Search results for "Random Variables"
showing 10 items of 37 documents
Longitudinal Investigation into Genetics in the Conservation of Metabolic Phenotypes in Danish and Chinese Twins
2016
Longitudinal twin studies on long term conservation of individual metabolic phenotypes can help to explore the genetic and environmental basis in maintaining metabolic homeostasis and metabolic health. We performed a longitudinal twin study on 12 metabolic phenotypes from Danish twins followed up for 12 years and Chinese twins traced for 7 years. The study covered a relatively large sample of 502 pairs of Danish adult twins with a mean age at intake of 38 years and a total of 181 Chinese adult twin pairs with a mean baseline age of 39.5 years. Bivariate twin models were fitted to the longitudinal measurements taken at two time points (at baseline and follow-up) to estimate the genetic and e…
A method for the probabilistic analysis of nonlinear systems
1995
Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an a…
Dynamics of Two Picophytoplankton Groups in Mediterranean Sea: Analysis of the Deep Chlorophyll Maximum by a Stochastic Advection-Reaction-Diffusion …
2013
A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for th…
Does Sedentary Behavior Predict Academic Performance in Adolescents or the Other Way Round? A Longitudinal Path Analysis.
2016
This study examined whether adolescents’ time spent on sedentary behaviors (academic, technological-based and social-based activities) was a better predictor of academic performance than the reverse. A cohort of 755 adolescents participated in a three-year period study. Structural Equation Modeling techniques were used to test plausible causal hypotheses. Four competing models were analyzed to determine which model best fitted the data. The Best Model was separately tested by gender. The Best Model showed that academic performance was a better predictor of sedentary behaviors than the other way round. It also indicated that students who obtained excellent academic results were more likely t…
Relations between structure and estimators in networks of dynamical systems
2011
The article main focus is on the identification of a graphical model from time series data associated with different interconnected entities. The time series are modeled as realizations of stochastic processes (representing nodes of a graph) linked together via transfer functions (representing the edges of the graph). Both the cases of non-causal and causal links are considered. By using only the measurements of the node outputs and without assuming any prior knowledge of the network topology, a method is provided to estimate the graph connectivity. In particular, it is proven that the method determines links to be present only between a node and its “kins”, where kins of a node consist of …
Scalable and Privacy-Preserving Admission Control for Smart Grids
2015
International audience; Energy demand and production need to be constantly matched in the power grid. The traditional paradigm to continuously adapt the production to the demand is challenged by the increasing penetration of more variable and less predictable energy sources, like solar photovoltaics and wind power. An alternative approach is the so called direct control of some inherently flexible electric loads to shape the demand. Direct control of deferrable loads presents analogies with flow admission control in telecommunication networks: a request for network resources (bandwidth or energy) can be delayed on the basis of the current network status in order to guarantee some performanc…
Backwards Martingales and Exchangeability
2020
With many data acquisitions, such as telephone surveys, the order in which the data come does not matter. Mathematically, we say that a family of random variables is exchangeable if the joint distribution does not change under finite permutations. De Finetti’s structural theorem says that an infinite family of E-valued exchangeable random variables can be described by a two-stage experiment. At the first stage, a probability distribution Ξ on E is drawn at random. At the second stage, independent and identically distributed random variables with distribution Ξ are implemented.
Forward and backward diffusion approximations for haploid exchangeable population models
2001
Abstract The class of haploid population models with non-overlapping generations and fixed population size N is considered such that the family sizes ν1,…,νN within a generation are exchangeable random variables. A criterion for weak convergence in the Skorohod sense is established for a properly time- and space-scaled process counting the number of descendants forward in time. The generator A of the limit process X is constructed using the joint moments of the offspring variables ν1,…,νN. In particular, the Wright–Fisher diffusion with generator Af(x)= 1 2 x(1−x)f″(x) appears in the limit as the population size N tends to infinity if and only if the condition lim N→∞ E((ν 1 −1) 3 )/(N Var …
Kernel methods and their derivatives: Concept and perspectives for the earth system sciences.
2020
Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However, kernel machines are still considered black-box models as the feature mapping is not directly accessible and difficult to interpret.The aim of this work is to show that it is indeed possible to interpret the functions learned by various kernel methods is intuitive despite their complexity. Specifically, we show that derivatives of these functions have a simple mathematical formulation, are easy to compute, and can be applied to many different problems. We n…
Bartlett formalism generating functions and Z-transforms in fluctuation and noise theory
1983
Abstract “La theorie des fonctions generatrices s'adapte elle meme et avec la plus grande generalite aux questions des probabilite les plus difficiles.” (Laplace, 1812) “An important part of probability theory consists of the derivation of the probability distribution of the sum of n random variables, each of which obeys a given probability law, and the development of asymptotic forms of these distributions valid for increasing n. Probability generating functions owe their dominant position to the simplification they permit to both problems. Their employment to obtain the successive moments of a probability distribution and to solve the difference equations of probability theory is ancillar…