scholarly journals Monitoring the post-containment COVID-19 crisis in Guadeloupe: Early-warning signals of destabilisation through bootstrapped probability density functions

2020 ◽  
Author(s):  
Meriem ALLALI ◽  
Patrick Portecop ◽  
Michel Carles ◽  
Dominique Gibert
Keyword(s):  
Probability Density ◽  
Early Warning ◽  
Warning Signal ◽  
Probability Density Functions ◽  
Density Functions ◽  
Control Points ◽  
Epidemic Spread ◽  
Data Clusters ◽  
Probability Densities ◽  
Simulated Case

We propose a method to detect early-warning information in relation with subtle changes occurring in the trend of evolution in data time series of the COVID-19 epidemic spread (e.g. daily new cases). The method is simple and easy to implement on laptop computers. It is designed to be able to provide reliable results even with very small amounts of data (i.e. ≈ 10 − 20). The results are given as compact graphics easy to interpret. The data are separated into two subsets: the old data used as control points to statistically define a "trend" and the recent data that are tested to evaluate their conformity with this trend. The trend is characterised by bootstrapping in order to obtain probability density functions of the expected misfit of each data point. The probability densities are used to compute distance matrices where data clusters and outliers are easily visually recognised. In addition to be able to detect very subtle changes in trend, the method is also able to detect outliers. A simulated case is analysed where R0 is slowly augmented (i.e. from 1.5 to 2.0 in 20 days) to pass from a stable damped control of the epidemic spread to an exponentially diverging situation. The method is able to give an early warning signal as soon as the very beginning of the R0 variation. Application to the data of Guadeloupe shows that a small destabilising event occurred in the data near April 30, 2020. This may be due to an increase of R0 ≈ 0.7 around April 13-15, 2020.

OPTIMUM MULTICHANNEL VELOCITY FILTERS

Geophysics ◽  
1968 ◽  
Vol 33 (1) ◽  
pp. 11-35 ◽  
Author(s):  
R. L. Sengbush ◽  
M. R. Foster
Keyword(s):  
Power Spectrum ◽  
Probability Density ◽  
Noise Suppression ◽  
Minimum Mean Square Error ◽  
Probability Density Functions ◽  
Linear Functions ◽  
Density Functions ◽  
Coherent Noise ◽  
Special Cases ◽  
Probability Densities

Optimum systems have been developed to correspond to the sub‐optimum moveout discrimination systems presented previously by several authors. The seismic data on the lth trace is assumed to be additive signal S with moveout [Formula: see text], coherent noise N with moveout [Formula: see text], and incoherent noise [Formula: see text], expressed [Formula: see text] where S, N, and [Formula: see text] are independent, second order stationary random processes and [Formula: see text] and [Formula: see text] are random variables with prescribed probability density functions. The signal estimate S⁁ is produced by filtering each trace with its corresponding filter [Formula: see text] and summing the outputs [Formula: see text] We choose the system of filters [Formula: see text] to make the signal estimate optimum in the Wiener sense (minimum mean‐square error of the signal ensemble). For the special cases discussed, the moveouts are linear functions of the trace number l determined by the moveout/trace τ for signal and [Formula: see text] for noise. Thus, the optimum system is determined by the probability densities of τ and [Formula: see text] together with the noise/signal power spectrum ratios [Formula: see text] and [Formula: see text]. In comparison, suboptimum systems are controlled completely by the cut‐off moveout/trace [Formula: see text]. Events whose moveout/trace falls within [Formula: see text] of the expected dip moveout/trace are accepted, and those falling outside this range are suppressed. Suboptimum systems can be derived from optimum systems by choosing probability densities for τ and [Formula: see text] that are uniform within the above ranges and letting [Formula: see text] be very large. Optimum systems have increased flexibility over suboptimum systems due to control over the probability density functions and the power spectrum ratios and allow increased noise suppression in selected regions of f‐k space.

scholarly journals Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

2021 ◽  
Vol 13 (12) ◽  
pp. 2307
Author(s):  
J. Javier Gorgoso-Varela ◽  
Rafael Alonso Ponce ◽  
Francisco Rodríguez-Puerta
Keyword(s):  
Probability Density ◽  
Linear Models ◽  
Pinus Halepensis ◽  
Beta Function ◽  
Probability Density Functions ◽  
Lidar Data ◽  
Density Functions ◽  
Minimum Diameter ◽  
Location Parameters ◽  
Diameter Distributions

