@misc{flickrgrowth, title = {Growth of the Flickr social network}, author = {Alan Mislove and Hema Swetha Koppula and Krishna P. Gummadi and Peter Druschel and Bobby Bhattacharjee}, booktitle = {In Proceedings of the 1 st Workshop on Online Social Networks(WOSN ' 08)}, note = {To appear}, year = 2008, location = {Seattle}, date = {August 2008}, description = {Online Social Networks Research @}, biburl = {http://www.bibsonomy.org/bibtex/244cc118a18e680c9c1488feaee864359/andreab}, keywords = {models flickr maxplanck dynamics social modeling network imported} } @inproceedings{1150476, title = {Structure and evolution of online social networks}, address = {New York, NY, USA}, author = {Ravi Kumar and Jasmine Novak and Andrew Tomkins}, booktitle = {KDD '06: Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining}, pages = {611--617}, publisher = {ACM}, year = 2006, url = {http://portal.acm.org/citation.cfm?id=1150476#}, location = {Philadelphia, PA, USA}, isbn = {1-59593-339-5}, doi = {http://doi.acm.org/10.1145/1150402.1150476}, description = {Structure and evolution of online social networks}, abstract = {In this paper, we consider the evolution of structure within large online social networks. We present a series of measurements of two such networks, together comprising in excess of five million people and ten million friendship links, annotated with metadata capturing the time of every event in the life of the network. Our measurements expose a surprising segmentation of these networks into three regions: singletons who do not participate in the network; isolated communities which overwhelmingly display star structure; and a giant component anchored by a well-connected core region which persists even in the absence of stars.We present a simple model of network growth which captures these aspects of component structure. The model follows our experimental results, characterizing users as either passive members of the network; inviters who encourage offline friends and acquaintances to migrate online; and linkers who fully participate in the social evolution of the network.}, biburl = {http://www.bibsonomy.org/bibtex/203874e666c56f22bce1b7db254420d77/andreab}, keywords = {models flickr structure 2006 social analysis network imported yahoo} } @book{urnmodelsbook, title = {Urn Models and Their Applications: An Approach to Modern Discrete Probability Theory}, address = {New York}, author = {Norman L. Johnson and Samuel Kotz}, publisher = {Wiley}, year = 1977, biburl = {http://www.bibsonomy.org/bibtex/21e48408318dd223af54c60ad063f2dd9/andreab}, keywords = {polya models d4.1 tagora urns statistics} } @article{1742-5468-2006-02-P02004, title = {Understanding scale invariance in a minimal model of complex relaxation phenomena}, author = {P I Hurtado and J Marro and P L Garrido}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, number = 02, pages = {P02004}, volume = 2006, year = 2006, url = {http://stacks.iop.org/1742-5468/2006/P02004}, abstract = {We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i. e., the model evolution is discontinuous and displays many scales in a way that closely resembles the relaxation in a large number of complex systems in nature. Such apparent scale invariance simply results in the model from summing over many exponential relaxations, each with a scale which is determined by the curvature of the domain wall at which the avalanche originates. The claim that scale invariance in a nonequilibrium setting is to be associated with criticality is therefore not supported. Some hints that may help in checking this experimentally are discussed.}, biburl = {http://www.bibsonomy.org/bibtex/2483235201d73b2181ea4e305cb7092f4/andreab}, keywords = {models physics modeling citingme imported scaling} } @article{colaiori2001, title = {Scaling, Optimality, and Landscape Evolution}, author = {Jayanth R. Banavar and Francesca Colaiori and Alessandro Flammini and Amosd Maritan and Andreae Rinaldo}, journal = {Journal of Statistical Physics}, number = 1, pages = {1-48}, volume = 104, year = 2001, description = {Banavar, Colaiori et al. paper on river network and landscape evolution.