C van Leeuwen

Neural correlates of priming on occluded figure interpretation in human fusiform cortex

The visual system rapidly completes a partially occluded figure. We probed the completion process by using priming in combination with neuroimaging techniques. Priming leads to more efficient visual processing and thus a reduction in neural activity in relevant brain areas. These areas were studied with high spatial resolution and temporal accuracy with focus on early perceptual processing. We recorded magnetoencephalographic responses from 10 human volunteers in a primed same-different task for test figures. The test figures were preceded by a sequence of two figures, a prime or control figure followed by an occluded figure. The prime figures were one of three possible interpretations of the occluded figures: global and local completions and mosaic interpretation. A significant priming effect was evident: in primed trials as compared with control trials, subjects responded faster and the latency was shorter in the magnetoencephalographic signal for the largest peak between 50 and 300 ms after the occluded figure onset. Tomographic and statistical parametric mapping analyses revealed stages of activation in occipitotemporal areas during occluded figure processing. Notably, we found significantly reduced activation in the right fusiform cortex between 120 and 200 ms after occluded figure onset for primed trials as compared with control trials. We also found significant spatiotemporal differences of local, global and mosaic interpretations for individual subjects but not across subjects. We conclude that modulation of activity in the right fusiform cortex may be a neural correlate of priming in the interpretation of an occluded figure, and that this area acts as a hub for different occluded figure interpretations in this early stage of perception.

Observers for Canonic Models of Neural Oscillators

We consider the problem of state and parameter estimation for a class of nonlinear oscillators defined as a system of coupled nonlinear ordinary differential equations. Observable variables are limited to a few components of state vector and an input signal. This class of systems describes a set of canonic models governing the dynamics of evoked potential in neural mem- branes, including Hodgkin-Huxley, Hindmarsh-Rose, FitzHugh-Nagumo, and Morris-Lecar mod- els. We consider the problem of state and parameter reconstruction for these models within the classical framework of observer design. This framework offers computationally-efficient solutions to the problem of state and parameter reconstruction of a system of nonlinear differential equa- tions, provided that these equations are in the so-called adaptive observer canonic form. We show that despite typical neural oscillators being locally observable they are not in the adaptive canonic observer form. Furthermore, we show that no parameter-independent diffeomorphism exists such that the original equations of these models can be transformed into the adaptive canonic observer form. We demonstrate, however, that for the class of Hindmarsh-Rose and FitzHugh-Nagumo models, parameter-dependent coordinate transformations can be used to render these systems into the adaptive observer canonical form. This allows reconstruction, at least partially and up to a (bi)linear transformation, of unknown state and parameter values with exponential rate of conver- gence. In order to avoid the problem of only partial reconstruction and at the same time to be able to deal with more general nonlinear models in which the unknown parameters enter the system nonlinearly, we present a new method for state and parameter reconstruction for these systems. The method combines advantages of standard Lyapunov-based design with more flexible design

Leaders do not look back, or do they?

We study the effect of adding to a directed chain of interconnected systems a directed feedback from the last element in the chain to the first. The problem is closely related to the fundamental question of how a change in network topology may influence the behavior of coupled systems. We begin the analysis by investigating a simple linear system. The matrix that specifies the system dynamics is the transpose of the network Laplacian matrix, which codes the connectivity of the network. Our analysis shows that for any nonzero complex eigenvalue � of this matrix, the following inequality holds: |ℑ�| |ℜ�| � cot � n . This bound is sharp, as it becomes an equality for an eigenvalue of a simple directed cycle with uniform interaction weights. The latter has the slowest decay of oscillations among all other network configurations with the same number of states. The result is generalized to directed rings and chains of identical nonlinear oscillators. For directed rings, a lower boundc for the connection strengths that guarantees asymptotic synchronization is found to follow a similar pattern: �c = 1 1−cos(2�/n) . Numerical

Decentralized adaptation in interconnected uncertain systems with nonlinear parametrization

We propose a technique for the design and analysis of decentralized adaptation algorithms in interconnected dynamical systems. Our technique does not require Lyapunov stability of the target dynamics and allows nonlinearly parameterized uncertainties. We show that for the considered class of systems, conditions for reaching the control goals can be formulated in terms of the nonlinear L 2 -gains of target dynamics of each interconnected subsystem. Equations for decentralized controllers and corresponding adaptation algorithms are also explicitly provided.

Unsupervised adaptive optimization of motion-sensitive systems guided by measurement uncertainty

We propose a design for adaptive optimization of sensory systems. We consider a network of sensors that measure stimulus parameters as well as the uncertainties associated with these measurements. No prior assumptions about the stimulation and measurement uncertainties are built into the system, and properties of stimulation are allowed to vary with time. We present two approaches: one is based on estimation of the local gradient of uncertainty, and the other on random adjustment of cell tuning. Either approach steers the network towards its optimal state.

Characterization and Computation of Partial Synchronization Manifolds for Diffusive Delay-Coupled Systems

Sometimes a network of dynamical systems shows a form of incomplete synchronization, characterized by synchronization of some but not all of its component systems. This type of incomplete synchronization is called partial synchronization or cluster synchronization. Partial synchronization is associated with the existence of partial synchronization manifolds, which are linear invariant subspaces of

A new method for adaptive brake control

\mathcal{C}

Non-uniform small-gain theorems for systems with unstable invariant sets

, the state space of the network of systems. We focus on partial synchronization manifolds in networks of identical systems, characterized by linear diffusive coupling described by a weighted graph, and allowing for time-delay in the coupling. We present equivalent existence criteria for partial synchronization manifolds in terms of invariant spaces, the block-structure of a reordered adjacency matrix, and the solvability of a Sylvester equation. We emphasize decomposable networks, according to the rational dependency structure of the coupling weights, and according to the delay values, respectively...

On the choice of coupling in a system of coupled maps: structure implies features

We consider the problem of minimizing the longitudinal braking distance for a single wheel rolling along a surface with unknown tyre-road characteristics. The friction coefficient is modelled by a nonlinear function of slip and tyre-road parameter which corresponds to the actual road conditions. Our method is based on recently proposed adaptive control technique that uses adaptation algorithms in integro-differential, or finite form. These algorithms are capable of dealing with nonlinear parametrizations, and they also ensure improved transient performance of the controlled system. We show that, for a class of practically relevant parameterizations of friction curves, it is possible to steer the system adaptively to the desired state without invoking sliding-mode or gain-scheduling control. At the same time we show that it is possible to estimate the optimal value of the tyre slip ensuring maximal braking force. These estimates, produced by essentially the standard PI algorithm, are used in the control loop to enhance efficiency of the brakes.

On a problem of time-varying learning rate influence on the adaptive system dynamics

We consider the problem of small-gain analysis of asymptotic behavior in interconnected nonlinear dynamic systems. Mathematical models of these systems are allowed to be uncertain and time-varying. In contrast to standard small-gain theorems that require global asymptotic stability of each interacting component in the absence of inputs, we consider interconnections of systems that can be critically stable and have infinite input-output L¿ gains. For this class of systems we derive small-gain conditions specifying state boundedness of the interconnection. The estimates of the domain in which the system¿s state remains are also provided. Conditions that follow from the main results of our paper are non-uniform in space. That is they hold generally only for a set of initial conditions in the system¿s state space. We show that under some mild continuity restrictions this set has a non-zero volume, hence such bounded yet potentially globally unstable motions are realizable with a non-zero probability. Proposed results can be used for the design and analysis of intermittent, itinerant and meta-stable dynamics which is the case in the domains of control of chemical kinetics, biological and complex physical systems, and non-linear optimization.