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Forthcoming events in this series
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Highly comparative time-series analysis: the empirical structure of time series and their methods
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Indirect Evidence and the Choice between Deterministic and Indeterministic Models.
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How errors in model-simulated internal variability could impact on Detection and Attribution
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Stochastic Parameterisation
Abstract
This will be a discussion on Stochastic Parameterisation, led by Hannah.
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Improving the Representation of Convective Clouds in Climate Models
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11:15
A hybrid sequential data assimilation scheme for model state and parameter estimation. POSTPONED TO A LATER DATE
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The sufficiency of two-point statistics for image analysis and synthesis
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Development of Tracking Software for Realistic Models of Bacterial Swimming Patterns
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Interacting expensive functions on rectangular and spherical domains
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Submarine Hunting and Other Applications of the Mathematics of Tracking. (NOTE Change of speaker and topic)
Abstract
The background for the multitarget tracking problem is presented
along with a new framework for solution using the theory of random
finite sets. A range of applications are presented including
submarine tracking with active SONAR, classifying underwater entities
from audio signals and extracting cell trajectories from biological
data.
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Differential Geometry Applied to Dynamical Systems
Abstract
This work aims to present a new approach called Flow Curvature Method
that applies Differential Geometry to Dynamical Systems. Hence, for a
trajectory curve, an integral of any n-dimensional dynamical system
as a curve in Euclidean n-space, the curvature of the trajectory or
the flow may be analytically computed. Then, the location of the
points where the curvature of the flow vanishes defines a manifold
called flow curvature manifold. Such a manifold being defined from
the time derivatives of the velocity vector field, contains
information about the dynamics of the system, hence identifying the
main features of the system such as fixed points and their stability,
local bifurcations of co-dimension one, centre manifold equation,
normal forms, linear invariant manifolds (straight lines, planes,
hyperplanes).
In the case of singularly perturbed systems or slow-fast dynamical
systems, the flow curvature manifold directly provides the slow
invariant manifold analytical equation associated with such systems.
Also, starting from the flow curvature manifold, it will be
demonstrated how to find again the corresponding dynamical system,
thus solving the inverse problem.
Moreover, the concept of curvature of trajectory curves applied to
classical dynamical systems such as Lorenz and Rossler models
enabled to highlight one-dimensional invariant sets, i.e. curves
connecting fixed points which are zero-dimensional invariant sets.
Such "connecting curves" provide information about the structure of
the attractors and may be interpreted as the skeleton of these
attractors. Many examples are given in dimension three and more.
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Feature selection for sparse data analysis, and best 'off the shelf
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Stochastic partial differential equations in reservoir property modeling
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History matching problems under training-image based geological model constraints
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