Subgroup Structure Research Articles

Social Influence in Social-Ecological Systems: Collaborative Capacity and Inter-Organizational Networks in the U.S. Sagebrush.

Collaborative governance has become a prominent, if not dominant, framework for thinking about multi-scalar and cross-jurisdictional environmental management. The literature broadly and consistently suggests that collaborative capacity and inter-organizational networks provide the institutional framework for addressing social-ecological system challenges. Surprisingly little scholarship addresses processes of social influence (or contagion) in social-ecological systems writ large, or more specifically as it relates to collaborative capacity. In this study, we consider the relationship between network position and structure and "collaborative capacity". We use a linear network autocorrelation model to establish a quantifiable, statistical relationship between an organizational-level outcome (collaborative capacity) for organizations that are relationally connected in a network addressing conservation and management issues in the U.S. sagebrush biome. We test three general hypotheses: (1) that social position - operationalized as network centrality - is related to collaborative capacity, (2) that subgroup or community structure - operationalized as modularity - is related to collaborative capacity, and (3) that there is a social contagion effect of collaborative capacity. Our results identify a positive relationship between collaborative capacity and organizations in positions of brokerage as well as evidence of a "collaborative capacity" contagion effect. This work contributes to our understanding of the role of bridging organizations and networks for large-scale environmental management.

The structure of finite groups whose elements outside a normal subgroup have prime power orders

The structure of groups in which every element has prime power order (CP-groups) is extensively studied. We first investigate the properties of group $G$ such that each element of $G\setminus N$ has prime power order. It is proved that $N$ is solvable or every non-solvable chief factor $H/K$ of $G$ satisfying $H\leq N$ is isomorphic to $PSL_2(3^f)$ with $f$ a 2-power. This partially answers the question proposed by Lewis in 2023, asking whether $G\cong M_{10}$ ? Furthermore, we prove that if each element $x\in G\backslash N$ has prime power order and ${\bf C}_G(x)$ is maximal in $G$ , then $N$ is solvable. Relying on this, we give the structure of group $G$ with normal subgroup $N$ such that ${\bf C}_G(x)$ is maximal in $G$ for any element $x\in G\setminus N$ . Finally, we investigate the structure of a normal subgroup $N$ when the centralizer ${\bf C}_G(x)$ is maximal in $G$ for any element $x\in N\setminus {\bf Z}(N)$ , which is a generalization of results of Zhao, Chen, and Guo in 2020, investigating a special case that $N=G$ for our main result. We also provide a new proof for Zhao, Chen, and Guo's results above.

Multilateral collaborative governance of Arctic shipping safety: Examining the impact of the Arctic Council via collaborative network analysis

Global climate change has dramatically reduced Arctic sea ice, opening new potential shipping routes, which has garnered international attention. This study explores the role of the Arctic Council in the collaborative governance network focused on Arctic shipping safety. For this purpose, a collection of 49 collaborative events initiated by international organisations and the Arctic Council was used as the data sample. These events are divided into two groups, one containing all the events and the other excluding those initiated by the Arctic Council. As a result, two collaborative networks are developed and evaluated based on network density, average path length, network transitivity, centrality indices (degree, closeness, betweenness), and clustering analysis. The results demonstrate that the Arctic Council significantly enhances the network density and transitivity of the international collaboration network, and reshapes core-periphery dynamics and cohesive subgroup structures. For instance, under the influence of the Arctic Council, Canada, France, and Japan surpass the United Kingdom in centrality (degree, closeness, betweenness). Results of the clustering coefficients reveal the Arctic Council's impact on connections among states, leading to shifts in collaboration patterns. Additionally, subgroup cohesion and density coefficients confirm the Arctic Council's role in promoting collaboration among states and restructuring governance networks.

