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The theoretical analysis of maritime accidents is a hot topic, but the time characteristics and dynamics of maritime accidents time series are still unclear. It is difficult to draw a clear conclusion from the cause analysis, so the accident is difficult to be predicted. To bridge this gap, this research analyzes the characteristics and evolution mechanism of maritime accidents time series from the perspective of complex network theory. The visual graph algorithm is used to model the complex network of maritime accidents data in 22 jurisdictions of the Yangtze River, map the time series into a complex network, and reveal the time characteristics and dynamics of maritime accidents time series based on the complex system theory. In the empirical analysis, degree distribution, clustering coefficient and network diameter are used to analyze the characteristics of time series. The results show that the degree distribution of maritime accidents time series network presents power-law characteristics in the macro and micro levels, which shows that the maritime accidents time series is scale-free. In addition, according to the clustering coefficient and network diameter, maritime accidents time series in the Yangtze River has the characteristics of small-world and hierarchical structure. The research of this manuscript shows that the occurrence of maritime accidents is not random events and does not follow specific patterns but presents the characteristics of complex systems, and this phenomenon is common. The analysis of maritime accidents time series by complex network theory can provide theoretical support for maritime traffic safety management., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Safety and Security Science

Background: Physiological and pathological brain aging plays a central role in brain network modulation. The aim of the present article was to assess the stability of a proposed method for evaluation of small-world (SW) characteristics for the study of the human connectome. Subjects and Methods: Eighty subjects were recruited: 36 young healthy controls, 32 elderly healthy controls, and 12 patients affected by Alzheimer's disease (AD). Electroencephalograms (EEGs) were recorded during six separate sessions (480 recordings) at an average intersession interval of 3.8 ± 0.2 days. We applied graph theory functions to the weighted and undirected networks obtained by the lagged linear coherence estimated by exact low-resolution electromagnetic tomography (eLORETA). We explored the following frequency bands: delta (2-4 Hz), theta (4-8 Hz), alpha 1 (8-10.5 Hz), alpha 2 (10.5-13 Hz), beta 1 (13-20 Hz), beta 2 (20-30 Hz), and gamma (30-40 Hz). Results: The proposed method for evaluation of SW characteristics exhibited good reproducibility and stability. Furthermore, results showed the pattern, Young>Elderly>AD, in low-frequency delta and theta bands and vice versa in the higher alpha band. Finally, a correlation with age was confirmed in healthy subjects, showing that the older the age, the higher the SW values for alpha 2. Discussion: Evidences from the present study confirm the stability of the SW index and suggest that the analysis of connectivity patterns evaluated from EEGs can be supported by the graph theory. The proposed method for evaluation of SW characteristics has shown good reproducibility and stability. This technique, applied to patient data, could provide more information on the pathophysiological processes underlying age-related brain disconnection, as well as on administration of rehabilitation treatments at the right time, which could allow patients to avoid unnecessary interventions. The graph analysis tools described in this study represent an intere

We propose a new model of exploration and exploitation, in which firms rely on local search for exploitation and on imitation for exploration. We assume that firms imitate the knowledge base of successful competitors, with imitation errors taking place depending on the social distance between the imitating firm and imitated firm in the network. The key model outcome, consistent with earlier empirical findings, holds that successful imitation generally occurs at an intermediate level of cognitive proximity because imitation at high cognitive distance is too error-prone, while for imitation at low cognitive distance there are typically no firms to imitate. A second outcome holds that social and cognitive proximity are substitutes. The model further shows that exploration by imitation is more beneficial in highly complex industries than in less complex industries, and that small-world networks yield the highest benefits for collective learning.

This case study is part of a research project based in Spain between 2011 and 2014 on the social institutions and affective processes involved in what is normally referred to as social movement. Our purpose is to study how information circulates in small-world networks in which the dynamics are modeled with a stochastic version of Greenberg–Hasting’s excitable model. This is a three-state model in which a node can be in an excited, passive, or susceptible state. Only in the susceptible state does a node interact with its neighbors in the small-world network, and its interaction depends on the probability of contagion. We introduce an infection probability, which is the only parameter in our implementation of Greenberg–Hasting’s model. The small-world network is characterized by a mean connectivity parameter and by a disorder parameter. The resulting dynamics are characterized by the average activity in the network. We have found transitions from inactive to active collective regimes, and we can induce this transition by varying. We search for different dynamics within small-world networks of citizens’ organizations by going through the following steps: identifying alliance patterns; looking for robust small-world attributes and how they are constructed; and interpreting the three modes of our model., Comunidad de Madrid, Depto. de Antropología Social y Psicología Social, Fac. de Ciencias Políticas y Sociología, TRUE, pub

Functional connectivity (FC) estimated from functional magnetic resonance imaging (fMRI) signals is important in understanding neural representation and information processing in cortical networks. However, due to a lack of "ground truth" FC pattern, the reliability and robustness of FC estimates are usually examined in downstream FC analysis tasks, such as performing participant's identification (also known as "fingerprinting"). In this paper, we propose to learn FC via a smooth graph learning framework. In particular, we treat each time frame of the fMRI time series as a graph signal on an underlying functional brain graph, and estimate the smooth graph functional connectivity (SGFC) by learning the weighted graph adjacency matrix based on graph signal smoothness assumption. We demonstrate that our approach gives rise to a natural and sparse graph representation of FC from which reliable graph measures can be extracted. Reliability of SGFC is evaluated in the context of fingerprinting and compared to correlation FC (CFC). SGFC achieves higher fingerprinting accuracy across several different experiment settings; the improvement is even more significant when a shorter fMRI scanning length is used for FC estimation. In addition to being reliable, we also validate the cognitive relevance of SGFC by using it to predict fluid intelligence. Finally, in evaluating topological measures of the sparse graph, SGFC reveals a more small-world and modular structure compared to CFC. Together, our results suggest that the smooth graph learning framework produces a naturally sparse, reliable, and cognitive-relevant representation of functional connectivity.

Background: Several studies investigated clinical and instrumental differences to make diagnosis of dementia in general and in Alzheimer's disease (AD) in particular with the aim to classify, at the individual level, AD patients and healthy controls cooperating with neuropsychological tests for an early diagnosis. Advanced network analysis of electroencephalographic (EEG) rhythms provides information on dynamic brain connectivity and could be used in classification processes. If successfully reached, this goal would add a low-cost, easily accessible, and non-invasive technique with neuropsychological tests. Objective: To investigate the possibility to automatically classify physiological versus pathological aging from cortical sources' connectivity based on a support vector machine (SVM) applied to EEG small-world parameter. Methods: A total of 295 subjects were recruited: 120 healthy volunteers and 175 AD. Graph theory functions were applied to undirected and weighted networks obtained by lagged linear coherence evaluated by eLORETA. A machine-learning classifier (SVM) was applied. EEG frequency bands were: delta (2-4 Hz), theta (4-8 Hz), alpha1 (8-10.5 Hz), alpha2 (10.5-13 Hz), beta1 (13-20 Hz), beta2 (20-30 Hz), and gamma (30-40 Hz). Results: The receiver operating characteristic curve showed AUC of 0.97±0.03 (indicating very high classification accuracy). The classifier showed 95% ±5% sensitivity, 96% ±3% specificity, and 95% ±3% accuracy for the classification. Conclusion: EEG connectivity analysis via a combination of source/connectivity biomarkers, highly correlating with neuropsychological AD diagnosis, could represent a promising tool in identification of AD patients. This approach represents a low-cost and non-invasive method, one that utilizes widely available techniques which, when combined, reach high sensitivity/specificity and optimal classification accuracy on an individual basis (0.97 of AUC).

