In this paper, we focus on computing an NE that optimizes a given objective function.

I left my toxic mums' group because I'd had enough of being judged Martina loved the idea of a baby signing class. As well as teaching her baby to communicate with simple hand gestures, she'd be able to meet other mothers in her area. But after the third session, Martina scooped up her newborn and walked out. She'd had enough of being judged. She says the other mothers scoffed at her parenting choices - she bottle-feeds her son - and seemed to disapprove of her choosing to deliver her baby by caesarean section.

Model selection is a pivotal process in the quantitative sciences, where researchers must navigate between numerous candidate models of varying complexity. Traditional information criteria, such as the corrected Akaike Information Criterion (AICc), Bayesian Information Criterion (BIC), and Mallows's $\mathit{C_p}$, are valuable tools for identifying optimal models. However, the exponential increase in candidate models with each additional model parameter renders the evaluation of these criteria for all models -- a strategy known as exhaustive, or brute-force, searches -- computationally prohibitive. Consequently, heuristic approaches like stepwise regression are commonly employed, albeit without guarantees of finding the globally-optimal model. In this study, we challenge the prevailing notion that non-monotonicity in information criteria precludes bounds on the search space. We introduce a simple but novel bound that enables the development of branch-and-bound algorithms tailored for these non-monotonic functions. We demonstrate that our approach guarantees identification of the optimal model(s) across diverse model classes, sizes, and applications, often with orders of magnitude computational speedups. For instance, in one previously-published model selection task involving $2^{32}$ (approximately 4 billion) candidate models, our method achieves a computational speedup exceeding 6,000. These findings have broad implications for the scalability and effectiveness of model selection in complex scientific domains.

Neurodivergent women in Software Engineering (SE) encounter distinctive challenges at the intersection of gender bias and neurological differences. To the best of our knowledge, no prior work in SE research has systematically examined this group, despite increasing recognition of neurodiversity in the workplace. Underdiagnosis, masking, and male-centric workplace cultures continue to exacerbate barriers that contribute to stress, burnout, and attrition. In response, we propose a hybrid methodological approach that integrates InclusiveMag's inclusivity framework with the GenderMag walkthrough process, tailored to the context of neurodivergent women in SE. The overarching design unfolds across three stages, scoping through literature review, deriving personas and analytic processes, and applying the method in collaborative workshops. We present a targeted literature review that synthesize challenges into cognitive, social, organizational, structural and career progression challenges neurodivergent women face in SE, including how under/late diagnosis and masking intensify exclusion. These findings lay the groundwork for subsequent stages that will develop and apply inclusive analytic methods to support actionable change.

Modelling across engineering, systems science, and formal methods remains limited by binary relations, implicit semantics, and diagram-centred notations that obscure multilevel structure and hinder mechanisation. Hypernetwork Theory (HT) addresses these gaps by treating the n-ary relation as the primary modelling construct. Each relation is realised as a typed hypersimplex - alpha (conjunctive, part-whole) or beta (disjunctive, taxonomic) - bound to a relation symbol R that fixes arity and ordered roles. Semantics are embedded directly in the construct, enabling hypernetworks to represent hierarchical and heterarchical systems without reconstruction or tool-specific interpretation. This paper presents the structural kernel of HT. It motivates typed n-ary relational modelling, formalises the notation and axioms (A1-A5) for vertices, simplices, hypersimplices, boundaries, and ordering, and develops a complete algebra of structural composition. Five operators - merge, meet, difference, prune, and split - are defined by deterministic conditions and decision tables that ensure semantics-preserving behaviour and reconcile the Open World Assumption with closure under rules. Their deterministic algorithms show that HT supports reproducible and mechanisable model construction, comparison, decomposition, and restructuring. The resulting framework elevates hypernetworks from symbolic collections to structured, executable system models, providing a rigorous and extensible foundation for mechanisable multilevel modelling.

