24,942 research outputs found
Levelable Sets and the Algebraic Structure of Parameterizations
Asking which sets are fixed-parameter tractable for a given parameterization
constitutes much of the current research in parameterized complexity theory.
This approach faces some of the core difficulties in complexity theory. By
focussing instead on the parameterizations that make a given set
fixed-parameter tractable, we circumvent these difficulties. We isolate
parameterizations as independent measures of complexity and study their
underlying algebraic structure. Thus we are able to compare parameterizations,
which establishes a hierarchy of complexity that is much stronger than that
present in typical parameterized algorithms races. Among other results, we find
that no practically fixed-parameter tractable sets have optimal
parameterizations
Construction of analysis-suitable planar multi-patch parameterizations
Isogeometric analysis allows to define shape functions of global
continuity (or of higher continuity) over multi-patch geometries. The
construction of such -smooth isogeometric functions is a non-trivial
task and requires particular multi-patch parameterizations, so-called
analysis-suitable (in short, AS-) parameterizations, to ensure
that the resulting isogeometric spaces possess optimal approximation
properties, cf. [7]. In this work, we show through examples that it is possible
to construct AS- multi-patch parameterizations of planar domains, given
their boundary. More precisely, given a generic multi-patch geometry, we
generate an AS- multi-patch parameterization possessing the same
boundary, the same vertices and the same first derivatives at the vertices, and
which is as close as possible to this initial geometry. Our algorithm is based
on a quadratic optimization problem with linear side constraints. Numerical
tests also confirm that isogeometric spaces over AS- multi-patch
parameterized domains converge optimally under mesh refinement, while for
generic parameterizations the convergence order is severely reduced
Optimal experimental designs for inverse quadratic regression models
In this paper optimal experimental designs for inverse quadratic regression
models are determined. We consider two different parameterizations of the model
and investigate local optimal designs with respect to the -, - and
-criteria, which reflect various aspects of the precision of the maximum
likelihood estimator for the parameters in inverse quadratic regression models.
In particular it is demonstrated that for a sufficiently large design space
geometric allocation rules are optimal with respect to many optimality
criteria. Moreover, in numerous cases the designs with respect to the different
criteria are supported at the same points. Finally, the efficiencies of
different optimal designs with respect to various optimality criteria are
studied, and the efficiency of some commonly used designs are investigated.Comment: 24 page
Revisiting the parametrization of Equation of State of Dark Energy via SNIa Data
In this paper, we revisit the parameterizations of the equation of state of
dark energy and point out that comparing merely the of different
fittings may not be optimal for choosing the "best" parametrization. Another
figure of merit for evaluating different parametrizations based on the area of
the band is proposed. In light of the analysis of some two-parameter
parameterizations and models based on available SNIa data, the area of
band seems to be a good figure of merit, especially in the situation that the
value of for different parametrizations are very close.
Therefore, we argue that both the area of the band and should be synthetically considered for choosing a better parametrization
of dark energy in the future experiments.Comment: 7 pages, contains 5 figures and 2 tables, accepted for publication in
MNRA
System-level, Input-output and New Parameterizations of Stabilizing Controllers, and Their Numerical Computation
It is known that the set of internally stabilizing controller
is non-convex, but it admits convex
characterizations using certain closed-loop maps: a classical result is the
{Youla parameterization}, and two recent notions are the {system-level
parameterization} (SLP) and the {input-output parameterization} (IOP). In this
paper, we address the existence of new convex parameterizations and discuss
potential tradeoffs of each parametrization in different scenarios. Our main
contributions are: 1) We first reveal that only four groups of stable
closed-loop transfer matrices are equivalent to internal stability: one of them
is used in the SLP, another one is used in the IOP, and the other two are new,
leading to two new convex parameterizations of . 2)
We then investigate the properties of these parameterizations after imposing
the finite impulse response (FIR) approximation, revealing that the IOP has the
best ability of approximating given FIR
constraints. 3) These four parameterizations require no \emph{a priori}
doubly-coprime factorization of the plant, but impose a set of equality
constraints. However, these equality constraints will never be satisfied
exactly in numerical computation. We prove that the IOP is numerically robust
for open-loop stable plants, in the sense that small mismatches in the equality
constraints do not compromise the closed-loop stability. The SLP is known to
enjoy numerical robustness in the state feedback case; here, we show that
numerical robustness of the four-block SLP controller requires case-by-case
analysis in the general output feedback case.Comment: 20 pages; 5 figures. Added extensions on numerial computation and
robustness of closed-loop parameterization
On the Equivalence of Youla, System-level and Input-output Parameterizations
A convex parameterization of internally stabilizing controllers is
fundamental for many controller synthesis procedures. The celebrated Youla
parameterization relies on a doubly-coprime factorization of the system, while
the recent system-level and input-output characterizations require no
doubly-coprime factorization but a set of equality constraints for achievable
closed-loop responses. In this paper, we present explicit affine mappings among
Youla, system-level and input-output parameterizations. Two direct implications
of the affine mappings are 1) any convex problem in Youla, system level, or
input-output parameters can be equivalently and convexly formulated in any
other one of these frameworks, including the convex system-level synthesis
(SLS); 2) the condition of quadratic invariance (QI) is sufficient and
necessary for the classical distributed control problem to admit an equivalent
convex reformulation in terms of Youla, system-level, or input-output
parameters.Comment: 8 pages, 3 figure
A framework for the evaluation of turbulence closures used in mesoscale ocean large-eddy simulations
We present a methodology to determine the best turbulence closure for an
eddy-permitting ocean model through measurement of the error-landscape of the
closure's subgrid spectral transfers and flux. We apply this method to 6
different closures for forced-dissipative simulations of the barotropic
vorticity equation on a f-plane (2D Navier-Stokes equation). Using a
high-resolution benchmark, we compare each closure's model of energy and
enstrophy transfer to the actual transfer observed in the benchmark run. The
error-landscape norms enable us to both make objective comparisons between the
closures and to optimize each closure's free parameter for a fair comparison.
The hyper-viscous closure most closely reproduces the enstrophy cascade,
especially at larger scales due to the concentration of its dissipative effects
to the very smallest scales. The viscous and Leith closures perform nearly as
well, especially at smaller scales where all three models were dissipative. The
Smagorinsky closure dissipates enstrophy at the wrong scales. The anticipated
potential vorticity closure was the only model to reproduce the upscale
transfer of kinetic energy from the unresolved scales, but would require
high-order Laplacian corrections in order to concentrate dissipation at the
smallest scales. The Lagrangian-averaged alpha-model closure did not perform
successfully for forced 2D isotropic Navier-Stokes: small-scale filamentation
is only slightly reduced by the model while small-scale roll-up is prevented.
Together, this reduces the effects of diffusion.Comment: 44 pages, 21 figures, 1 Appendix, submitted to Ocean Modelin
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