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At least 19 records

Terminal attractors in neural networks

A new type of attractor (terminal attractors) for content-addressable memory, associative memory, and pattern recognition in artificial neural networks operating in continuous time is introduced. The idea of a terminal attractor is based upon a violation of the Lipschitz condition at a fixed point. As a result, the fixed point becomes a singular solution which envelopes the family of regular solutions, while each regular solution approaches such an attractor in finite time. It will be shown that terminal attractors can be incorporated into neural networks such that any desired set of these attractors with prescribed basins is provided by an appropriate selection of the synaptic weights. The applications of terminal attractors for content-addressable and associative memories, pattern recognition, self-organization, and for dynamical training are illustrated.

Zak, Michail↗

Terminal attractors for addressable memory in neural networks

A new type of attractors - terminal attractors - for an addressable memory in neural networks operating in continuous time is introduced. These attractors represent singular solutions of the dynamical system. They intersect (or envelope) the families of regular solutions while each regular solution approaches the terminal attractor in a finite time period. It is shown that terminal attractors can be incorporated into neural networks such that any desired set of these attractors with prescribed basins is provided by an appropriate selection of the weight matrix.

Zak, Michail↗

Multiple Quasi-Equilibria of the ITCZ and the Origin of Monsoon Onset: Rotational ITCZ Attractors - Part 2

Chao's numerical and theoretical work on multiple quasi-equilibria of the intertropical convergence zone (ITCZ) and the origin of monsoon onset is extended to solve two additional puzzles. One is the highly nonlinear dependence on latitude of the "force" acting on the ITCZ due to earth's rotation, which makes the multiple quasi-equilibria of the ITCZ and monsoon onset possible. The other is the dramatic difference in such dependence when different cumulus parameterization schemes are used in a model. Such a difference can lead to a switch between a single ITCZ at the equator and a double ITCZ, when a different cumulus parameterization scheme is used. Sometimes one of the double ITCZ can diminish and only the other remain, but still this can mean different latitudinal locations for the single ITCZ. A single idea based on two off-equator attractors for the ITCZ, due to earth's rotation and symmetric with respect to the equator, and the dependence of the strength and size of these attractors on the cumulus parameterization scheme solves both puzzles. The origin of these rotational attractors, explained in Part I, is further discussed. The "force" acting on the ITCZ due to earth's rotation is the sum of the "forces" of the two attractors. Each attractor exerts on the ITCZ a "force" of simple shape in latitude; but the sum gives a shape highly varying in latitude. Also the strength and the domain of influence of each attractor vary, when change is made in the cumulus parameterization. This gives rise to the high sensitivity of the "force" shape to cumulus parameterization. Numerical results, of experiments using Goddard's GEOS general circulation model, supporting this idea are presented. It is also found that the model results are sensitive to changes outside of the cumulus parameterization. The significance of this study to El Nino forecast and to tropical forecast in general is discussed.

Chao, Winston C.↗

A search for X-ray emission associated with the great attractor

A search is reported for X-ray emission associated with the object, dubbed the 'great attractor', which has been postulated as the cause of the coherent deviations from the Hubble flow which are observed in nearby parts of the universe. The hypothesis that a substantial fraction of the dynamical mass of the great attractor exists in the form of rich clusters of galaxies is ruled out. The possibility is considered that a substantial fraction of the mass of the great attractor could exist in a form which would increase the apparently diffuse X-ray surface brightness. The observational upper limit to the diffuse X-ray sky surface brightness enhancement in the general direction of the great attractor allows interesting limits to be set on the fraction of the dynamical mass of the great attractor which can exist in the form of X-ray-luminous material.

