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Human mobility has been empirically observed to exhibit Levy flight characteristics and behaviour with powerlaw distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Levy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a powerlaw distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a powerlaw distribution, providing an explanation to the emergence of Levy Walk patterns that characterize human mobility patterns.
The analogies and differences between biological and cultural evolution have been explored by evolutionary biologists, historians, engineers and linguists alike. Two well known domains of cultural change are language and technology. Both share some traits relating the evolution of species, but technological change is very difficult to study. A major challenge in our way towards a scientific theory of technological evolution is how to properly define evolutionary trees or clades and how to weight the role played by horizontal transfer of information. Here we study the large scale historical development of programming languages, which have deeply marked social and technological advances in the last half century. We analyse their historical connections using network theory and reconstructed phylogenetic networks. Using both data analysis and network modelling, it is shown that their evolution is highly uneven, marked by innovation events where new languages are created out of improved combinations of different structural components belonging to previous languages. These radiation events occur in a bursty pattern and are tied to novel technological and social niches. The method can be extrapolated to other systems and consistently captures the major classes of languages and the widespread horizontal design exchanges, revealing a punctuated evolutionary path.
Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest  essential in determining reward and penalty  is frequently an ambiguous task due to the incomplete (partially filled) nature of competition networks. Here we introduce the [ldquo]Natural Ranking,[rdquo] an unambiguous ranking method applicable to a round robin tournament, and formulate an analytical model based on the Bayesian formula for inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in resolving important issues of ranking by applying it to realworld competition networks.
The "smallworld effect" is the observation that one can find a short chain of acquaintances, often of no more than a handful of individuals, connecting almost any two people on the planet. It is often expressed in the language of networks, where it is equivalent to the statement that most pairs of individuals are connected by a short path through the acquaintance network. Although the smallworld effect is wellestablished empirically for contemporary social networks, we argue here that it is a relatively recent phenomenon, arising only in the last few hundred years: for most of mankind's tenure on Earth the social world was large, with most pairs of individuals connected by relatively long chains of acquaintances, if at all. Our conclusions are based on observations about the spread of diseases, which travel over contact networks between individuals and whose dynamics can give us clues to the structure of those networks even when direct network measurements are not available. As an example we consider the spread of the Black Death in 14thcentury Europe, which is known to have traveled across the continent in welldefined waves of infection over the course of several years. Using established epidemiological models, we show that such wavelike behavior can occur only if contacts between individuals living far apart are exponentially rare. We further show that if longdistance contacts are exponentially rare, then the shortest chain of contacts between distant individuals is on average a long one. The observation of the wavelike spread of a disease like the Black Death thus implies a network without the smallworld effect.
Highspeed cameras reveal when insects become selforganizing.
Support is growing for a decadesold physics idea suggesting that localized episodes of disordered brain activity help keep the overall system in healthy balance
Physicists have identified a mechanism that may help explain Zipf's law – a unique pattern of behavior found in disparate systems, including complex biological ones. The journal Physical Review Letters is publishing their mathematical models, which demonstrate how Zipf's law naturally arises when a sufficient number of units react to a hidden variable in a system.
Novelties are a familiar part of daily life. They are also fundamental to the evolution of biological systems, human society, and technology. By opening new possibilities, one novelty can pave the way for others in a process that Kauffman has called “expanding the adjacent possible”. The dynamics of correlated novelties, however, have yet to be quantified empirically or modeled mathematically. Here we propose a simple mathematical model that mimics the process of exploring a physical, biological, or conceptual space that enlarges whenever a novelty occurs. The model, a generalization of Polya's urn, predicts statistical laws for the rate at which novelties happen (Heaps' law) and for the probability distribution on the space explored (Zipf's law), as well as signatures of the process by which one novelty sets the stage for another. We test these predictions on four data sets of human activity: the edit events of Wikipedia pages, the emergence of tags in annotation systems, the sequence of words in texts, and listening to new songs in online music catalogues. By quantifying the dynamics of correlated novelties, our results provide a starting point for a deeper understanding of the adjacent possible and its role in biological, cultural, and technological evolution.
Alan Turing, the British mathematician (19121954), is famous for a number of breakthroughs, which altered the course of the 20th century. In 1936 he published a paper, which laid the foundation of computer science, providing the first formal concept of a computer algorithm. He next played a pivotal role in the Second World War, designing the machines which cracked the German military codes, enabling the Allies to defeat the Nazis in several crucial battles. And in the late 1940's he turned his attention to artificial intelligence and proposed a challenge, now called the Turing test, which is still important to the field today. His contribution to mathematical biology is less famous, but was no less profound. He published just one paper (1952), but it triggered a whole new field of mathematical enquiry into pattern formation. He discovered that a system with just 2 molecules could, at least in theory, create spotty or stripy patterns if they diffused and chemically interacted in just the right way. His mathematical equations showed that starting from uniform condition (ie. a homogeneous distribution – no pattern) they could spontaneously selforganise their concentrations into a repetitive spatial pattern. This theory has come to be accepted as an explanation of fairly simple patterns such as zebra stripes and even the ridges on sand dunes, but in embryology it has been resisted for decades as an explanation of how structures such as fingers are formed. Now a group of researchers from the Multicellular Systems Biology lab at the CRG, led by ICREA Research Professor James Sharpe, has provided the long soughtfor data which confirms that the fingers and toes are patterned by a Turing mechanism. "It complements their recent paper (Science 338:1476, 2012), which provided evidence that Hox genes and FGF signaling modulated a hypothetical Turing system. However, at that point the Turing molecules themselves were still not identified, and so this remained as the critical unsolved piece of the puzzle. The new study completes the picture, by revealing which signaling molecules act as the Turing system" says James Sharpe, coauthor of the study.
