16,264 research outputs found
Consistent Dynamic Mode Decomposition
We propose a new method for computing Dynamic Mode Decomposition (DMD)
evolution matrices, which we use to analyze dynamical systems. Unlike the
majority of existing methods, our approach is based on a variational
formulation consisting of data alignment penalty terms and constitutive
orthogonality constraints. Our method does not make any assumptions on the
structure of the data or their size, and thus it is applicable to a wide range
of problems including non-linear scenarios or extremely small observation sets.
In addition, our technique is robust to noise that is independent of the
dynamics and it does not require input data to be sequential. Our key idea is
to introduce a regularization term for the forward and backward dynamics. The
obtained minimization problem is solved efficiently using the Alternating
Method of Multipliers (ADMM) which requires two Sylvester equation solves per
iteration. Our numerical scheme converges empirically and is similar to a
provably convergent ADMM scheme. We compare our approach to various
state-of-the-art methods on several benchmark dynamical systems
Soft computing applications in dynamic model identification of polymer extrusion process
This paper proposes the application of soft computing to deal with the constraints in conventional modelling techniques of the dynamic extrusion process. The proposed technique increases the efficiency in utilising the available information during the model identification. The resultant model can be classified as a ‘grey-box model’ or has been termed as a ‘semi-physical model’ in the context. The extrusion process contains a number of parameters that are sensitive to the operating environment. Fuzzy ruled-based system is introduced into the analytical model of the extrusion by means of sub-models to approximate those operational-sensitive parameters. In drawing the optimal structure for the sub-models, a hybrid algorithm of genetic algorithm with fuzzy system (GA-Fuzzy) has been implemented. The sub-models obtained show advantages such as linguistic interpretability, simpler rule-base and less membership functions. The developed model is adaptive with its learning ability through the steepest decent error back-propagation algorithm. This ability might help to minimise the deviation of the model prediction when the operational-sensitive parameters adapt to the changing operating environment in the real situation. The model is first evaluated through simulations on the consistency of model prediction to the theoretical analysis. Then, the effectiveness of adaptive sub-models in approximating the operational-sensitive parameters during the operation is further investigated
Blazes: Coordination Analysis for Distributed Programs
Distributed consistency is perhaps the most discussed topic in distributed
systems today. Coordination protocols can ensure consistency, but in practice
they cause undesirable performance unless used judiciously. Scalable
distributed architectures avoid coordination whenever possible, but
under-coordinated systems can exhibit behavioral anomalies under fault, which
are often extremely difficult to debug. This raises significant challenges for
distributed system architects and developers. In this paper we present Blazes,
a cross-platform program analysis framework that (a) identifies program
locations that require coordination to ensure consistent executions, and (b)
automatically synthesizes application-specific coordination code that can
significantly outperform general-purpose techniques. We present two case
studies, one using annotated programs in the Twitter Storm system, and another
using the Bloom declarative language.Comment: Updated to include additional materials from the original technical
report: derivation rules, output stream label
The Consistency of Partial Observability for PDEs
In this paper, a new definition of observability is introduced for PDEs. It
is a quantitative measure of partial observability. The quantity is proved to
be consistent if approximated using well posed approximation schemes. A first
order approximation of an unobservability index using empirical gramian is
introduced. For linear systems with full state observability, the empirical
gramian is equivalent to the observability gramian in control theory. The
consistency of the defined observability is exemplified using a Burgers'
equation.Comment: 28 pages, 3 figure
On the Convergence of Finite Element Methods for Hamilton-Jacobi-Bellman Equations
In this note we study the convergence of monotone P1 finite element methods
on unstructured meshes for fully non-linear Hamilton-Jacobi-Bellman equations
arising from stochastic optimal control problems with possibly degenerate,
isotropic diffusions. Using elliptic projection operators we treat
discretisations which violate the consistency conditions of the framework by
Barles and Souganidis. We obtain strong uniform convergence of the numerical
solutions and, under non-degeneracy assumptions, strong L2 convergence of the
gradients.Comment: Keywords: Bellman equations, finite element methods, viscosity
solutions, fully nonlinear operators; 18 pages, 1 figur
Revisiting Kawasaki dynamics in one dimension
Critical exponents of the Kawasaki dynamics in the Ising chain are
re-examined numerically through the spectrum gap of evolution operators
constructed both in spin and domain wall representations. At low temperature
regimes the latter provides a rapid finite-size convergence to these exponents,
which tend to for instant quenches under ferromagnetic
couplings, while approaching to in the antiferro case. The spin
representation complements the evaluation of dynamic exponents at higher
temperature scales, where the kinetics still remains slow.Comment: 11 pages, 8 figure
Statistical exponential formulas for homogeneous diffusion
Let denote the -homogeneous -Laplacian, for . This paper proves that the unique bounded, continuous viscosity
solution of the Cauchy problem \left\{ \begin{array}{c} u_{t} \ - \ (
\frac{p}{ \, N + p - 2 \, } ) \, \Delta^{1}_{p} u ~ = ~ 0 \quad \mbox{for}
\quad x \in \mathbb{R}^{N}, \quad t > 0 \\ \\ u(\cdot,0) ~ = ~ u_{0} \in BUC(
\mathbb{R}^{N} ) \end{array} \right. is given by the exponential formula
where the statistical operator is defined by with , when and by with , when . Possible extensions to problems with Dirichlet boundary conditions and to
homogeneous diffusion on metric measure spaces are mentioned briefly
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