Search results for "distribution function"
showing 10 items of 348 documents
Is there an absolutely continuous random variable with equal probability density and cumulative distribution functions in its support? Is it unique? …
2014
This paper inquires about the existence and uniqueness of a univariate continuous random variable for which both cumulative distribution and density functions are equal and asks about the conditions under which a possible extrapolation of the solution to the discrete case is possible. The issue is presented and solved as a problem and allows to obtain a new family of probability distributions. The different approaches followed to reach the solution could also serve to warn about some properties of density and cumulative functions that usually go unnoticed, helping to deepen the understanding of some of the weapons of the mathematical statistician’s arsenal.
Optimal calculation of the pair correlation function for an orthorhombic system
2012
We present a new computational method to calculate arbitrary pair correlation functions of an orthorombic system in the most efficient way. The algorithm is demonstrated by the calculation of the radial distribution function of shock compressed liquid hydrogen.
Average versus local structure in K2NiF4-type LaSrAlO4: direct experimental evidence of local cationic ordering
2012
The long-range ordering of a crystalline material can be accurately determined by analyzing the Bragg intensities and positions. In contrast, direct observation of short-range ordering in crystalline materials, which is increasingly considered of fundamental importance to unravel the structure-property relationships that underpin their technological applications, is a challenging task. In this study we have investigated the structure of LaSrAlO4, a representative example of compounds with the K2NiF4-type structure. By the combined use of synchrotron and neutron diffraction, pair distribution function analysis, Al-27 MQMAS NMR and atomistic simulations we have highlighted differences between…
Automatic detection of large dense-core vesicles in secretory cells and statistical analysis of their intracellular distribution.
2010
Analyzing the morphological appearance and the spatial distribution of large dense-core vesicles (granules) in the cell cytoplasm is central to the understanding of regulated exocytosis. This paper is concerned with the automatic detection of granules and the statistical analysis of their spatial locations in different cell groups. We model the locations of granules of a given cell as a realization of a finite spatial point process and the point patterns associated with the cell groups as replicated point patterns of different spatial point processes. First, an algorithm to segment the granules using electron microscopy images is proposed. Second, the relative locations of the granules with…
Real-Time Observation of “Soft” Magic-Size Clusters during Hydrolysis of the Model Metallodrug Bismuth Disalicylate
2021
International audience; Colloidal bismuth therapeutics have been used for hundreds of years, yet remain mysterious. Here we report an X-ray pair distribution function (PDF) study of the solvolysis of bismuth disalicylate, a model for the metallodrug bismuth subsalicylate (Pepto-Bismol). This reveals catalysis by traces of water, followed by multistep cluster growth. The ratio of the two major species, {Bi9O7} and {Bi38O44}, depends on exposure to air, time, and the solvent. The solution-phase cluster structures are of significantly higher symmetry in comparison to solid-state analogues, with reduced off-center Bi3+ displacements. This explains why such “magic-size” clusters can be both stab…
An expansion–coalescence model to track gas bubble populations in magmas
2016
Abstract We propose a kinetic model that statistically describes the growth by decompression, exsolution and coalescence of a polydisperse population of gas bubbles in a silicate melt. The model is homogeneous in space and its main variable is a distribution function representing the probability to find a bubble of volume v and mass m at time t. The volume and mass growth rates are described by a simplification of the classical monodisperse bubble growth model. This simplification, which shortens computational time, removes the coupling between mass evolution and an advection–diffusion equation describing the behavior of the volatile concentration in the melt. We formulate three coalescence…
On the first- and second-order statistics of the capacity of N*Nakagami-m channels for applications in cooperative networks
2012
This article deals with the derivation and analysis of the statistical properties of the instantaneous channel capacitya of N*Nakagami-m channels, which has been recently introduced as a suitable stochastic model for multihop fading channels. We have derived exact analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the instantaneous channel capacity of N*Nakagami-m channels. For large number of hops, we have studied the first-order statistics of the instantaneous channel capacity by assuming that the fading amplitude of the channel can approximately be modeled as a lognor…
Fractional Fourier transform dual random phase encoding of time-varying signals
2008
Optical techniques have shown great potential in the field of information security to encode high-security images. Among several established methods, a double-random phase encryption technique (DRPE) for encoding a primary image into stationary white noise was developed by using the analogy between Fresnel diffraction patterns and the fractional Fourier transform (FrFT-DRPE). In this case, additional keys are obtained through the knowledge of the fractional orders of the FrFTs. In this work we propose an encoding setup for time-varying signals, mainly for short-haul fiber optics link applications, that can be considered as the temporal analogue of the spatial FrFT-DRPE. The behavior of the …
The Influence of LOS Components on the Statistical Properties of the Capacity of Amplify-and-Forward Channels
2009
Also available from publisher: http://dx.doi.org/10.4236/wsn.2009.11002 Amplify-and-forward channels in cooperative networks provide a promising improvement in the network coverage and system throughput. Under line-of-sight (LOS) propagation conditions in such cooperative networks, the overall fading channel can be modeled by a double Rice process. In this article, we have stud-ied the statistical properties of the capacity of double Rice fading channels. We have derived the analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level- crossing rate (LCR), and average duration of fades (ADF) of the channel capacity. The obtained results ar…
Investigating the cooling rate dependence of amorphous silica: A computer simulation study
1996
We use molecular dynamics computer simulations to study the dependence of the properties of amorphous silica on the cooling rate with which the glass has been produced. In particular we show that the density, the glass transition temperature, the radial distribution function and the distribution of the size of the rings depend on the cooling rate.