We review the article by Ferrer-i-Cancho & Solé (2001) on the word co-occurrence networks of the British National Corpus, improving it and expanding it in multiple directions. First, we replace the statistically flawed criterion to filter out non-statistically significant co-occurrences by a new method that is a combination of Fisher's Exact Test and a Holm-Bonferroni's Correction to control for multiple comparisons. Second, we introduce new measures such as closeness centrality to measure vertex-vertex distance and we discover that significant co-occurrences reported by our method are mostly composed by words with larger centrality. Also we study the degree mixing of the network using the mixing coefficient, defined by Newman, to determine the disassortative nature of the words in the corpus. Third, we study common phenomena over word co-occurrence networks, like the small-world condition and the emergence of Zipf's Law. We discover that networks whose non-significant co-occurrences are filtered out lose the condition of small-world, while non-filtered networks exhibit it, but for both of them we find a double Zipf's Law with different exponents for the regimes in the degree distribution. Fourth, we investigate the effect of randomizing the corpus and the significance level on the properties of the network. We find that the original filtering technique is not able to determine a lack of significance in word co-occurrences from a randomized corpus. Also, we add a discussion on the significance level we have used for the filtering, such that it has an impact on the different properties exhibited by the resulting network after the filtering. To conclude, we try to tie the results from our analysis to human language phenomena, like the existence of two different registries in human language to achieve a successful communication, as reported by Ferrer-i-Cancho.

In vitro electrophysiological investigation of neural activity at a network level holds tremendous potential for elucidating underlying features of brain function (and dysfunction). In standard neural network modelling systems, however, the fundamental three-dimensional (3D) character of the brain is a largely disregarded feature. This widely applied neuroscientific strategy affects several aspects of the structure-function relationships of the resulting networks, altering network connectivity and topology, ultimately reducing the translatability of the results obtained. As these model systems increase in popularity, it becomes imperative that they capture, as accurately as possible, fundamental features of neural networks in the brain, such as small-worldness. In this report, we combine in vitro neural cell culture with a biologically compatible scaffolding substrate, surface-grafted polymer particles (PPs), to develop neural networks with 3D topology. Furthermore, we investigate their electrophysiological network activity through the use of 3D multielectrode arrays. The resulting neural network activity shows emergent behaviour consistent with maturing neural networks capable of performing computations, i.e. activity patterns suggestive of both information segregation (desynchronized single spikes and local bursts) and information integration (network spikes). Importantly, we demonstrate that the resulting PP-structured neural networks show both structural and functional features consistent with small-world network topology.

In vitro electrophysiological investigation of neural activity at a network level holds tremendous potential for elucidating underlying features of brain function (and dysfunction). In standard neural network modelling systems, however, the fundamental three-dimensional (3D) character of the brain is a largely disregarded feature. This widely applied neuroscientific strategy affects several aspects of the structure-function relationships of the resulting networks, altering network connectivity and topology, ultimately reducing the translatability of the results obtained. As these model systems increase in popularity, it becomes imperative that they capture, as accurately as possible, fundamental features of neural networks in the brain, such as small-worldness. In this report, we combine in vitro neural cell culture with a biologically compatible scaffolding substrate, surface-grafted polymer particles (PPs), to develop neural networks with 3D topology. Furthermore, we investigate their electrophysiological network activity through the use of 3D multielectrode arrays. The resulting neural network activity shows emergent behaviour consistent with maturing neural networks capable of performing computations, i.e. activity patterns suggestive of both information segregation (desynchronized single spikes and local bursts) and information integration (network spikes). Importantly, we demonstrate that the resulting PP-structured neural networks show both structural and functional features consistent with small-world network topology.

In vitro electrophysiological investigation of neural activity at a network level holds tremendous potential for elucidating underlying features of brain function (and dysfunction). In standard neural network modelling systems, however, the fundamental three-dimensional (3D) character of the brain is a largely disregarded feature. This widely applied neuroscientific strategy affects several aspects of the structure-function relationships of the resulting networks, altering network connectivity and topology, ultimately reducing the translatability of the results obtained. As these model systems increase in popularity, it becomes imperative that they capture, as accurately as possible, fundamental features of neural networks in the brain, such as small-worldness. In this report, we combine in vitro neural cell culture with a biologically compatible scaffolding substrate, surface-grafted polymer particles (PPs), to develop neural networks with 3D topology. Furthermore, we investigate their electrophysiological network activity through the use of 3D multielectrode arrays. The resulting neural network activity shows emergent behaviour consistent with maturing neural networks capable of performing computations, i.e. activity patterns suggestive of both information segregation (desynchronized single spikes and local bursts) and information integration (network spikes). Importantly, we demonstrate that the resulting PP-structured neural networks show both structural and functional features consistent with small-world network topology.

In vitro electrophysiological investigation of neural activity at a network level holds tremendous potential for elucidating underlying features of brain function (and dysfunction). In standard neural network modelling systems, however, the fundamental three-dimensional (3D) character of the brain is a largely disregarded feature. This widely applied neuroscientific strategy affects several aspects of the structure-function relationships of the resulting networks, altering network connectivity and topology, ultimately reducing the translatability of the results obtained. As these model systems increase in popularity, it becomes imperative that they capture, as accurately as possible, fundamental features of neural networks in the brain, such as small-worldness. In this report, we combine in vitro neural cell culture with a biologically compatible scaffolding substrate, surface-grafted polymer particles (PPs), to develop neural networks with 3D topology. Furthermore, we investigate their electrophysiological network activity through the use of 3D multielectrode arrays. The resulting neural network activity shows emergent behaviour consistent with maturing neural networks capable of performing computations, i.e. activity patterns suggestive of both information segregation (desynchronized single spikes and local bursts) and information integration (network spikes). Importantly, we demonstrate that the resulting PP-structured neural networks show both structural and functional features consistent with small-world network topology.

