Alzheimer's disease (AD) is a progressive neurodegenerative disorder that remains a global challenge due to its complex pathology and the lack of definitive diagnostic tools. This paper introduces an innovative approach to predicting and analyzing Alzheimer's disease by constructing signed brain network models and leveraging signed graph neural network technologies. By modeling the brain network as a signed graph that incorporates both positive and negative correlations, we capture the nuanced interactions between brain regions more effectively than traditional methods. We utilize graph convolutional networks (GCNs) and their variants to process these signed brain networks, significantly improving the accuracy of Alzheimer's disease prediction. Comparative analysis reveals that the signed graph model outperforms its unsigned counterparts in diagnostic precision (with an improvement of at least 19%), emphasizing the importance of incorporating negative correlations in neural interactions. Furthermore, precisely because of the additional negative edge information that we can utilize both positive and negative attention matrices, derived from these prediction tasks, to determine important brain region biomarkers. This work is an attempt to systematically validate the role of negative information through comparisons of different signed graph variants, which holds particular promise for enhancing Alzheimer's disease diagnostic accuracy at early stages. We believe that this approach will have significant clinical applications in the future.

The analysis of social networks and community detection is a central theme in Artificial Intelligence. One line of research deals with finding groups of agents that could work together to achieve a certain goal. To this end, different notions of so-called clusters or communities have been introduced in the literature of graphs and networks. Among these, a defensive alliance is a kind of quantitative group structure. However, all studies on alliances so far have ignored one aspect that is central to the formation of alliances on a very intuitive level, assuming that the agents are preconditioned concerning their attitude towards other agents: they prefer to be in some group (or in an alliance) together with the agents they like, so that they are happy to help each other towards their common aim, possibly then working against the agents outside of their group that they dislike. Signed networks were introduced in the psychology literature to model liking and disliking between agents, generalizing graphs in a natural way. Hence, we propose the novel notion of a defensive alliance in the context of signed networks. We then investigate several natural algorithmic questions related to this notion. These, and also combinatorial findings, connect our notion to that of correlation clustering, which is a well-established idea of finding groups of agents within a signed network. Also, we introduce a new structural parameter for signed graphs, the signed neighborhood diversity snd, and exhibit a snd-parameterized algorithm that finds one of the smallest defensive alliances in a signed graph.

Signed networks with both positive and negative links have gained considerable attention over the past several years. Community detection is among the main challenges for signed network analysis. It aims to find mutually antagonistic groups such that entities within the same group have as many positive relationships as possible and entities between different groups have as many negative relationships as possible. Most existing algorithms for community detection in signed networks aim to provide a hard partition of the network where any node should belong to a single community. However, overlapping communities, where a node is allowed to belong to multiple communities, widely exist in many real-world networks. Another disadvantage of some existing algorithms is that the number of final clusters k should be an input of the clustering process. It may however be the case that we do not know k in advance. In this paper, to offer improvements to existing algorithms, we propose a new clustering method for signed networks, the Signed Quasi-clique Merger (SQCM) algorithm. This algorithm detects the meaningful clusters (i.e. subgraphs with high friendly density) from the networks directly, where the friendly density of a subgraph [Formula: see text] is defined as [Formula: see text]. We construct a hierarchically nested system to illustrate their inclusion relationships. The output of SQCM is a smaller hierarchical tree, which clearly highlights meaningful clusters. During the clustering process, we do not need to know the number of final clusters k in advance; the algorithm is able to detect it on its own. Another important feature of SQCM is overlapping clustering or multi-membership. Its effectiveness is demonstrated through rigorous experiments involving both benchmark and randomly generated signed networks.

The complex network of relationships between countries provides an abundance of data from which intelligence analysts must synthesize useful interpretations that effectively inform foreign policy and security decision making. In this work, a network of foreign policy event interactions is developed and then used to describe the state of the international system by estimating the behavioral distances from all relevant actors to the US. Using a graph theoretic approach, we develop a tool for estimating behavioral distances through direct network links when behavior is present, and indirect network paths when direct behavior is unobserved. The international system is examined in temporal aggregations of 60 and 30 days prior to and following the 1991 Gulf War and the 2003 invasion of Iraq. Both periods see distancing from the US as the wars approach, and a partial return to the prior state by 60 days after the initiation of conflict. The overall position of the US and the response of other nations towards the US indicates that the systemic leadership role of the US is diminished in behavioral relationships with a moderate number of actors.

Extremist political movements have proliferated on the web in recent years due to the advent of minimal publication costs coupled with near universal access, resulting in what appears to be an abundance of groups that hover on the fringe of many socially divisive issues. Whether white-supremacist, neo- Nazi, anti-abortion, black separatist, radical Christian, animal rights, or violent environmentalists, all have found a home (and voice) on the Web. These groups form social networks whose ties are predicated primarily on shared political goals. Little is known about these groups, their interconnections, their animosities, and most importantly, their growth and development and studies such as the Dark Web Project, while considering domestic extremists, have focused primarily on international terrorist groups. Yet here in the US, there has been a complex social dynamic unfolding as well. While left-wing radicalism declined throughout the 80s and 90s, right wing hate groups began to flourish. Today, the web offers a place for any brand of extremism, but little is understood about their current growth and development. While there is much to gain from in-depth studies of the content provided by these sites, there is also a surprising amount of information contained in their online network structure as manifested in links between and among these web sites. Our research follows the idea that much can be known about you by the company you keep. In this paper, we propose an approach to measure the intrinsic relationships (i.e., similarities) of a set of extremist web pages. In this model, the web presence of a group is thought of as a node in a social network and the links between these pages are the ties between groups. This approach takes the bi-directional hyperlink structure of web pages and, based on similarity scores, applies an effective multi-membership clustering algorithm known as the quasi clique merger method to cluster these web pages using a derived hierarchical tree. The experimental results show that this new similarity measurement and hierarchical clustering algorithm gives an improvement over traditional link based clustering methods.

The problem of sorting by reciprocal translocations (abbreviated as SBT) arises from the field of comparative genomics, which is to find a shortest sequence of reciprocal translocations that transforms one genome Pi into another genome Gamma, with the restriction that Pi and Gamma contain the same genes. SBT has been proved to be polynomial-time solvable, and several polynomial algorithms have been developed. In this paper, we show how to extend Bergeron's SBT algorithm to include insertions and deletions, allowing to compare genomes containing different genes. In particular, if the gene set of Pi is a subset (or superset, respectively) of the gene set of Gamma, we present an approximation algorithm for transforming Pi into Gamma by reciprocal translocations and deletions (insertions, respectively), providing a sorting sequence with length at most OPT + 2, where OPT is the minimum number of translocations and deletions (insertions, respectively) needed to transform Pi into Gamma; if Pi and Gamma have different genes but not containing each other, we give a heuristic to transform Pi into Gamma by a shortest sequence of reciprocal translocations, insertions, and deletions, with bounds for the length of the sorting sequence it outputs. At a conceptual level, there is some similarity between our algorithm and the algorithm developed by El Mabrouk which is used to sort two chromosomes with different gene contents by reversals, insertions, and deletions.