scholarly journals The Sherrington–Kirkpatrick spin glass model in the presence of a random field with a joint Gaussian probability density function for the exchange interactions and random fields

2014 ◽  
Vol 397 ◽  
pp. 1-16 ◽  
Author(s):  
Ioannis A. Hadjiagapiou
Keyword(s):  
Probability Density Function ◽  
Random Field ◽  
Spin Glass ◽  
Probability Density ◽  
Density Function ◽  
Random Fields ◽  
Exchange Interactions ◽  
Spin Glass Model ◽  
Gaussian Probability Density Function ◽  
Glass Model

scholarly journals A Phenomenological Epidemic Model Based On the Spatio-Temporal Evolution of a Gaussian Probability Density Function

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2000
Author(s):  
Domingo Benítez ◽  
Gustavo Montero ◽  
Eduardo Rodríguez ◽  
David Greiner ◽  
Albert Oliver ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Epidemic Model ◽  
Temporal Evolution ◽  
Growth Models ◽  
Model Fit ◽  
Gaussian Probability Density Function ◽  
Spatio Temporal

A novel phenomenological epidemic model is proposed to characterize the state of infectious diseases and predict their behaviors. This model is given by a new stochastic partial differential equation that is derived from foundations of statistical physics. The analytical solution of this equation describes the spatio-temporal evolution of a Gaussian probability density function. Our proposal can be applied to several epidemic variables such as infected, deaths, or admitted-to-the-Intensive Care Unit (ICU). To measure model performance, we quantify the error of the model fit to real time-series datasets and generate forecasts for all the phases of the COVID-19, Ebola, and Zika epidemics. All parameters and model uncertainties are numerically quantified. The new model is compared with other phenomenological models such as Logistic Grow, Original, and Generalized Richards Growth models. When the models are used to describe epidemic trajectories that register infected individuals, this comparison shows that the median RMSE error and standard deviation of the residuals of the new model fit to the data are lower than the best of these growing models by, on average, 19.6% and 35.7%, respectively. Using three forecasting experiments for the COVID-19 outbreak, the median RMSE error and standard deviation of residuals are improved by the performance of our model, on average by 31.0% and 27.9%, respectively, concerning the best performance of the growth models.

Facts about the gaussian probability density function

1995 ◽  
Vol 59 (1-4) ◽  
pp. 289-306 ◽  
Author(s):  
B. Aldershof ◽  
J.S. Marron ◽  
B.U. Park ◽  
M.P. Wand
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Gaussian Probability Density Function

scholarly journals Level Sets of Random Fields and Applications: Specular Points and Wave Crests

2010 ◽  
Vol 2010 ◽  
pp. 1-22
Author(s):  
Esteban Flores ◽  
José R. León R
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Random Fields ◽  
Level Sets ◽  
Two Dimensions ◽  
Level Curve ◽  
Curvilinear Integral ◽  
The Waves ◽  
Rice Formula

We apply Rice's multidimensional formulas, in a mathematically rigorous way, to several problems which appear in random sea modeling. As a first example, the probability density function of the velocity of the specular points is obtained in one or two dimensions as well as the expectation of the number of specular points in two dimensions. We also consider, based on a multidimensional Rice formula, a curvilinear integral with respect to the level curve. It follows that its expected value allows defining the Palm distribution of the angle of the normal of the curve that defines the waves crest. Finally, we give a new proof of a general multidimensional Rice formula, valid for all levels, for a stationary and smooth enough random fields X:ℝd→ℝj(d>j).

scholarly journals Evaluation of a Flexible Single Ice Microphysics and a Gaussian Probability-Density-Function Macrophysics Scheme in a Single Column Model

Atmosphere ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 638
Author(s):  
Jiabo Li ◽  
Xindong Peng ◽  
Xiaohan Li ◽  
Yanluan Lin ◽  
Wenchao Chu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Water Content ◽  
Density Function ◽  
Liquid Water ◽  
Cloud Fraction ◽  
Gaussian Probability Density Function ◽  
Single Column ◽  
Ice Water Content ◽  
Ice Water

Scale-aware parameterizations of subgrid scale physics are essentials for multiscale atmospheric modeling. A single-ice (SI) microphysics scheme and Gaussian probability-density-function (Gauss-PDF) macrophysics scheme were implemented in the single-column Global-to-Regional Integrated forecast System model (SGRIST) and they were tested using the Tropical Warm Pool-International Cloud Experiment (TWP-ICE) and the Atmospheric Radiation Measurement Southern Great Plains Experiment in 1997 (ARM97). Their performance was evaluated against observations and other reference schemes. The new schemes simulated reasonable precipitation with proper fluctuations and peaks, ice, and liquid water contents, especially in lower levels below 650 hPa during the wet period in the TWP-ICE. The root mean square error (RMSE) of the simulated cloud fraction was below 200 hPa was 0.10/0.08 in the wet/dry period, which showed an obvious improvement when compared to that, i.e., 0.11/0.11 of original scheme. Accumulated ice water content below the melting level decreased by 21.57% in the SI. The well-matched average liquid water content displayed between the new scheme and observations, which was two times larger than those with the referencing scheme. In the ARM97 simulations, the SI scheme produced considerable ice water content, especially when convection was active. Low-level cloud fraction and precipitation extremes were improved using the Gauss-PDF scheme, which displayed the RMSE of cloud fraction of 0.02, being only half of the original schemes. The study indicates that the SI and Gauss-PDF schemes are promising approaches to simplify the microphysics process and improve the low-level cloud modeling.

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