Internet's Critical Path Horizon

Internet is known to display a highly heterogeneous structure and complex fluctuations in its traffic dynamics. Congestion seems to be an inevitable result of user's behavior coupled to the network dynamics and it effects should be minimized by choosing appropriate routing strategies. But what are the requirements of routing depth in order to optimize the traffic flow? In this paper we analyse the behavior of Internet traffic with a topologically realistic spatial structure as described in a previous study (S-H. Yook et al. ,Proc. Natl Acad. Sci. USA, {\bf 99} (2002) 13382). The model involves self-regulation of packet generation and different levels of routing depth. It is shown that it reproduces the relevant key, statistical features of Internet's traffic. Moreover, we also report the existence of a critical path horizon defining a transition from low-efficient traffic to highly efficient flow. This transition is actually a direct consequence of the web's small world architecture exploited by the routing algorithm. Once routing tables reach the network diameter, the traffic experiences a sudden transition from a low-efficient to a highly-efficient behavior. It is conjectured that routing policies might have spontaneously reached such a compromise in a distributed manner. Internet would thus be operating close to such critical path horizon.Comment: 8 pages, 8 figures. To appear in European Journal of Physics B (2004

The long and winding road : accidents and tinkering in software standardization

Software is based on universal principles but not its development. Relating software to hardware is never automatic or easy. Attempts to optimize software production and drastically reduce their costs (like in hardware) have been very restricted. Instead, highly-skilled and experienced individuals are ultimately responsible for project success. The long and convoluted path towards useful and reliable software is often plagued by idiosyncratic accidents and emergent complexity. It was expected that software standardisation would remove these sources of unwanted diversity by aiming at controllable development processes, universal programming languages, and toolkits of reusable software components. However, limited adoption of development standards suggests that we still do not understand why software is so difficult to produce. Software standardisation has been limited by our poor understanding of humans? role at the origin of technological diversity

A simple spatiotemporal evolution model of a transmission power grid

In this paper, we present a model for the spatial and temporal evolution of a particularly large human-made network: the 400-kV French transmission power grid. This is based on 1) an attachment procedure that diminishes the connection probability between two nodes as the network grows and 2) a coupled cost function characterizing the available budget at every time step. Two differentiated and consecutive processes can be distinguished: a first global space-filling process and a secondary local meshing process that increases connectivity at a local level. Results show that even without power system engineering design constraints (i.e., population and energy demand), the evolution of a transmission network can be remarkably explained by means of a simple attachment procedure. Given a distribution of resources and a time span, the model can also be used to generate the probability distribution of cable lengths at every time step, thus facilitating network planning. Implications for network's fragility are suggested as a starting point for new design perspectives in this kind of infrastructures.Peer ReviewedPostprint (author's final draft

Rashevsky’s dream: A physico-mathematical foundation of history and culture

La famosa serie de ciencia ficción Fundación, escrita por Isaac Asimov, explora la idea de que el futuro de las sociedades no solo es predecible, sino que puede incluso ser diseñado. En el mundo de ficción de Asimov, se presenta una ciencia multidisciplinar llamada psicohistoria que combina las matemáticas, la psicología y la historia para predecir acontecimientos futuros. Nicolas Rashevsky, el padre de la biología matemática, dio credibilidad a la existencia de principios universales que sustenten la evolución cultural humana mediante modelos matemáticos. Su visión todavía no se ha realizado plenamente, ya que nuestra capacidad para predecir e incluso para diseñar la ingeniería necesaria es muy fragmentaria. Dos obstáculos importantes son la confusión con respecto al papel de los modelos matemáticos y las limitaciones de los conjuntos de datos actuales. Los avances recientes en la investigación sobre sistemas complejos, simulaciones computacionales y bases de datos a gran escala están allanando el camino para el desarrollo de una verdadera teoría matemática de la historia humana.; La famosa sèrie de ciència-ficció Fundació, escrita per Isaac Asimov, explora la idea que el futur de les societats no solament és predictible, sinó que fins i tot es pot dissenyar. En el món de ficció d’Asimov, es presenta una ciència multidisciplinària anomenada psicohistòria que combina les matemàtiques, la psicologia i la història per a predir esdeveniments futurs. Nicolas Rashevsky, el pare de la biologia matemàtica, va donar credibilitat a l’existència de principis universals que sustenten l’evolució cultural humana per mitjà de models matemàtics. La seua visió encara no s’ha realitzat plenament, ja que la nostra capacitat per a predir i fins i tot per a dissenyar l’enginyeria necessària és molt fragmentària. Dos obstacles importants són la confusió respecte al paper dels models matemàtics i les limitacions dels conjunts de dades actuals. Els avanços recents en la investigació sobre sistemes complexos, simulacions computacionals i bases de dades a gran escala estan aplanant el camí per al desenvolupament d’una vertadera teoria matemàtica de la història humana.; The popular science fiction series Foundation penned by Isaac Asimov explores the idea that the course of the future of societies is not only predictable but can be engineered as well. In Asimov’s fictional world, a multidisciplinary science called psychohistory combines mathematics, psychology, and history to predict future events. Nicolas Rashevsky, the father of mathematical biology, lent credibility to the existence of universal principles underpinning human cultural evolution using mathematical models. His vision remains to be fully realized, as our capacity to predict and even engineer is very fragmented. Two main obstacles are a misunderstanding of the role of mathematical models and the limitations of current datasets. Recent advances in complex systems research, computer-based simulations, and large-scale databases, are paving the way towards fully developing a mathematical theory of human history