Gregory S. Duane

K-winner networks

A special class of mutually inhibitory networks is analyzed, and parameters for reliable K-winner performance are presented. The network dynamics are modeled using interactive activation, and results are compared with the sigmoid model. For equal external inputs, network parameters that select the units with the larger initial activations (the network converges to the nearest stable state) are derived. Conversely, for equal initial activations, networks that select the units with larger external inputs (the network converges to the lowest energy stable state) are derived. When initial activations are mixed with external inputs, anomalous behavior results. These discrepancies are analyzed with several examples. Restrictions on initial states are derived which ensure accurate K-winner performance when unequal external inputs are used.

Data Assimilation as Synchronization of Truth and Model: Experiments with the Three-Variable Lorenz System*

Abstract The potential use of chaos synchronization techniques in data assimilation for numerical weather prediction models is explored by coupling a Lorenz three-variable system that represents “truth” to another that represents “the model.” By adding realistic “noise” to observations of the master system, an optimal value of the coupling strength was clearly identifiable. Coupling only the y variable yielded the best results for a wide range of higher coupling strengths. Coupling along dynamically chosen directions identified by either singular or bred vectors could improve upon simpler chaos synchronization schemes. Generalized synchronization (with the parameter r of the slave system different from that of the master) could be easily achieved, as indicated by the synchronization of two identical slave systems coupled to the same master, but the slaves only provided partial information about regime changes in the master. A comparison with a standard data assimilation technique, three-dimensional variat...

Co-occurrence of Northern and Southern Hemisphere Blocks as Partially Synchronized Chaos

Abstract Teleconnections between the midlatitudes of the Northern and Southern Hemispheres are diagnosed in National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis data and separately in European Centre for Medium-Range Weather Forecasts reanalysis data. The teleconnections are manifested as a small but significant tendency for blocking to occur simultaneously in the two hemispheres, though at different longitudes and different relative latitudes, during boreal winters over the period 1979–94 in both datasets. One way to explain the correlations between blocking events is as an instance of synchronized chaos, the tendency of some coupled chaotic systems to synchronize, permanently or intermittently, regardless of initial conditions. As the coupling is weakened, the systems no longer synchronize completely, but small correlations between the states of the coupled systems are observed instead. In previous work, such behavior was observed in an idealized coupled-hemi...

A multi-model ensemble method that combines imperfect models through learning

Abstract. In the current multi-model ensemble approach climate model simulations are combined a posteriori. In the method of this study the models in the ensemble exchange information during simulations and learn from historical observations to combine their strengths into a best representation of the observed climate. The method is developed and tested in the context of small chaotic dynamical systems, like the Lorenz 63 system. Imperfect models are created by perturbing the standard parameter values. Three imperfect models are combined into one super-model, through the introduction of connections between the model equations. The connection coefficients are learned from data from the unperturbed model, that is regarded as the truth. The main result of this study is that after learning the super-model is a very good approximation to the truth, much better than each imperfect model separately. These illustrative examples suggest that the super-modeling approach is a promising strategy to improve weather and climate simulations.

Weak Atlantic-Pacific Teleconnections as Synchronized Chaos

Abstract The relationship between blocking events in the Atlantic and Pacific sectors of the Northern Hemisphere midlatitudes is investigated in a Vautard–Legras two-layer quasigeostrophic channel model with two sectors, each sector forced by a separate baroclinic jet. It is found that the exchange of medium-scale eddies tends to cause anticorrelation between blocking events in the two sectors, while the large-scale flow components tend to cause positive correlation. The net correlation in blocking is more positive when the jets are skewed latitudinally, a result that is confirmed in the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data and separately in a long run of a global circulation model (GCM). The anticorrelating effect of the eddy exchange follows from the tendency of two distinct, coextensive, chaotically vacillating channel flows to synchronize when their corresponding medium-scale eddy components are coupled (a physically unreali...

