17 Result(s)
within
T. Geisel
Complex Systems
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Article
Recurrent host mobility in spatial epidemics: beyond reaction-diffusion
Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modeled by diffusion in space or on metapolulation networks. Alternatively,...
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Article
Dynamical synapses causing self-organized criticality in neural networks
Self-organized criticality1 is one of the key concepts to describe the emergence of complexity in natural systems. The concept asserts that a system self-organizes into a critical state where system observables a...
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Chapter and Conference Paper
Pattern formation in the develo** visual cortex: Topological defects, their generation, motion, and annihilation
The pinwheel-like arrangement of iso-orientation domains around orientation centers is a ubiquitous structural element of orientation preference maps in primary visual cortex. We show that activity-dependent s...
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Chapter and Conference Paper
A Cortical Interpretation of ASSOMs
Self-organizing maps have been successfully used to model map formation in the visual cortex of mammals. When applying natural images as stimuli, properties of the maps obtained for low-dimensional input manif...
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Chapter and Conference Paper
Analysing the Context Dependence of Receptive Fields in Visual Cortex
Stimuli outside the classical receptive field of orientation-selective cells in the visual cortex can strongly modulate the response properties of these cells. Normally, stimuli with orientation contrasts lead...
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Article
Analyzing phase transitions in high-dimensional self-organizing maps
The self-organizing map (SOM), a widely used algorithm for the unsupervised learning of neural maps, can be formulated in a low-dimensional ‘feature map’ variant which requires prespecified parameters (‘featur...
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Chapter and Conference Paper
Linear and Nonlinear Dynamics in the Development of Orientation Preference Maps
The formation of feature-maps in the develo** visual cortex has become a central system for the study of cooperative phenomena in large neural networks, both theoretically[1, 2] and experimentally [3, 4]. Wi...
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Chapter and Conference Paper
Lévy walks in chaotic systems: Useful formulas and recent applications
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Article
Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation
Synchronous network excitation is believed to play an outstanding role in neuronal information processing. Due to the stochastic nature of the contributing neurons, however, those synchronized states are diffi...
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Article
Formation of field discontinuities and islands in visual cortical maps
The representations of visual hemifields in the extrastriate areas of various species exhibit field discontinuities and islands. We propose that these violations of retinotopy are a developmental consequence o...
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Chapter
The Formation of Representations in the Visual Cortex
We give an introduction to activity-dependent learning in self-organizing neural networks and consider applications to the formation of representations (retinotopic maps) in the visual cortex. In particular we...
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Chapter
Optimal Smoothness of Orientation Preference Maps
We propose a mathematical description for the spatial organization of orientation preference in the visual cortex. The theory is derived from the principle of optimal smoothness and predicts the spatial patter...
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Chapter
Network Dynamics and Correlated Spikes
Oscillatory neuronal responses have been suspected to reveal assembly formation via synchronization. We analyse these data in terms of a hidden-state model, the parameters of which are estimated directly from ...
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Chapter
Alternating Predictable and Unpredictable States in Data From Cat Visual Cortex
Visual inspection of data from cat visual cortex reveals, that the recently discovered 50-Hz-oscillations do not consist of a permanent oscillatory signal during the whole period of stimulation, but instead di...
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Chapter
Field Discontinuities and Islands in a Model of Cortical Map Formation
The existence of field discontinuities, i.e. discontinuities in cortical maps of the retina is well established by neurophysiological investigations in a variety of species [1–4]. In cat, additional geometric ano...
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Chapter and Conference Paper
The role of KAM-tori for the dynamics of nonlinear quantum systems
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Chapter
Deterministic Diffusion — A Quality of Chaos
This paper reports on chaotic systems that can exhibit a deterministic “random” walk as an additional chaotic quality. This diffusive motion is generated within the dynamical system and not by external random ...
