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Cees van Leeuwen

Publications and source records attributed to Cees van Leeuwen.

At least 19 recordsLinked to original sources
arXiv2026

Self-regulated emergence of heavy-tailed weight distributions in evolving complex network architectures

The nervous system continuously adjusts connection strengths and reorganizes its structure to form and maintain complex connectivity patterns with heavy-tailed weight distributions. We propose a parsimonious model in which structural and synaptic plasticity are driven by common diffusion dynamics. Synaptic plasticity alone generates heavy-tailed weight distributions, but only when activity spreading remains predominantly local. However, when combined with structural plasticity through adaptive rewiring, the model also generates these distributions with more extensive activity flow. Furthermore, adaptive rewiring produces complex network structures with convergent-divergent circuits. These circuits contain motifs that are pervasive in nervous systems and are responsible for context-sensitive signal propagation and enhanced signal to noise ratios. Our model robustly reproduces these results across diverse dynamical regimes while capturing key connectivity features of both C. elegans and mouse brain networks. These findings suggest that the underlying principles are shared across species of varying complexity.

q-bio.NC↗
arXiv2024

Basic principles drive self-organization of brain-like connectivity structure

The brain can be considered as a system that dynamically optimizes the structure of anatomical connections based on the efficiency requirements of functional connectivity. To illustrate the power of this principle in organizing the complexity of brain architecture, we portray the functional connectivity as diffusion on the current network structure. The diffusion drives adaptive rewiring, resulting in changes to the network to enhance its efficiency. This dynamic evolution of the network structure generates, and thus explains, modular small-worlds with rich club effects, f eatures commonly observed in neural anatomy. Taking wiring length and propagating waves into account leads to the morphogenesis of more specific neural structures that are stalwarts of the detailed brain functional anatomy, such as parallelism, divergence, convergence, super-rings, and super-chains. By showing how such structures emerge, largely independently of their specific biological realization, we offer a new conjecture on how natural and artificial brain-like structures can be physically implemented.

q-bio.NC↗
arXiv2022

Functional and spatial rewiring jointly generate convergent-divergent units in self-organizing networks

Self-organization through adaptive rewiring of random neural networks generates brain-like topologies comprising modular small-world structures with rich club effects, merely as the product of optimizing the network topology. In the nervous system, spatial organization is optimized no less by rewiring, through minimizing wiring distance and maximizing spatially aligned wiring layouts. We show that such spatial organization principles interact constructively with adaptive rewiring, contributing to establish the networks' connectedness and modular structures. We use an evolving neural network model with weighted and directed connections, in which neural traffic flow is based on consensus and advection dynamics, to show that wiring cost minimization supports adaptive rewiring in creating convergent-divergent unit structures. Convergent-divergent units consist of a convergent input-hub, connected to a divergent output-hub via subnetworks of intermediate nodes, which may function as the computational core of the unit. The prominence of minimizing wiring distance in the dynamic evolution of the network determines the extent to which the core is encapsulated from the rest of the network, i.e., the context-sensitivity of its computations. This corresponds to the central role convergent-divergent units play in establishing context-sensitivity in neuronal information processing.

q-bio.NC↗
arXiv2021

Adaptive rewiring of random neural networks generates convergent-divergent units

Brain networks are adaptively rewired continually, adjusting their topology to bring about functionality and efficiency in sensory, motor and cognitive tasks. In model neural network architectures, adaptive rewiring generates complex, brain-like topologies. Present models, however, cannot account for the emergence of complex directed connectivity structures. We tested a biologically plausible model of adaptive rewiring in directed networks, based on two algorithms widely used in distributed computing: advection and consensus. When both are used in combination as rewiring criteria, adaptive rewiring shortens path length and enhances connectivity. When keeping a balance between advection and consensus, adaptive rewiring produces convergent-divergent units consisting of convergent hub nodes, which collect inputs from pools of sparsely connected, or local, nodes and project them via densely interconnected processing nodes onto divergent hubs that broadcast output back to the local pools. Convergent-divergent units operate within and between sensory, motor, and cognitive brain regions as their connective core, mediating context-sensitivity to local network units. By showing how these structures emerge spontaneously in directed networks models, adaptive rewiring offers self-organization as a principle for efficient information propagation and integration in the brain.