Jahoda, Keith↗

ATTRACTOR: Toward Trustworthy and Trusted Autonomous Systems

The question of what it means and what it takes for an autonomous system to consider another autonomous system justifiably trustworthy must be addressed by all who seek to integrate intelligent machine agents into real-world operations. A satisfactory answer to this question is an essential component in accepting autonomous machine decision-making in safety-critical and time-critical environments, such as aviation. Historically, simulation platforms for test and evaluation of complex systems have proven to be effective in assessing performance and contributing to decisions on the fitness of systems to operate in current general and commercial aviation airspace. Moreover, simulations have informed the definition of safety-critical constraints. However, as machine systems progressively take on responsibilities for decision-making traditionally supplied by humans, simulations require enhancement. Mixed reality simulation that integrates real-world platforms and data or high-fidelity simulation data in a sim-to-flight paradigm provides insight into agent interaction and the rationale behind autonomous agent decision-making as well as the capacity for seamless integrated implementation, testing, and operation of systems. Strong simulation capabilities are especially important in the presence of algorithms that hold great promise in decision-making yet increase the uncertainty in the system. Autonomy Teaming and TRAjectories for Complex Trusted Operational Reliability (ATTRACTOR) is a subproject of NASA’s Convergent Aeronautics Solutions (CAS) Project. ATTRACTOR’s objective is to build a basis for understanding trust and trustworthiness in multi-agent autonomous teams, and thus to inform future certification of safety-critical and time-critical autonomous systems in aviation. Because the concepts of trust and trustworthiness must be addressed in a context, ATTRACTOR has chosen Search and Rescue (SAR) in dynamic and unstructured environments, with emphasis on search, as its design reference mission (DRM). During dynamic planning and execution of trajectory-based operations, autonomous agents determine their trajectories given an assigned mission or missions and call for assistance from an appropriate teammate when needed. This experience along with the attendant human-machine and machine-machine interactions, serve as a platform for developing approaches to identifying and measuring trustworthiness and increasing trust. In this paper, we give an overview of some of ATTRACTOR’s research and development activities, findings, and ongoing work.

ATTRACTOR↗

A search for a dynamical attractor in Cygnus X-1

A method used for searching for low-dimensional attractors in fluctuating signals is applied to the aperiodicity observed in Cyg X-1. The analysis technique for determining the dimension of an attractor given its light curve, and the practical limitations in applying the technique, are described. The requirement of large amounts of low-noise data is found to be very important in using the technique. No low-dimensional attractor is found for the set of Cyg X-1 data used, but evidence of an attractor with large dimension may be present.

Lochner, James C.↗

Strange attractors in weakly turbulent Couette-Taylor flow

An experiment is conducted on the transition from quasi-periodic to weakly turbulent flow of a fluid contained between concentric cylinders with the inner cylinder rotating and the outer cylinder at rest. Power spectra, phase-space portraits, and circle maps obtained from velocity time-series data indicate that the nonperiodic behavior observed is deterministic, that is, it is described by strange attractors. Various problems that arise in computing the dimension of strange attractors constructed from experimental data are discussed and it is shown that these problems impose severe requirements on the quantity and accuracy of data necessary for determining dimensions greater than about 5. In the present experiment the attractor dimension increases from 2 at the onset of turbulence to about 4 at a Reynolds number 50-percent above the onset of turbulence.

Brandstater, A.↗

Thermal attractor in chaotic convection with high-Prandtl-number fluids

The onset of chaotic convection in large-Prandtl-number fluids has been found to occur in the form of elongated cells with aperiodic boundary-layer instabilities. The dynamics of this phenomenon has been monitored in the physical domain, and also in the spectral and phase spaces. In order to describe more precisely the underlying mechanisms of chaotic thermal convection, the notion of 'thermal attractor' is introduced in the physical domain and a systematic study is conducted of the evolution of the spectral energy surfaces. A relationship between this thermal attractor and the presence of a strange attractor in the phase space is proposed.

Vincent, Alain P.↗

Modelling the slow climatic attractor

Attempts to model the evolution of the slow-response parts of the climatic system such as the global ice mass are reviewed, and the fundamental laws governing the complete complex multidomain slow system, called the slow climatic attractor, are analyzed. The uses of paleoclimatic records are discussed, and a low-order model for the late Quaternary variations that constitutes a credible global representation of the slow climatic attractor is presented. It is shown that although according to the model the climatic system is centered on an unstable equilibrium, the points of the limit cycle attractor are quite stable and robust. It is also noted that one major deficiency of the model is its inability to portray the geographic spatial variability of climatic mean states. However, at least with regard to atmospheric CO2, estimates of the geographic fields of all significant atmospheric and surface boundary layer climate variables are deducible.

