scholarly journals Continuous distribution model for the investigation of complex molecular architectures near interfaces with scattering techniques

2011 ◽  
Vol 110 (10) ◽  
pp. 102216 ◽  
Author(s):  
Prabhanshu Shekhar ◽  
Hirsh Nanda ◽  
Mathias Lösche ◽  
Frank Heinrich
Keyword(s):  
Continuous Distribution ◽  
Distribution Model ◽  
Molecular Architectures

scholarly journals Compatibility of quantitative X-ray spectroscopy with continuous distribution models of water at ambient conditions

2019 ◽  
Vol 116 (10) ◽  
pp. 4058-4063 ◽  
Author(s):  
Johannes Niskanen ◽  
Mattis Fondell ◽  
Christoph J. Sahle ◽  
Sebastian Eckert ◽  
Raphael M. Jay ◽  
...  
Keyword(s):  
Liquid Water ◽  
Pair Correlation ◽  
Continuous Distribution ◽  
Emission Spectra ◽  
Mean Value ◽  
Distribution Model ◽  
Ambient Conditions ◽  
Distribution Models ◽  
X Ray ◽  
Atomic Ionization

The phase diagram of water harbors controversial views on underlying structural properties of its constituting molecular moieties, its fluctuating hydrogen-bonding network, as well as pair-correlation functions. In this work, long energy-range detection of the X-ray absorption allows us to unambiguously calibrate the spectra for water gas, liquid, and ice by the experimental atomic ionization cross-section. In liquid water, we extract the mean value of 1.74 ± 2.1% donated and accepted hydrogen bonds per molecule, pointing to a continuous-distribution model. In addition, resonant inelastic X-ray scattering with unprecedented energy resolution also supports continuous distribution of molecular neighborhoods within liquid water, as do X-ray emission spectra once the femtosecond scattering duration and proton dynamics in resonant X-ray–matter interaction are taken into account. Thus, X-ray spectra of liquid water in ambient conditions can be understood without a two-structure model, whereas the occurrence of nanoscale-length correlations within the continuous distribution remains open.

scholarly journals On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 555
Author(s):  
Chénangnon Frédéric Tovissodé ◽  
Sèwanou Hermann Honfo ◽  
Jonas Têlé Doumatè ◽  
Romain Glèlè Kakaï
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Probability Distributions ◽  
Continuous Distribution ◽  
Simple Expression ◽  
Distribution Model ◽  
Stochastic Representation ◽  
Gamma Distributions ◽  
The Family ◽  
Jensen Shannon Divergence

Most existing flexible count distributions allow only approximate inference when used in a regression context. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under-, and over-dispersion). The new method, referred to as “balanced discretization”, consists of discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation (probabilistic rounding) in terms of the continuous distribution. For illustrative purposes, we develop the family of balanced discrete gamma distributions that can model equi-, under-, and over-dispersed count data. This family of count distributions is appropriate for building flexible count regression models because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we show that under the equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersions, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data are Poisson distributed.

The Lung Allocation Score and Its Relevance

2021 ◽  
Vol 42 (03) ◽  
pp. 346-356
Author(s):  
Dennis M. Lyu ◽  
Rebecca R. Goff ◽  
Kevin M. Chan
Keyword(s):  
Pulmonary Hypertension ◽  
Lung Disease ◽  
Organ Procurement ◽  
Continuous Distribution ◽  
Severity Of Illness ◽  
Wait Time ◽  
The United States ◽  
Distribution Model ◽  
Wait List ◽  
Lung Allocation Score

AbstractLung transplantation in the United States, under oversight by the Organ Procurement Transplantation Network (OPTN) in the 1990s, operated under a system of allocation based on location within geographic donor service areas, wait time of potential recipients, and ABO compatibility. On May 4, 2005, the lung allocation score (LAS) was implemented by the OPTN Thoracic Organ Transplantation Committee to prioritize patients on the wait list based on a balance of wait list mortality and posttransplant survival, thus eliminating time on the wait list as a factor of prioritization. Patients were categorized into four main disease categories labeled group A (obstructive lung disease), B (pulmonary hypertension), C (cystic fibrosis), and D (restrictive lung disease/interstitial lung disease) with variables within each group impacting the calculation of the LAS. Implementation of the LAS led to a decrease in the number of wait list deaths without an increase in 1-year posttransplant survival. LAS adjustments through the addition, modification or elimination of covariates to improve the estimates of patient severity of illness, have since been made in addition to establishing criteria for LAS value exceptions for pulmonary hypertension patients. Despite the success of the LAS, concerns about the prioritization, and transplantation of older, sicker individuals have made some aspects of the LAS controversial. Future changes in US lung allocation are anticipated with the current development of a continuous distribution model that incorporates the LAS, geographic distribution, and unaccounted aspects of organ allocation into an integrated score.