q-bio.NC↗
arXiv2019

Increasing the Detectability of Phase-Amplitude Coupling

Background: In electrical brain signals such as Local Field Potential (LFP) and Electroencephalogram (EEG), oscillations emerge as a result of neural network activity. The oscillations extend over several frequency bands. Between their dominant components, various couplings can be observed. Of these, Phase-Amplitude Coupling (PAC) is intensively studied in relation to brain function. In the time-frequency domain, however, PAC measurement faces a dilemma in the choice of filter bandwidth. For a frequency m modulating a frequency n, filters narrowly tuned around the latter frequency will miss the modulatory components at frequencies n+m and n-m; wide band tuning will pass increasing levels of noise. New Method: Our CFC measurement uses three identical narrow band filters with center frequencies located on n-m, n, and n+m. The method therefore is free from the bandwidth dilemma. Comparison with Existing Method(s): The method was tested on diagnostic artificial signals modeled on local field potentials and compared with four established PAC detection algorithms. While the proposed method detected the simulated PAC in high frequency resolution, the other methods detected with poor frequency resolution, or completely missed the PAC. Conclusion: Using the proposed triplet-filter banks instead of wideband filtering allows for high resolution detection of PAC. Moreover, the method successfully detected PAC in wide range of modulation frequency. Finally, bandwidth is not chosen subjectively in our new method which makes the comparison of PAC more convenient among different studies.

eess.SP↗
arXiv2015

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 $λ$ of this matrix, the following inequality holds: $\frac{|\Im λ|}{|\Re λ|} \leq \cot\fracπ{n}$. 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 bound $σ_c$ for the connection strengths that guarantees asymptotic synchronization is found to follow a similar pattern: $σ_c=\frac{1}{1-\cos\left( 2π/n\right)} $. Numerical analysis revealed that, depending on the network size $n$, multiple dynamic regimes co-exist in the state space of the system. In addition to the fully synchronous state a rotating wave solution occurs. The effect is observed in networks exceeding a certain critical size. The emergence of a rotating wave highlights the importance of long chains and loops in networks of oscillators: the larger the size of chains and loops, the more sensitive the network dynamics becomes to removal or addition of a single connection.

math.DS↗
arXiv2013

Adaptive Observers and Parameter Estimation for a Class of Systems Nonlinear in the Parameters

We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be nonlinearly parameterized functions of state and time. Reconstruction of state and parameter values is based on the concepts of weakly attracting sets and non-uniform convergence and is subjected to persistency of excitation conditions. In absence of nonlinear parametrization the resulting observers reduce to standard estimation schemes. In this respect, the proposed method constitutes a generalization of the conventional canonical adaptive observer design.

math.OC↗
arXiv2010

Observers for canonic models of neural oscillators

We consider the problem of state and parameter estimation for a wide class of nonlinear oscillators. Observable variables are limited to a few components of state vector and an input signal. The problem of state and parameter reconstruction is viewed 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 equations, 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 convergence. In order to avoid the problem of only partial reconstruction and 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 and analysis techniques based on the non-uniform small-gain theorems. Effectiveness of the method is illustrated with simple numerical examples.

q-bio.NC↗
arXiv2007

Invariant template matching in systems with spatiotemporal coding: a vote for instability

We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, translation, and rotation as well as unmodeled ones. Biological and neural systems require that these perturbations be processed through a minimal number of channels by simple adaptation mechanisms. We found that the most suitable mathematical framework to meet this requirement is that of weakly attracting sets. This framework provides us with a normative and unifying solution to the pattern recognition problem. We analyze the consequences of its explicit implementation in neural systems. Several properties inherent to the systems designed in accordance with our normative mathematical argument coincide with known empirical facts. This is illustrated in mental rotation, visual search and blur/intensity adaptation. We demonstrate how our results can be applied to a range of practical problems in template matching and pattern recognition.

