In ultrasound imaging, various statistical distributions have been proposed to model the first-order statistics of the amplitude of the echo envelope. We present an overview of these distributions based on their compound representation, which comprises three aspects: the modulated distribution (Rice or Nakagami); the modulating distribution (gamma, inverse Gaussian or even generalized inverse Gaussian); and the modulated parameters (the diffuse signal power with or without the coherent signal component or the coherent signal power). This unifying point of view makes the comparison of the various models conceptually easier. In particular, we discuss the implications of the modulated parameters on the mean intensity and the signal-to-noise ratio of the intensity in the case of a vanishing diffuse signal. We conclude that the homodyned K-distribution is the only model among the literature for which the parameters have a physical meaning that is consistent with the limiting case, although the other distributions may fit real data.

A Critical Review and Uniformized Representation of Statistical Distributions Modeling the Ultrasound Echo Envelope

Reducing the energy consumption of a wireless cellular network is an important and urgent problem. This paper studies the effect of cell sizes on the energy consumed by the network, assuming base station technologies of today and the future. Making cell sizes too small or too large can significantly increase energy consumption. We show that the optimal cell size from an energy perspective depends on a number of factors, including base station technology, data rates, and traffic demands. Given that traffic varies significantly during a day, dynamically adjusting cell sizes can help reduce energy consumption. We propose a practical, 2-level scheme that adjusts cell sizes between two fixed values, and show an energy saving of up to 40%. The paper also proposes some self-organizing techniques to allow this dynamic cell size adjustment.

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Breathe to stay cool: adjusting cell sizes to reduce energy consumption

Circular data are common in biological studies. The most fundamental question that can be asked of a sample of circular data is whether it suggests that the underlying population is uniformly distributed around the circle, or whether it is concentrated around at least one preferred direction (e.g. a migratory goal or activity phase). We compared the statistical power of five commonly used tests (the Rayleigh test, the V-test, Watson’s test, Kuiper’s test and Rao’s spacing test) across a range of different unimodal scenarios. The V-test showed higher power for symmetrical distributions, Rao’s spacing performed worst for all explored unimodal distributions tested and the remaining three tests showed very similar performance. However, the V-test only applies if the hypothesis is restricted to one (pre-specified) direction of interest. In all other unimodal cases, we recommend using the Rayleigh test. Much less explored is the multimodal case with data concentrated around several directions. We performed power simulations for a variety of multimodal situations, testing the performance of the widely used Rayleigh, Rao’s, Watson, and Kuiper’s tests as well as the more recent Bogdan and Hermans-Rasson tests. Our analyses of alternative statistical methods show that the commonly used tests lack statistical power in many of multimodal cases. Transformation of the raw data (e.g. doubling the angles) can overcome some of the issues, but only in the case of perfect f-fold symmetry. However, the Hermans-Rasson method, which is not yet implemented in any software package, outcompetes the alternative tests (often by substantial margins) in most of the multimodal situations explored. We recommend the wider uptake of the powerful but hitherto neglected Hermans-Rasson method. In summary, we provide guidance for biologists helping them to make decisions when testing circular data for single or multiple departures from uniformity.

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Circular data in biology: advice for effectively implementing statistical procedures.

Previously, we introduced a monkey model for human frontal midline theta oscillations as a possible neural correlate of attention. It was based on homologous theta oscillations found in the monkey's prefrontal and anterior cingulate cortices (areas 9 and 32) in a self-initiated hand-movement task. However, it has not been confirmed whether theta activity in the monkey model consistently appears in other situations demanding attention. Here, we examined the detailed properties of theta oscillations in four variations of forewarned reaction time tasks with warning (S1) and imperative (S2) stimuli. We characterized the theta oscillations generated exclusively in areas 9 and 32, as follows: 1) in the S1-S2 interval where movement preparation and reward expectation were presumably involved, the theta power was higher than in the pre-S1 period; 2) in the no-go trials of go/no-go tasks instructed by S1, the theta power in the S1-S2 interval was lower than in the pre-S1 period in an asymmetrical reward condition, whereas it was moderately higher in a symmetrical condition; 3) the theta power after reward delivery was higher than in the unrewarded trials; 4) the theta power in the pre-S1 period was higher than in the resting condition; and 5) when the monkey had to guess the S1-S2 duration internally without seeing S2, the theta power in the pre-S1 period was higher than in the original S1-S2 experiment. These findings suggest that attentional loads associated with different causes can induce the same theta activity, thereby supporting the consistency of attention-dependent theta oscillations in our model.

Theta Oscillations in Primate Prefrontal and Anterior Cingulate Cortices in Forewarned Reaction Time Tasks

In this paper, we introduce a new class of distributions which is obtained by compounding the extended Weibull and power series distributions. The compounding procedure follows the same set-up carried out by Adamidis and Loukas (1998) and defines at least new 68 sub-models. This class includes some well-known mixing distributions, such as the Weibull power series (Morais and Barreto-Souza, 2010) and exponential power series (Chahkandi and Ganjali, 2009) distributions. Some mathematical properties of the new class are studied including moments and generating function. We provide the density function of the order statistics and obtain their moments. The method of maximum likelihood is used for estimating the model parameters and an EM algorithm is proposed for computing the estimates. Special distributions are investigated in some detail. An application to a real data set is given to show the flexibility and potentiality of the new class of distributions.

John William Strutt

Papers

Scientific Papers: On the Resultant of a large number of Vibrations of the same Pitch and of arbitrary Phase