Dynamically combining climate models to "supermodel" the tropical Pacific

We construct an interactive ensemble of two different climate models to improve simulation of key aspects of tropical Pacific climate. Our so-called supermodel is based on two atmospheric general circulation models (AGCMs) coupled to a single ocean GCM, which is driven by a weighted average of the air-sea fluxes. Optimal weights are determined using a machine learning algorithm to minimize sea surface temperature errors over the tropical Pacific. This coupling strategy synchronizes atmospheric variability in the two AGCMs over the equatorial Pacific, where it improves the representation of ocean-atmosphere interaction and the climate state. In particular, the common double Intertropical Convergence Zone error is suppressed, and the positive Bjerknes feedback improves substantially to match observations well, and the negative heat flux feedback is also much improved. This study supports the concept of supermodeling as a promising multimodel ensemble strategy to improve weather and climate predictions.

Synchronicity from Synchronized Chaos

The synchronization of loosely-coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical concept of “synchronicity”—the commonplace notion that related eventsmysteriously occur at the same time. When extended to continuous media and/or large discrete arrays, and when general (non-identical) correspondences are considered between states, intermittent synchronous relationships indeed become ubiquitous. Meaningful synchronicity follows naturally if meaningful events are identified with coherent structures, defined by internal synchronization between remote degrees of freedom; a condition that has been posited as necessary for synchronizability with an external system. The important case of synchronization between mind and matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system, as in meteorological data assimilation. Evidence for the ubiquity of synchronization is reviewed along with recent proposals that: (1) synchronization of different models of the same objective process may be an expeditious route to improved computational modeling and may also describe the functioning of conscious brains; and (2) the nonlocality in quantum phenomena implied by Bell’s theorem may be explained in a variety of deterministic (hidden variable) interpretations if the quantum world resides on a generalized synchronization “manifold”.

Violations of Bell's Inequality in Synchronized Hyperchaos

Motivated by a parallel between quantum cryptography and chaos synchronization cryptography, we construct a Bells inequality for a pair of synchronously coupled variable-order Generalized Rossler Systems, with arbitrarily binarized final states. In the infinite-order limit, although dynamical parameters cannot be extracted from the coupling signal in finite time, the inequality is violated, as with entangled quantum states. The violations are weaker than in quantum theory, vanishing as the differences between corresponding parameters of the coupled systems become small. The fact that Bells inequality can be violated for a pair of classical systems that are not discernibly connected supports the possibility of a realist interpretation of quantum mechanics.

Data Assimilation as Artificial Perception and Supermodeling as Artificial Consciousness

Data assimilation is naturally conceived as the synchronization of two systems, “truth” and “model”, coupled through a limited exchange of information (observed data) in one direction. Though investigated most thoroughly in meteorology, the task of data assimilation arises in any situation where a predictive computational model is updated in run time by new observations of the target system, including the case where that model is a perceiving biological mind. In accordance with a view of a semi-autonomous mind evolving in synchrony with the material world, but not slaved to it, the goal is to prescribe a coupling between truth and model for maximal synchronization. It is shown that optimization leads to the usual algorithms for assimilation via Kalman Filtering under a weak linearity assumption. For nonlinear systems with model error and sampling error, the synchronization view gives a recipe for calculating covariance inflation factors that are usually introduced on an ad hoc basis. Consciousness can be framed as self-perception, and represented as a collection of models that assimilate data from one another and collectively synchronize. The combination of internal and external synchronization is examined in an array of models of spiking neurons, coupled to each other and to a stimulus, so as to segment a visual field. The inter-neuron coupling appears to enhance the overall synchronization of the model with reality.

Jet Alignment in a Two-Layer Quasigeostrophic Channel Using One-Dimensional Grid Warping

Because of position errors traditional methods of data assimilation can broaden and weaken jets or other flow structures leading to reduced forecast skill. Here a technique to assimilate properties of coherent structures is developed and tested. Focusing on jets, the technique identifies jets in both the modeled and observed fields and warps the model grid so that the jet positions are better aligned prior to further assimilation of observations. The technique is tested using optimal interpolation on the flow in a two-layer quasigeostrophic channel. The results show that a simple and fast jet position correction algorithm can significantly improve the skill of a 12-h forecast. Furthermore, the results indicate that this method of position correction maintains its utility when observations become sparse.