cs.CV↗
arXiv2006

Non-uniform Small-gain Theorems for Systems with Unstable Invariant Sets

We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This, however, is neither a necessary requirement, nor is it always useful. Systems may, for instance, be inherently unstable (e.g. intermittent, itinerant, meta-stable) or the problem statement may include requirements that cannot be satisfied with stable solutions. This is often the case in general optimization problems and in nonlinear parameter identification or adaptation. Conventional techniques for these cases rely either on detailed knowledge of the system's vector-fields or require boundeness of its states. The presently proposed method relies only on estimates of the input-output maps and steady-state characteristics. The method requires the possibility of representing the system as an interconnection of a stable, contracting, and an unstable, exploratory part. We illustrate with examples how the method can be applied to problems of analyzing the asymptotic behavior of locally unstable systems as well as to problems of parameter identification and adaptation in the presence of nonlinear parametrizations. The relation of our results to conventional small-gain theorems is discussed.

math.DS↗
arXiv2006

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.

math.OC↗
arXiv2005

Adaptation and Parameter Estimation in Systems with Unstable Target Dynamics and Nonlinear Parametrization

We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the target set is nonequilibrium and in general unstable in the Lyapunov sense. Mathematical models of uncertainties are allowed to be nonlinearly parametrized, smooth, and monotonic functions of linear functionals of the parameters. We illustrate with applications how the proposed method leads to control algorithms. In particular we show that the mere existence of nonlinear operator gains for the desired dynamics guarantees that system solutions are bounded, reach a neighborhood of the target set, and mismatches between the modeled uncertainties and uncertainty compensator vanish with time. The proposed class of algorithms can also serve as parameter identification procedures. In particular, standard persistent excitation suffices to ensure exponential convergence of the estimated to the actual values of the parameters. When a weak, nonlinear version of the persistent excitation condition is satisfied, convergence is asymptotic. The approach extends to a broader class of parameterizations where the monotonicity restriction holds only locally. In this case excitation with oscillations of sufficiently high frequency ensure convergence.

math.OC↗
arXiv2004

Adaptive Regulation to Invariant Sets

A new framework for adaptive regulation to invariant sets is proposed. Reaching the target dynamics (invariant set) is to be ensured by state feedback while adaptation to parametric uncertainties is provided by additional adaptation algorithm. We show that for a sufficiently large class of nonlinear systems it is possible to adaptively steer the system trajectories to the desired non-equilibrium state without requiring knowledge or existence of a specific strict Lyapunov function.

math.OC↗
arXiv2004

Adaptation and nonlinear parametrization: nonlinear dynamics prospective

We consider adaptive control problem in presence of nonlinear parametrization of uncertainties in the model. It is shown that despite traditional approaches require for domination in the control loop during adaptation, it is not often necessary to use such energy inefficient compensators it in wide range of applications. In particular, we show that recently introduced adaptive control algorithms in finite form which are applicable to monotonic parameterized systems can be extended to general smooth non-monotonic parametrization. These schemes do not require any damping or domination in control inputs.

math.OC↗
arXiv2004

Parameter estimation and control for a class of systems with nonlinear parametrization

We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show that under this restriction standard persistent excitation suffices to ensure exponentially fast convergence of the estimates to the actual values of unknown parameters. Subsequently, our approach is extended to cases in which the monotonicity assumption holds only locally. We show that excitation with high-frequency of oscillations is sufficient to ensure convergence. Two practically relevant examples are given in order to illustrate the effectiveness of the approach.

math.DS↗
arXiv2003

Adaptive Algorithms in Finite Forms

We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired performance characteristics and a class of nonlinearly parameterized systems, first to augment the tuning error function and design the adaptation scheme in the form of ordinary differential equations. The resulting augmentation is allowed to depend on state derivatives. To deal with these, we suggest the realization of the adaptation scheme in an algebraic-integral form. Because of the explicit dependance on the state of the original system such adaptation schemes are referred to as adaptive algorithms in it finite form instead of differential ones. Sufficient conditions for the existence of finite form realizations are proposed. These conditions lead to the necessity to find a solution of a system of partial differential equations, which in general is not an easy task. In order to resolve this problem we suggest to embed the original system dynamics into one of a higher order, thus replacing it by a simple integration of a function with respect to a single scalar argument. Several full-state feedback finite form realizations are presented and illustrated with examples.

math.OC↗