Related papers: Majority Boolean networks classifying density: str…

This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the…

Traditional clustering methods often perform clustering with low-level indiscriminative representations and ignore relationships between patterns, resulting in slight achievements in the era of deep learning. To handle this problem, we…

We propose a new latent Boolean feature model for complex networks that captures different types of node interactions and network communities. The model is based on a new concept in graph theory, termed the Boolean intersection…

We study regularization in the context of small sample-size learning with over-parameterized neural networks. Specifically, we shift focus from architectural properties, such as norms on the network weights, to properties of the internal…

Networks (or graphs) are used to model the dyadic relations between entities in a complex system. In cases where there exists multiple relations between the entities, the complex system can be represented as a multilayer network, where the…

We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree…

The roles of different nodes within a network are often understood through centrality analysis, which aims to quantify the capacity of a node to influence, or be influenced by, other nodes via its connection topology. Many different…

We present a compact matrix formulation of the modularity, a commonly used quality measure for the community division in a network. Using this formulation we calculate the density of modularities, a statistical measure of the probability of…

Given the ground state wavefunction for an interacting lattice model, we define a "correlation density matrix"(CDM) for two disjoint, separated clusters $A$ and $B$, to be the density matrix of their union, minus the direct product of their…

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…

Polarization, understood as a division into mutually hostile groups, is a common feature of social systems. It is studied in Structural Balance Theory (SBT) in terms of semicycles in signed networks. However, enumerating semicycles is…

We generalize Condorcet's jury theorem (CJT) to socially connected populations in which agents revise discrete choices on a network in the presence of zealots. Free agents receive privately informative signals about the correct alternative…

This paper addresses the task of set prediction using deep learning. This is important because the output of many computer vision tasks, including image tagging and object detection, are naturally expressed as sets of entities rather than…

Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs,…

We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the…

There are hierarchical characteristics in the network and how to effectively reveal the hierarchical characteristics in the network is a problem in the research of network structure. If a node is assigned to the community to which it…

The density classification task is a famous problem in the theory of cellular automata. It is unsolvable for deterministic automata, but recently solutions for stochastic cellular automata have been found. One of them is a set of stochastic…

We propose a Multi-Task Learning (MTL) paradigm based deep neural network architecture, called MTCNet (Multi-Task Crowd Network) for crowd density and count estimation. Crowd count estimation is challenging due to the non-uniform scale…

Deep neural networks have achieved remarkable success, yet our understanding of how they learn remains limited. These models can learn high-dimensional tasks, which is generally statistically intractable due to the curse of dimensionality.…

We study here the problem of determining the majority type in an arbitrary connected network, each vertex of which has initially two possible types. The vertices may have a few additional possible states and can interact in pairs only if…