In vitro electrophysiological investigation of neural activity at a network level holds tremendous potential for elucidating underlying features of brain function (and dysfunction). In standard neural network modelling systems, however, the fundamental three-dimensional (3D) character of the brain is a largely disregarded feature. This widely applied neuroscientific strategy affects several aspects of the structure-function relationships of the resulting networks, altering network connectivity and topology, ultimately reducing the translatability of the results obtained. As these model systems increase in popularity, it becomes imperative that they capture, as accurately as possible, fundamental features of neural networks in the brain, such as small-worldness. In this report, we combine in vitro neural cell culture with a biologically compatible scaffolding substrate, surface-grafted polymer particles (PPs), to develop neural networks with 3D topology. Furthermore, we investigate their electrophysiological network activity through the use of 3D multielectrode arrays. The resulting neural network activity shows emergent behaviour consistent with maturing neural networks capable of performing computations, i.e. activity patterns suggestive of both information segregation (desynchronized single spikes and local bursts) and information integration (network spikes). Importantly, we demonstrate that the resulting PP-structured neural networks show both structural and functional features consistent with small-world network topology.

Many real life complex networks consists of a tremendous amount of nodes and edges which make them difficult to extract and analyze. This thesis aims to examine what network prop- erties that can be deduced when considering small samples of a complex network and how well they correspond to the characteristics of the complete network. This is of importance as sampling will most likely be the de facto method when analyzing complex networks in the future. The study examine the scale-free property, the small-world property and the com- munity structure of the network spanned by the KTH domain. The method consisted of gathering data about the network through sampling it in a breadth-first manner using a web crawler. The samples was then compared with respect to each property. The results was that good approximations of the scale-free property could be made from small samples of the KTH network. However, no good approximation could be made about the small-world property using the sampling technique. Good approximations about a node’s community affiliation could be observed. However, general conclusions of the com- plete network’s community structures could not be made. To summarize, the result indi- cate that small samples can be used to approximate some properties of the complete KTH network. However, to determine if the result is true for the general case more research is necessary., Komplexa nätverk i vår omvärld består av ett stort antal hörn och kanter vilket gör dem svå- ra att extrahera och analysera. Denna rapport undersöker vilka nätverksegenskaper som kan härledas vid undersökningen av små stickprov av ett nätverk och hur bra dessa representerar egenskaperna hos det fullständiga nätverket. Detta är av betydelse eftersom användandet av små stickprov kommer troligtvis att vara standarden vid undersökningar av nätverk i framtiden. Denna studie undersökte scale-free egenskapen, small-world egenskapen och community strukturen för nätverket som omfattas av KTH domaänen. Metoden innefattade att samla in data om nätverket genom stickprov baserat på en bredden-först sökning. Detta realiserades genom att använda en sökrobot. Sedan jämfördes de olika stickproven med avseende på de olika nätverksegenskaperna. Resultetat visade att nätverkets scale-free egenskap kunde approximaeras med små stickprov. Däremot var det inte möjligt att approximera nätverkets small-world egenskap genom användet av den givna stickprovsmetoden. Goda approximationer observerades för att avgöra ett hörns community tillhörighet men den allmäna community strukturen kunde inte approximeras. Sammanfattningsvis visade resultatet att stickprov kan användas för att approximera vissa egenskaper hos det fullständiga KTH nätverket men att mer forskning krävs för att avgöra om resultaten kan generaliseras.

Many real life complex networks consists of a tremendous amount of nodes and edges which make them difficult to extract and analyze. This thesis aims to examine what network prop- erties that can be deduced when considering small samples of a complex network and how well they correspond to the characteristics of the complete network. This is of importance as sampling will most likely be the de facto method when analyzing complex networks in the future. The study examine the scale-free property, the small-world property and the com- munity structure of the network spanned by the KTH domain. The method consisted of gathering data about the network through sampling it in a breadth-first manner using a web crawler. The samples was then compared with respect to each property. The results was that good approximations of the scale-free property could be made from small samples of the KTH network. However, no good approximation could be made about the small-world property using the sampling technique. Good approximations about a node’s community affiliation could be observed. However, general conclusions of the com- plete network’s community structures could not be made. To summarize, the result indi- cate that small samples can be used to approximate some properties of the complete KTH network. However, to determine if the result is true for the general case more research is necessary., Komplexa nätverk i vår omvärld består av ett stort antal hörn och kanter vilket gör dem svå- ra att extrahera och analysera. Denna rapport undersöker vilka nätverksegenskaper som kan härledas vid undersökningen av små stickprov av ett nätverk och hur bra dessa representerar egenskaperna hos det fullständiga nätverket. Detta är av betydelse eftersom användandet av små stickprov kommer troligtvis att vara standarden vid undersökningar av nätverk i framtiden. Denna studie undersökte scale-free egenskapen, small-world egenskapen och community strukturen för nätverket som omfattas av KTH domaänen. Metoden innefattade att samla in data om nätverket genom stickprov baserat på en bredden-först sökning. Detta realiserades genom att använda en sökrobot. Sedan jämfördes de olika stickproven med avseende på de olika nätverksegenskaperna. Resultetat visade att nätverkets scale-free egenskap kunde approximaeras med små stickprov. Däremot var det inte möjligt att approximera nätverkets small-world egenskap genom användet av den givna stickprovsmetoden. Goda approximationer observerades för att avgöra ett hörns community tillhörighet men den allmäna community strukturen kunde inte approximeras. Sammanfattningsvis visade resultatet att stickprov kan användas för att approximera vissa egenskaper hos det fullständiga KTH nätverket men att mer forskning krävs för att avgöra om resultaten kan generaliseras.

Objective Epilepsy is characterized by unpredictable and sudden paroxysmal neuronal firing occurrences and sometimes evolving in clinically evident seizure. To predict seizure event, small-world characteristic in nine minutes before seizure, divided in three 3-min periods (T0, T1, T2) were investigated. Methods Intracerebral recordings were obtained from 10 patients with drug resistant focal epilepsy examined by means of stereotactically implanted electrodes; analysis was focused in a period of low spiking (Baseline) and during two seizures. Networks’ architecture is undirected and weighted. Electrodes’ contacts close to epileptic focus are the vertices, edges are weighted by mscohere (=magnitude squared coherence). Results Differences were observed between Baseline and T1 and between Baseline and T2 in theta band; and between Baseline and T1, Baseline and T2, and near-significant difference between T0 and T2 in Alpha 2 band. Moreover, an intra-band index was computed for small worldness as difference between Theta and Alpha 2. It was found a growing index trend from Baseline to T2. Conclusions Cortical network features a specific pre-seizure architecture which could predict the incoming epileptic seizure. Significance Through this study future researches could investigate brain connectivity modifications approximating a clinical seizure also in order to address a preventive therapy.

