Key Node Discovery Algorithm Based on Multiple Relationships and Multiple Features in Social Networks

The key nodes play important roles in the processes of information propagation and opinion evolution in social networks. Previous work rarely considered multiple relationships and features into key node discovery algorithms at the same time. Based on the relational networks including the forwarding network, replying network, and mentioning network in a social network, this paper first proposes an algorithm of the overlapping user relational network to extract different relational networks with same nodes. Integrated with these relational networks, a multirelationship network is established. Subsequently, a key node discovery (KND) algorithm is presented on the basis of the shortest path, degree centrality, and random walk features in the multirelationship network. The advantages of the proposed KND algorithm are proved by the SIR propagation model and the normalized discounted cumulative gain on the multirelationship networks and single-relation networks. The experiment’s results show that the proposed KND method for finding the key nodes is superior to other baseline methods on different networks.

Meaningful comparisons with ordinal-scale items

Ordinal rating scales---say that from *strongly agree* to *strongly disagree* with a proposition---are exceedingly popular in psychological research. Yet, there is often a lingering question of whether metric-level descriptions of the results and parametric tests are appropriate. We consider a different problem, perhaps one that supersedes the ordinal-vs-metric issue: When is it appropriate to use single relations---say, a difference in central tendencies---to compare two ratings distributions? In this paper, we propose a set of models to guide researchers in drawing meaningful inferences from ordinal scales. We develop four statistical models that represent possible relations across two ratings distributions: a null model, a parametric single-relation model, a nonparametric single-relation model, and a multiple-relations model that accounts for complex effects. We show how these models can be compared in light of data with Bayes factors and illustrate their usefulness with two real-world examples. We also provide a freely available web applet for researchers who wish to adopt the approach.

Multiple testing; when is many too much?

In almost all medical research, more than a single hypothesis is being tested or more than a single relation is being estimated. Testing multiple hypotheses increases the risk of drawing a false-positive conclusion. We briefly discuss this phenomenon, which is often called multiple testing. Also, methods to mitigate the risk of false-positive conclusions are discussed.

ON SOLVABILITY OF CERTAIN EQUATIONS OF ARBITRARY LENGTH OVER TORSION-FREE GROUPS

Let G be a nontrivial torsion-free group and $s\left( t \right) = {g_1}{t^{{\varepsilon _1}}}{g_2}{t^{{\varepsilon _2}}} \ldots {g_n}{t^{{\varepsilon _n}}} = 1\left( {{g_i} \in G,{\varepsilon_i} = \pm 1} \right)$ be an equation over G containing no blocks of the form ${t^{- 1}}{g_i}{t^{ - 1}},{g_i} \in G$ . In this paper, we show that $s\left( t \right) = 1$ has a solution over G provided a single relation on coefficients of s(t) holds. We also generalize our results to equations containing higher powers of t. The later equations are also related to Kaplansky zero-divisor conjecture.

Finding globally optimal macrostructure in multiple relation, mixed-mode social networks

From the outset, computational sociologists have stressed leveraging multiple relations when blockmodeling social networks. Despite this emphasis, the majority of published research over the past 40 years has focused on solving blockmodels for a single relation. When multiple relations exist, a reductionist approach is often employed, where the relations are stacked or aggregated into a single matrix, allowing the researcher to apply single relation, often heuristic, blockmodeling techniques. Accordingly, in this article, we develop an exact procedure for the exploratory blockmodeling of multiple relation, mixed-mode networks. In particular, given (a) [Formula: see text] actors, (b) [Formula: see text] events, (c) an [Formula: see text] binary one-mode network depicting the ties between actors, and (d) an [Formula: see text] binary two-mode network representing the ties between actors and events, we use integer programming to find globally optimal [Formula: see text] image matrices and partitions, where [Formula: see text] and [Formula: see text] represent the number of actor and event positions, respectively. Given the problem’s computational complexity, we also develop an algorithm to generate a minimal set of non-isomorphic image matrices, as well as a complementary, easily accessible heuristic using the network analysis software Pajek. We illustrate these concepts using a simple, hypothetical example, and we apply our techniques to a terrorist network.

MR-GCN: Multi-Relational Graph Convolutional Networks based on Generalized Tensor Product

Graph Convolutional Networks (GCNs) have been extensively studied in recent years. Most of existing GCN approaches are designed for the homogenous graphs with a single type of relation. However, heterogeneous graphs of multiple types of relations are also ubiquitous and there is a lack of methodologies to tackle such graphs. Some previous studies address the issue by performing conventional GCN on each single relation and then blending their results. However, as the convolutional kernels neglect the correlations across relations, the strategy is sub-optimal. In this paper, we propose the Multi-Relational Graph Convolutional Network (MR-GCN) framework by developing a novel convolution operator on multi-relational graphs. In particular, our multi-dimension convolution operator extends the graph spectral analysis into the eigen-decomposition of a Laplacian tensor. And the eigen-decomposition is formulated with a generalized tensor product, which can correspond to any unitary transform instead of limited merely to Fourier transform. We conduct comprehensive experiments on four real-world multi-relational graphs to solve the semi-supervised node classification task, and the results show the superiority of MR-GCN against the state-of-the-art competitors.

The first law of general quantum resource theories

We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.

Topological Properties of Multigranular Rough sets on Fuzzy Approximation Spaces

One of the extensions of the basic rough set model introduced by Pawlak in 1982 is the notion of rough sets on fuzzy approximation spaces. It is based upon a fuzzy proximity relation defined over a Universe. As is well known, an equivalence relation provides a granularization of the universe on which it is defined. However, a single relation defines only single granularization and as such to handle multiple granularity over a universe simultaneously, two notions of multigranulations have been introduced. These are the optimistic and pessimistic multigranulation. The notion of multigranulation over fuzzy approximation spaces were introduced recently in 2018. Topological properties of rough sets are an important characteristic, which along with accuracy measure forms the two facets of rough set application as mentioned by Pawlak. In this article, the authors introduce the concept of topological property of multigranular rough sets on fuzzy approximation spaces and study its properties.