Recently, there has been much interest in the resilience of complex networks to random failures and intentional attacks. The study of the network robustness is particularly important by several occasions. In one hand a higher degree of robustness to errors and attacks may be desired for maintaining the information flow in communication networks under attacks. On the other hand planning a very limited attack aimed at fragmenting a network by removal of minimum number of the most important nodes might have significant usage in drug design. Many real world networks were found to display scale free topology including WWW, the internet, social networks or regulatory gene and protein networks. In the recent studies it was shown that while these networks have a surprising error tolerance, their scale-free topology makes them fragile under intentional attack, leaving the scientists a challenge on how to improve the networks robustness against attacks. In this thesis, we studied the protein domain co-occurrence network of yeast which displays scale free topology generated with data from Biomart which links to Pfam database. Several networks obtained from protein domain co-occurrence network having exactly the same connectivity distribution were compared under attacks to investigate the assumption that the different networks with the same connectivity distribution do not need to have the same attack tolerances. In addition to this, we considered that the networks with the same connectivity distribution have higher attack tolerance as we organize the same resources in a better way. Then, we checked for the variations of attack tolerance of the networks with the same connectiviy distributions. Furthermore, we investigated whether there is an evolutionary mechanism for having networks with higher or lower attack tolerances for the same connectivity distribution. As a result of these investigations, the different networks with the same connectivity distribution do not have the same attack tolerances under attack. In addition to this, it was observed that the networks with the same connectivity distribution have higher attack tolerances as organizing the same resources in a better way which implies that there is an evolutionary mechanism for having networks with higher attack tolerance for the same connectivity distribution.

Converging evidence from a variety of fields, including psychiatry, suggests that the temporal correlates of the brain’s resting state could serve as essential markers of a healthy and efficient brain. We use ketamine to induce schizophrenia-like states in 32 healthy individuals to examine the brain’s resting states using fMRI. We found a global reduction in temporal variability quantified by the time series’ standard deviation and an increase in scale-free properties quantified by the Hurst exponent representing the signal self-affinity over time. We also found network-specific and frequency-specific effects of ketamine on these temporal measures. Our results confirm prior studies in aging, sleep, anesthesia, and psychiatry suggesting that increased self-affinity and decreased temporal variability of the brain resting state could indicate a compromised and inefficient brain state. Our results expand our systemic view of the temporal structure of the brain and shed light on promising biomarkers in psychiatry

In a celebrated series of experimental observations, starling flocks have been shown to be characterized by scale-free, long-ranged spatial correlations in their velocity fluctuations. While this is expected for velocity orientation correlations on the basis of simple symmetry-breaking arguments, the same scaling-free behaviour for speed (i.e. the absolute value of birds’ velocity) correlations cannot be explained by the same symmetry-based argument. Possible explanations so far put forward required the implicit or explicit fine-tuning of a speed control parameter. In this work we explore a different possibility, investigating the effects of the experimental discrete temporal sampling of individual bird trajectories. We argue that observed velocity may well be a time coarse-grained observable, that is, the sum over many faster course corrections taken by the bird. A simple argument shows such a time coarse-grained speed to be linked with the squared fluctuations of (soft modes) transversal velocities, which may thus acquire a long-range correlation. Our idea is numerically tested by measuring spatial correlations between coarse-grained speeds in the on-lattice equilibrium XY model and the off-lattice out-of-equilibrium Vicsek model in two dimensions. Saturation of the speed correlation length is found in the equilibrium XY model, while in the non-equilibrium Vicsek model ordered symmetry-broken phase shows scale-free behaviour with a correlation length ξ is found to be proportional to system size L. We conclude that in non-equilibrium flocking models, the temporal coarse-graining procedure is able to reproduce scale-free behaviour at system sizes which are relevant to the experimental observations. We believe that this mechanism might find applications beyond the case of starling flocks and perhaps be relevant for other experimental observations of collective motion.

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.

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Networks are all around us, all the time. From the biochemistry of our cells to the web of friendships across the planet. From the circuitry of modern electronics to chains of historical events. A network is the result of the forces that shaped it. Thus the principles of network formation can be, to some extent, deciphered from the network itself. All such information comprises the structure of the network. The study of network structure is the core of modern network science. This thesis centres around three aspects of network structure: What kinds of network structures are there and how can they be measured? How can we build models for network formation that give the structure of networks in the real world? How does the network structure affect dynamical systems confined to the networks? These questions are discussed using a variety of statistical, analytical and modelling techniques developed by physicists, mathematicians, biologists, chemists, psychologists, sociologists and anthropologists. My own research touches all three questions. In this thesis I present works trying to answer: What is the best way to protect a network against sinister attacks? How do groups form in friendship networks? Where do traffic jams appear in a communication network? How is cellular metabolism organised? How do Swedes flirt on the Internet? . . . and many other questions.

