Fülöp Bazsó

Fuzzy communities and the concept of bridgeness in complex networks

We consider the problem of fuzzy community detection in networks, which complements and expands the concept of overlapping community structure. Our approach allows each vertex of the graph to belong to multiple communities at the same time, determined by exact numerical membership degrees, even in the presence of uncertainty in the data being analyzed. We create an algorithm for determining the optimal membership degrees with respect to a given goal function. Based on the membership degrees, we introduce a measure that is able to identify outlier vertices that do not belong to any of the communities, bridge vertices that have significant membership in more than one single community, and regular vertices that fundamentally restrict their interactions within their own community, while also being able to quantify the centrality of a vertex with respect to its dominant community. The method can also be used for prediction in case of uncertainty in the data set analyzed. The number of communities can be given in advance, or determined by the algorithm itself, using a fuzzified variant of the modularity function. The technique is able to discover the fuzzy community structure of different real world networks including, but not limited to, social networks, scientific collaboration networks, and cortical networks, with high confidence.

Prediction of the main cortical areas and connections involved in the tactile function of the visual cortex by network analysis.

We explored the cortical pathways from the primary somatosensory cortex to the primary visual cortex (V1) by analysing connectional data in the macaque monkey using graph‐theoretical tools. Cluster analysis revealed the close relationship of the dorsal visual stream and the sensorimotor cortex. It was shown that prefrontal area 46 and parietal areas VIP and 7a occupy a central position between the different clusters in the visuo‐tactile network. Among these structures all the shortest paths from primary somatosensory cortex (3a, 1 and 2) to V1 pass through VIP and then reach V1 via MT, V3 and PO. Comparison of the input and output fields suggested a larger specificity for the 3a/1‐VIP‐MT/V3‐V1 pathways among the alternative routes. A reinforcement learning algorithm was used to evaluate the importance of the aforementioned pathways. The results suggest a higher role for V3 in relaying more direct sensorimotor information to V1. Analysing cliques, which identify areas with the strongest coupling in the network, supported the role of VIP, MT and V3 in visuo‐tactile integration. These findings indicate that areas 3a, 1, VIP, MT and V3 play a major role in shaping the tactile information reaching V1 in both sighted and blind subjects. Our observations greatly support the findings of the experimental studies and provide a deeper insight into the network architecture underlying visuo‐tactile integration in the primate cerebral cortex.

Reconstructing Cortical Networks: Case of Directed Graphs with High Level of Reciprocity

The problem of prediction of yet uncharted connections in the large scale network of the cerebral cortex is addressed. Our approach was determined by the fact that the cortical network is highly reciprocal although directed, i.e. the input and output connection patterns of vertices are slightly different. In order to solve the problem of predicting missing connections in the cerebral cortex, we propose a probabilistic method, where vertices are grouped into two clusters based on their outgoing and incoming edges, and the probability of a connection is determined by the cluster affiliations of the vertices involved. Our approach allows accounting for differences in the incoming and outgoing connections, and is free from assumptions about graph properties. The method is general and applicable to any network for which the connectional structure is mapped to a sufficient extent. Our method allows the reconstruction of the original visual cortical network with high accuracy, which was confirmed after comparisons with previous results. For the first time, the effect of extension of the visual cortex was also examined on graph reconstruction after complementing it with the subnetwork of the sensorimotor cortex. This additional connectional information further improved the graph reconstruction. One of our major findings is that knowledge of definitely nonexistent connections may significantly improve the quality of predictions regarding previously uncharted edges as well as the understanding of the large scale cortical organization.

