Optimal network topologies for information transmission in active networks

This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is optimal for information transmission. By optimal, we mean that the network is able to transmit a large amount of information, it possesses a large number of communication channels, and it is robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.Comment: 20 pages, 12 figure

Cycles and interactions : A mathematician among biologists

The backbone of this thesis is the interdisciplinary interaction between dynamic systems theory and a selection of biological problems. Each chapter focuses in one problem, namely plankton dynamics, cell development paths and sleep-wake dynamics. Despite these topics may seem disconnected, they share an important feature: all of them show cyclic behaviour under certain circumstances. In the present thesis we show that cyclic (or chaotic) behaviour is deeply related with plankton biodiversity. We also use cycles to show, in an intuitive way, that Waddington’s epigenetic landscapes (a common visual tool in stem cell research) are poorly defined, and we provide a practical solution to this. Lastly, we provide an algorithm to forecast a transition between synchronized and non-synchronized cyclic systems (such as normal sleep – insomnia, or normal hearth functioning – arrhythmia), with potential applications in medical sciences

Color Image Segmentation Based on Modified Kuramoto Model

AbstractA new approach for color image segmentation is proposed based on Kuramoto model in this paper. Firstly, the classic Kuramoto model which describes a global coupled oscillator network is changed to be one that is locally coupled to simulate the neuron activity in visual cortex and to describe the influence for phase changing by external stimuli. Secondly, a rebuilt method of coupled neuron activities is proposed by introducing and computing instantaneous frequency. Three oscillating curves corresponding to the pixel values of R, G, B for color image are formed by the coupled network and are added up to produce the superposition of oscillation. Finally, color images are segmented according to the synchronization of the oscillating superposition by extracting and checking the frequency of the oscillating curves. The performance is compared with that from other representative segmentation approaches

Functional connectivity signatures of visual-motor coordination using spectral dynamical analysis

Visual-motor coordination is an essential function of human motion control, which requires interactions of multiple brain regions. Visual tracking is a behavioural task that requires intensive visual-motor coordination, which makes it a good paradigm to study the underlying mechanism of visual-motor coordination. In this research, tracking paradigm was used to study the visual-motor coordination, and both behaviour and electroencephalography (EEG) functional connectivity were analysed. The behavioural analysis explored the anticipatory characteristic of human motion control. In the tracking paradigm, participants were asked to trace a target moving with constant speed along a circular trajectory. Two different types of tracking paradigm were applied in the research. Firstly, the full visibility tracking trials were performed, in which participants had the full visibility of the target movement. Participants showed weak anticipatory behaviour in the full visibility tracking trials. In order to observe stronger anticipatory behaviour, the intermittent tracking trials were then performed, in which two target-invisible zones were added. It was found that participants applied two distinctive control modes of visual-motor coordination in the target-visible zone and target-invisible zone, respectively. The result showed that the target-invisible zone made participants perform anticipatory control of visual tracking. In order to identify the brain activities related to visual processing and motion control separately in the visual-motor feedback loops, two reference conditions were designed and compared with the tracking trials. The functional connectivity was defined using phase-locking synchrony, and both static and dynamical features of the network were investigated. For static analysis, the time-averaged graphical properties of functional connectivity were investigated. To investigate dynamical properties, a new dynamical network analysis method was developed based on eigenvector representation of functional connectivity. Both static and dynamic analyses demonstrated significant differences between cortical functional connectivity networks of open and closed visual-motor loop. Additionally, the dynamical network analysis also revealed that the EEG network related to visualmotor coordination undergoes a meta-stable state dynamics in the prime eigenvector space. This method can also potentially be applied to other network system to reveal the meta-stable states structure