scholarly journals Constraints on the paleoelevation history of the Eastern Cordillera of Colombia from its palynological record

Geosphere ◽  
2021 ◽  
Author(s):  
Peter Molnar ◽  
Lina C. Pérez-Angel
Keyword(s):  
Probability Distributions ◽  
Objective Assessment ◽  
Probability Density Functions ◽  
Fossil Pollen ◽  
Density Functions ◽  
Fossil Plants ◽  
Eastern Cordillera ◽  
Surface Uplift ◽  
Complete Knowledge ◽  
History Of

We attempted to make an objective assessment of whether fossil pollen assemblages from the Sabana de Bogotá require surface uplift of ~2000 m since 6–3 Ma, as has been argued. We relied on recently published elevation ranges of plants for which fossil pollen has been found in sites 2000–2500 m high in the Sabana de Bogotá. The elevation ranges of fossil plants do not overlap, suggesting that those ranges may be too narrow. By weighting these elevation ranges by percentages of corresponding fossil pollen and summing them, we estimated probability density functions for past elevations. These probability distributions of past elevations overlap present-day elevations and therefore do not require surface uplift since deposition of the pollen. Fossil pollen assemblages include pollen from some plant taxa for which we do not know present-day elevation ranges, and therefore, with a more complete knowledge of elevation distributions, tighter constraints on elevations should be obtainable. The elevation of the oldest assemblage, from Tequendama, which lies at the southern edge of the Sabana de Bogotá and is thought to date from 16 to 6 Ma, is least well constrained. Although our analysis permits no change in elevation since the pollen was deposited, we consider 1000–2000 m of elevation gain since 15 Ma to be likely and consistent with an outward growth of the Eastern Cordillera.

A New Approach to Probability in Engineering Design and Optimization

1984 ◽  
Vol 106 (1) ◽  
pp. 5-10 ◽  
Author(s):  
J. N. Siddall
Keyword(s):  
Probability Density ◽  
Engineering Design ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Density Functions ◽  
New Approach ◽  
Design And Optimization ◽  
Evolutionary Technique ◽  
Probability And Statistics

The anomalous position of probability and statistics in both mathematics and engineering is discussed, showing that there is little consensus on concepts and methods. For application in engineering design, probability is defined as strictly subjective in nature. It is argued that the use of classical methods of statistics to generate probability density functions by estimating parameters for assumed theoretical distributions should be used with caution, and that the use of confidence limits is not really meaningful in a design context. Preferred methods are described, and a new evolutionary technique for developing probability distributions of new random variables is proposed. Although Bayesian methods are commonly considered to be subjective, it is argued that, in the engineering sense, they are really not. A general formulation of the probabilistic optimization problem is described, including the role of subjective probability density functions.

scholarly journals Arrival Traffic Separations Modelling By Using Continuous Probability Distributions

2019 ◽  
Vol 285 ◽  
pp. 00013
Author(s):  
Adrian Pawełek ◽  
Piotr Lichota
Keyword(s):  
Mathematical Model ◽  
Quantitative Analysis ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Air Traffic ◽  
Density Functions ◽  
Traffic Intensity ◽  
Traffic Data ◽  
Model Application ◽  
Comparing Distributions

This article presents a method that allows to analyze selected aspects of past arrival traffic by modelling distributions of time separations of arriving aircraft in a chosen navigationpoint of Terminal Manoeuvring Area with the use of continuous probability distributions. Modelling arriving aircraft time separations distribution with continuous probability density functions allows to apply various mathematical tools to analyze separations distributions. Moreover, by comparing distributions parameters, quantitative analysis of separations for days with various arrival traffic intensity can be performed. Assumptions, mathematical model, application in the exemplary experimental scenario with an airport and days with low and high traffic intensity, and results are presented in this article. Real air traffic data was used for the experimental scenario. Outcomes show that the method can be used for air traffic post-analysis, e.g assessment of maintaining separation.

scholarly journals The Metalog Distributions

2016 ◽  
Vol 13 (4) ◽  
pp. 243-277 ◽  
Author(s):  
Thomas W. Keelin
Keyword(s):  
Decision Analysis ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Cumulative Distribution ◽  
Density Functions ◽  
Creative Commons ◽  
Discrete Methods ◽  
Actual Decision ◽  
New System

