ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP

Let G be a permutation group on a set $\Omega $ of size t. We say that $\Lambda \subseteq \Omega $ is an independent set if its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset of $\Lambda $ . We define the height of G to be the maximum size of an independent set, and we denote this quantity $\textrm{H}(G)$ . In this paper, we study $\textrm{H}(G)$ for the case when G is primitive. Our main result asserts that either $\textrm{H}(G)< 9\log t$ or else G is in a particular well-studied family (the primitive large–base groups). An immediate corollary of this result is a characterization of primitive permutation groups with large relational complexity, the latter quantity being a statistic introduced by Cherlin in his study of the model theory of permutation groups. We also study $\textrm{I}(G)$ , the maximum length of an irredundant base of G, in which case we prove that if G is primitive, then either $\textrm{I}(G)<7\log t$ or else, again, G is in a particular family (which includes the primitive large–base groups as well as some others).

La vicinanza solidale in contesti di vulnerabilità familiare. La partecipazione nella comunità come strada per ricostruire i tessuti sociali

Family vulnerability is a particular social situation, characterised by high levels of relational complexity, with serious consequences for the fulfilment of the developmental needs of a child. In the framework of the P.I.P.P.I. Programme (Programme of Intervention for the Prevention of Institutionalisation), social support is intended as a form of solidarity between families that aims to help a family through the support of another family, or individuals. In order to face vulnerability and social exclusion, P.I.P.P.I. promotes the mobilisation of these resources. The paper is therefore focused on a case study based in Sondrio (Italy), carried out within the P.I.P.P.I. Programme. The professionals together with the researchers tested their understanding, also promoting dialogue-meetings with families. These dialogical and interactive contexts generated new and unexpected interpretations of this phenomenon, framing it into an educational process that meets the needs of children and families, and promoting community participation as a way to reconstruct local social networks as well.

Fieldworking the relational complexity of organizations

PurposeThe purpose of this paper is to present researcher's reflexive writing about emergent events in research collaborations as a way of responding to the process-figurational sociology of Norbert Elias in the practice of organizational ethnography.Design/methodology/approachDrawing parallels between Norbert Elias' figurative account of social life and auto-ethnographic methodology, this paper re-articulates the entanglement of social researchers in organizational ethnographic work. Auto-ethnographic narration is explored as means to inquire from within the emerging relational complexity constituted by organizational dynamics. Writing about emergent events in the research process becomes a way of inquiring into the social figurations between the involved stakeholders; thus nurturing sense-making and increasing the awareness and sensitivity of the researcher to her own entanglement with the relational complexity of the organization under study.FindingsIn the paper, we argue that the writing of auto-ethnographic narratives of emergent field encounters is a process of inquiry that continuously depicts the temporal development of the relational complexity in organizations. Viewing that from the perspective of Elias' concept of figuration, we find a common commitment to the processual nature of research processes, which insists on moving beyond objectifying empirical insights.Originality/valueThis paper encourages awareness of the interdependency between ourselves as social researchers and field actors as we engage with the field. It moves beyond simplifying the ethnographic research agenda to that of “studying” and “describing” organizations. It offers unique insights into the organizational context, and increased sensitivity toward the social entanglement of the experiences that we, ourselves, as researchers are part of.

Navigating Increasing Levels of Relational Complexity: Perceptual, Analogical, and System Mappings

Relational thinking involves comparing abstract relationships between mental representations that vary in complexity; however, this complexity is rarely made explicit during everyday comparisons. This study explored how people naturally navigate relational complexity and interference using a novel relational match-to-sample (RMTS) task with both minimal and relationally directed instruction to observe changes in performance across three levels of relational complexity: perceptual, analogy, and system mappings. Individual working memory and relational abilities were examined to understand RMTS performance and susceptibility to interfering relational structures. Trials were presented without practice across four blocks, and participants received feedback after each attempt to guide learning. Experiment 1 instructed participants to select the target that best matched the sample, whereas Experiment 2 additionally directed participants' attention to same and different relations. Participants in Experiment 2 demonstrated improved performance when solving analogical mappings, suggesting that directing attention to relational characteristics affected behavior. Higher performing participants—those with above-chance performance on the final block of system mappings—solved more analogical RMTS problems and had greater visuospatial working memory, abstraction, verbal analogy, and scene analogy scores compared to lower performers. Lower performers were less dynamic in their performance across blocks and demonstrated negative relationships between analogy and system mapping accuracy, suggesting increased interference between these relational structures. Participant performance on RMTS problems did not change monotonically with relational complexity, suggesting that increases in relational complexity places nonlinear demands on working memory. We argue that competing relational information causes additional interference, especially in individuals with lower executive function abilities.

The Difficulty to Break a Relational Complexity Network Can Predict Air Traffic Controllers’ Mental Workload and Performance in Conflict Resolution

Objective: To test the network disentangling model for explaining air traffic controllers’ (ATCos) conflict resolution performance. The network rigidity index (NRI), and the steps to break the relational complexity network following a central-available-node-first rule, was hypothesized to explain the overall task demand, whereas marginal-effort-decrease rule was expected to explain the actual operational outcome. Background: Understanding the conflict resolution process of ATCos is important for aviation safety and efficiency. However, linear models are insufficient. We proposed a new model that ATCos behavior can be largely considered as a process to break the relational complexity network, in which nodes represent the aircraft while links represent the cognitive complexity to understand the aircraft dyad relationship. Method: Twenty-one professional ATCos completed 27 conflict resolution scenarios that varied in the NRI and other control variables. Multilevel regression analyses were performed to understand the influence of the NRI on the number of interventions, mental workload, and unresolved rate. A cross-validation was performed to evaluate the predictive power of the model. Results: NRI influenced ATCos intervention number in a curvilinear manner, which further leads to ATCo’s mental workload. The deviance between the number of interventions and the NRI was strongly linked with unresolved rate. Cross-validation suggests that the models predictions are robust. Conclusion: The network disentangling model provides a useful theory-driven way to explain controllers’ conflict resolution workload and other important performance outcomes such as intervention probability. Application: The proposed model can potentially be used for workload management, sector design, and intelligent decision support tool development.

“If I Want to Feel My Feelings, I’ll See a Bloody Shrink”: Learning From the Shadow Side of Experiential Learning

This article discusses the value of learning from a psychodynamic approach to experiential learning. This approach is used to help students experience and understand the emotional and relational complexity of leading and managing within organizations. From this perspective, experiential learning means engaging with emotions and with embedded relations of power, to unsettle expectations of how organizations work. Here, we consider the professor’s role, which is to help students work with and through the emotional dynamics generated in work relationships, even when those dynamics are difficult to bear and the overriding impulse is to avoid or defend against them. In this way, students are being supported to better understand how organizations are emotional places, not how individuals within organizations can “manage” emotion.

Recognizing and Resolving Ethical Issues

Counseling stepfamilies necessitates appreciating the relational complexity of this family constellation and the impact of these relational schema on the provisions of ethical counseling. Clinicians need to recognize common ethical concerns as specific to stepfamilies and learn how to resolve these potential concerns in a manner that enhances therapeutic service and honors the ethical aspirations of the counseling profession.