981 research outputs found
The Existence of Linear Selection and the Quotient Lifting Property
Lifting properties for Banach spaces are studied. An alternate version of the
lifting property due to Lindenstrass and Tzafriri is proposed and a
characterization, up to isomorphism, is given. The quotient lifting property
for pairs of Banach spaces , with proximinal in , is considered
and several conditions for the property to hold are given.Comment: 16 pages and 2 figure
Choosing Lag Lengths in Nonlinear Dynamic Models
Given that it is quite impractical to use standard model selection criteria in a nonlinear modeling context, the builders of nonlinear models often choose lag length by setting it equal to the lag length chosen for a linear autoregression of the data. This paper studies the performance of this procedure in a variety of circumstances, and then proposes some new and simple model selection procedures, based on linear approximations of the nonlinear forms. The idea here is to apply standard selection criteria to these linear approximations, rather than to autoregressions that make no provision for nonlinear behavior. A simulation study compares the properties of these proposed procedures with the properties of linear selection procedures.Nonlinear time series models, Neural networks, Model selection criteria, Polynomial approximations, Volterra expansions.
The linear selections of metric projections in the Lp spaces
AbstractA characterization is given of those subspaces of Lp space whose metric projection is linear, and of L1, which is finitely codimensional, whose metric projection admits a linear selection
The Markoff-Automaton - a New Algorithm for Simulating the Time--Evolution of Large Stochastic Dynamic Systems
We describe a new algorithm for simulating complex Markoff-processes. We have
used a reaction-cell method in order to simulate arbitrary reactions. It can be
used for any kind of RDS on arbitrary topologies, including fractal dimensions
or configurations not being related to any spatial geometry. The events within
a single cell are managed by an event handler which has been implemented
independently of the system studied. The method is exact on the Markoff level
including the correct treatment of finite numbers of molecules. To demonstrate
its properties, we apply it on a very simple reaction-diffusion-systems (RDS).
The chemical equations A+A -> inert and A+B -> inert in 1 to 4 dimensions serve
as models for systems whose dynamics on an intermediate time scale are governed
by fluctuations. We compare our results to the analytic approach by the scaling
ansatz. The simulations confirm the exponents of the A+B system within
statistical errors, including the logarithmic corrections in the dimension d=2.
The method is capable to simulate the crossover from the reaction to diffusion
limited regime, which is defined by a crossover time depending on the system
size.Comment: 29 Pages, uuencoded, compressed Dvi file, 89kB. pictures included as
uuencoded, compressed tar file, 32 Kb full postscript version (191KB)
available at
http://summa.physik.hu-berlin.de:80/papers/ThomasFricke/rdcompphys.ps.
Cosmological constraints from Sunyaev-Zeldovich cluster counts: an approach to account for missing redshifts
The accumulation of redshifts provides a significant observational bottleneck
when using galaxy cluster surveys to constrain cosmological parameters. We
propose a simple method to allow the use of samples where there is a fraction
of the redshifts that are not known. The simplest assumption is that the
missing redshifts are randomly extracted from the catalogue, but the method
also allows one to take into account known selection effects in the
accumulation of redshifts. We quantify the reduction in statistical precision
of cosmological parameter constraints as a function of the fraction of missing
redshifts for simulated surveys, and also investigate the impact of making an
incorrect assumption for the distribution of missing redshifts.Comment: 6 pages, 5 figures, accepted by Ap
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