263,120 research outputs found
Basin structure of optimization based state and parameter estimation
Most data based state and parameter estimation methods require suitable
initial values or guesses to achieve convergence to the desired solution, which
typically is a global minimum of some cost function. Unfortunately, however,
other stable solutions (e.g., local minima) may exist and provide suboptimal or
even wrong estimates. Here we demonstrate for a 9-dimensional Lorenz-96 model
how to characterize the basin size of the global minimum when applying some
particular optimization based estimation algorithm. We compare three different
strategies for generating suitable initial guesses and we investigate the
dependence of the solution on the given trajectory segment (underlying the
measured time series). To address the question of how many state variables have
to be measured for optimal performance, different types of multivariate time
series are considered consisting of 1, 2, or 3 variables. Based on these time
series the local observability of state variables and parameters of the
Lorenz-96 model is investigated and confirmed using delay coordinates. This
result is in good agreement with the observation that correct state and
parameter estimation results are obtained if the optimization algorithm is
initialized with initial guesses close to the true solution. In contrast,
initialization with other exact solutions of the model equations (different
from the true solution used to generate the time series) typically fails, i.e.
the optimization procedure ends up in local minima different from the true
solution. Initialization using random values in a box around the attractor
exhibits success rates depending on the number of observables and the available
time series (trajectory segment).Comment: 15 pages, 2 figure
Asymptotically stable phase synchronization revealed by autoregressive circle maps
A new type of nonlinear time series analysis is introduced, based on phases,
which are defined as polar angles in spaces spanned by a finite number of
delayed coordinates. A canonical choice of the polar axis and a related
implicit estimation scheme for the potentially underlying auto-regressive
circle map (next phase map) guarantee the invertibility of reconstructed phase
space trajectories to the original coordinates. The resulting Fourier
approximated, Invertibility enforcing Phase Space map (FIPS map) is well suited
to detect conditional asymptotic stability of coupled phases. This rather
general synchronization criterion unites two existing generalisations of the
old concept and can successfully be applied e.g. to phases obtained from ECG
and airflow recordings characterizing cardio-respiratory interaction.Comment: PDF file, 232 KB, 24 pages, 3 figures; cheduled for Phys. Rev. E
(Nov) 200
State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing
Determining the magnitude and location of neural sources within the brain
that are responsible for generating magnetoencephalography (MEG) signals
measured on the surface of the head is a challenging problem in functional
neuroimaging. The number of potential sources within the brain exceeds by an
order of magnitude the number of recording sites. As a consequence, the
estimates for the magnitude and location of the neural sources will be
ill-conditioned because of the underdetermined nature of the problem. One
well-known technique designed to address this imbalance is the minimum norm
estimator (MNE). This approach imposes an regularization constraint that
serves to stabilize and condition the source parameter estimates. However,
these classes of regularizer are static in time and do not consider the
temporal constraints inherent to the biophysics of the MEG experiment. In this
paper we propose a dynamic state-space model that accounts for both spatial and
temporal correlations within and across candidate intracortical sources. In our
model, the observation model is derived from the steady-state solution to
Maxwell's equations while the latent model representing neural dynamics is
given by a random walk process.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS483 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Power series approximations for two-class generalized processor sharing systems
We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are nonempty, a customer of queue 1 is served with probability beta, and a customer of queue 2 is served with probability 1-beta. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating function U(z (1),z (2)) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary value problems. Then, we propose to use the same functional equation to obtain a power series for U(z (1),z (2)) in beta. The first coefficient of this power series corresponds to the priority case beta=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations for the mean stationary queue lengths are obtained from combining truncated power series and Pad, approximation
A hierarchy for modeling high speed propulsion systems
General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery, such as inlets, ramjets, and scramjets. The discussion is separated into four areas: (1) computational fluid dynamics models for the entire nonlinear system or high order nonlinear models; (2) high order linearized models derived from fundamental physics; (3) low order linear models obtained from the other high order models; and (4) low order nonlinear models (order here refers to the number of dynamic states). Included in the discussion are any special considerations based on the relevant control system designs. The methods discussed are for the quasi-one-dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, including moving normal shocks, hammershocks, simple subsonic combustion via heat addition, temperature dependent gases, detonations, and thermal choking. The report also contains a comprehensive list of papers and theses generated by this grant
Continuous-time VIX dynamics: on the role of stochastic volatility of volatility
This paper examines the ability of several different continuous-time one- and two-factor jump-diffusion models to capture the dynamics of the VIX volatility index for the period between 1990 and 2010. For the one-factor models we study affine and non-affine specifications, possibly augmented with jumps. Jumps in one-factor models occur frequently, but add surprisingly little to the ability of the models to explain the dynamic of the VIX. We present a stochastic volatility of volatility model that can explain all the time-series characteristics of the VIX studied in this paper. Extensions demonstrate that sudden jumps in the VIX are more likely during tranquil periods and the days when jumps occur coincide with major political or economic events. Using several statistical and operational metrics we find that non-affine one-factor models outperform their affine counterparts and modeling the log of the index is superior to modeling the VIX level directly
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