Dimension and coverage of multiple-models structures using clustering techniques

In this work a method for building multiple-model structures is presented. A clustering algorithm that uses data from the system is employed to define the architecture of the multiple-model, including the size of the region covered by each model, and the number of models. A heating ventilation and air conditioning system is used as a testbed of the proposed method.

First-dimension separation with the MicroRotoforTM cell prior to SDS-PAGE and LC-MS/MS analysis

Free-flow isoelectric focusing (IEF) is a gel-free method for separating proteins based on their isoelectric point (pl) in a liquid environment and in the presence of carrier ampholytes. this method has been used with the RotoforTM cell at the preparative scale to fractionate proteins from samples containing several hundred milligrams of protein; see the refeences listed in Bio-Rad bulletin 3152. the MicroRotofor cell applies the same method to much sl=maller protein samples without dilution, separating and recoverng milligram quantities of protein in a total volume of about 2 ml.

Neurofuzzy design and model construction of nonlinear dynamical processes from data

A common problem in many data based modelling algorithms such as associative memory networks is the problem of the curse of dimensionality. In this paper, a new two-stage neurofuzzy system design and construction algorithm (NeuDeC) for nonlinear dynamical processes is introduced to effectively tackle this problem. A new simple preprocessing method is initially derived and applied to reduce the rule base, followed by a fine model detection process based on the reduced rule set by using forward orthogonal least squares model structure detection. In both stages, new A-optimality experimental design-based criteria we used. In the preprocessing stage, a lower bound of the A-optimality design criterion is derived and applied as a subset selection metric, but in the later stage, the A-optimality design criterion is incorporated into a new composite cost function that minimises model prediction error as well as penalises the model parameter variance. The utilisation of NeuDeC leads to unbiased model parameters with low parameter variance and the additional benefit of a parsimonious model structure. Numerical examples are included to demonstrate the effectiveness of this new modelling approach for high dimensional inputs.

Low-order dynamical behavior in the martian atmosphere: Diagnosis of general circulation model results

The hypothesis of a low dimensional martian climate attractor is investigated by the application of the proper orthogonal decomposition (POD) to a simulation of martian atmospheric circulation using the UK Mars general circulation model (UK-MGCM). In this article we focus on a time series of the interval between autumn and winter in the northern hemisphere, when baroclinic activity is intense. The POD is a statistical technique that allows the attribution of total energy (TE) to particular structures embedded in the UK-MGCM time-evolving circulation. These structures are called empirical orthogonal functions (EOFs). Ordering the EOFs according to their associated energy content, we were able to determine the necessary number to account for a chosen amount of atmospheric TE. We show that for Mars a large fraction of TE is explained by just a few EOFs (with 90% TE in 23 EOFs), which apparently support the initial hypothesis. We also show that the resulting EOFs represent classical types of atmospheric motion, such as thermal tides and transient waves. Thus, POD is shown to be an efficient method for the identification of different classes of atmospheric modes. It also provides insight into the non-linear interaction of these modes.

The control of dynamical systems by neural networks

In this paper the use of neural networks for the control of dynamical systems is considered. Both identification and feedback control aspects are discussed as well as the types of system for which neural networks can provide a useful technique. Multi-layer Perceptron and Radial Basis function neural network types are looked at, with an emphasis on the latter. It is shown how basis function centre selection is a critical part of the implementation process and that multivariate clustering algorithms can be an extremely useful tool for finding centres.

The CloudSat mission and the A-train: a new dimension of space-based observations of clouds and precipitation

CloudSat is a satellite experiment designed to measure the vertical structure of clouds from space. The expected launch of CloudSat is planned for 2004, and once launched, CloudSat will orbit in formation as part of a constellation of satellites (the A-Train) that includes NASA's Aqua and Aura satellites, a NASA-CNES lidar satellite (CALIPSO), and a CNES satellite carrying a polarimeter (PARASOL). A unique feature that CloudSat brings to this constellation is the ability to fly a precise orbit enabling the fields of view of the CloudSat radar to be overlapped with the CALIPSO lidar footprint and the other measurements of the constellation. The precision and near simultaneity of this overlap creates a unique multisatellite observing system for studying the atmospheric processes essential to the hydrological cycle.The vertical profiles of cloud properties provided by CloudSat on the global scale fill a critical gap in the investigation of feedback mechanisms linking clouds to climate. Measuring these profiles requires a combination of active and passive instruments, and this will be achieved by combining the radar data of CloudSat with data from other active and passive sensors of the constellation. This paper describes the underpinning science and general overview of the mission, provides some idea of the expected products and anticipated application of these products, and the potential capability of the A-Train for cloud observations. Notably, the CloudSat mission is expected to stimulate new areas of research on clouds. The mission also provides an important opportunity to demonstrate active sensor technology for future scientific and tactical applications. The CloudSat mission is a partnership between NASA's JPL, the Canadian Space Agency, Colorado State University, the U.S. Air Force, and the U.S. Department of Energy.

Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec−1) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Separating the dynamical effects of climate change and ozone depletion. Part II: Southern Hemisphere troposphere

The separate effects of ozone depleting substances (ODSs) and greenhouse gases (GHGs) on forcing circulation changes in the Southern Hemisphere extratropical troposphere are investigated using a version of the Canadian Middle Atmosphere Model (CMAM) that is coupled to an ocean. Circulation-related diagnostics include zonal wind, tropopause pressure, Hadley cell width, jet location, annular mode index, precipitation, wave drag, and eddy fluxes of momentum and heat. As expected, the tropospheric response to the ODS forcing occurs primarily in austral summer, with past (1960-99) and future (2000-99) trends of opposite sign, while the GHG forcing produces more seasonally uniform trends with the same sign in the past and future. In summer the ODS forcing dominates past trends in all diagnostics, while the two forcings contribute nearly equally but oppositely to future trends. The ODS forcing produces a past surface temperature response consisting of cooling over eastern Antarctica, and is the dominant driver of past summertime surface temperature changes when the model is constrained by observed sea surface temperatures. For all diagnostics, the response to the ODS and GHG forcings is additive: that is, the linear trend computed from the simulations using the combined forcings equals (within statistical uncertainty) the sum of the linear trends from the simulations using the two separate forcings. Space time spectra of eddy fluxes and the spatial distribution of transient wave drag are examined to assess the viability of several recently proposed mechanisms for the observed poleward shift in the tropospheric jet.