The metalog distributions constitute a new system of continuous univariate probability distributions designed for flexibility, simplicity, and ease/speed of use in practice. The system is comprised of unbounded, semibounded, and bounded distributions, each of which offers nearly unlimited shape flexibility compared to previous systems of distributions. Explicit shape-flexibility comparisons are provided. Unlike other distributions that require nonlinear optimization for parameter estimation, the metalog quantile functions and probability density functions have simple closed-form expressions that are quantile parameterized linearly by cumulative-distribution-function data. Applications in fish biology and hydrology show how metalogs may aid data and distribution research by imposing fewer shape constraints than other commonly used distributions. Applications in decision analysis show how the metalog system can be specified with three assessed quantiles, how it facilities Monte Carlo simulation, and how applying it aided an actual decision that would have been made wrongly based on commonly used discrete methods. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. You are free to download this work and share with others for any purpose, except commercially, if you distribute your contributions under the same license as the original, and you must attribute this work as “Decision Analysis. Copyright © 2016 The Author(s). https://doi.org/10.1287/deca.2016.0338 , used under a Creative Commons Attribution License: https://creativecommons.org/licenses/by-nc-sa/4.0/ .”

scholarly journals Cenozoic uplift of the Central Andes in northern Chile and Bolivia—reconciling paleoaltimetry with the geological evolution

2016 ◽  
Vol 53 (11) ◽  
pp. 1227-1245 ◽  
Author(s):  
Simon Lamb
Keyword(s):  
Lower Crust ◽  
Central Andes ◽  
Crustal Thickening ◽  
Direct Result ◽  
Western Margin ◽  
Crustal Shortening ◽  
Eastern Cordillera ◽  
Surface Uplift ◽  
Geological Evolution ◽  
History Of

The Cenozoic geological evolution of the Central Andes, along two transects between ∼17.5°S and 21°S, is compared with paleo-topography, determined from published paleo-altimetry studies. Surface and rock uplift are quantified using simple 2-D models of crustal shortening and thickening, together with estimates of sedimentation, erosion, and magmatic addition. Prior to ∼25 Ma, during a phase of amagmatic flat-slab subduction, thick-skinned crustal shortening and thickening (nominal age of initiation ∼40 Ma) was focused in the Eastern and Western Cordilleras, separated by a broad basin up to 300 km wide and close to sea level, which today comprises the high Altiplano. Surface topography at this time in the Altiplano and the western margin of the Eastern Cordillera appears to be ∼1 km lower than anticipated from crustal thickening, which may be due to the pull-down effect of the subducted slab, coupled to the overlying lithosphere by a cold mantle wedge. Oligocene steepening of the subducted slab is indicated by the initiation of the volcanic arc at ∼27–25 Ma, and widespread mafic volcanism in the Altiplano between 25 and 20 Ma. This may have resulted in detachment of mantle lithosphere and possibly dense lower crust, triggering 1–1.5 km of rapid uplift (over ≪5 Myrs) of the Altiplano and western margin of the Eastern Cordillera and establishing the present day lithospheric structure beneath the high Andes. Since ∼25 Ma, surface uplift has been the direct result of crustal shortening and thickening, locally modified by the effects of erosion, sedimentation, and magmatic addition from the mantle. The rate of crustal shortening and thickening varies with location and time, with two episodes of rapid shortening in the Altiplano, lasting <5 Myrs, that are superimposed on a long-term history of ductile shortening in the lower crust, driven by underthrusting of the Brazilian Shield on the eastern margin.

scholarly journals Exact and Approximate Weighted Model Integration with Probability Density Functions Using Knowledge Compilation

2019 ◽  
Vol 33 ◽  
pp. 7825-7833 ◽  
Author(s):  
Pedro Zuidberg Dos Martires ◽  
Anton Dries ◽  
Luc De Raedt
Keyword(s):  
Probability Density ◽  
Probabilistic Reasoning ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Knowledge Compilation ◽  
Model Integration ◽  
Weight Functions ◽  
Density Functions ◽  
Model Counting ◽  
Weighted Model

Weighted model counting has recently been extended to weighted model integration, which can be used to solve hybrid probabilistic reasoning problems. Such problems involve both discrete and continuous probability distributions. We show how standard knowledge compilation techniques (to SDDs and d-DNNFs) apply to weighted model integration, and use it in two novel solvers, one exact and one approximate solver. Furthermore, we extend the class of employable weight functions to actual probability density functions instead of mere polynomial weight functions.