It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and also scale-free (the degrees are distributed according to a power law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems that are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances the probabilistic and simulation techniques and, therefore, it provides a better understanding of the modeled systems. In this paper we find the radius, diameter, clustering coefficient and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks that has been considered for modeling real-life complex systems., Peer Reviewed, Postprint (author's final draft)

© 2015. Graph theory (GT) is a powerful framework for quantifying topological features of neuroimaging-derived functional and structural networks. However, false positive (FP) connections arise frequently and influence the inferred topology of networks. Thresholding is often used to overcome this problem, but an appropriate threshold often relies on a priori assumptions, which will alter inferred network topologies.Four common network metrics (global efficiency, mean clustering coefficient, mean betweenness and smallworldness) were tested using a model tractography dataset. It was found that all four network metrics were significantly affected even by just one FP. Results also show that thresholding effectively dampens the impact of FPs, but at the expense of adding significant bias to network metrics.In a larger number (n= 248) of tractography datasets, statistics were computed across random group permutations for a range of thresholds, revealing that statistics for network metrics varied significantly more than for non-network metrics (i.e., number of streamlines and number of edges). Varying degrees of network atrophy were introduced artificially to half the datasets, to test sensitivity to genuine group differences. For some network metrics, this atrophy was detected as significant (p<. 0.05, determined using permutation testing) only across a limited range of thresholds.We propose a multi-threshold permutation correction (MTPC) method, based on the cluster-enhanced permutation correction approach, to identify sustained significant effects across clusters of thresholds. This approach minimises requirements to determine a single threshold a priori. We demonstrate improved sensitivity of MTPC-corrected metrics to genuine group effects compared to an existing approach and demonstrate the use of MTPC on a previously published network analysis of tractography data derived from a clinical population.In conclusion, we show that there are large biases and instab

Neuronal dynamics display a complex spatiotemporal structure involving the precise, context-dependent coordination of activation patterns across a large number of spatially distributed regions. Functional magnetic resonance imaging (fMRI) has played a central role in demonstrating the nontrivial spatial and topological structure of these interactions, but thus far has been limited in its capacity to study their temporal evolution. Here, using high-resolution resting-state fMRI data obtained from the Human Connectome Project, we mapped time-resolved functional connectivity across the entire brain at a subsecond resolution with the aim of understanding how nonstationary fluctuations in pairwise interactions between regions relate to large-scale topological properties of the human brain. We report evidence for a consistent set of functional connections that show pronounced fluctuations in their strength over time. The most dynamic connections are intermodular, linking elements from topologically separable subsystems, and localize to known hubs of default mode and fronto-parietal systems. We found that spatially distributed regions spontaneously increased, for brief intervals, the efficiency with which they can transfer information, producing temporary, globally efficient network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time, possibly achieving a balance between efficient information-processing and metabolic expenditure.

Developmental dyslexia is a neurobiological deficit characterized by persistent difficulty in learning to read in children and adults who otherwise possess normal intelligence. Functional and structural connectivity data suggest that developmental dyslexia could be a disconnection syndrome. However, whether abnormalities in connectivity exist in beginning readers at-risk for reading difficulties is unknown. Using graph-theoretical analysis, we investigated differences in global and regional topological properties of structural brain networks in 42 beginning readers with (FH+) and without (FH-) familial risk for reading difficulties. We constructed separate structural correlation networks based on measures of surface area and cortical thickness. Results revealed changes in topological properties in brain regions known to be abnormal in dyslexia (left supramarginal gyrus, left inferior frontal gyrus) in the FH+ group mainly in the network constructed from measures of cortical surface area. We also found alterations in topological properties in regions that are not often advertised as dyslexia but nonetheless play important role in reading (left posterior cingulate, hippocampus, and left precentral gyrus). To our knowledge, this is the first report of altered topological properties of structural correlation networks in children at risk for reading difficulty, and motivates future studies that examine the mechanisms underlying how these brain networks may mediate the influences of family history on reading outcome.

Functional network connectivity (FNC) is a method of analyzing the temporal relationship of anatomical brain components, comparing the synchronicity between patient groups or conditions. We use functional-connectivity measures between independent components to classify between Schizophrenia patients and healthy controls during resting-state. Connectivity is measured using a variety of graph-theoretic connectivity measures such as graph density, average path length, and small-worldness. The Schizophrenia patients showed significantly less clustering (transitivity) among components than healthy controls (p < 0.05, corrected) with networks less likely to be connected, and also showed lower small-world connectivity than healthy controls. Using only these connectivity measures, an SVM classifier (without parameter tuning) could discriminate between Schizophrenia patients and healthy controls with 65% accuracy, compared to 51% chance. This implies that the global functional connectivity between resting-state networks is altered in Schizophrenia, with networks more likely to be disconnected and behave dissimilarly for diseased patients. We present this research finding as a tutorial using the publicly available COBRE dataset of 146 Schizophrenia patients and healthy controls, provided as part of the 1000 Functional Connectomes Project. We demonstrate preprocessing, using independent component analysis (ICA) to nominate networks, computing graph-theoretic connectivity measures, and finally using these connectivity measures to either classify between patient groups or assess between-group differences using formal hypothesis testing. All necessary code is provided for both running command-line FSL preprocessing, and for computing all statistical measures and SVM classification within R. Collectively, this work presents not just findings of diminished FNC among resting-state networks in Schizophrenia, but also a practical connectivity tutorial.

This thesis examines the urban morphology of fifty cities using spatial syntax analysis. The analysis compares the urban street networks of European, USA, Islamic and East Asian cities. Street connectivity was the main metric and natural roads were the basis for the analysis. The aim of the study was to analyze determine how sensitive space syntax methods are for uncovering the hierarchical patterns of urban street networks and examining their scale-free and small-world properties. Street data was collected from OpenStreetMap. ArcGIS 10 with the Axwoman extension was used to study the hierarchical levels of street networks. Matlab provided the platform to examine the scale-free property of street data. Pajek software was used to measure the small-world behavior. Based on the hierarchical representation, the fifty sample cities were classified into different groups and their scale-free and small-world properties were studied. From a traditionally morphological perspective, it was found that some cities in Europe have a close-knit cellular and organic urban morphology. Cities in the USA exhibit gridiron patterns on the whole. Some Islamic cities have special urban structure with houses grouped around the cul-de-sac lanes. Several of the East Asian cities studied also have grid forms. According to the space syntax analysis, urban street networks that have a connectivity value greater than the average value were less than 40%. The results showed that for most cities, the street connectivity distribution follows a power-law distribution and exhibits scale-free properties. Urban street networks of all sample cities were found to have a small-world property. Space syntax cannot detect all of the morphological patterns recognized in traditional morphological studies. The method can, however, efficiently quantify the spatial configuration of a large sample. Space syntax’s topological and scaling metrics thus provide a way to compare urban street networks. These metrics can t

Functional network connectivity (FNC) is a method of analyzing the temporal relationship of anatomical brain components, comparing the synchronicity between patient groups or conditions. We use functional-connectivity measures between independent components to classify between Schizophrenia patients and healthy controls during resting-state. Connectivity is measured using a variety of graph-theoretic connectivity measures such as graph density, average path length, and small-worldness. The Schizophrenia patients showed significantly less clustering (transitivity) among components than healthy controls (p < 0.05, corrected) with networks less likely to be connected, and also showed lower small-world connectivity than healthy controls. Using only these connectivity measures, an SVM classifier (without parameter tuning) could discriminate between Schizophrenia patients and healthy controls with 65% accuracy, compared to 51% chance. This implies that the global functional connectivity between resting-state networks is altered in Schizophrenia, with networks more likely to be disconnected and behave dissimilarly for diseased patients. We present this research finding as a tutorial using the publicly available COBRE dataset of 146 Schizophrenia patients and healthy controls, provided as part of the 1000 Functional Connectomes Project. We demonstrate preprocessing, using independent component analysis (ICA) to nominate networks, computing graph-theoretic connectivity measures, and finally using these connectivity measures to either classify between patient groups or assess between-group differences using formal hypothesis testing. All necessary code is provided for both running command-line FSL preprocessing, and for computing all statistical measures and SVM classification within R. Collectively, this work presents not just findings of diminished FNC among resting-state networks in Schizophrenia, but also a practical connectivity tutorial.

