Kronecker graphs are a construction for generating graphs for modeling systems. The method constructs a sequence of graphs from a small base graph by iterating the Kronecker product. [1] A variety of generalizations of Kronecker graphs exist. [2]
The Graph500 benchmark for supercomputers is based on the use of a stochastic version of Kronecker graphs. Stochastic kronecker graph is a kronecker graph with each component of the matrix made by real numbers between 0 and 1. The stochastic version of kronecker graph eliminates the staircase effect, which happens due to large multiplicity of kronecker graph. [3]
Artificial neural networks are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains.
In graph theory, the shortest path problem is the problem of finding a path between two vertices in a graph such that the sum of the weights of its constituent edges is minimized.
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles Network theory and Percolation.
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P(k) of nodes in the network having k connections to other nodes goes for large values of k as
In graph theory, a clustering coefficient is a measure of the degree to which nodes in a graph tend to cluster together. Evidence suggests that in most real-world networks, and in particular social networks, nodes tend to create tightly knit groups characterised by a relatively high density of ties; this likelihood tends to be greater than the average probability of a tie randomly established between two nodes.
In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.
A recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some nodes to affect subsequent input to the same nodes. Their ability to use internal state (memory) to process arbitrary sequences of inputs makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition. The term "recurrent neural network" is used to refer to the class of networks with an infinite impulse response, whereas "convolutional neural network" refers to the class of finite impulse response. Both classes of networks exhibit temporal dynamic behavior. A finite impulse recurrent network is a directed acyclic graph that can be unrolled and replaced with a strictly feedforward neural network, while an infinite impulse recurrent network is a directed cyclic graph that can not be unrolled.
In probability theory and machine learning, the multi-armed bandit problem is a problem in which a fixed limited set of resources must be allocated between competing (alternative) choices in a way that maximizes their expected gain, when each choice's properties are only partially known at the time of allocation, and may become better understood as time passes or by allocating resources to the choice. This is a classic reinforcement learning problem that exemplifies the exploration–exploitation tradeoff dilemma. The name comes from imagining a gambler at a row of slot machines, who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. The multi-armed bandit problem also falls into the broad category of stochastic scheduling.
A multifractal system is a generalization of a fractal system in which a single exponent is not enough to describe its dynamics; instead, a continuous spectrum of exponents is needed.
In the study of complex networks, a network is said to have community structure if the nodes of the network can be easily grouped into sets of nodes such that each set of nodes is densely connected internally. In the particular case of non-overlapping community finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But overlapping communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community(ies), and less likely to be connected if they do not share communities. A related but different problem is community search, where the goal is to find a community that a certain vertex belongs to.
A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to. This set of functions in effect determines a topology (connectivity) on the set of variables, which then become nodes in a network. Usually, the dynamics of the system is taken as a discrete time series where the state of the entire network at time t+1 is determined by evaluating each variable's function on the state of the network at time t. This may be done synchronously or asynchronously.
The clique percolation method is a popular approach for analyzing the overlapping community structure of networks. The term network community has no widely accepted unique definition and it is usually defined as a group of nodes that are more densely connected to each other than to other nodes in the network. There are numerous alternative methods for detecting communities in networks, for example, the Girvan–Newman algorithm, hierarchical clustering and modularity maximization.
Multi-particle collision dynamics (MPC), also known as stochastic rotation dynamics (SRD), is a particle-based mesoscale simulation technique for complex fluids which fully incorporates thermal fluctuations and hydrodynamic interactions. Coupling of embedded particles to the coarse-grained solvent is achieved through molecular dynamics.
Philippe Blanchard has been a Professor of Mathematical Physics at Faculty of Physics, Bielefeld University since 1980. He is both director of the Research Center BiBoS and deputy managing director of the Center for Interdisciplinary Research at Bielefeld University.
Exponential Random Graph Models (ERGMs) are a family of statistical models for analyzing data from social and other networks. Examples of networks examined using ERGM include knowledge networks, organizational networks, colleague networks, social media networks, networks of scientific development, and others.
A recursive neural network is a kind of deep neural network created by applying the same set of weights recursively over a structured input, to produce a structured prediction over variable-size input structures, or a scalar prediction on it, by traversing a given structure in topological order. Recursive neural networks, sometimes abbreviated as RvNNs, have been successful, for instance, in learning sequence and tree structures in natural language processing, mainly phrase and sentence continuous representations based on word embedding. RvNNs have first been introduced to learn distributed representations of structure, such as logical terms. Models and general frameworks have been developed in further works since the 1990s.
The Louvain method for community detection is a method to extract communities from large networks created by Blondel et al. from the University of Louvain. The method is a greedy optimization method that appears to run in time where is the number of nodes in the network.
The stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized by being connected with one another with particular edge densities. For example, edges may be more common within communities than between communities. Its mathematical formulation has been firstly introduced in 1983 in the field of social network by Paul W. Holland et al. The stochastic block model is important in statistics, machine learning, and network science, where it serves as a useful benchmark for the task of recovering community structure in graph data.
Emotion recognition in conversation (ERC) is a sub-field of emotion recognition, that focuses on mining human emotions from conversations or dialogues having two or more interlocutors. The datasets in this field are usually derived from social platforms that allow free and plenty of samples, often containing multimodal data. Self- and inter-personal influences play critical role in identifying some basic emotions, such as, fear, anger, joy, surprise, etc. The more fine grained the emotion labels are the harder it is to detect the correct emotion. ERC poses a number of challenges, such as, conversational-context modeling, speaker-state modeling, presence of sarcasm in conversation, emotion shift across consecutive utterances of the same interlocutor.
Matthias Grossglauser is a Swiss communication engineer. He is a professor of computer science at EPFL and co-director of the Information and Network Dynamics Laboratory (INDY) at EPFL's School of Computer and Communication Sciences School of Basic Sciences.