scholarly journals A Continuous Distribution Model to Predict a Long-term Selection Response Taking the Effect of Reproduction into Account

1988 ◽  
Vol 59 (6) ◽  
pp. 548-553
Author(s):  
Akira NISHIDA ◽  
Yoshitaka NAGAMINE ◽  
Katsuhiro MIURA ◽  
Masahiro SATOH
Keyword(s):  
Continuous Distribution ◽  
Selection Response ◽  
Distribution Model ◽  
Term Selection

scholarly journals A Skewed Model Combining Triangular and Exponential Features: The Two-faced Distribution and its Statistical Properties

2016 ◽  
Vol 35 (4) ◽  
Author(s):  
Maurizio Brizzi
Keyword(s):  
Distribution Function ◽  
Parameter Estimation ◽  
Goodness Of Fit ◽  
Cumulative Distribution Function ◽  
Continuous Distribution ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Model Combining ◽  
Left And Right ◽  
Expected Values

A new continuous distribution model is introduced, joining triangular and exponential features, respectively on the left and right side of a hinge point. The cumulative distribution function is derived, as well as the first three moments. Expected values and the Pearson index of skewness are tabulated. A possible step-by-step approach to parameter estimation is outlined. An application to Italian geographical data is given, referring to a set of municipalities classified by population, showing a very satisfactory goodness of fit.

scholarly journals On the Discretization of Continuous Probability Distributions for Flexible Count Regression

2021 ◽  
Author(s):  
Chénangnon Frédéric Tovissodé ◽  
Romain Glèlè Kakaï ◽  
Sèwanou Hermann Honfo ◽  
Jonas Têlé Doumatè
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Probability Distributions ◽  
Continuous Distribution ◽  
Simple Expression ◽  
Distribution Model ◽  
Stochastic Representation ◽  
Gamma Distributions ◽  
The Family ◽  
Jensen Shannon Divergence

Most existing flexible count regression models allow only approximate inference. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under- and overdispersion). The new method, referred as “balanced discretization”, consists in discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation in terms of the continuous distribution. For illustrative purposes, we have developed the family of balanced discrete gamma distributions which can model equi-, under- and overdispersed count data. This family of count distributions is appropriate for building flexible count regressionmodels because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we have shown that under equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersion, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data is Poisson distributed.

Calculation of structure images of crystalline defects

1978 ◽  
Vol 36 (1) ◽  
pp. 282-283
Author(s):  
M.A. O'Keefe ◽  
Sumio Iijima
Keyword(s):  
Diffuse Scattering ◽  
Computing Time ◽  
Continuous Distribution ◽  
Sampling Interval ◽  
Reciprocal Space ◽  
Objective Lens ◽  
Lattice Images ◽  
Slice Method ◽  
Space Cell ◽  
Beam Lattice

We have extended the multi-slice method of computating many-beam lattice images of perfect crystals to calculations for imperfect crystals using the artificial superlattice approach. Electron waves scattered from faulted regions of crystals are distributed continuously in reciprocal space, and all these waves interact dynamically with each other to give diffuse scattering patterns.In the computation, this continuous distribution can be sampled only at a finite number of regularly spaced points in reciprocal space, and thus finer sampling gives an improved approximation. The larger cell also allows us to defocus the objective lens further before adjacent defect images overlap, producing spurious computational Fourier images. However, smaller cells allow us to sample the direct space cell more finely; since the two-dimensional arrays in our program are limited to 128X128 and the sampling interval shoud be less than 1/2Å (and preferably only 1/4Å), superlattice sizes are limited to 40 to 60Å. Apart from finding a compromis superlattice cell size, computing time must be conserved.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

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