modularity is one of the prominent features of complex networks that divides the structure of these networks into community groups. So far, many methods have been used to identify communities in complex networks, but some of these methods have local optimizations that affect the order of processing nodes and the final solution. In this paper, a new method for finding communities in complex networks using split and merge is proposed. In this method, minimum spanning tree is used as a tool to detect dissimilarity between nodes. In the partitioning process, the edges that show the most dissimilarity are removed in the minimum spanning tree to create smaller groups of nodes in a community. In the merging process, each group is merged with the neighboring group whose combination has the highest increase in modularity compared to other neighboring groups. The results of experiments conducted on real networks and artificial networks show that the method proposed in this article has a good accuracy for identifying communities in complex networks.

Massive modularity Hypothesis of Mind assumes that the mind is composed largely, or perhaps even entirely, of modules. Since the publication of modularity of the Mind (Fodor, 1983) modularity has occupied a central role in the studies of mind and cognitive science. But in philosophy there is no agreement about this role. In this paper, first I propose that many of these problems are the effects of the Fodorian base of Massive modularity Hypothesis, and then I suggest taking Simon’s works on complexity as a proper base for modularity. In the last section of this paper, I consider two common characteristics of mind, i.e. domain- specificity and encapsulation, and argue that in shadow of Massive modularity Hypothesis these characteristics can be explained better.

In this paper, relying on the clustering of complex networks that can determine large scale features of ‎the network, we study 48 financial markets across the world. To this end, we develop a modularity ‎maximization method for directed and weighted networks. According to the linear correlation measure, ‎we construct the adjacency matrix, and by using the theory of random matrices, we divide the space of ‎eigenvalues of our matrix into two irrelevant and relevant fragments. By considering the temporal ‎window and its evolution over time series, our results demonstrate that in the vicinity of so-called ‎financial crisis clusters, which are often affected by geographical characteristics, are formed and from the ‎perspective of complex networks, they show more random behavior‎.‎‎

Abstract. In this paper, we have introduced and studied the notion of a fuzzy independent pair and obtain some properties of fuzzy α-modular pairs and independent pairs.

We address the throughput maximization problem for downlink transmission in DF-relay-assisted cognitive radio networks (CRNs) based on simultaneous wireless information and power transfer (SWIPT) capability. In this envisioned network, multiple-input multiple-output (MIMO) relay and secondary user (SU) equipment are designed to handle both radio frequency (RF) signal energy harvesting and SWIPT functional tasks. Additionally, the cognitive base station (CBS) communicates with the SU only via the MIMO relay. Based on the considered network model, several combined constraints of the main problem complicate the solution. Therefore, in this paper, we apply heuristic guidelines within the convex optimization framework to handle this complexity. First, consider the problem of maximizing throughput on both sides of the relay separately. Second, each side progresses to solve the complex problem optimally by adopting strategies for solving sub-problems. Finally, these optimal solutions are synthesized by proposing a heuristic iterative power allocation algorithm that satisfies the combinatorial constraints with short convergence times. The performance of the optimal proposed algorithm (OPA) is evaluated against benchmark algorithms via numerical results on optimality, convergence time, constraints’ compliance, and imperfect channel state information (CSI) on the CBS-PU link.

In literature, for the four common classes of uninorms, the modularity equation has been solved except for the kind of ones having continuous underlying functions. This paper is devoted to solving the modularity equation involving two uninorms with continuous underlying functions.We discuss this modularity equation in detail by dividing the main section into two parts. The structure characterization of the two uninorms is almost completely obtained and it is found that they are equal in the unit square except in a subdomain.

The focus of this paper is to investigate the modularity equation involving uninorms and Mayor's aggregation operators.  Necessary and sufficient conditions are established for this equation. And, it finds that themodularity equation of a Mayor's aggregation operator over a uninorm is reduced to the modularityof a commutative semi-t-norm over a uninorm and the modularity equation of a uninorm over a Mayor's aggregation operator is reduced to the modularity equation of a uninorm over a commutative semi-t-conorm. Among them, the cases of a uninorm which is locally internal on the boundary are studied in \cite{Su_Riera_Aguilera_Torrens_2019}. In this paper, we consider whether the neutral element $e$ of the uninorm is idempotent element of the Mayor's aggregation operator in modularity equation to get solutions in the corresponding cases.

As social networks grow, they become more and more complex and analyzing them becomes complicated. One way to reduce this complexity is to divide the network into subnets, which are also called communities. Dividing social networks into desirable communities can help the analysts and experts to understand the behavior and function of the networks. Community detection in networks is a challenging topic in network science and various methods have been proposed for that. modularity maximization is one of the state-of-the-art methods suggested for community detection. modularity maximization is an NP-hard problem meaning that no polynomial-time algorithm exists that could solve the problem optimally unless P=NP. One group of approaches that could solve such problems is the approximate algorithms. Identifying the influential nodes has many important applications in social networks. This technique could also be used in community detection. To maximize the modularity, in this paper, we propose approximate algorithms based on identifying the influential nodes and their influence domain. We used the concept of scale-free networks to prove the approximate factor. Experiments on real-world networks show that the proposed algorithm can compete with the state-of-the-art methods of community detection algorithms.

In the cognitive sciences, two distinct theories have been proposed about the structure of the human mind, both of which are evolutionary but also different. One of them is the theory of evolutionary psychology and its related claim to the massive modularity hypothesis, which considers the mind as a set of modules. Another is the simple heuristic and its related claim to the existence of an adaptive toolbox in cognitive methods that assigns mind guidance to the existence of a set of heuristics. Both theories seek to explain cultural diversity by applying these modules/ heuristics. Although proponents of each do not routinely mention the existence of another theory, both theories, both the massive modularity hypothesis and the existing idea of heuristics in the mind, seek to provide explanations not only from an evolutionary perspective but also in comparative psychology (Which compares the behavior of non-human species) are also acceptable. They also want to explain how cognitive processes are processed in our minds. However, at first, there are reasons to think that these theories offer explanations of human cognition that are incompatible with each other or undermine each other. What is challenged in this article is how a human being, who has always been influenced by a variety of heuristics, cognitive biases, and irrationality in reasoning, judgment, and decision-making during the process of evolution, can have a massive modular cognitive structure in its mind. And be organized to have a logical function