Brain connectivity analyses show considerable promise for understanding how our neural pathways gradually break down in aging and Alzheimer's disease (AD). Even so, we know very little about how the brain's networks change in AD, and which metrics are best to evaluate these changes. To better understand how AD affects brain connectivity, we analyzed anatomical connectivity based on 3-T diffusion-weighted images from 111 subjects (15 with AD, 68 with mild cognitive impairment, and 28 healthy elderly; mean age, 73.7±7.6 SD years). We performed whole brain tractography based on the orientation distribution functions, and compiled connectivity matrices showing the proportions of detected fibers interconnecting 68 cortical regions. We computed a variety of measures sensitive to anatomical network topology, including the structural backbone--the so-called "k-core"--of the anatomical network, and the nodal degree. We found widespread network disruptions, as connections were lost in AD. Among other connectivity measures showing disease effects, network nodal degree, normalized characteristic path length, and efficiency decreased with disease, while normalized small-worldness increased, in the whole brain and left and right hemispheres individually. The normalized clustering coefficient also increased in the whole brain; we discuss factors that may cause this effect. The proportions of fibers intersecting left and right cortical regions were asymmetrical in all diagnostic groups. This asymmetry may intensify as disease progressed. Connectivity metrics based on the k-core may help understand brain network breakdown as cognitive impairment increases, revealing how degenerative diseases affect the human connectome.

Developmental dyslexia is a neurobiological deficit characterized by persistent difficulty in learning to read in children and adults who otherwise possess normal intelligence. Functional and structural connectivity data suggest that developmental dyslexia could be a disconnection syndrome. However, whether abnormalities in connectivity exist in beginning readers at-risk for reading difficulties is unknown. Using graph-theoretical analysis, we investigated differences in global and regional topological properties of structural brain networks in 42 beginning readers with (FH+) and without (FH-) familial risk for reading difficulties. We constructed separate structural correlation networks based on measures of surface area and cortical thickness. Results revealed changes in topological properties in brain regions known to be abnormal in dyslexia (left supramarginal gyrus, left inferior frontal gyrus) in the FH+ group mainly in the network constructed from measures of cortical surface area. We also found alterations in topological properties in regions that are not often advertised as dyslexia but nonetheless play important role in reading (left posterior cingulate, hippocampus, and left precentral gyrus). To our knowledge, this is the first report of altered topological properties of structural correlation networks in children at risk for reading difficulty, and motivates future studies that examine the mechanisms underlying how these brain networks may mediate the influences of family history on reading outcome.

A data-driven realistic design and evaluation of vehicular mobility has been particularly challenging due to a lack of large-scale real-world measurements in the research community. Current research methodologies rely on artificial scenarios, random connectivity, and use small and biased samples. In this paper, we perform a combined study to learn the structure and connectivity of urban streets and modeling and characterization of vehicular traffic densities on them. Our dataset is a collection of more than 222 thousand routes and 25 million vehicular mobility images from 1091 online web cameras located in six different regions of the world. Our results centered around four major observations: i. Study shows that driving routes and visiting locations of regions demonstrate power-law distribution, indicating a planned or recently designed road infrastructure. ii. We represent regions by network graphs in which nodes are camera locations and edges are urban streets that connect the nodes. Such representation exhibits small world properties with short path lengths and large clustering coefficient. iii. Traffic densities show 80% temporal correlation during several hours of a day. iv. Modeling traffic densities against known theoretical distributions show less than 5% deviation for heavy-trailed models such as log-logistic and log-gamma distributions. We believe this work will provide a much-needed contribution to the research community for design and evaluation of future vehicular networks and smart cities.

This thesis examines the urban morphology of fifty cities using spatial syntax analysis. The analysis compares the urban street networks of European, USA, Islamic and East Asian cities. Street connectivity was the main metric and natural roads were the basis for the analysis. The aim of the study was to analyze determine how sensitive space syntax methods are for uncovering the hierarchical patterns of urban street networks and examining their scale-free and small-world properties. Street data was collected from OpenStreetMap. ArcGIS 10 with the Axwoman extension was used to study the hierarchical levels of street networks. Matlab provided the platform to examine the scale-free property of street data. Pajek software was used to measure the small-world behavior. Based on the hierarchical representation, the fifty sample cities were classified into different groups and their scale-free and small-world properties were studied. From a traditionally morphological perspective, it was found that some cities in Europe have a close-knit cellular and organic urban morphology. Cities in the USA exhibit gridiron patterns on the whole. Some Islamic cities have special urban structure with houses grouped around the cul-de-sac lanes. Several of the East Asian cities studied also have grid forms. According to the space syntax analysis, urban street networks that have a connectivity value greater than the average value were less than 40%. The results showed that for most cities, the street connectivity distribution follows a power-law distribution and exhibits scale-free properties. Urban street networks of all sample cities were found to have a small-world property. Space syntax cannot detect all of the morphological patterns recognized in traditional morphological studies. The method can, however, efficiently quantify the spatial configuration of a large sample. Space syntax’s topological and scaling metrics thus provide a way to compare urban street networks. These metrics can t

The paper analyzes how the structure of social networks affects innovation diffusion and competition under different information regimes. Diffusion is modeled as the result of idiosyncratic adoption thresholds, local network effectsand information diffusion (broadcasting and demonstration effect from previous adopters). A high social cohesion decreases the probability of one innovation cornering the market. Nonetheless, with imperfect information, in small–world networks the higher speed of diffusion produced by the low average distance increases this probability. A low social cohesion also increases the probability of falling into traps of under–adoption. However, such probability is significantly lower with imperfect information, because such regime is characterized by higher levels of market concentrations and this reduces the frictions due to the coexistence of non–compatible product innovations.

The paper analyzes how the structure of social networks affects innovation diffusion and competition under different information regimes. Diffusion is modeled as the result of idiosyncratic adoption thresholds, local network effectsand information diffusion (broadcasting and demonstration effect from previous adopters). A high social cohesion decreases the probability of one innovation cornering the market. Nonetheless, with imperfect information, in small–world networks the higher speed of diffusion produced by the low average distance increases this probability. A low social cohesion also increases the probability of falling into traps of under–adoption. However, such probability is significantly lower with imperfect information, because such regime is characterized by higher levels of market concentrations and this reduces the frictions due to the coexistence of non–compatible product innovations.

