Understanding scaling through history-dependent processes with collapsing sample space

History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample-space, or their set of possible outcomes, reduces as they age. We demonstrate that these sample-space reducing (SSR) processes necessarily lead to Zipf's law in the rank distributions of their outcomes. We show that by adding noise to SSR processes the corresponding rank distributions remain exact power-laws, $p(x)\sim x^{-\lambda}$, where the exponent directly corresponds to the mixing ratio of the SSR process and noise. This allows us to give a precise meaning to the scaling exponent in terms of the degree to how much a given process reduces its sample-space as it unfolds. Noisy SSR processes further allow us to explain a wide range of scaling exponents in frequency distributions ranging from $\alpha = 2$ to $\infty$. We discuss several applications showing how SSR processes can be used to understand Zipf's law in word frequencies, and how they are related to diffusion processes in directed networks, or ageing processes such as in fragmentation processes. SSR processes provide a new alternative to understand the origin of scaling in complex systems without the recourse to multiplicative, preferential, or self-organised critical processes.Comment: 7 pages, 5 figures in Proceedings of the National Academy of Sciences USA (published ahead of print April 13, 2015

Equilibria in the Tangle

We analyse the Tangle --- a DAG-valued stochastic process where new vertices get attached to the graph at Poissonian times, and the attachment's locations are chosen by means of random walks on that graph. These new vertices, also thought of as "transactions", are issued by many players (which are the nodes of the network), independently. The main application of this model is that it is used as a base for the IOTA cryptocurrency system (www.iota.org). We prove existence of "almost symmetric" Nash equilibria for the system where a part of players tries to optimize their attachment strategies. Then, we also present simulations that show that the "selfish" players will nevertheless cooperate with the network by choosing attachment strategies that are similar to the "recommended" one.Comment: 33 pages, 11 figure

Double Whammy - How ICT Projects are Fooled by Randomness and Screwed by Political Intent

The cost-benefit analysis formulates the holy trinity of objectives of project management - cost, schedule, and benefits. As our previous research has shown, ICT projects deviate from their initial cost estimate by more than 10% in 8 out of 10 cases. Academic research has argued that Optimism Bias and Black Swan Blindness cause forecasts to fall short of actual costs. Firstly, optimism bias has been linked to effects of deception and delusion, which is caused by taking the inside-view and ignoring distributional information when making decisions. Secondly, we argued before that Black Swan Blindness makes decision-makers ignore outlying events even if decisions and judgements are based on the outside view. Using a sample of 1,471 ICT projects with a total value of USD 241 billion - we answer the question: Can we show the different effects of Normal Performance, Delusion, and Deception? We calculated the cumulative distribution function (CDF) of (actual-forecast)/forecast. Our results show that the CDF changes at two tipping points - the first one transforms an exponential function into a Gaussian bell curve. The second tipping point transforms the bell curve into a power law distribution with the power of 2. We argue that these results show that project performance up to the first tipping point is politically motivated and project performance above the second tipping point indicates that project managers and decision-makers are fooled by random outliers, because they are blind to thick tails. We then show that Black Swan ICT projects are a significant source of uncertainty to an organisation and that management needs to be aware of

Graph-based Security and Privacy Analytics via Collective Classification with Joint Weight Learning and Propagation

Many security and privacy problems can be modeled as a graph classification problem, where nodes in the graph are classified by collective classification simultaneously. State-of-the-art collective classification methods for such graph-based security and privacy analytics follow the following paradigm: assign weights to edges of the graph, iteratively propagate reputation scores of nodes among the weighted graph, and use the final reputation scores to classify nodes in the graph. The key challenge is to assign edge weights such that an edge has a large weight if the two corresponding nodes have the same label, and a small weight otherwise. Although collective classification has been studied and applied for security and privacy problems for more than a decade, how to address this challenge is still an open question. In this work, we propose a novel collective classification framework to address this long-standing challenge. We first formulate learning edge weights as an optimization problem, which quantifies the goals about the final reputation scores that we aim to achieve. However, it is computationally hard to solve the optimization problem because the final reputation scores depend on the edge weights in a very complex way. To address the computational challenge, we propose to jointly learn the edge weights and propagate the reputation scores, which is essentially an approximate solution to the optimization problem. We compare our framework with state-of-the-art methods for graph-based security and privacy analytics using four large-scale real-world datasets from various application scenarios such as Sybil detection in social networks, fake review detection in Yelp, and attribute inference attacks. Our results demonstrate that our framework achieves higher accuracies than state-of-the-art methods with an acceptable computational overhead.Comment: Network and Distributed System Security Symposium (NDSS), 2019. Dataset link: http://gonglab.pratt.duke.edu/code-dat