Network growing mechanisms are used to construct random networks that have structural behaviors similar to existing networks such as genetic networks, in efforts of understanding the evolution of complex topologies. Popular mechanisms, such as preferential attachment, are capable of preserving network features such as the degree distribution. However, little is known about such randomly grown structures regarding robustness to disturbances (e.g., edge deletions). Moreover, preferential attachment does not target optimizing the network's functionality, such as information flow. Here, we consider a network to be optimal if it's natural functionality is relatively high in addition to possessing some degree of robustness to disturbances. Specifically, a robust network would continue to (1) transmit information, (2) preserve it's connectivity and (3) preserve internal clusters post failures. In efforts to pinpoint features that would possibly replace or collaborate with the degree of a node as criteria for preferential attachment, we present a case study on both; undirected and directed networks. For undirected networks, we make a case study on wireless sensor networks in which we outline a strategy using Support Vector Regression. For Directed networks, we formulate an Integer Linear Program to gauge the exact transcriptional regulatory network optimal structures, from there on we can identify variations in structural features post optimization.

nÃo hà / Na primeira parte deste trabalho, empregamos uma rede neural artificial (RNA) treinada com algoritmo back-propagation para inferir a volatilidade dos gases liquefeitos de petrÃleo (GLP) produzidos em uma torre de fracionamento de lÃquido de gÃs natural (LGN). Os resultados obtidos indicam que a RNA fornece melhores respostas do que um simulador desenvolvido com base fenomenolÃgica que se encontra em fase de implementaÃÃo na planta em estudo. Na segunda parte da dissertaÃÃo, o nosso objetivo primordial à demonstrar que os fluxogramas de processos de refinarias de petrÃleo podem estar intrinsecamente associados à topologias de redes complexas, que sÃo scale-free, exibem efeitos de mundo pequeno e possuem organizaÃÃo hierÃrquica. A emergÃncia dessas propriedades em redes artificiais à explicada como uma consequÃncia dos princÃpios usados no design de projeto dos processos, os quais incluem regras heurÃsticas e tÃcnicas algorÃtmicas. Esperamos que esses resultados sejam tambÃm vÃlidos para plantas quÃmicas de diferentes tipos e capacidades. / In the first part of this work we apply an artificial neural network (ANN) trained with a back-propagation algorithm to predict the volatility of liquefied petroleum gases (LPG) produced from a fractionation tower of natural gas liquid (NGL). Our analysis indicate that the ANN scheme provides better results than a simulator developed based phenomenological which is currently being implemented in the plant under study. In the second part, our primary objective is to demonstrate that flowsheets of oil refineries can be intrinsically associated to complex network topologies, which are scale-free, display small-word effect and have hierarchical organization. The emergence of these properties artificial networks is explained as a consequence of the design principles used in the processâ design, which include heuristics rules and algorithmic techniques. We expect these results to be also valid for chemical plants of different types and capacities.

<p>Networks are all around us, all the time. From the biochemistry of our cells to the web of friendships across the planet. From the circuitry of modern electronics to chains of historical events. A network is the result of the forces that shaped it. Thus the principles of network formation can be, to some extent, deciphered from the network itself. All such information comprises the structure of the network. The study of network structure is the core of modern network science. This thesis centres around three aspects of network structure: What kinds of network structures are there and how can they be measured? How can we build models for network formation that give the structure of networks in the real world? How does the network structure affect dynamical systems confined to the networks? These questions are discussed using a variety of statistical, analytical and modelling techniques developed by physicists, mathematicians, biologists, chemists, psychologists, sociologists and anthropologists. My own research touches all three questions. In this thesis I present works trying to answer: What is the best way to protect a network against sinister attacks? How do groups form in friendship networks? Where do traffic jams appear in a communication network? How is cellular metabolism organised? How do Swedes flirt on the Internet? . . . and many other questions.</p>