Demands on the quality and reliability of Volunteered Geographic Information have increased because of its rising popularity. Due to the less controlled data entry, there is a risk that people provide false or inaccurate information to the database. One factor that affects the effect of such updates is the network structure of the database schema, which might reveal the database’s robustness against different kinds of false updates. Therefore, network analyses are needed. The aim is to analyse GIS data models, stored in UML class diagrams, for scale-free and small-world properties. Moreover, a robustness analysis is to be carried out on selected data models in order to find out their error and attack tolerance against, for example, false updates. Three graphs were specified from the UML class diagrams: (1) class graphs: classes as nodes and their interactive relationships as connections; (2) attribute graphs: classes and attributes as nodes, with connections between the classes and their attributes; and (3) schema graphs: attributes as nodes and their interactive relationships inside and outside the tables as links. The analysed class diagrams were stored in XMI, and therefore transformed with XSLT to the Pajek network format. Thereafter, small-world and scale-free analyses as well as a robustness analysis were performed on the graphs. The results from the scale-free analyses showed no strict power-laws. Nevertheless, the classes’ relationships and attributes, and the betweenness in the schema graphs were long-tailed distributed. Furthermore, the schema graphs had small-world properties, and the analysed class and schema graphs were robust against errors but fragile against attacks. In a network structure perspective, these results indicate that false updates on random tables of a database should usually do little harm, but falsely updating the most central cells or tables may cause big damage. Consequently, it may be necessary to monitor and constrain sensitive ce

Demands on the quality and reliability of Volunteered Geographic Information have increased because of its rising popularity. Due to the less controlled data entry, there is a risk that people provide false or inaccurate information to the database. One factor that affects the effect of such updates is the network structure of the database schema, which might reveal the database’s robustness against different kinds of false updates. Therefore, network analyses are needed. The aim is to analyse GIS data models, stored in UML class diagrams, for scale-free and small-world properties. Moreover, a robustness analysis is to be carried out on selected data models in order to find out their error and attack tolerance against, for example, false updates. Three graphs were specified from the UML class diagrams: (1) class graphs: classes as nodes and their interactive relationships as connections; (2) attribute graphs: classes and attributes as nodes, with connections between the classes and their attributes; and (3) schema graphs: attributes as nodes and their interactive relationships inside and outside the tables as links. The analysed class diagrams were stored in XMI, and therefore transformed with XSLT to the Pajek network format. Thereafter, small-world and scale-free analyses as well as a robustness analysis were performed on the graphs. The results from the scale-free analyses showed no strict power-laws. Nevertheless, the classes’ relationships and attributes, and the betweenness in the schema graphs were long-tailed distributed. Furthermore, the schema graphs had small-world properties, and the analysed class and schema graphs were robust against errors but fragile against attacks. In a network structure perspective, these results indicate that false updates on random tables of a database should usually do little harm, but falsely updating the most central cells or tables may cause big damage. Consequently, it may be necessary to monitor and constrain sensitive ce

Purpose/Aim: To find power structures within the blog network. Material/Method: Using keywords to find all available blog posts about the National Defence Radio Establishment from the blog search engine Twingly, and thereafter using the same blog search engine to find inlinks from other blogs, to those posts. The data is set into the context of the small-world networks models of Duncan J. Watts and rich-club models of Sergi Valverde och Ricard V. Sole. Main results: 5183 unique blogs have written about the subject in 22779 blog posts to which 28128 inlinks from other blogposts are made. Just over one fifth of the blogs are linkted to each other in one big network, where the remaining blogs stand without any ingoing or outgoing links. The first bloggers are the one who continue to write for longer period of time and also the ones who attracts most inlinks. The blogosphere around this subject is highly connected, shows features as one would find in a small-world network, displays a power-law distribution for inlinks and is highly clustered around a few rich- club nodes.

Purpose/Aim: To find power structures within the blog network. Material/Method: Using keywords to find all available blog posts about the National Defence Radio Establishment from the blog search engine Twingly, and thereafter using the same blog search engine to find inlinks from other blogs, to those posts. The data is set into the context of the small-world networks models of Duncan J. Watts and rich-club models of Sergi Valverde och Ricard V. Sole. Main results: 5183 unique blogs have written about the subject in 22779 blog posts to which 28128 inlinks from other blogposts are made. Just over one fifth of the blogs are linkted to each other in one big network, where the remaining blogs stand without any ingoing or outgoing links. The first bloggers are the one who continue to write for longer period of time and also the ones who attracts most inlinks. The blogosphere around this subject is highly connected, shows features as one would find in a small-world network, displays a power-law distribution for inlinks and is highly clustered around a few rich- club nodes.

The objective of this study was to test, in single subjects, the hypothesis that the signs of voluntary movement- related neural activity would first appear in the prefrontal region, then move to both the medial frontal and posterior parietal regions, progress to the medial primary motor area, lateralize to the contralateral primary motor area and finally involve the cerebellum (where feedbackinitiated error signals are computed). Six subjects performed voluntary finger movements while DC coupled EEG was recorded from 64 scalp electrodes. Event-related potentials (ERPs) averaged on the movements were analysed both before and after independent component analysis (ICA) combined with dipole source analysis (DSA) of the independent components. Both a simple topographic analysis of undecomposed ERPs and the ICA/DSA analysis suggested that the original hypothesis was inadequate. The major departure from its predictions was that, while activity over many brain regions did appear at the expected times, it also appeared at unexpected times. Overall, the results suggest that the neuroscientific ‘standard model’, in which neural activity occurs sequentially in a series of discrete local areas each specialized for a particular function, may reflect the true situation less well than models in which large areas of brain shift simultaneously into and out of common activity states.

The objective of this study was to test, in single subjects, the hypothesis that the signs of voluntary movement- related neural activity would first appear in the prefrontal region, then move to both the medial frontal and posterior parietal regions, progress to the medial primary motor area, lateralize to the contralateral primary motor area and finally involve the cerebellum (where feedbackinitiated error signals are computed). Six subjects performed voluntary finger movements while DC coupled EEG was recorded from 64 scalp electrodes. Event-related potentials (ERPs) averaged on the movements were analysed both before and after independent component analysis (ICA) combined with dipole source analysis (DSA) of the independent components. Both a simple topographic analysis of undecomposed ERPs and the ICA/DSA analysis suggested that the original hypothesis was inadequate. The major departure from its predictions was that, while activity over many brain regions did appear at the expected times, it also appeared at unexpected times. Overall, the results suggest that the neuroscientific ‘standard model’, in which neural activity occurs sequentially in a series of discrete local areas each specialized for a particular function, may reflect the true situation less well than models in which large areas of brain shift simultaneously into and out of common activity states.