}, abstract = {A nonlinear model is studied which describes the evolution of a landscape under the effects of erosion and regeneration by geologic uplift by mean of a simple differential equation. The equation, already in wide use among geomorphologists and in that context obtained phenomenologically, is here derived by reparametrization invariance arguments and exactly solved in dimension d=1. Results of numerical simulations in d=2 show that the model is able to reproduce the critical scaling characterizing landscapes associated with natural river basins. We show that configurations minimizing the rate of energy dissipation (optimal channel networks) are stationary solutions of the equation describing the landscape evolution. Numerical simulations show that a careful annealing of the equation in the presence of additive noise leads to configurations very close to the global minimum of the dissipated energy, characterized by mean field exponents. We further show that if one considers generalized river network configurations in which splitting of the flow (i.e., braiding) and loops are allowed, the minimization of the dissipated energy results in spanning loopless configurations, under the constraints imposed by the continuity equations. This is stated in the form of a general theorem applicable to generic networks, suggesting that other branching structures occurring in nature may possibly arise as optimal structures minimizing a cost function.}, biburl = {http://www.bibsonomy.org/bibtex/21116c03c4e127f16a232e13bdb93d4e3/andreab}, keywords = {models physics rivernetworks modeling review statistical} } @article{goltsev-2006-73, title = {k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects}, author = {A. V. Goltsev and S. N. Dorogovtsev and J. F. F. Mendes}, journal = {Physical Review E}, pages = 056101, volume = 73, year = 2006, url = {http://www.citebase.org/abstract?id=oai:arXiv.org:cond-mat/0602611}, description = {[cond-mat/0602611] k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects}, abstract = {We develop the theory of the k-core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the k-core percolation is an unusual, hybrid phase transition with a jump emergence of the k-core as at a first order phase transition but also with a critical singularity as at a continuous transition. We describe the properties of the k-core, explain the meaning of the order parameter for the k-core percolation, and reveal the origin of the specific critical phenomena. We demonstrate that a so-called ``corona'' of the k-core plays a crucial role (corona is a subset of vertices in the k-core which have exactly k neighbors in the k-core). It turns out that the k-core percolation threshold is at the same time the percolation threshold of finite corona clusters. The mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point. We show that a random removal of even one vertex from the k-core may result in the collapse of a vast region of the k-core around the removed vertex. The mean size of this region diverges at the critical point. We find an exact mapping of the k-core percolation to a model of cooperative relaxation. This model undergoes critical relaxation with a divergent rate at some critical moment.}, biburl = {http://www.bibsonomy.org/bibtex/251186ba16a6e366133245628b780071c/andreab}, keywords = {networks models model physics kcore theory percolation simulation network imported graphs} } @misc{alvarezhamelin-2006, title = {The dynamical collision network in granular gases}, author = {Jose Ignacio Alvarez-Hamelin and Andrea Puglisi}, year = 2006, url = {http://www.citebase.org/abstract?id=oai:arXiv.org:cond-mat/0609341}, description = {[cond-mat/0609341] The dynamical collision network in granular gases}, abstract = {We dynamically construct the interaction network in a granular gas, using the sequence of collisions collected in an MD event driven simulation of inelastic hard disks from time 0 till time t. The network is decomposed into its k-core structure: particles in a core of index k have collided at least k times with other particles in the same core. The difference between cores k+1 and k is the so-called k-shell, and the set of all shells is a complete and on-overlapping decomposition of the system. Because of energy dissipation, the gas cools down: its initial spatially homogeneous dynamics, characterized by the Haff law, i.e. a t^{-2} energy decay, is unstable towards a strongly inhomogeneous phase with clusters and vortices, where energy decays as t^{-1}. The clear transition between those two phases appears in the evolution of the k-shells structure in the collision network. In the homogeneous regime the k-shell structure evolves as in a growing network with fixed number of vertices and randomly added links: the shell distribution is strongly peaked around the most populated shell, which has an index k\_{max} ~ 0.9 with the average number of collisions experienced by a particle. During the final non-homogeneous regime a growing fraction of collisions is concentrated in small, almost closed, 'communities' of particles: k\_{max} is no more linear in and the distribution of shells becomes extremely large developing a power-law tail ~ k^{-3} for high shell indexes. We propose the k-shell decomposition as a quantitative characterization of Molecular Chaos violation.