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Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
Controlling a complex network towards a desire state is of great importance in many applications. Existing works present an approximate algorithm to find the driver nodes used to control partial nodes of the network. However, the driver…
We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
This paper presents a model-based, unsupervised algorithm for recovering word boundaries in a natural-language text from which they have been deleted. The algorithm is derived from a probability model of the source that generated the text.…
Introduced recently, the concept of hierarchical degree allows a more complete characterization of the topological context of a node in a complex network than the traditional node degree. This article presents analytical characterization…
We investigate various aspects of the statistics of leaders in growing network models defined by stochastic attachment rules. The leader is the node with highest degree at a given time (or the node which reached that degree first if there…
We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…
Sentence ordering aims at arranging a list of sentences in the correct order. Based on the observation that sentence order at different distances may rely on different types of information, we devise a new approach based on multi-granular…
Master equations are of fundamental importance in modeling stochastic dynamical systems.However, solving master equations is challenging due to the exponential increase in the number of possible states or trajectories with the dimension of…
Automata networks are a versatile model of finite discrete dynamical systems composed of interacting entities (the automata), able to embed any directed graph as a dynamics on its space of configurations (the set of vertices, representing…
We propose a direct-to-word sequence model which uses a word network to learn word embeddings from letters. The word network can be integrated seamlessly with arbitrary sequence models including Connectionist Temporal Classification and…
Real-world networks grow over time; statistical models based on node exchangeability are not appropriate. Instead of constraining the structure of the \textit{distribution} of edges, we propose that the relevant symmetries refer to the…
Consensus strategies find a variety of applications in distributed coordination and decision making in multi-agent systems. In particular, average consensus plays a key role in a number of applications and is closely associated with two…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
Natural language correction has the potential to help language learners improve their writing skills. While approaches with separate classifiers for different error types have high precision, they do not flexibly handle errors such as…
Identifying the most influential nodes in information networks has been the focus of many research studies. This problem has crucial applications in various contexts, such as controlling the propagation of viruses or rumours in real-world…
The brain must robustly store a large number of memories, corresponding to the many events encountered over a lifetime. However, the number of memory states in existing neural network models either grows weakly with network size or recall…