The Estimation of Wind Speed and Wind Power Characteristics in Taiwan

2014 ◽  
Vol 535 ◽  
pp. 145-148
Author(s):  
Jeeng Min Ling ◽  
Kunkerati Lublertlop
Keyword(s):  
Wind Speed ◽  
Probability Density ◽  
Wind Power ◽  
Probability Distributions ◽  
Weibull Model ◽  
Probability Density Functions ◽  
Density Functions ◽  
Power Characteristics ◽  
Wind Characteristic ◽  
Better Than

In this paper, the Weibull, Gamma, Lognormal, Rayleigh probability density functions (PDF) were used to statistically analyze the characteristics of wind speed and evaluate the energy based on hourly records from years of 2004 to 2009 at 24 locations in Taiwan. Weibull model shows the best goodness probability density function for estimating behavior of wind characteristic within six years at 7 sites of weather station better than using the Gamma and Rayleigh model. The annual mean wind power density is estimated and compared by different index. The feasibility of probability distributions at different locations were investigated.

Review Of Some Mathematical And Physical Subjects

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Random Variable ◽  
Probability Density Functions ◽  
Density Functions ◽  
Discrete Random Variables ◽  
Actual Learning ◽  
The Given ◽  
Selection Of ◽  
Comprehensive Discussion

This chapter reviews some subjects in mathematics and physics that are used in different contexts throughout this book. The selection of subjects and the level of their coverage reflect the author’s perception of what potential users of this text were exposed to in their earlier studies. Therefore, only brief overview is given of some subjects while somewhat more comprehensive discussion is given of others. In neither case can the coverage provided substitute for the actual learning of these subjects that are covered in detail by many textbooks. A random variable is an observable whose repeated determination yields a series of numerical values (“realizations” of the random variable) that vary from trial to trial in a way characteristic of the observable. The outcomes of tossing a coin or throwing a die are familiar examples of discrete random variables. The position of a dust particle in air and the lifetime of a light bulb are continuous random variables. Discrete random variables are characterized by probability distributions; Pn denotes the probability that a realization of the given random variable is n. Continuous random variables are associated with probability density functions P(x): P(x1)dx denotes the probability that the realization of the variable x will be in the interval x1 . . . x1+dx.

Probability Density Functions

2019 ◽  
pp. 108-130
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Bayesian Inference ◽  
Probability Distribution ◽  
Probability Density ◽  
Probability Distributions ◽  
Random Variable ◽  
Probability Density Functions ◽  
Density Functions ◽  
Normal Distributions ◽  
Likelihood Profile ◽  
Variable Probability

This chapter builds on probability distributions. Its focus is on general concepts associated with probability density functions (pdf’s), which are distributions associated with continuous random variables. The continuous uniform and normal distributions are highlighted as examples of pdf’s. These and other pdf’s can be used to specify prior distributions, likelihoods, and/or posterior distributions in Bayesian inference. Although this chapter specifically focuses on the continuous uniform and normal distributions, the concepts discussed in this chapter will apply to other continuous probability distributions. By the end of the chapter, the reader should be able to define and use the following terms for a continuous random variable: random variable, probability distribution, parameter, probability density, likelihood, and likelihood profile.

scholarly journals RSSI Probability Density Functions Comparison Using Jensen-Shannon Divergence and Pearson Distribution

Technologies ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 26
Author(s):  
Antonios Lionis ◽  
Konstantinos P. Peppas ◽  
Hector E. Nistazakis ◽  
Andreas Tsigopoulos
Keyword(s):  
Probability Density ◽  
Atmospheric Turbulence ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Index Structure ◽  
Optical Channel ◽  
Density Functions ◽  
Free Space Optical ◽  
Leibler Divergence ◽  
Jensen Shannon Divergence

The performance of a free-space optical (FSO) communications link suffers from the deleterious effects of weather conditions and atmospheric turbulence. In order to better estimate the reliability and availability of an FSO link, a suitable distribution needs to be employed. The accuracy of this model depends strongly on the atmospheric turbulence strength which causes the scintillation effect. To this end, a variety of probability density functions were utilized to model the optical channel according to the strength of the refractive index structure parameter. Although many theoretical models have shown satisfactory performance, in reality they can significantly differ. This work employs an information theoretic method, namely the so-called Jensen–Shannon divergence, a symmetrization of the Kullback–Leibler divergence, to measure the similarity between different probability distributions. In doing so, a large experimental dataset of received signal strength measurements from a real FSO link is utilized. Additionally, the Pearson family of continuous probability distributions is also employed to determine the best fit according to the mean, standard deviation, skewness and kurtosis of the modeled data.

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