Convergence and divergence are mostly reciprocated properties of the connections in the network of cortical areas

Cognition is based on the integrated functioning of hierarchically organized cortical processing streams in a manner yet to be clarified. Because integration fundamentally depends on convergence and the complementary notion of divergence of the neuronal connections, we analysed integration by measuring the degree of convergence/divergence through the connections in the network of cortical areas. By introducing a new index, we explored the complementary convergent and divergent nature of connectional reciprocity and delineated the backward and forward cortical sub-networks for the first time. Integrative properties of the areas defined by the degree of convergence/divergence through their afferents and efferents exhibited distinctive characteristics at different levels of the cortical hierarchy. Areas previously identified as hubs exhibit information bottleneck properties. Cortical networks largely deviate from random graphs where convergence and divergence are balanced at low reciprocity level. In the cortex, which is dominated by reciprocal connections, balance appears only by further increasing the number of reciprocal connections. The results point to the decisive role of the optimal number and placement of reciprocal connections in large-scale cortical integration. Our findings also facilitate understanding of the functional interactions between the cortical areas and the information flow or its equivalents in highly recurrent natural and artificial networks.

Accuracy of joint entropy and mutual information estimates

In practice, researchers often face the problem of being able to collect only one, possibly large, dataset, and they are forced to make inferences from a single sample. Based on the results of the polarisation operator technique of Bowman et al (1969), we computed the dependence of joint entropy and mutual information estimates on the sample size in terms of asymptotic series. These expressions enabled us to control the bias of the estimates caused by finite sample sizes and obtain an expression for the accuracies. The result is important in data mining when joint entropy and mutual information are used to find interdependences within large data sets with unknown underlying structures.

Optimization of the hexapod robot walking by genetic algorithm

In building walking hexapod robot great time and effort is needed to optimize robot walking. When simulating robotic gaits, several parameters affect simulation output. These parameters need to be optimized in order to achieve optimal robot movement. Genetic algorithm is used to optimize parameters in the simulation.

Channel noise in Hodgkin–Huxley model neurons

Abstract We study the effect of channel noise on the firing properties of the Hodgkin–Huxley equations. The spectral properties of the currents and corresponding Hurst indices are determined, and their relevance for information processing is discussed. The interspike interval histograms and their properties are also discussed.

The effect of synaptic depression on stochastic resonance

Abstract Stochastic resonance is a mechanism, where noise plays a beneficial role in amplifying weak signals arriving to some nonlinear system. A possible way to improve the signal-to-noise ratio (SNR) of the output of the system is to use several realizations, and sum and average the output of them in a proper way. In neural systems the different synaptic strengths play important role in the averaging. Earlier studies neglected the effect of the possible rapid synaptic plasticity on stochastic resonance, and tacitly assumed constant synaptic strengths. Here, we systematically examined in a small integrate-and-fire network the interaction between stochasticity and synaptic modifiability, namely synaptic depression. This kind of plasticity mechanism increased the SNR in some parameter regions.

A statistical approach to neural population dynamics: Theory, algorithms, simulations

Abstract Our goal is to give a general theory of population dynamics within the framework of kinetic theory. We describe a computational model for simulating large-scale population phenomena. The behaviour of the underlying ‘average single cell’ is also given. The model is suitable for describing various population phenomena, such as different hippocampal activities and orientation selectivity in the primary visual cortex.

What makes the prefrontal cortex so appealing in the era of brain imaging? A network analytical perspective

It is thought that the prefrontal cortex (PFC) subserves cognitive control processes by coordinating the flow of information in the cerebral cortex. In the network of cortical areas the central position of the PFC makes difficult to dissociate processing and the cognitive function mapped to this region, especially when using whole brain imaging techniques, which can detect frequently activated regions. Accordingly, the present study showed particularly high rate of increase of published studies citing the PFC and imaging as compared to other fields of the neurosciences on the PubMed. Network measures used to characterize the role of the areas in signal flow indicated specialization of the different regions of the PFC in cortical processing. Notably, areas of the dorsolateral PFC and the anterior cingulate cortex, which received the highest number of citations, were identified as global convergence points in the network. These prefrontal regions also had central position in the dominant cluster consisted exclusively by the associational areas of the cortex. We also present findings relevant to models suggesting that control processes of the PFC are depended on serial processing, which results in bottleneck effects. The findings suggest that PFC is best understood via its role in cortical information processing.