Recently it has been shown that many networks associated with complex systems are small-world (they have both a large local clustering and a small diameter) and they are also scale-free (the degrees are distributed according to a power-law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems which are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances the probabilistic and simulation techniques and, therefore, it provides a better understanding of the systems modeled. In this paper we find the radius, diameter, clustering and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks which has been considered for modeling real life complex systems. Moreover a routing algorithm is proposed.

We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads to a self-consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network. We test our similarity measure on computer-generated networks for which the expected results are known, and on a number of real-world networks., QC 20100525

The next step in the understanding of the genome organization, after the determination of complete sequences, involves proteomics. The proteome includes the whole set of protein-protein interactions, and two recent independent studies have shown that its topology displays a number of surprising features shared by other complex networks, both natural and artificial. In order to understand the origins of this topology and its evolutionary implications, we present a simple model of proteome evolution that is able to reproduce many of the observed statistical regularities reported from the analysis of the yeast proteome. Our results suggest that the observed patterns can be explained by a process of gene duplication and diversification that would evolve proteome networks under a selection pressure, favoring robustness against failure of its individual components., Postprint (author's final draft)

Cílem práce je definice vztahu závislosti klasifikace pacientů postižených neurodegenerativním onemocněním na volbě parcelačního atlasu. Součástí práce je aplikace analýzy funkční konektivity a výpočtu grafových metrik dle metody publikované Olafem Spornsem a Mikailem Rubinovem [1] na fMRI datech naměřených na CEITEC MU. Aplikaci předchází teoretická rešerše parcelačních atlasů pro segmentování mozku ze snímků fMRI a rešerše matematických metod klasifikace, jako i klasifikátorů neurodegenerativních onemocnění. První kapitoly práce přináší teoretický základ poznatkůl z oblasti magnetické a funkční magnetické rezonance. Definovány jsou fyzikální principy metody, podmínky a průběh akvizice obrazových dat. Třetí kapitola shrnuje grafové metriky použité dále v diplomové práci pro analýzu a klasifikování grafů. Práce přináší stručný přehled parcelačních metod, se zaměřením na parcelaci pomoci atlasů. Po teoretické rešerši metod zkoumání funkční konektivity a matematických metod klasifikací, byly poznatky použity pro realizaci parcelací, výpočet grafových metrik a následnou klasifikaci fMRI snímků 96 subjektů vždy do jedné ze dvou tříd s využitím binárních klasifikátocí metodou podpůrných vektorů a lineární diskriminační analýzy. Data klasifikována v této práci byla naměřena na pacientech s Parkinsonovou chorobou (PD), s Alzheimerovou chorobou (AD), s Mírní kognitivní poruchou (MCI), s kombinací nemocí PD a MCI a na subjektech patřících do kontrolní skupiny zdravých jedinců. Pro předzpracování a pro analýzu je v práci využito prostředí MATLAB a toolboxy SPM12 a Brain Connectivity Toolbox., The aim of the thesis is to define the dependency of the classification of patients affected by neurodegenerative diseases on the choice of the parcellation atlas. Part of this thesis is the application of the functional connectivity analysis and the calculation of graph metrics according to the method published by Olaf Sporns and Mikail Rubinov [1] on fMRI data measured at CEITEC MU. The application is preceded by the theoretical research of parcellation atlases for brain segmentation from fMRI frames and the research of mathematical methods for classification as well as classifiers of neurodegenerative diseases. The first chapters of the thesis brings a theoretical basis of knowledge from the field of magnetic and functional magnetic resonance imaging. The physical principles of the method, the conditions and the course of acquisition of image data are defined. The third chapter summarizes the graph metrics used in the diploma thesis for analyzing and classifying graphs. The paper presents a brief overview of the brain segmentation methods, with the focuse on the atlas-based segmentation. After a theoretical research of functional connectivity methods and mathematical classification methods, the findings were used for segmentation, calculation of graph metrics and for classification of fMRI images obtained from 96 subjects into the one of two classes using Binary classifications by support vector machines and linear discriminatory analysis. The data classified in this study was measured on patiens with Parkinson’s disease (PD), Alzheimer’s disease (AD), Mild cognitive impairment (MCI), a combination of PD and MCI and subjects belonging to the control group of healthy individuals. For pre-processing and analysis, the MATLAB environment, the SPM12 toolbox and The Brain Connectivity Toolbox were used.

Cílem práce je definice vztahu závislosti klasifikace pacientů postižených neurodegenerativním onemocněním na volbě parcelačního atlasu. Součástí práce je aplikace analýzy funkční konektivity a výpočtu grafových metrik dle metody publikované Olafem Spornsem a Mikailem Rubinovem [1] na fMRI datech naměřených na CEITEC MU. Aplikaci předchází teoretická rešerše parcelačních atlasů pro segmentování mozku ze snímků fMRI a rešerše matematických metod klasifikace, jako i klasifikátorů neurodegenerativních onemocnění. První kapitoly práce přináší teoretický základ poznatkůl z oblasti magnetické a funkční magnetické rezonance. Definovány jsou fyzikální principy metody, podmínky a průběh akvizice obrazových dat. Třetí kapitola shrnuje grafové metriky použité dále v diplomové práci pro analýzu a klasifikování grafů. Práce přináší stručný přehled parcelačních metod, se zaměřením na parcelaci pomoci atlasů. Po teoretické rešerši metod zkoumání funkční konektivity a matematických metod klasifikací, byly poznatky použity pro realizaci parcelací, výpočet grafových metrik a následnou klasifikaci fMRI snímků 96 subjektů vždy do jedné ze dvou tříd s využitím binárních klasifikátocí metodou podpůrných vektorů a lineární diskriminační analýzy. Data klasifikována v této práci byla naměřena na pacientech s Parkinsonovou chorobou (PD), s Alzheimerovou chorobou (AD), s Mírní kognitivní poruchou (MCI), s kombinací nemocí PD a MCI a na subjektech patřících do kontrolní skupiny zdravých jedinců. Pro předzpracování a pro analýzu je v práci využito prostředí MATLAB a toolboxy SPM12 a Brain Connectivity Toolbox., The aim of the thesis is to define the dependency of the classification of patients affected by neurodegenerative diseases on the choice of the parcellation atlas. Part of this thesis is the application of the functional connectivity analysis and the calculation of graph metrics according to the method published by Olaf Sporns and Mikail Rubinov [1] on fMRI data measured at CEITEC MU. The application is preceded by the theoretical research of parcellation atlases for brain segmentation from fMRI frames and the research of mathematical methods for classification as well as classifiers of neurodegenerative diseases. The first chapters of the thesis brings a theoretical basis of knowledge from the field of magnetic and functional magnetic resonance imaging. The physical principles of the method, the conditions and the course of acquisition of image data are defined. The third chapter summarizes the graph metrics used in the diploma thesis for analyzing and classifying graphs. The paper presents a brief overview of the brain segmentation methods, with the focuse on the atlas-based segmentation. After a theoretical research of functional connectivity methods and mathematical classification methods, the findings were used for segmentation, calculation of graph metrics and for classification of fMRI images obtained from 96 subjects into the one of two classes using Binary classifications by support vector machines and linear discriminatory analysis. The data classified in this study was measured on patiens with Parkinson’s disease (PD), Alzheimer’s disease (AD), Mild cognitive impairment (MCI), a combination of PD and MCI and subjects belonging to the control group of healthy individuals. For pre-processing and analysis, the MATLAB environment, the SPM12 toolbox and The Brain Connectivity Toolbox were used.