Design of consensus and cluster consensus controller for first-order nonlinear multi-agent systems based on subgroup structure

It is well known that nonlinear multi-agent systems (MASs) with a directed topology can reach a consensus if the global coupling coefficient is strong enough. In this paper, we propose a novel distributed protocol based on the subgroup structure. Our results demonstrate that the MAS design can follow a part-to-whole approach, starting with subgroups and gradually building up to a more complex system. We firstly consider two cases for the MASs: one with a single leader and one with a leader group, where agents within the leader group can communicate with each other, but cannot receive the information of other group. We show that followers can track the leader or group leaders if intra-coupling within the subgroup and information strength received by the root node are above a certain threshold. Next, we investigate cluster consensus and practical cluster consensus for the Laplacian matrix with unequal row sum, equal row sum, and mixing of partitioned matrices. Our results reveal that row sum and community structure of the partitioned matrix are crucial in determining the final state of each agent. Our proposed control protocol is highly flexible and relies only on the cluster structure and information received by the root node, rather than global information. Moreover, our method is not limited to tracking problems, cooperative control, or multi-objective control, and can accommodate new group agents joining the system, making it highly adaptable. We provide illustrative examples to demonstrate the effectiveness of our approach.

Normed Amenability and Bounded Cohomology over Non-Archimedean Fields

We study continuous bounded cohomology of totally disconnected locally compact groups with coefficients in a non-Archimedean valued field K \mathbb {K} . To capture the features of classical amenability that induce the vanishing of bounded cohomology with real coefficients, we start by introducing the notion of normed K \mathbb {K} -amenability, of which we prove an algebraic characterization. It implies that normed K \mathbb {K} -amenable groups are locally elliptic, and it relates an invariant, the norm of a K \mathbb {K} -amenable group, to the order of its discrete finite p p -subquotients, where p p is the characteristic of the residue field of K \mathbb {K} . Moreover, we prove a characterization of discrete normed K \mathbb {K} -amenable groups in terms of vanishing of bounded cohomology with coefficients in K \mathbb {K} . The algebraic characterization shows that normed K \mathbb {K} -amenability is a very restrictive condition, so the bounded cohomological one suggests that there should be plenty of groups with rich bounded cohomology with trivial K \mathbb {K} coefficients. We explore this intuition by studying the injectivity and surjectivity of the comparison map, for which surprisingly general statements are available. Among these, we show that if either K \mathbb {K} has positive characteristic or its residue field has characteristic 0 0 , then the comparison map is injective in all degrees. If K \mathbb {K} is a finite extension of Q p \mathbb {Q}_p , we classify unbounded and non-trivial quasimorphisms of a group and relate them to its subgroup structure. For discrete groups, we show that suitable finiteness conditions imply that the comparison map is an isomorphism; this applies in particular to finitely presented groups in degree 2 2 . A motivation as to why the comparison map is often an isomorphism, in stark contrast with the real case, is given by moving to topological spaces. We show that over a non-Archimedean field, bounded cohomology is a cohomology theory in the sense of Eilenberg–Steenrod, except for a weaker version of the additivity axiom which is however equivalent for finite disjoint unions. In particular there exists a Mayer–Vietoris sequence, the main missing piece for computing real bounded cohomology.

Robust Integrative Analysis via Quantile Regression with Homogeneity and Sparsity

Integrative analysis plays a critical role in integrating heterogeneous data from multiple datasets to provide a comprehensive view of the overall data features. However, in multiple datasets, outliers and heavy-tailed data can render least squares estimation unreliable. In response, we propose a Robust Integrative Analysis via Quantile Regression (RIAQ) that accounts for homogeneity and sparsity in multiple datasets. The RIAQ approach is not only able to identify latent homogeneous coefficient structures but also recover the sparsity of high-dimensional covariates via double penalty terms. The integration of sample information across multiple datasets improves estimation efficiency, while a sparse model improves model interpretability. Furthermore, quantile regression allows the detection of subgroup structures under different quantile levels, providing a comprehensive picture of the relationship between response and high-dimensional covariates. We develop an efficient alternating direction method of multipliers (ADMM) algorithm to solve the optimization problem and study its convergence. We also derive the parameter selection consistency of the modified Bayesian information criterion. Numerical studies demonstrate that our proposed estimator has satisfactory finite-sample performance, especially in heavy-tailed cases.

