Biomedical subjects

Michael Menzinger

Publications and source records attributed to Michael Menzinger.

11 recordsLinked to original sources

PubMed2005

Pattern formation by boundary forcing in convectively unstable, oscillatory media with and without differential transport.

Convectively unstable, open reactive flows of oscillatory media, whose phase is fixed or periodically modulated at the inflow boundary, are known to result in stationary and traveling waves, respectively. The latter are implicated in biological segmentation. The boundary-controlled pattern selection by this flow-distributed oscillator (FDO) mechanism has been generalized to include differential flow (DIFI) and differential diffusion (Turing) modes. Our present goal is to clarify the relationships among these mechanisms in the general case where there is differential flow as well as differential diffusion. To do so we analyze the dispersion relation for linear perturbations in the presence of periodic boundary forcing, and show how the solutions are affected by differential transport. We find that the DIFI and FDO modes are closely related and lie in the same frequency range, while the Turing mechanism gives rise to a distinct set of unstable modes in a separate frequency range. Finally, we substantiate the linear analysis by nonlinear simulations and touch upon the issue of competition of spatial modes.

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PubMed2005

Flow-distributed oscillation, flow-velocity modulation, and resonance.

We examine the effects of a periodically varying flow velocity on the standing- and traveling-wave patterns formed by the flow-distributed oscillation mechanism. In the kinematic (or diffusionless) limit, the phase fronts undergo a simple, spatiotemporally periodic longitudinal displacement. On the other hand, when the diffusion is significant, periodic modulation of the velocity can disrupt the wave pattern, giving rise in the downstream region to traveling waves whose frequency is a rational multiple of the velocity perturbation frequency. We observe frequency locking at ratios of 1:1, 2:1, and 3:1, depending on the amplitude and frequency of the velocity modulation. This phenomenon can be viewed as a novel, rather subtle type of resonant forcing.

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PubMed2005

Clustering and the synchronization of oscillator networks.

By manipulating the clustering coefficient of a network without changing its degree distribution, we examine the effect of clustering on the synchronization of phase oscillators on networks with Poisson and scale-free degree distributions. For both types of networks, increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies. Surprisingly, in scale-free networks, clustering promotes the synchronization of the most connected nodes (hubs) even though it inhibits global synchronization. As a result, they show an additional, advanced transition instead of a single synchronization threshold. This cluster-enhanced synchronization of hubs may be relevant to the brain that is scale-free and highly clustered.

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PubMed2004

Control of chemical pattern formation by a clock-and-wavefront type mechanism.

The segmentation of many animals ranging from insects to mammals involves the sequential formation of stationary stripes of gene expression that are perpendicular to the growth axis of the developing embryo. This process has been accounted for by a variety of theoretical "clock-and-wavefront" type models that involve the arrest of an oscillation (the clock) at a moving boundary (the wavefront). Here, we demonstrate experimentally that progressive arrest of a homogeneous oscillation can control the symmetry as well as the wavelength of spatial structures in a chemical system. We show how a spontaneously formed, labyrinthine pattern can be converted into a pattern composed of ordered, parallel stripes and confirm a previously predicted proportionality between the wavelength and the period of the homogeneous oscillation. Our experiments provide the first experimental demonstration of a general mechanism for the control of pattern formation that has been hypothesized to operate in the context of biological morphogenesis.

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PubMed2003

General theory of nonlinear flow-distributed oscillations.

We outline a general theory for the analysis of flow-distributed standing and traveling wave patterns in one-dimensional, open flows of oscillatory chemical media, emphasizing features that are generic to a variety of kinetic models. We draw particular attention to the cases far from a Hopf bifurcation and far from the so-called kinematic or zero-diffusion limit. We introduce a nonlinear formalism for both traveling and stationary waves and show that the wave forms and their amplitudes depend on a single reduced transport parameter that quantifies the departure from the kinematic limit. The nonlinear formalism can be applied to systems with more complex types of bifurcations (canards, period doublings, etc.).

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PubMed2003

Topology and computational performance of attractor neural networks.

