Abstract: The rapid pace of urbanization has made the transport infrastructure of prime importance for efficient functioning of cities. This pace is putting ever increasing load on public transport services. The public transport services are offered by both formal and informal sector. Looking at the dependency of people on public transport services and inadequacy of formal public transport services, its generate apt conditions for flourishing of informal public transport services. This establishes the need to get insight into informal public transport services. Informal public transport services are the services provided by the private owners without fix route and stoppages. The network that emerges on this basis, caters effectively to user’s expectations and appears to be highly integrated with city fabric. It helps to connects the formal public transport services, neighborhood in the proximity and provides last mile connectivity. It also offers variety of options to the commuter that may be flexible and economical. To have better understanding of network of informal public transport services, Complexity science concepts are applied to derive an analytical framework.The research explores inter-connectedness and inter-dependence, emergence,role of adaptive agents, and self-organisation in the network of informal public transport services.Further it explores the co-evolution within network of informal public transport services and also with formal public transport services. The research further highlights the potential of informal public transport services in complementing the formal public transport services.

Abstract: Cascading failures are frequently observed in networked systems and remain a major threat to the reliability of network-like infrastructure such as power grids, public transportation systems or financial markets. Furthermore, the interdependence of such systems on one another increases their vulnerability to failure, especially when compared to function of a single network viewed in isolation. Here we consider a classic model of cascading failure, the BTW sandpile model, on a system of interdependent networks. Recent study (PNAS 109, 12, E680-E689, 2012) of the sandpile model on modular random graphs has demonstrated that there exist an optimal level of connectivity between systems which suppresses the largest cascades in each network. Higher connectivity, however, increases capacity and total possible load of the system, raising the frequency of large avalanches. We build upon this result by considering more realistic scenario of coupling between two networks. Rather than connecting the nodes of both networks fully at random, randomly selected sites in one network are connected preferentially to a location topologically most similar in the second layer. We demonstrate that for both random graphs and two-dimensional lattices high level of such preferential connections suppresses large cascades seen otherwise in the random connection case. The probability of large cascades reaches a minimal value as seen in the earlier work and is kept constant at that magnitude for any connectivity higher than optimal. Finally, we discuss limitations of the multiple branching process approximation in estimating the impact of cascading failures on realistic networks. We show that preferential inter-layer connections create large-scale loops, which are responsible for limiting the size of observed cascades. Our work suggests that connectivity between systems can be topologically optimized as to limit impact of cascading failures in networks of networks.

Abstract: It is known that the presence of short loops (clustering) is an important source of error in the tree-based theories [Gleeson et al PRE 2012; Faqeeh et al, PRE 2015]. Despite this fact, the message passing (MP) approach for bond percolation [Karrer and Newman PRL 2010], which is a state-of-the-art tree-based theory, was shown to perform surprisingly well on several clustered networks. On the other hand, on some real-world networks that MP performs poorly, a significant part of error cannot be explained by the presence of short loops [Faqeeh et al, PRE 2015]. This indicates the presence of an unknown source of error and a phenomenon not captured by theories. We show [Faqeeh et al arXiv:1508.05590, 2015] that a type of finite size effect, which is independent of the total number of nodes or links of the network, is an important source of inaccuracy of theories such as MP. This type of finite size effect, which we refer to as “limited mixing”, occurs in modular networks in which the number of interlinks between pairs of modules is finite and sufficiently small. We demonstrate that, due to limited mixing, coexisting percolating clusters emerge in networks, while it is commonly assumed that only one percolating cluster can exist in networks (see for example [Melnik et al, Chaos 2014; Colomer-de-Simón et al, PRX 2014]). We show that this assumption is an important source of error in MP. We develop an approach called modular message passing (MMP) to describe and verify these observations. Moreover, we show that the MMP theory improves significantly over the predictions of MP for percolation on synthetic networks with limited mixing and also on several real-world networks. These findings have important implications for understanding the robustness of networks and in quantifying epidemic outbreaks in the susceptible-infected-recovered model of disease spread.

Abstract: In this work we study the transportation congestion problem in multiplex networks. We prove analytically and experimentally that the structure of multiplex networks can induce congestion for flows that otherwise would be decongested if the individual layers were not interconnected [1]. In transportation dynamics, a node starts to be congested when it is required to process elements at its maximum processing rate. The onset of congestion is known to be attained at a critical load which is inverse proportional to the network betweenness (i.e. the largest betweeness of all nodes). We show that the multiplex betweenness depends on intra-layer paths, inter-layer paths, and on the migration of shortest paths between layers. This last contribution unbalances, in a highly non-linear way, the distribution of shortest paths among the layers. Some approximations are possible to grasp the effect of the different contributions to the onset of congestion. In particular, the fraction of shortest paths fully contained within layers is basically 1, and so, the main factor influencing the traffic dynamics is the migration of shortest paths from the less efficient layer to the most efficient one. Then, we can approximate the multiplex betweenness and compute the congestion induced by a multiplex as the situation in which a multiplex network reaches congestion with less load than the worst of its layers when operating individually. Evaluation on several multiplex topologies show that the boundaries obtained by our approximations determine accurately the regions where the multiplex induces congestion. The observed cooperative phenomenon reminds the Braess' paradox in which adding extra capacity to a network when the moving entities selfishly choose their route can in some cases reduce overall performance. [1] Solé-Ribalta, Albert, Sergio Gómez, and Alex Arenas. "Congestion induced by the structure of multiplex networks." Physical Review Letters 116 (2016) 108701.

Abstract: One of the most fundamental properties of complex systems is that their evolution exhibits path-dependence. This implies a substantial departure from standard approaches of statistical physics. Complementarily, their statistical properties are usually governed by power-laws and scaling patters, in opposition to the generalised presence of exponential and gaussian distributions found in standard approaches. It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space Reducing processes (SSRP) offer an alternative new mechanism to understand the emergence of scaling in countless processes. The corresponding power law exponents are related to noise levels in the process. In this talk we will show that the emergence of scaling is not limited to the simplest SSRPs, but holds for a huge domain of stochastic processes which reduce their sampling space as they unfold, in spite of being characterized by non-uniform prior distributions. In the absence of noise, the scaling exponents converge to −1 (Zipf’s law) for almost all prior distributions. As a consequence it becomes possible to fully understand targeted diffusion on weighted directed networks and its associated scaling laws law in node visit distributions. The presence of cycles can be properly interpreted as playing the same role as noise in SSRPs and, accordingly, determine the scaling exponents. Our results have two immediate consequences: At the theoretical level, they offer a clear link between the emergence of scaling and path-dependence. At the applied level, the result that Zipf’s law emerges as a generic feature of diffusion on networks, regardless of its details, and that the exponent of visiting times is related to the amount of cycles in a network could be relevant for applications in traffic-, transport- and supply chain management.