Central limit theorems for Gaussian polytopes

Bárány, Imre; Vu, Van

doi:10.1214/009117906000000791

Cited by 103 publications

(85 citation statements)

References 17 publications

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“…Analyzing the multiple-scale entropy of physiological signals the Richman-Moormanentropy was applied [7]. Supposing that the Gauss-type pink-noise at physiologic signals is a good approximation due to the central limit theorem [8]. The covariance matrix is necessary for characterizing the multidimensional Gauss-distribution.…”

Section: Homeostasis and Entropymentioning

confidence: 99%

On the Dynamic Equilibrium in Homeostasis

Hegyi¹,

Vincze²,

Szász³

2012

OJBIPHY

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We studied the homeostatic equilibrium of the healthy organism. The homeostasis is controlled by oppositely effective physiologic feedback signal-pairs in various timescales. We show the entropy of every signal in this state is identical and constant: SE = 1.8. The controlling physiological signals fluctuate around their average values. The fluctuation is time-fractal, (pink-noise), which characterizes the homeostasis. The aging is the degradation of the competing pairs of signals, decreasing the complexity of the organism. This way, the color of the noise gradually changes to brown. A special scaling process occurs during the aging: the exponent of the frequency dependence of the power density function grows in this process from 1 to 2, but the homeostasis of the system is unchanged.

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Section: Homeostasis and Entropymentioning

confidence: 99%

On the Dynamic Equilibrium in Homeostasis

Hegyi¹,

Vincze²,

Szász³

2012

OJBIPHY

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“…Moreover, it can be seen from (2) that the measurements generated by a target are following Gaussian distribution. For Gaussian distribution, most data stochastically is distributed inside the interval between the expectation plus threefold variances and the expectation minus threefold variances [20]. So d c in our paper is determined by…”

Section: Determination Of D C and The Cluster Centermentioning

confidence: 96%

A Measurement Set Partitioning Algorithm Based on CFSFDP for Multiple Extended Target Tracking in PHD Filter

Gong¹,

Cui²

2021

RADIOENGINEERING

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The extended target probability hypothesis density (ET-PHD) filter is a promising approach for multiple extended target tracking. One crucial problem of the ET-PHD filter is partitioning the measurement set. This paper proposes a partitioning algorithm based on clustering by fast search and find density peaks (CFSFDP). Firstly, we adopt CFSFDP algorithm to partition the measurement set and the field theory is introduced to determine the cutoff distance of the CFSFDP algorithm. Then, the cluster center of the CFSFDP algorithm is determined according to solved cutoff distance and measurement rate. Finally, as the CFSFDP algorithm cannot handle the case in which targets are spatially close, an improved sub-partitioning method is implemented. Simulation results show that the proposed algorithm has less computational complexity and stronger robustness than the existing algorithm without losing tracking performance.

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“…There are many established methods in the literature to calculate CIs [33]. The most simple and basic method is normal approximation using central limit theorem [34], [35]. This approximation fails when the trial entries are too low orω (a) x t s is very close to 0 or 1.…”

Section: Confidence Interval For Binomial Proportionsmentioning

confidence: 99%

Definitions of Demand Flexibility for Aggregate Residential Loads

Sajjad

Chicco

Napoli

2016

IEEE Trans. Smart Grid

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Nowadays, enhanced knowledge of the nature of the electricity demand is achieved through the progressively increasing deployment of smart meters and advanced data analysis techniques. One of the major challenges is to exploit this knowledge to support the introduction of strategies to modify the demand according to relevant objectives to be achieved, like users' participation in demand response programmes. A key point for facing this challenge is to characterize the demand flexibility. In spite of many discussions about the concept of flexibility, the few mathematical definitions of flexibility available do not address the variation in time of the overall demand aggregation. This paper starts from the analysis of time-variable patterns of aggregate residential customers, ending up with suitable definitions of expected flexibility for aggregate demand. These definitions are based on assessing positive and negative pattern variations and are identified from the analysis of the collective behavior of the aggregate users. A set of results is shown for different numbers of aggregate customers, by considering different values of the averaging time step for load pattern representation.

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Central limit theorems for Gaussian polytopes

Cited by 103 publications

References 17 publications

On the Dynamic Equilibrium in Homeostasis

On the Dynamic Equilibrium in Homeostasis

A Measurement Set Partitioning Algorithm Based on CFSFDP for Multiple Extended Target Tracking in PHD Filter

Definitions of Demand Flexibility for Aggregate Residential Loads

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