Abstract--Traditional efforts to measure historical structural oppression struggle with cross-national validity due to the unique, locally specified histories of exclusion, colonization, and social status in each country, and often have relied on structured indices that privilege material resources while overlooking lived, identity-based exclusion. We introduce a novel framework for oppression measurement that leverages Large Language Models (LLMs) to generate context-sensitive scores of lived historical disadvantage across diverse geopolitical settings. Using unstructured self-identified ethnicity utterances from a multilingual COVID-19 global study, we design rule-guided prompting strategies that encourage models to produce interpretable, theoretically grounded estimations of oppression. We systematically evaluate these strategies across multiple state-of-the-art LLMs. Our results demonstrate that LLMs, when guided by explicit rules, can capture nuanced forms of identity-based historical oppression within nations. This approach provides a complementary measurement tool that highlights dimensions of systemic exclusion, offering a scalable, cross-cultural lens for understanding how oppression manifests in data-driven research and public health contexts. The study of racial and ethnic inequality remains central to sociological research, with extensive research documenting how structural oppression is reproduced in historical and contemporary contexts [1]-[3]. Oppression can be understood as a social hierarchy in which some groups subject other groups to lower status and to systemic exclusion, dehumanization, and disadvantage. In public health and sociology, this oppression is closely aligned with definitions of systemic and structural racism, which describe racism as deeply embedded in laws, policies, institutional practices, and social norms that sustain widespread inequities, violence, and disadvantage over time [1]. Foundational works have demonstrated how ethnic and national hierarchies shape access to power, life opportunities, autonomy, and sovereignty, for example, primarily through institutionalized mechanisms such as legal structures, educational systems, and healthcare access, among others [2].

This study introduces a hybrid neuro-symbolic framework that achieves deterministic detection of statutory inconsistency in complex law. We use the U.S. Internal Revenue Code (IRC) as a case study because its complexity makes it a fertile domain for identifying conflicts. Our research offers a solution for detecting inconsistent provisions by combining Large Language Models (LLMs) with symbolic logic. LLM-based methods can support compliance, fairness, and statutory drafting, yet tax-specific applications remain sparse. A key challenge is that such models struggle with hierarchical processing and deep structured reasoning, especially over long text. This research addresses these gaps through experiments using GPT-4o, GPT-5, and Prolog. GPT-4o was first used to translate Section 121 into Prolog rules and refine them in SWISH. These rules were then incorporated into prompts to test whether Prolog-augmented prompting improved GPT-4o's inconsistency detection. GPT-4o, whether prompted with natural language alone or with Prolog augmentation, detected the inconsistency in only one of three strategies (33 percent accuracy), but its reasoning quality differed: natural-language prompting achieved 100 percent rule coverage, while Prolog-augmented prompting achieved 66 percent, indicating more incomplete statutory analysis. In contrast to probabilistic prompting, the hybrid Prolog model produced deterministic and reproducible results. Guided by GPT-5 for refinement, the model formalized the IRC section's competing interpretations and successfully detected an inconsistency zone. Validation tests confirm that the Prolog implementation is accurate, internally consistent, deterministic, and capable of autonomously identifying inconsistencies. These findings show that LLM-assisted formalization, anchored in symbolic logic, enables transparent and reliable statutory inconsistency detection.

We consider a structured multi-label prediction problem where the labels are organized under implication and mutual exclusion constraints.

There are other approaches (e.g., [ Here, if all team members play strategies according to an NE minimizing the adversary's utility, the Eq.(1c) ensures that binary variable This space is represented by Eq.(1), which involves nonlinear terms in Eq.(1a) Section 3.4 shows that our techniques can significantly reduce the time The procedure of CRM is shown in Algorithm 2, which is illustrated in Appendix A. A collection N of subsets of players is a binary collection if: 1. { i | i N } N ; Eqs.(1b)-(1g), (3), and (4) is the space of NEs. Example 1 provides an example of N .