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Higher-order data are often compressed into pairwise co-occurrence counts, but this can hide how pairs are assembled into triples. We ask for the largest possible difference in deterministic cascade size between simple 3-uniform hypergraphs with the same labeled exact pair-codegree matrix. Starting from two active vertices, a triple activates its third vertex when its other two are active. We define M₂(n) as the maximum closure-size gap inside any projection fiber on n vertices. A direct proof gives M₂(n)=0 for 2≤n≤5 and M₂(n)=n−3 for n≥6. The upper bound follows because equal codegrees force both cascades either to stop at two or reach at least three vertices. A five-edge Pasch-trade-plus-context construction attains the bound and extends to every larger n. Fresh exhaustive enumeration of all 2²⁰ simple 3-uniform hypergraphs on six labeled vertices independently checks the first ambiguous order, a maximum gap of three, and edge thresholds: four edges for different final sets, five for different sizes, and seven when non-isomorphism is additionally required on six vertices. Two separately implemented censuses agree on 69 shared summary fields. The result is a precise warning about information lost under pairwise compression for one abstract deterministic closure rule; it is not an empirical claim about real epidemics or social networks.
Background: Diabetic peripheral neuropathy (DPN) affects at least half of people with diabetes and is a major risk factor for foot ulceration and amputation. Because nerve damage is least reversible late, a screening method's value depends on whether it can be delivered widely and early, not accuracy. Methods: This narrative review compared four DPN detection methods, nerve conduction studies, clinical sensory tests, plantar pressure analysis, and wearable gait sensing, across cost, setup, time, scalability, and accuracy. Results: Accuracy and scalability traded off. Nerve conduction studies are the accepted reference standard for large-fiber function but too specialist-dependent for population screening, while the cheapest test, the 10-gram monofilament, suits advanced disease better than early disease. Sensor-based methods report high accuracy from small, internally validated samples. Conclusion: No method is simultaneously cheap, fast, accurate, and sensitive to early disease. The unmet need is a scalable test externally validated for early detection.
Background. Off-exchange venues executed a record 51.8% of United States equity share volume in January 2025. A widely repeated interpretation attributes this migration to machine learning embedded in matching and routing infrastructure. This paper tests whether public data can support that attribution, and reports what they support instead.\n\nMethods. Six datasets were compiled from FINRA, SEC, and ESMA publications, from enforcement releases, and from the peer-reviewed and working-paper literature, and are provided in full with a calculation workbook in which every derived statistic is a live formula. A three-tier evidence protocol separates directly measured values from author-derived arithmetic and from interpretive attribution, and ten robustness tests are reported alongside the results they test.\n\nResults. In share terms, non-ATS off-exchange venues account for 86.3% of the 14.6 percentage-point rise in off-exchange share since 2019, a result robust to endpoint and window variation but not to dollar denomination, under which the figure falls to 54.1%. The 15.93 basis-point price-impact differential between retail and institutional execution indicates lower adverse selection in retail flow and is not, as it is often read, an execution penalty borne by retail investors. Sixteen enforcement actions totaling $330.15 million cluster in 2015 to 2018, and none alleges conduct involving a machine-learning system.\n\nConclusion. The public record establishes a compositional shift toward bilateral internalization, a segmented market, and a disclosure regime that has not been updated for model-driven venues. It does not establish that machine learning caused any of these. The governance question stands without the attribution, and a difference-in-differences design using audit-trail microdata is specified that would settle it.
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Research archive records
Colorectal cancer (CRC) is a multifactorial disease in which chronic inflammation, intestinal dysbiosis, and immune dysregulation converge to simultaneously promote tumor progression and immune evasion. These alterations activate inflammatory signaling pathways and generate a tumor microenvironment that is both pro-inflammatory and immunosuppressive, fostering angiogenesis, epithelial–mesenchymal transition (EMT), and resistance to apoptosis. The aim of this study was to analyze the relationship between inflammatory mediators, immune cells, and CRC progression during the 2020–2025 period, identifying potential immunomodulatory therapeutic targets. A systematic and descriptive review was conducted using PubMed, Scopus, and Web of Science, including in vitro, in vivo, and clinical studies focused on cytokines and the tumor microenvironment. The findings showed that sustained activation of the JAK/STAT3, NF-κB, and SMAD pathways, together with disruption of the intestinal barrier, contributes to maintaining a chronically inflammatory microenvironment. Cytokines such as IL-6, TNF-α, IL-10, and TGF-β exhibit a dual role, initially exerting protective functions but later promoting tumor development. Additionally, M2 macrophage polarization, neutrophil accumulation, and the expansion of regulatory T cells were associated with immunosuppression and metastatic potential.
Our project investigates how the physical features of a Kerr black hole influence gravitational-wave ringdown oscillations after a binary black hole merger. Using a computational model based on quasi-normal mode approximations, the model generates inspiral, merger, and ringdown waveforms while allowing the final black hole's mass, dimensionless spin, mode composition, and detector noise level to be adjusted.The simulation also used frequency-domain analysis, including a power spectrum, to identify dominant ringdown frequencies.The results showed that increasing final black hole mass lowered the quasi-normal mode frequency and stretched the waveform over a longer timescale, while increasing spin produced more sustained oscillations with longer damping behavior times. The model also showed that detector noise distorted the waveform but did not fully remove the main ringdown structure. These findings support the hypothesis that Kerr black hole properties leave measurable signatures in gravitational-wave ringdown signals. Although the simulation is simplified and does not replace full numerical relativity or real detector analysis, it shows how computational modeling can connect general relativity, signal processing, and observable gravitational-wave behavior.This project provides a visual way to explore how black hole mass and spin can be inferred from post-merger oscillations.
Health and social care systems operate amid workforce shortages, financial constraints, demographic ageing, and rising demand, with the quality of leadership increasingly recognised as a key influence on patient safety, staff retention, organisational culture, and service performance. This report critically reviews leadership theories commonly applied within the sector, including transformational, transactional, servant, and authentic leadership, alongside major motivational frameworks developed by Maslow, Herzberg, Vroom, and Taylor, and models of team development and leadership proposed by Tuckman, Belbin, and Adair. Drawing on peer reviewed evidence, regulatory and workforce reports, and the author's leadership practice in educational and clinical support roles, the review finds that no single leadership theory is sufficient in isolation. Transformational and authentic leadership are consistently associated with psychological safety, job satisfaction, staff engagement, and patient safety, while transactional approaches remain important for governance, accountability, and regulatory compliance. Evidence on motivation indicates that hygiene factors can prevent dissatisfaction, whereas intrinsic motivators such as recognition, autonomy, meaningful work, and professional growth are more important for sustaining engagement. Workforce turnover is strongly influenced by workload, burnout, and inadequate organisational support. Performance management is most effective when it is developmental rather than punitive, while effective teams depend on shared goals, clear roles, open communication, trust, and adaptive management. Overall, sustainable performance in health and social care requires a blended, compassionate, inclusive, and accountable approach to leadership that balances organisational governance with workforce wellbeing and is supported by continuous improvement, benchmarking, and ongoing leadership development.
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