661 research outputs found
Lyapunov-based online parameter estimation in continuous fluidized bed spray agglomeration processes
Laplace deconvolution with noisy observations
In the present paper we consider Laplace deconvolution for discrete noisy
data observed on the interval whose length may increase with a sample size.
Although this problem arises in a variety of applications, to the best of our
knowledge, it has been given very little attention by the statistical
community. Our objective is to fill this gap and provide statistical treatment
of Laplace deconvolution problem with noisy discrete data. The main
contribution of the paper is explicit construction of an asymptotically
rate-optimal (in the minimax sense) Laplace deconvolution estimator which is
adaptive to the regularity of the unknown function. We show that the original
Laplace deconvolution problem can be reduced to nonparametric estimation of a
regression function and its derivatives on the interval of growing length T_n.
Whereas the forms of the estimators remain standard, the choices of the
parameters and the minimax convergence rates, which are expressed in terms of
T_n^2/n in this case, are affected by the asymptotic growth of the length of
the interval.
We derive an adaptive kernel estimator of the function of interest, and
establish its asymptotic minimaxity over a range of Sobolev classes. We
illustrate the theory by examples of construction of explicit expressions of
Laplace deconvolution estimators. A simulation study shows that, in addition to
providing asymptotic optimality as the number of observations turns to
infinity, the proposed estimator demonstrates good performance in finite sample
examples
Topological interactions in a Boltzmann-type framework
We consider a finite number of particles characterised by their positions and
velocities. At random times a randomly chosen particle, the follower, adopts
the velocity of another particle, the leader. The follower chooses its leader
according to the proximity rank of the latter with respect to the former. We
study the limit of a system size going to infinity and, under the assumption of
propagation of chaos, show that the limit equation is akin to the Boltzmann
equation. However, it exhibits a spatial non-locality instead of the classical
non-locality in velocity space. This result relies on the approximation
properties of Bernstein polynomials
Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes
New algorithms for computing of asymptotic expansions for stationary
distributions of nonlinearly perturbed semi-Markov processes are presented. The
algorithms are based on special techniques of sequential phase space reduction,
which can be applied to processes with asymptotically coupled and uncoupled
finite phase spaces.Comment: 83 page
Random Feature Models for Learning Interacting Dynamical Systems
Particle dynamics and multi-agent systems provide accurate dynamical models
for studying and forecasting the behavior of complex interacting systems. They
often take the form of a high-dimensional system of differential equations
parameterized by an interaction kernel that models the underlying attractive or
repulsive forces between agents. We consider the problem of constructing a
data-based approximation of the interacting forces directly from noisy
observations of the paths of the agents in time. The learned interaction
kernels are then used to predict the agents behavior over a longer time
interval. The approximation developed in this work uses a randomized feature
algorithm and a sparse randomized feature approach. Sparsity-promoting
regression provides a mechanism for pruning the randomly generated features
which was observed to be beneficial when one has limited data, in particular,
leading to less overfitting than other approaches. In addition, imposing
sparsity reduces the kernel evaluation cost which significantly lowers the
simulation cost for forecasting the multi-agent systems. Our method is applied
to various examples, including first-order systems with homogeneous and
heterogeneous interactions, second order homogeneous systems, and a new sheep
swarming system
Population balance modelling of polydispersed particles in reactive flows
Polydispersed particles in reactive flows is a wide subject area encompassing a range of dispersed flows with particles, droplets or bubbles that are created, transported and possibly interact within a reactive flow environment - typical examples include soot formation, aerosols, precipitation and spray combustion. One way to treat such problems is to employ as a starting point the Newtonian equations of motion written in a Lagrangian framework for each individual particle and either solve them directly or derive probabilistic equations for the particle positions (in the case of turbulent flow). Another way is inherently statistical and begins by postulating a distribution of particles over the distributed properties, as well as space and time, the transport equation for this distribution being the core of this approach. This transport equation, usually referred to as population balance equation (PBE) or general dynamic equation (GDE), was initially developed and investigated mainly in the context of spatially homogeneous systems. In the recent years, a growth of research activity has seen this approach being applied to a variety of flow problems such as sooting flames and turbulent precipitation, but significant issues regarding its appropriate coupling with CFD pertain, especially in the case of turbulent flow. The objective of this review is to examine this body of research from a unified perspective, the potential and limits of the PBE approach to flow problems, its links with Lagrangian and multi-fluid approaches and the numerical methods employed for its solution. Particular emphasis is given to turbulent flows, where the extension of the PBE approach is met with challenging issues. Finally, applications including reactive precipitation, soot formation, nanoparticle synthesis, sprays, bubbles and coal burning are being reviewed from the PBE perspective. It is shown that population balance methods have been applied to these fields in varying degrees of detail, and future prospects are discussed
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