On its own, a single starling doesn't elicit much fuss. It's a tennisballsized bird, glossy black in winter, purplish or green in summer, and in autumn, sometimes speckled with white spots. But when starlings congregate in flocks of hundreds of thousands over open fields (something scientists call a "murmuration") they pitch and arc and rush at one another in a bizarre choreography that's puzzled naturalists for hundreds of years. A whole catalog of YouTube videos has documented the black shapes in flight, a movement that looks like the birds are attached to a giant rhythmic gymnast's invisible ribbon.
A review of the science behind problem solving, how it functions in the brain and how we can do it better.
A new computer game, No Man’s Sky, demonstrates a new way to build computer games filled with diverse flora and fauna. Sean Murray, one of the creators of the computer game No Man’s Sky, can’t guarantee that the virtual universe he is building is infinite, but he’s certain that, if it isn’t, nobody will ever find out. “If you were to visit one virtual planet every second,” he says, “then our own sun will have died before you’d have seen them all.” No Man’s Sky is a video game quite unlike any other. Developed for Sony’s PlayStation 4 by an improbably small team (the original fourperson crew has grown only to 10 in recent months) at Hello Games, an independent studio in the south of England, it’s a game that presents a traversable universe in which every rock, flower, tree, creature, and planet has been “procedurally generated” to create a vast and diverse play area.
Prevalence and use of Twitter among scholars (Infographic on Prevalence and use of Twitter among scholars http://t.co/skulthbeMe)

Watch as this colony forms a daisy chain to pull a millipede—a behavior researchers have never seen before.
We study the conditions for persistent cooperation in an offlattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius ${r}_{P}$, which accounts for the population viscosity, and an interaction radius ${r}_{\mathrm{int}}$, which defines the instantaneous contact network for the game dynamics. We show that, differently from the ${r}_{P}=0$ case, the model with finitesized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases, in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.
Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network [ldquo]mobile[rdquo] can effectively suppress extreme events. A striking, resonancelike phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.
A small perturbation in a system's parameter can convert its attractor from chaotic to periodic, where the probability of obtaining a chaotic regime scales as a power law with respect to the perturbation size.
Artur Avila’s solutions to ubiquitous problems in chaos theory have “changed the face of the field,” earning him Brazil’s first Fields Medal.
The first study of dialects on Twitter reveals global patterns that have never been observed before.
The temporal statistics exhibited by written correspondence appear to be media dependent, with features which have so far proven difficult to characterize. We explain the origin of these difficulties by disentangling the role of spontaneous activity from decisionbased prioritizing processes in human dynamics, clocking all waiting times through each agent's ``proper time'' measured by activity. This unveils the same fundamental patterns in written communication across all media (letters, email, sms), with response times displaying truncated powerlaw behavior and average exponents near $$${}\frac{3}{2}$. When standard time is used, the response time probabilities are theoretically predicted to exhibit a bimodal character, which is empirically borne out by our newly collected yearslong data on email. These perspectives on the temporal dynamics of human correspondence should aid in the analysis of interaction phenomena in general, including resource management, optimal pricing and routing, information sharing, and emergency handling.
The emergent processes driving cultural history are a product of complex interactions among large numbers of individuals, determined by difficulttoquantify historical conditions. To characterize these processes, we have reconstructed aggregate intellectual mobility over two millennia through the birth and death locations of more than 150,000 notable individuals. The tools of network and complexity theory were then used to identify characteristic statistical patterns and determine the cultural and historical relevance of deviations. The resulting network of locations provides a macroscopic perspective of cultural history, which helps us to retrace cultural narratives of Europe and North America using largescale visualization and quantitative dynamical tools and to derive historical trends of cultural centers beyond the scope of specific events or narrow time intervals.
Mathematical model shows how hundreds of starlings coordinate their movements in flight. A flock of starlings flies as one, a spectacular display in which each bird flits about as if in a wellchoreographed dance. Everyone seems to know exactly when and where to turn. Now, for the first time, researchers have measured how that knowledge moves through the flock—a behavior that mirrors certain quantum phenomena of liquid helium.
We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors' states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network. We compute an Influence Matrix (IM) in which each element characterizing the influence of an agent on another agent in the network. We use the IM to predict the bias of each normal agent and thus predict which competitor will win. Furthermore, we compare the IM criterion with seven node centrality measures to predict the winner. We find that the competitor with higher Katz Centrality in an undirected network or higher PageRank in a directed network is most likely to be the winner. These findings may shed new light on the role of network structure in competition and to what extent could competitors adjust network structure so as to win the competition.
One of the most common strategies in studying complex systems is to investigate and interpret whether any “hidden order” is present by fitting observed statistical regularities via data analysis and then reproducing such regularities with longtime or equilibrium dynamics from some generative model. Unfortunately, many different models can possess indistinguishable longtime dynamics, so the above recipe is often insufficient to discern the relative quality of competing models. In this paper, we use the example of collective online behavior to illustrate that, by contrast, timedependent modeling can be very effective at disentangling competing generative models of a complex system.
Psychologists have always puzzled over why people in Sweden were slower to start smoking and slower to stop. Now a group of mathematicians have worked out why.
