183,011 research outputs found
Modeling and simulating chemical reactions
Many students are familiar with the idea of modeling chemical reactions in terms of ordinary differential equations. However, these deterministic reaction rate equations are really a certain large-scale limit of a sequence of finer-scale probabilistic models. In studying this hierarchy of models, students can be exposed to a range of modern ideas in applied and computational mathematics. This article introduces some of the basic concepts in an accessible manner and points to some challenges that currently occupy researchers in this area. Short, downloadable MATLAB codes are listed and described
Nonlinear State-Space Models for Microeconometric Panel Data
In applied microeconometric panel data analyses, time-constant random effects and first-order Markov chains are the most prevalent structures to account for intertemporal correlations in limited dependent variable models. An example from health economics shows that the addition of a simple autoregressive error terms leads to a more plausible and parsimonious model which also captures the dynamic features better. The computational problems encountered in the estimation of such models - and a broader class formulated in the framework of nonlinear state space models - hampers their widespread use. This paper discusses the application of different nonlinear filtering approaches developed in the time-series literature to these models and suggests that a straightforward algorithm based on sequential Gaussian quadrature can be expected to perform well in this setting. This conjecture is impressively confirmed by an extensive analysis of the example application
Probabilistic load flow in systems with high wind power penetration
This paper proposes a method for solving a probabilistic load flows that takes into account the uncertainties of wind
generation, but also of load and conventional
systems. The method uses a combination of methods including cumulant, point estimate and convolution. Cornish Fisher expansion series are also used to find the CDF. The method is of especial application to estimate active power flows through lines
Generalizing the first-difference correlated random walk for marine animal movement data
Animal telemetry data are often analysed with discrete time movement models
assuming rotation in the movement. These models are defined with equidistant
distant time steps. However, telemetry data from marine animals are observed
irregularly. To account for irregular data, a time-irregularised
first-difference correlated random walk model with drift is introduced. The
model generalizes the commonly used first-difference correlated random walk
with regular time steps by allowing irregular time steps, including a drift
term, and by allowing different autocorrelation in the two coordinates. The
model is applied to data from a ringed seal collected through the Argos
satellite system, and is compared to related movement models through
simulations. Accounting for irregular data in the movement model results in
accurate parameter estimates and reconstruction of movement paths. Measured by
distance, the introduced model can provide more accurate movement paths than
the regular time counterpart. Extracting accurate movement paths from uncertain
telemetry data is important for evaluating space use patterns for marine
animals, which in turn is crucial for management. Further, handling irregular
data directly in the movement model allows efficient simultaneous analysis of
several animals
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