Saltzman, Barry↗

The dimension of attractors underlying periodic turbulent Poiseuille flow

A lower bound on the Liapunov dimenison, D-lambda, of the attractor underlying turbulent, periodic Poiseuille flow at a pressure-gradient Reynolds number of 3200 is calculated, on the basis of a coarse-grained (16x33x8) numerical solution, to be approximately 352. Comparison of Liapunov exponent spectra from this and a higher-resolution (16x33x16) simulation on the same spatial domain shows these spectra to have a universal shape when properly scaled. On the basis of these scaling properties, and a partial exponent spectrum from a still higher-resolution (32x33x32) simulation, it is argued that the actual dimension of the attractor underlying motion of the given computational domain is approximately 780. It is suggested that this periodic turbulent shear flow is deterministic chaos, and that a strange attractor does underly solutions to the Navier-Stokes equations in such flows.

Keefe, Laurence↗

Optical implementation of terminal-attractor-based associative memory

For the purpose of reducing the spurious states in a Hopfield neural net for associative memory, we invoke terminal attractors. In achieving the optical implementation of the terminal-attractor-based associative memory (TABAM) as described in this paper, we first prove the existence of the terminal-attractor model with binary neuron representation. We then present several one- and two-dimensional optical architectures for the TABAM. Finally, as an example, we experimentally demonstrate an inner-product optical neural model using liquid-crystal spatial light modulators with engineering approximations and discuss how to apply the inner-product model to build a two-dimensional parallel processing TABAM.

Liu, Hua-Kuang↗

A study of roll attractor and wing rock of delta wings at high angles of attack

Wing rock is a high angle of attack dynamic phenomenon of limited cycle motion predominantly in roll. The wing rock is one of the limitations to combat effectiveness of the fighter aircraft. Roll Attractor is the steady state or equilibrium trim angle (phi(sub trim)) attained by the free-to-roll model, held at some angle of attack, and released form rest at a given initial roll (bank) angle (phi(sub O)). Multiple roll attractors are attained at different trim angles depending on initial roll angle. The test facility (Vigyan's low speed wind tunnel) and experimental work is presented here along with mathematical modelling of roll attractor phenomenon and analysis and comparison of predictions with experimental data.

Niranjana, T.↗

An Unipolar Terminal-Attractor Based Neural Associative Memory with Adaptive Threshold and Perfect Convergence

For the first time, a unipolar terminal-attractor based neural associative memory (TABAM)system with adaptive threshold and perfect convergence is presented. By adaptively setting thethreshold values for the dynamic iteration for the unipolar binary neuron states with terminal-attractors and inner-product approach, we demonstrate via computer simulation the achievement ofperfect convergence and correct retrieval. The simulation is completed with a small number of storedstates (M) and a small number of neurons (N) but a large M/N ratio. An experiment with exclusive-or logic operation using LCTV SLMs is used to show feasibility of the optoelectronic implementationof the models.

Associative↗

Upper semicontinuous global attractors for viscous flow

A particular form of regularization of the Navier-Stokes equations is studied. It is shown that as the regularization parameter goes to zero, the global attractor for the regularized system converges to the global attractor for the conventional Navier-Stokes system.

Ou, Yuh-Roung↗

A chaotic attractor in timing noise from the Vela pulsar?

Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.

Harding, Alice K.↗

Connecting coherent structures and strange attractors

A concept of turbulence derived from nonlinear dynamical systems theory suggests that turbulent solutions to the Navier-Stokes equations are restricted to strange attractors, and, by implication, that turbulent phenomenology must find some expression or source in the structure of these mathematical objects. Examples and discussions are presented to link coherent structures to some of the commonly known characteristics of strange attractors. Basic to this link is a geometric interpretation of conditional sampling techniques employed to educe coherent structures that offers an explanation for their appearance in measurements as well as their size.

Keefe, Laurence R.↗

Optoelectronic Terminal-Attractor-Based Associative Memory

Report presents theoretical and experimental study of optically and electronically addressable optical implementation of artificial neural network that performs associative recall. Shows by computer simulation that terminal-attractor-based associative memory can have perfect convergence in associative retrieval and increased storage capacity. Spurious states reduced by exploiting terminal attractors.

Liu, Hua-Kuang↗