Ένα φαινόμενο που έκανε την εμφάνισή του τα τελευταία χρόνια είναι η μελέτη μεγάλων δικτύων που εμφανίζουν μια ιεραρχική δομή ανεξαρτήτως κλίμακας (large scale-free networks). Μια παραδοσιακή μέθοδος μοντελοποίησης δικτύων είναι η χρήση γραφημάτων και η χρησιμοποίηση αποτελεσμάτων που προκύπτουν από την Θεωρία Γράφων. Όμως στα κλασικά μοντέλα που έχουν μελετηθεί, δυο κόμβοι του ίδιου γραφήματος έχουν την ίδια πιθανότητα να συνδέονται με οποιουσδήποτε δυο άλλους κόμβους. Αυτός ο τρόπος μοντελοποίησης αποτυγχάνει να περιγράψει πολλά δίκτυα της καθημερινής ζωής, όπως δίκτυα γνωριμιών όπου οι κόμβοι συμβολίζουν ανθρώπους και συνδέονται μεταξύ τους αν γνωρίζονται άμεσα. Σε ένα τέτοιο δίκτυο είναι αναμενόμενο δυο φίλοι κάποιου ατόμου να έχουν μεγαλύτερη πιθανότητα να γνωρίζονται μεταξύ τους από ότι δυο τυχαία επιλεγμένοι ξένοι. Αυτό ακριβώς το φαινόμενο ονομάζεται συσσωμάτωση (clustering) και είναι χαρακτηριστικό για τα εν λόγω δίκτυα. Είναι γεγονός ότι πολλά δίκτυα που συναντώνται στη φύση αλλά και πάρα πολλά ανθρωπογενή δίκτυα εντάσσονται σε αυτήν την κατηγορία. Παραδείγματα τέτοιων είναι τα δίκτυα πρωτεϊνών, δίκτυα τροφικών αλυσίδων, επιδημικής διάδοσης ασθενειών, δίκτυα ηλεκτρικού ρεύματος, υπολογιστών, ιστοσελίδων του Παγκόσμιου Ιστού, δίκτυα γνωριμιών, επιστημονικών αναφορών (citations) κ.α. . Παρότι φαίνεται να άπτονται πολλών επιστημών όπως η Φυσική, η Βιολογία, η Κοινωνιολογία και η Πληροφορική, δεν έχουν τύχει ευρείας μελέτης, καθώς μέχρι στιγμής έλειπαν πραγματικά μεγάλα δίκτυα για πειραματική μελέτη (κενό που καλύφθηκε με την ανάπτυξη του Παγκόσμιου Ιστού). Μέχρι σήμερα δεν έχουν φωτιστεί όλα εκείνα τα σημεία και τα μεγέθη που είναι χαρακτηριστικά για αυτά τα δίκτυα και που πρέπει να εστιάσει η επιστημονική έρευνα, παρόλα αυτά έχει γίνει κάποια πρόοδος. Μια τέτοια έννοια που μπορεί να εκφραστεί με πολλά μεγέθη είναι η έννοια της κεντρικότητας (centrality) ενός κόμβου στο δίκτυο. Η χρησιμότητα ενός τέτοιου μεγέθους, αν μπορεί να οριστεί, είναι προφανής, για παράδειγμα στον τομέα της εσκεμμένης «επίθεσης» σε ένα τέτοιο δίκτυο (π.χ. δίκτυο υπολογιστών). Η ακριβής όμως συσχέτιση της κεντρικότητας με τα άλλα χαρακτηριστικά μεγέθη του δικτύου, όπως η συσσωμάτωση, δεν είναι γνωστή. Στόχος της εργασίας είναι να εμβαθύνει στην έννοια της κεντρικότητας, και χρησιμοποιεί σαν πεδίο πειραματισμών τον χώρο της εσκεμμένης επίθεσης σε ανεξάρτητα κλίμακας δίκτυα. Στο πλαίσιο αυτό γίνεται μια συνοπτική παρουσίαση των μοντέλων δικτύων που έχουν προταθεί μέχρι σήμερα και αναλύεται η έννοια της κεντρικότητας μέσω των παραδοσιακών ορισμών της από την επιστήμη της Κοινωνιολογίας. Στη συνέχεια προτείνεται μια σειρά ορισμών της κεντρικότητας που την συνδέουν με μεγέθη του δικτύου όπως ο συντελεστής συσσωμάτωσης. Η καταλληλότητα των ορισμών αυτών διαπιστώνεται στην πράξη, εξομοιώνοντας πειραματικά επιθέσεις σε ανεξάρτητα κλίμακας μεγάλα δίκτυα και χρησιμοποιώντας στρατηγικές επίθεσης που βασίζονται σε αυτές. / A trend in recent years is the study of large networks which possess a hierarchical structure independent of the current scale (large scale-free networks). A traditional method of network modelling is the use of graphs and the usage of results based on Graph Theory. Until recently, the classical models studied, describe the probability of two random vertices connecting with each other as equal for all pairs of vertices. This modelling fails to describe many everyday networks such as acquaintance networks, where the vertices are individuals and connect with an edge if they know each other