Cílem práce je definice vztahu závislosti klasifikace pacientů postižených neurodegenerativním onemocněním na volbě parcelačního atlasu. Součástí práce je aplikace analýzy funkční konektivity a výpočtu grafových metrik dle metody publikované Olafem Spornsem a Mikailem Rubinovem [1] na fMRI datech naměřených na CEITEC MU. Aplikaci předchází teoretická rešerše parcelačních atlasů pro segmentování mozku ze snímků fMRI a rešerše matematických metod klasifikace, jako i klasifikátorů neurodegenerativních onemocnění. První kapitoly práce přináší teoretický základ poznatkůl z oblasti magnetické a funkční magnetické rezonance. Definovány jsou fyzikální principy metody, podmínky a průběh akvizice obrazových dat. Třetí kapitola shrnuje grafové metriky použité dále v diplomové práci pro analýzu a klasifikování grafů. Práce přináší stručný přehled parcelačních metod, se zaměřením na parcelaci pomoci atlasů. Po teoretické rešerši metod zkoumání funkční konektivity a matematických metod klasifikací, byly poznatky použity pro realizaci parcelací, výpočet grafových metrik a následnou klasifikaci fMRI snímků 96 subjektů vždy do jedné ze dvou tříd s využitím binárních klasifikátocí metodou podpůrných vektorů a lineární diskriminační analýzy. Data klasifikována v této práci byla naměřena na pacientech s Parkinsonovou chorobou (PD), s Alzheimerovou chorobou (AD), s Mírní kognitivní poruchou (MCI), s kombinací nemocí PD a MCI a na subjektech patřících do kontrolní skupiny zdravých jedinců. Pro předzpracování a pro analýzu je v práci využito prostředí MATLAB a toolboxy SPM12 a Brain Connectivity Toolbox., The aim of the thesis is to define the dependency of the classification of patients affected by neurodegenerative diseases on the choice of the parcellation atlas. Part of this thesis is the application of the functional connectivity analysis and the calculation of graph metrics according to the method published by Olaf Sporns and Mikail Rubinov [1] on fMRI data measured at CEITEC MU. The application is preceded by the theoretical research of parcellation atlases for brain segmentation from fMRI frames and the research of mathematical methods for classification as well as classifiers of neurodegenerative diseases. The first chapters of the thesis brings a theoretical basis of knowledge from the field of magnetic and functional magnetic resonance imaging. The physical principles of the method, the conditions and the course of acquisition of image data are defined. The third chapter summarizes the graph metrics used in the diploma thesis for analyzing and classifying graphs. The paper presents a brief overview of the brain segmentation methods, with the focuse on the atlas-based segmentation. After a theoretical research of functional connectivity methods and mathematical classification methods, the findings were used for segmentation, calculation of graph metrics and for classification of fMRI images obtained from 96 subjects into the one of two classes using Binary classifications by support vector machines and linear discriminatory analysis. The data classified in this study was measured on patiens with Parkinson’s disease (PD), Alzheimer’s disease (AD), Mild cognitive impairment (MCI), a combination of PD and MCI and subjects belonging to the control group of healthy individuals. For pre-processing and analysis, the MATLAB environment, the SPM12 toolbox and The Brain Connectivity Toolbox were used.

Cílem práce je definice vztahu závislosti klasifikace pacientů postižených neurodegenerativním onemocněním na volbě parcelačního atlasu. Součástí práce je aplikace analýzy funkční konektivity a výpočtu grafových metrik dle metody publikované Olafem Spornsem a Mikailem Rubinovem [1] na fMRI datech naměřených na CEITEC MU. Aplikaci předchází teoretická rešerše parcelačních atlasů pro segmentování mozku ze snímků fMRI a rešerše matematických metod klasifikace, jako i klasifikátorů neurodegenerativních onemocnění. První kapitoly práce přináší teoretický základ poznatkůl z oblasti magnetické a funkční magnetické rezonance. Definovány jsou fyzikální principy metody, podmínky a průběh akvizice obrazových dat. Třetí kapitola shrnuje grafové metriky použité dále v diplomové práci pro analýzu a klasifikování grafů. Práce přináší stručný přehled parcelačních metod, se zaměřením na parcelaci pomoci atlasů. Po teoretické rešerši metod zkoumání funkční konektivity a matematických metod klasifikací, byly poznatky použity pro realizaci parcelací, výpočet grafových metrik a následnou klasifikaci fMRI snímků 96 subjektů vždy do jedné ze dvou tříd s využitím binárních klasifikátocí metodou podpůrných vektorů a lineární diskriminační analýzy. Data klasifikována v této práci byla naměřena na pacientech s Parkinsonovou chorobou (PD), s Alzheimerovou chorobou (AD), s Mírní kognitivní poruchou (MCI), s kombinací nemocí PD a MCI a na subjektech patřících do kontrolní skupiny zdravých jedinců. Pro předzpracování a pro analýzu je v práci využito prostředí MATLAB a toolboxy SPM12 a Brain Connectivity Toolbox., The aim of the thesis is to define the dependency of the classification of patients affected by neurodegenerative diseases on the choice of the parcellation atlas. Part of this thesis is the application of the functional connectivity analysis and the calculation of graph metrics according to the method published by Olaf Sporns and Mikail Rubinov [1] on fMRI data measured at CEITEC MU. The application is preceded by the theoretical research of parcellation atlases for brain segmentation from fMRI frames and the research of mathematical methods for classification as well as classifiers of neurodegenerative diseases. The first chapters of the thesis brings a theoretical basis of knowledge from the field of magnetic and functional magnetic resonance imaging. The physical principles of the method, the conditions and the course of acquisition of image data are defined. The third chapter summarizes the graph metrics used in the diploma thesis for analyzing and classifying graphs. The paper presents a brief overview of the brain segmentation methods, with the focuse on the atlas-based segmentation. After a theoretical research of functional connectivity methods and mathematical classification methods, the findings were used for segmentation, calculation of graph metrics and for classification of fMRI images obtained from 96 subjects into the one of two classes using Binary classifications by support vector machines and linear discriminatory analysis. The data classified in this study was measured on patiens with Parkinson’s disease (PD), Alzheimer’s disease (AD), Mild cognitive impairment (MCI), a combination of PD and MCI and subjects belonging to the control group of healthy individuals. For pre-processing and analysis, the MATLAB environment, the SPM12 toolbox and The Brain Connectivity Toolbox were used.