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

scholarly journals A synergy of the velocity gradients technique and the probability density functions for identifying gravitational collapse in self-absorbing media

2021 ◽  
Vol 502 (2) ◽  
pp. 1768-1784
Author(s):  
Yue Hu ◽  
A Lazarian
Keyword(s):  
Magnetic Fields ◽  
Probability Density ◽  
Column Density ◽  
Mass Density ◽  
Probability Density Functions ◽  
Emission Lines ◽  
Density Functions ◽  
Star Forming ◽  
Velocity Gradients ◽  
Self Gravity

ABSTRACT The velocity gradients technique (VGT) and the probability density functions (PDFs) of mass density are tools to study turbulence, magnetic fields, and self-gravity in molecular clouds. However, self-absorption can significantly make the observed intensity different from the column density structures. In this work, we study the effects of self-absorption on the VGT and the intensity PDFs utilizing three synthetic emission lines of CO isotopologues 12CO (1–0), 13CO (1–0), and C18O (1–0). We confirm that the performance of VGT is insensitive to the radiative transfer effect. We numerically show the possibility of constructing 3D magnetic fields tomography through VGT. We find that the intensity PDFs change their shape from the pure lognormal to a distribution that exhibits a power-law tail depending on the optical depth for supersonic turbulence. We conclude the change of CO isotopologues’ intensity PDFs can be independent of self-gravity, which makes the intensity PDFs less reliable in identifying gravitational collapsing regions. We compute the intensity PDFs for a star-forming region NGC 1333 and find the change of intensity PDFs in observation agrees with our numerical results. The synergy of VGT and the column density PDFs confirms that the self-gravitating gas occupies a large volume in NGC 1333.

scholarly journals Interactive design of probability density functions for shape grammars

2015 ◽  
Vol 34 (6) ◽  
pp. 1-13 ◽  
Author(s):  
Minh Dang ◽  
Stefan Lienhard ◽  
Duygu Ceylan ◽  
Boris Neubert ◽  
Peter Wonka ◽  
...  
Keyword(s):  
Probability Density ◽  
Probability Density Functions ◽  
Interactive Design ◽  
Density Functions ◽  
Shape Grammars

scholarly journals The Impact of Probability Density Functions Assessment on Model Performance for Slope Stability Analysis

Geosciences ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 322
Author(s):  
Evelina Volpe ◽  
Luca Ciabatta ◽  
Diana Salciarini ◽  
Stefania Camici ◽  
Elisabetta Cattoni ◽  
...  
Keyword(s):  
Probability Density ◽  
Central Italy ◽  
Model Performance ◽  
Probability Density Functions ◽  
Slope Instability ◽  
Complex Nature ◽  
Density Functions ◽  
Umbria Region ◽  
Input Variables ◽  
The Impact

The development of forecasting models for the evaluation of potential slope instability after rainfall events represents an important issue for the scientific community. This topic has received considerable impetus due to the climate change effect on territories, as several studies demonstrate that an increase in global warming can significantly influence the landslide activity and stability conditions of natural and artificial slopes. A consolidated approach in evaluating rainfall-induced landslide hazard is based on the integration of rainfall forecasts and physically based (PB) predictive models through deterministic laws. However, considering the complex nature of the processes and the high variability of the random quantities involved, probabilistic approaches are recommended in order to obtain reliable predictions. A crucial aspect of the stochastic approach is represented by the definition of appropriate probability density functions (pdfs) to model the uncertainty of the input variables as this may have an important effect on the evaluation of the probability of failure (PoF). The role of the pdf definition on reliability analysis is discussed through a comparison of PoF maps generated using Monte Carlo (MC) simulations performed over a study area located in the Umbria region of central Italy. The study revealed that the use of uniform pdfs for the random input variables, often considered when a detailed geotechnical characterization for the soil is not available, could be inappropriate.

BASIC ELEMENTS OF BIOLOGICAL COMPUTATIONAL SYSTEMS

1994 ◽  
Vol 05 (02) ◽  
pp. 313-315 ◽  
Author(s):  
CHARLES H. ANDERSON
Keyword(s):  
Probability Density ◽  
Probability Density Functions ◽  
Density Functions ◽  
Cortical Circuits ◽  
Computational Environment ◽  
Computational Systems

This paper explores some basic representational and implementation issues arising from the premise that cortical circuits operate on probability density functions to reason about analog quantities. Some insight is provided into why neurobiological systems can appear messy, while at the same time provide a rich and robust computational environment.

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