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We study rare events in networks with both internal and external noise, and develop a general formalism for analyzing rare events that combines pair-quenched techniques and large-deviation theory. The probability distribution, shape, and…
Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…
Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production…
Random forests construct each tree with a different, randomised representation of the feature space. Their uniform voting cannot correct errors in regions where trees with incorrect representations probabilistically outnumber correct ones,…
In this paper we investigate image classification with computational resource limits at test time. Two such settings are: 1. anytime classification, where the network's prediction for a test example is progressively updated, facilitating…
Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
The rate at which nodes in evolving social networks acquire links (friends, citations) shows complex temporal dynamics. Preferential attachment and link copying models, while enabling elegant analysis, only capture rich-gets-richer effects,…
We present a new model of the evolutionary dynamics and the growth of on-line social networks. The model emulates people's strategies for acquiring information in social networks, emphasising the local subjective view of an individual and…
We study a version of the Tangled Nature model of evolutionary ecology redefined in a phenotype space where mutants have properties correlated to their parents. The model has individual-based dynamics whilst incorporating species scale…
Life on earth is distinguished by long-lived correlations in time. The patterns of material organization that characterize living organisms today are contingent on events that occurred billions of years ago. This contingency is a necessary…
We investigate the spectra of adjacency matrices of multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two random networks, the spectra of the…
The problem of reconstructing evolutionary trees or phylogenies is of great interest in computational biology. A popular model for this problem assumes that we are given the set of leaves (current species) of an unknown binary tree and the…
We investigate a degree-biased cutting process on random recursive trees, where each vertex is deleted with probability proportional to its degree. We establish the splitting property and derive the explicit distribution of the number of…
In several real-world networks like the Internet, WWW etc., the number of links grow in time in a non-linear fashion. We consider growing networks in which the number of outgoing links is a non-linear function of time but new links between…
This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…
We consider the discrete-time threshold-$\theta \ge 2$ contact process on a random r-regular graph on n vertices. In this process, a vertex with at least \theta occupied neighbors at time t will be occupied at time t+1 with probability p,…
Random walks on dynamic graphs have received increasingly more attention from different academic communities over the last decade. Despite the relatively large literature, little is known about random walks that construct the graph where…
Many complex systems change their structure over time, in these cases dynamic networks can provide a richer representation of such phenomena. As a consequence, many inference methods have been generalized to the dynamic case with the aim to…
We study the problem of building a maximum lifetime data collection tree for periodic convergecast applications in wireless sensor networks. We experimentally observe that if two nodes transmit same number of data packets, the amount of…