Commuting Probability for Approximate Subgroups of a Finite Group

Abstract For subsets $X,Y$ of a finite group G, we write $\mathrm{Pr} (X,Y)$ for the probability that two random elements $x\in X$ and $y\in Y$ commute. This paper addresses the relation between the structure of an approximate subgroup $A\subseteq G$ and the probabilities $\mathrm{Pr} (A,G)$ and $\mathrm{Pr} (A,A)$. The following results are obtained. Theorem 1.1: Let A be a K-approximate subgroup of a finite group G, and let $\mathrm{Pr} (A,G)\geq\epsilon\gt0$. There are two $(\epsilon, K)$-bounded positive numbers γ and K0 such that G contains a normal subgroup T and a K0-approximate subgroup B such that $|A\cap B|\ge \gamma\; {\mathrm{max}}\{|A|,|B|\}$ while the index $[G:T]$ and the order of the commutator subgroup $[T,\langle B \rangle]$ are $(\epsilon, K)$-bounded. Theorem 1.2: Let A be a K-approximate subgroup of a finite group G, and let $\mathrm{Pr} (A,A)\geq\epsilon\gt0$. There are two $(\epsilon, K)$-bounded positive numbers γ and s and a subgroup $C\leq G$ such that $|C \cap A^2| \gt \gamma |A|$ and $|C^{\prime}|\leq s$. In particular, A is contained in the union of at most $\gamma^{-1}K^2$ left cosets of the subgroup C. It is also shown that the above results admit approximate converses.

Isotropy groups of the action of orthogonal *congruence on Hermitian matrices

We present a procedure which enables the computation and the description of structures of isotropy subgroups of the group of complex orthogonal matrices with respect to the action of *congruence on Hermitian matrices. A key ingredient in our proof is an algorithm giving solutions of a certain rectangular block (complex-alternating) upper triangular Toeplitz matrix equation.

Hyperbolic quantum color codes with normal subgroup structure derived from the Reidemeister–Schreier method

Hyperbolic quantum color codes with normal subgroup structure derived from the Reidemeister–Schreier method

2-Adic Galois Images of Non-CM Isogeny-Torsion Graphs Defined over ℚ

Let E be a Q -isogeny class of elliptic curves defined over Q without CM. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in E and an edge for each Q -isogeny of prime degree that maps one elliptic curve in E to another elliptic curve in E , with the degree recorded as a label of the edge. An isogeny-torsion graph is an isogeny graph where, in addition, we label each vertex with the abstract group structure of the torsion subgroup over Q of the corresponding elliptic curve. Then, the main statement of the article is a classification of the 2-adic Galois image that occurs at each vertex of all isogeny-torsion graphs consisting of elliptic curves defined over Q without CM.

Radiant toric varieties and unipotent group actions

We consider complete toric varieties X such that a maximal unipotent subgroup U of the automorphism group Aut(X) acts on X with an open orbit. It turns out that such varieties can be characterized by several remarkable properties. We study the set of Demazure roots of the corresponding complete fan, describe the structure of a maximal unipotent subgroup U in Aut(X), and find all regular subgroups in U that act on X with an open orbit.

Octonions, Albert vectors and the group E6(F)

–We present a uniform approach to the construction of the groups of type E 6 over arbitrary fields without using Lie theory. This gives a simple description of the group generators and some of the subgroup structure. In the finite case our approach also permits relatively straightforward computation of the group order.

Heterogeneous quantile regression for longitudinal data with subgroup structures

Subgroup analysis for modeling longitudinal data with heterogeneity across all individuals has drawn attention in the modern statistical learning. In this paper, we focus on heterogeneous quantile regression model and propose to achieve variable selection, heterogeneous subgrouping and parameter estimation simultaneously, by using the smoothed generalized estimating equations in conjunction with the multi-directional separation penalty. The proposed method allows individuals to be divided into multiple subgroups for different heterogeneous covariates such that estimation efficiency can be gained through incorporating individual correlation structure and sharing information within subgroups. A data-driven procedure based on a modified BIC is applied to estimate the number of subgroups. Theoretical properties of the oracle estimator given the underlying true subpopulation information are firstly provided and then it is shown that the proposed estimator is equivalent to the oracle estimator under some conditions. The finite-sample performance of the proposed estimators is studied through simulations and an application to an AIDS dataset is also presented.

Subgroup detection in the heterogeneous partially linear additive Cox model

In the analysis of survival data, it is crucial to consider individual heterogeneities related to therapy, gender, and genetics as they can impact the validity of conclusions. The heterogeneous partially linear additive Cox model offers a versatile and useful approach for addressing these variations by incorporating both heterogeneous linear components and homogeneous additive components. We propose a subgroup detection method for this model under right-censoring using B-spline smoothing technique to approximate the additive functions. Without imposing any specific subgroup structure, we generate an objective function by combining a log partial likelihood function with a fusion penalty. To estimate parameters and detect subgroups simultaneously, we employ a majorized alternating direction method of multipliers (ADMM) algorithm. Furthermore, we establish oracle properties and model selection consistency for the proposed penalised estimator. Simulation studies and real data analysis on breast cancer demonstrate the performance of our method.