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world, and scale-free topologies. The random configuration is the most efficient for storage and retrieval of patterns by the network as a whole. However, in the scale-free case retrieval errors are not distributed uniformly among the nodes. The portion of a pattern encoded by the subset of highly connected nodes is more robust and efficiently recognized than the rest of the pattern. The scale-free network thus achieves a very strong partial recognition. The implications of these findings for brain function and social dynamics are suggestive.

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PubMed2003

Bistable gradient networks. I. Attractors and pattern retrieval at low loading in the thermodynamic limit.

We examine the large-network, low-loading behavior of an attractor neural network, the so-called bistable gradient network (BGN), and compare it with that of the Hopfield network (HN). We use analytical and numerical methods to characterize the attractor states of the network and their basins of attraction. The energy landscape of BGN is more complex than that of the HN and depends on the strength of the coupling among units. At weak coupling, the BGN acts as a highly selective associative memory; the input must be close to the one of the stored patterns in order to be recognized. A category of spurious attractors occurs which is not present in the HN. Stronger coupling results in a transition to a more Hopfield-like regime with large basins of attraction. The basins of attraction for spurious attractors are noticeably suppressed compared to the Hopfield case, even though the Hebbian synaptic structure is the same and there is no stochastic noise.

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PubMed2003

Bistable gradient networks. II. Storage capacity and behavior near saturation.

We examine numerically the storage capacity and the behavior near saturation of an attractor neural network consisting of bistable elements with an adjustable coupling strength, the bistable gradient network. For strong coupling, we find evidence of a first-order "memory blackout" phase transition, as in the Hopfield network. For weak coupling, on the other hand, there is no evidence of such a transition and memorized patterns can be stable even at high levels of loading. The enhanced storage capacity comes, however, at the cost of imperfect retrieval of the patterns from corrupted versions.

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PubMed2002

Stabilization of stationary excitation pulses in an open flow without long-range inhibition.

We study numerically and experimentally the stabilization of stationary excitation pulses in an open flow system. Since all the species have equal flow and diffusion coefficients, stabilization of stationary pulses by long-range inhibition is excluded. Upstream propagating pulses slow down as they approach the inflow boundary, where a constant forcing establishes a downstream extending subexcitable boundary layer. When the flow velocity is low, successive pulses vanish as they reach the subexcitable region. When the flow velocity is increased, the incoming pulses pile up near the inflow one after the other to form a stationary and space-periodic structure. This occurs in such a manner that the system remembers and stores the number of incoming pulses. We show that flow-induced stabilization of stationary pulses involves a mechanism by which the upstream subexcitable region and the flow cause the arrest of the pulse front and the pulse back, respectively. We discuss how the flow-stabilized structures compare to, and are different from those stabilized by a long-ranged, diffusive inhibition and from those observed in boundary-forced open flows of media showing relaxation-type oscillations.

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PubMed1999

On the local stability of limit cycles.

Orbital stability of limit cycles is the result of the competing local tendencies of perturbations from the cycle to decay (during phases of local stability) and to grow (during phases of local instability), averaged over a cycle. We examine this coexistence of attractive and repulsive phases on limit cycles, including the local rates of expansion and contraction of phase space volumes. This is done in a frame of reference that moves along the orbit, to partially decouple motions tangential and perpendicular to the cycle. Dynamical systems used for illustration are the generalized Bonhoeffer-van-der-Pol and Rossler models, both far from and near to different types of bifurcations. Finally, it is shown that the nonuniformity of local stability in phase space affects the response of limit cycle oscillators to perturbations and gives rise to their phase-dependent response. (c) 1999 American Institute of Physics.

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PubMedDate not supplied

Reconstruction of noisy patterns by bistable gradient neural-like network.

An attractor bistable gradient neural-like network (BGN) described in Chinarov and Menzinger (BioSystems 55 (2000) 137) is applied to restoration of unknown patterns, which have been highly corrupted by multiplicative and additive Gaussian white noise. This becomes possible due to competitive advantage of BGN that derives from it: nice generalization capabilities, existence of the unique attractor with the lowest energy that is worked out when several patterns are stored by the network, and fast guaranteed convergence to this attractor.

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