the CFAR algorithm based on the Gaussian Distribution.

Xiaofeng Li - One of the best experts on this subject based on the ideXlab platform.

  • Ship detection in SAR image based on the Alpha-Stable Distribution
    Sensors, 2008
    Co-Authors: Changcheng Wang, Mingsheng Liao, Xiaofeng Li
    Abstract:

    This paper describes an improved Constant False Alarm Rate (CFAR) ship detection algorithm in spaceborne synthetic aperture radar (SAR) image based on AlphaStable Distribution model. Typically, the CFAR algorithm uses the Gaussian Distribution model to describe statistical characteristics of a SAR image background clutter. However, the Gaussian Distribution is only valid for multilook SAR images when several radar looks are averaged. As sea clutter in SAR images shows spiky or heavy-tailed characteristics, the Gaussian Distribution often fails to describe background sea clutter. In this study, we replace the Gaussian Distribution with the Alpha-Stable Distribution, which is widely used in impulsive or spiky signal processing, to describe the background sea clutter in SAR images. In our proposed algorithm, an initial step for detecting possible ship targets is employed. Then, similar to the typical two-parameter CFAR algorithm, a local process is applied to the pixel identified as possible target. A RADARSAT-1 image is used to validate this Alpha-Stable Distribution based algorithm. Meanwhile, known ship location data during the time of RADARSAT-1 SAR image acquisition is used to validate ship detection results. Validation results show improvements of the new CFAR algorithm based on the Alpha-Stable Distribution over the CFAR algorithm based on the Gaussian Distribution.

Mingsheng Liao - One of the best experts on this subject based on the ideXlab platform.

  • using sar images to detect ships from sea clutter
    IEEE Geoscience and Remote Sensing Letters, 2008
    Co-Authors: Mingsheng Liao, Changcheng Wang, Yong Wang, Liming Jiang
    Abstract:

    An innovative constant false alarm rate (CFAR) algorithm was studied for ship detection using synthetic aperture radar (SAR) images of the sea. Two advances were achieved. An alpha-Stable Distribution rather than a traditional Weibull or -Distribution was used to model the Distribution of sea clutter. The Distribution of sea clutter in a SAR image was typically heterogeneous, caused mainly by variable wind and current conditions. Image segmentation was carried out to improve the homogeneity of the Distribution in each subimage or region. In comparison with ship detection using the CFAR algorithms based on the Weibull or K -Distribution, our algorithm detected the most number of ships with the smallest number of false alarms.

  • Ship detection in SAR image based on the Alpha-Stable Distribution
    Sensors, 2008
    Co-Authors: Changcheng Wang, Mingsheng Liao, Xiaofeng Li
    Abstract:

    This paper describes an improved Constant False Alarm Rate (CFAR) ship detection algorithm in spaceborne synthetic aperture radar (SAR) image based on AlphaStable Distribution model. Typically, the CFAR algorithm uses the Gaussian Distribution model to describe statistical characteristics of a SAR image background clutter. However, the Gaussian Distribution is only valid for multilook SAR images when several radar looks are averaged. As sea clutter in SAR images shows spiky or heavy-tailed characteristics, the Gaussian Distribution often fails to describe background sea clutter. In this study, we replace the Gaussian Distribution with the Alpha-Stable Distribution, which is widely used in impulsive or spiky signal processing, to describe the background sea clutter in SAR images. In our proposed algorithm, an initial step for detecting possible ship targets is employed. Then, similar to the typical two-parameter CFAR algorithm, a local process is applied to the pixel identified as possible target. A RADARSAT-1 image is used to validate this Alpha-Stable Distribution based algorithm. Meanwhile, known ship location data during the time of RADARSAT-1 SAR image acquisition is used to validate ship detection results. Validation results show improvements of the new CFAR algorithm based on the Alpha-Stable Distribution over the CFAR algorithm based on the Gaussian Distribution.

Doyne J Farmer - One of the best experts on this subject based on the ideXlab platform.

  • measuring productivity dispersion a parametric approach using the levy alpha Stable Distribution
    Social Science Research Network, 2019
    Co-Authors: Jangho Yang, Torsten Heinrich, Julian Winkler, Francois Lafond, Pantelis Koutroumpis, Doyne J Farmer
    Abstract:

    Productivity levels and growth are extremely heterogeneous among firms. A vast literature has developed to explain the origins of productivity shocks, their dispersion, evolution and their relationship to the business cycle. We examine in detail the Distribution of labor productivity levels and growth, and observe that they exhibit heavy tails. We propose to model these Distributions using the four parameter Levy Stable Distribution, a natural candidate deriving from the generalised Central Limit Theorem. We show that it is a better fit than several standard alternatives, and is remarkably consistent over time, countries and sectors. In all samples considered, the tail parameter is such that the theoretical variance of the Distribution is infinite, so that the sample standard deviation increases with sample size. We find a consistent positive skewness, a markedly different behaviour between the left and right tails, and a positive relationship between productivity and size. The Distributional approach allows us to test different measures of dispersion and find that productivity dispersion has slightly decreased over the past decade.