}, biburl = {http://www.bibsonomy.org/bibtex/24d8844a74d4a378c21ae7fdf939d2ed3/andreab}, keywords = {models model granular physics kcore simulation network imported statistics} } @article{Mitzenmacher2006, title = {Editorial: The Future of Power Law Research}, author = {Michael Mitzenmacher}, journal = {Internet Mathematics }, number = 4, pages = { 525-534}, volume = 2, year = 2006, abstract = {Abstract. I argue that power law research must move from focusing on observation, in- terpretation, and modeling of power law behavior to instead considering the challenging problems of validation of models and control of systems. }, biburl = {http://www.bibsonomy.org/bibtex/22d4f0ca387048bfefafec9d74b3bc0a8/andreab}, keywords = {models law editorial d4.1 article paper power tagora research} } @article{preMitzenmacher2004, title = {A Brief History of Generative Models for Power Law and Lognormal Distributions - submission version}, author = {Michael Mitzenmacher}, journal = {submitted to Internet Mathematics }, pages = { }, year = { 2004}, abstract = {Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a rich and long history, spanning many fields. Indeed, several recently proposed models from the computer science community have antecedents in work from decades ago. Here, I briefly survey some of this history, focusing on underlying generative models that lead to these distributions. One finding is that lognormal and power law distributions connect quite naturally, and hence, it is not surprising that lognormal distributions have arisen as a possible alternative to power law distributions across many fields. }, biburl = {http://www.bibsonomy.org/bibtex/236d933318b0e03fab1987ea7d9639b38/andreab}, keywords = {law model d4.1 zipf paper submission models article yule power simon tagora review} } @article{Mitzenmacher2004, title = {A Brief History of Generative Models for Power Law and Lognormal Distributions}, author = {Michael Mitzenmacher}, journal = {Internet Mathematics }, number = 2, pages = { 226-251}, volume = 1, year = { 2004}, biburl = {http://www.bibsonomy.org/bibtex/27cef5c65c8874e9d263a188b08993dfb/andreab}, keywords = {models law model zipf d4.1 article paper yule power tagora simon review} } @inproceedings{DBLP:conf/acl/Baayen91, title = {A Stochastic Process for Word Frequency Distributions.}, author = {R. Harald Baayen}, booktitle = {ACL}, pages = {271-278}, year = 1991, bibsource = {DBLP, http://dblp.uni-trier.de}, description = {DBLP Record 'conf/acl/Baayen91'}, biburl = {http://www.bibsonomy.org/bibtex/25130f4955af49c18e6339ae833dfe006/andreab}, keywords = {model zipf d4.1 mandelbrot frequency distribution stochastic imported statistics models words language simon tagora linguistics} } @article{willis, title = {Re-inventing Willis}, author = {M.V. Simkin and V.P. Roychowdhury}, year = 2006, url = {http://arxiv.org/abs/physics/0601192}, abstract = {Scientists often re-invent things which were long known. Here we review these activities as related to the mechanism of producing power law distributions, originally proposed in 1922 by Yule to explain experimental data on the sizes of biological genera, collected by Willis. We estimate that scientists are busy re-discovering America about 2/3 of time.}, biburl = {http://www.bibsonomy.org/bibtex/211ff73ed92f9fcbd9f997ed83f7d17e9/andreab}, keywords = {models urn model physics d4.1 theory attachment tagora preferetial network} } @misc{cattuto2006, title = {Collaborative Tagging and Semiotic Dynamics}, author = {C. Cattuto and V. Loreto and L. Pietronero}, year = 2006, url = {http://xxx.lanl.gov/abs/cs.CY/0605015}, biburl = {http://www.bibsonomy.org/bibtex/2992e0ffa73972fa69f6c58b89e7ab236/andreab}, keywords = {models sapienza d4.1 collaborative tagging theory tagora} }