Exploration or exploitation orientation, subgroup structure and organizational knowledge creation

ABSTRACT Significant performance differences in the process of knowledge creation may exist between organisations with exploratory and exploitative tendencies due to differences in their inner network structures. This study focuses on the subgroups widespread in intra-organisational networks and their structural characteristics. We construct an agent-based model that describes the two different organisational learning models that exist in organisations – exploration-oriented and exploitation-oriented. We find that higher network density in each subgroup helps increase the speed of knowledge creation but depletes the idiosyncratic sets of beliefs and leads to premature convergence. Only when the network scale is large enough or the organisation tends to focus more on exploration can a sparse network play a positive role in knowledge creation. Moderate levels of cross-group links prevent exploitation-oriented organisations from entering the stagnation stage of knowledge growth and increase the knowledge creation performance of exploration-oriented organisations. Knowledge creation performance in exploitation-oriented organisations depends more on boundary hubs than on internal hubs. The presence of twofold hubs can improve knowledge creation performance without significantly reducing the dissimilarity of collective beliefs.

Profiles of psychological flexibility in Japan: A conceptual replication

This study aimed to conceptually replicate previous research. It detected subgroups of psychological flexibility (PF), which are based on the overall PF subcomponent, using latent class analysis and examined the relationships among the subgroups, well-being, and psychological distress. A total of 672 Japanese community sample participants completed the online survey. Analyses revealed three distinct profiles, namely, high-, moderate-, and low-PF groups. Well-being and psychological distress significantly differed across the groups. The high-PF group exhibited the highest levels of well-being and the lowest levels of distress, while the opposite results are true for the low-PF group. Furthermore, the high-PF group included more men than women and older participants. These results were almost consistent with previous data and demonstrated the stability of the subgroup structures of the PF level. The study discussed future directions for the PF profiles and cultural variables.

Subgroup analysis for the functional linear model

Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended to allow heterogeneous coefficient functions across different subgroups of subjects. The greatest challenge is that the subgroup structure is usually unknown to us. To this end, we develop a penalization-based approach which innovatively applies the penalized fusion technique to simultaneously determine the number and structure of subgroups and coefficient functions within each subgroup. An effective computational algorithm is derived. We also establish the oracle properties and estimation consistency. Extensive numerical simulations demonstrate its superiority compared to several competing methods. The analysis of an air quality dataset leads to interesting findings and improved predictions.

Image restoration with group sparse representation and low‐rank group residual learning

AbstractImage restoration, as a fundamental research topic of image processing, is to reconstruct the original image from degraded signal using the prior knowledge of image. Group sparse representation (GSR) is powerful for image restoration; it however often leads to undesirable sparse solutions in practice. In order to improve the quality of image restoration based on GSR, the sparsity residual model expects the representation learned from degraded images to be as close as possible to the true representation. In this article, a group residual learning based on low‐rank self‐representation is proposed to automatically estimate the true group sparse representation. It makes full use of the relation among patches and explores the subgroup structures within the same group, which makes the sparse residual model have better interpretation furthermore, results in high‐quality restored images. Extensive experimental results on two typical image restoration tasks (image denoising and deblocking) demonstrate that the proposed algorithm outperforms many other popular or state‐of‐the‐art image restoration methods.

Some connections between galois group and free group

Free Group and Galois Theory are both new contents of modern mathematics with being widely studied, while there are few studies about the connections between them. We can find that the automorphisms in the definition of Galois Group is like the symbols in free group. The structure of subgroups in free groups is a significant subject which is originated from the Group Theory. Thus, this paper will introduce some basic theorems of Galois Group, free group and give a proof of the set of every subfield of a field is isomorphic to a free Galois Group.

Narrow normal subgroups of Coxeter groups and of automorphism groups of Coxeter groups

Abstract By definition, a group is called narrow if it does not contain a copy of a non-abelian free group. We describe the structure of finite and narrow normal subgroups in Coxeter groups and their automorphism groups.