Using a constraint satisfaction formulation with rotational symmetry reduction, we exhibit configurations of 2n points on the n×n grid for every 2≤n≤60 with no three collinear. These computations resolved every previously open case through n=60. We describe the formulation, computational search, and empirical scaling of the method.
Mycobacterium tuberculosis remains the leading cause of death from a single infectious pathogen globally despite decades of effective chemotherapy. In 2024, an estimated 10·7 million people developed tuberculosis, including approximately 620 000 people living with HIV (PLHIV), and tuberculosis caused an estimated 1·23 million deaths overall, including approximately 150 000 deaths among PLHIV. Men accounted for more than half of the cases, and children represented a substantial burden, reflecting ongoing transmission and diagnostic gaps. Approximately a quarter of the world's population has been infected with M tuberculosis, with immunological evidence of previous or current infection. This population includes groups at increased risk of progression to tuberculosis disease, particularly those with recent infection, HIV, undernutrition, young age, or other clinical and social vulnerabilities. Following 3 years of COVID-19-related setbacks, global tuberculosis incidence declined modestly (1%) from 2023 to 2024 but remains higher than in 2020 and far off-track to meet the 2025 WHO End TB Strategy milestones. Case detection improved to 8·3 million notifications (78% of estimated incident cases), supported by expanded molecular diagnostics; however, prevalence surveys continue to reveal substantial proportions of bacteriologically confirmed but asymptomatic tuberculosis, highlighting persistent transmission and missed diagnoses. 30 high-burden countries accounted for 87% of cases, led by India, Indonesia, the Philippines, China, Pakistan, Nigeria, the Democratic Republic of the Congo, and Bangladesh. M tuberculosis-HIV co-infection remains a major driver of mortality in sub-Saharan Africa. Drug-resistant tuberculosis threatens progress: of 390 000 estimated multidrug-resistant or rifampicin-resistant tuberculosis cases in 2024, only 42% initiated treatment, although treatment success improved to 71%. Tuberculosis-preventive treatment reached 5·3 million people, including 58% of PLHIV and 25% of eligible household contacts, well below global targets. Persistent undernutrition, poverty, HIV, diabetes, smoking, alcohol use, air pollution, migration, and conflict continue to shape tuberculosis epidemiology. With financing at only 27% of global targets, accelerated prevention, proactive case finding, social protection, and sustained political commitment are essential to eliminate tuberculosis.
Tuberculosis treatment has undergone its most profound transformation since the launch of the standardised DOTS strategy in 1994. Since 2020, a series of pivotal randomised trials, including TB-PRACTECAL, ZeNix, Nix-TB, endTB, BEAT-TB, SHINE, and Study 31/A5349, have redefined the management of both drug-susceptible and drug-resistant tuberculosis. These studies have enabled shorter, fully oral regimens with improved efficacy and safety across adult and paediatric populations, including people with HIV, and have driven major updates to WHO treatment guidelines. Despite these advances, tuberculosis remains the leading cause of death from a single infectious agent worldwide, with substantial mortality occurring before treatment initiation due to delayed diagnosis and pretreatment loss to follow-up, and additional deaths during treatment related to advanced disease, drug resistance, comorbidities, and challenges with treatment tolerance and adherence. In 2024, an estimated 10·7 million people developed tuberculosis of whom approximately 390 000 developed multidrug-resistant (MDR) or rifampicin-resistant (RR) tuberculosis. Tuberculosis caused an estimated 1·23 million deaths globally, including approximately 150 000 deaths attributable to MDR tuberculosis or RR tuberculosis. Outcomes remain poorest among people with HIV, young children (who rarely access treatment and prevention), migrants, and displaced populations. The tuberculosis drug development pipeline in 2026 is more advanced than at any time since the introduction of rifampicin. Novel and repurposed compounds, including DprE1 inhibitors, next-generation oxazolidinones (including TBAJ-587 and TBAJ-876), cytochrome bc1 inhibitors, and long-acting formulations, are in late-stage evaluation. Host-directed therapies are also advancing as adjunctive strategies to reduce inflammation-mediated tissue damage and long-term morbidity, although they remain investigational. This Series paper synthesises advances in adult and paediatric tuberculosis therapeutics from Nov 15, 2020, to Jan 15, 2026, and highlights priorities to translate therapeutic innovation into equitable population-level effects.
Background Advanced monitoring instruments can provide detailed assessment of work of breathing in patients with acute hypoxaemic respiratory failure (AHRF) managed with non-invasive respiratory support (NRS). Despite increasing availability, uptake in routine clinical practice remains limited. Beyond technical performance, implementation depends on acceptability to both patients and healthcare practitioners. This study explored perceptions of acceptability to inform sustainable clinical implementation. Methods We conducted a multicentre qualitative study across two hospitals. Semi-structured interviews were undertaken with former adult patients who experienced AHRF requiring non-invasive respiratory support (n = 10) and multidisciplinary critical care practitioners (n = 20). Data were analysed using reflexive thematic analysis and mapped to the Theoretical Framework of Acceptability. Results Patients described AHRF and non-invasive respiratory support as distressing experiences characterised by fear, sensory overload, loss of agency, and physical discomfort. Acceptability of advanced monitoring was highly conditional: non-invasive, non-restrictive instruments were favoured, particularly when visual feedback enhanced understanding and reassurance. Invasive or cumbersome monitoring was rejected due to added distress and perceived ethical burden, although some patients retrospectively tolerated discomfort reflecting on survival benefit. Practitioners described AHRF assessment and delivery of non-invasive respiratory support as cognitively demanding and complex, shaped by uncertainty, workload, time pressure, and limited standardised guidance. Monitoring was acceptable when intuitive, easy to interpret, feasible within workflow, and informed clinical decision-making. Visual, real-time, low-burden, non-invasive modalities were viewed favourably, whereas invasive or technically complex tools raised concerns regarding patient distress, training requirements, and feasibility. Conclusion Acceptability of advanced respiratory monitoring during non-invasive respiratory support is shaped by lived experience of illness, treatment burden, and clinical uncertainty. Instruments that are non-invasive, visually interpretable, and clinically meaningful are most acceptable to patients and practitioners. Implications for clinical practice Advanced respiratory monitoring appears most acceptable when non-invasive, visually interpretable, and feasible within routine workflows. Monitoring providing clear, real-time information without adding patient burden can enhance patient engagement and support clinical assessment, multidisciplinary communication, and decision-making. Implementation should prioritise structured training, and integration within standardised care pathways to maximise clinical value without increasing workload.
Personalized public transit routing in public transit systems remains challenging due to the difficulty of capturing and integrating diverse user preferences into routing algorithms. This paper presents ChatPlanner, a novel framework that leverages Large Language Models (LLMs) to enable preference-aware public transit routing. Our approach employs fine-tuned LLMs with Retrieval-Augmented Generation (RAG) to extract routing parameters and interpret conversationally expressed preferences from natural language queries as preference scores, subsequently integrating these preferences into the objective function of a public transit routing algorithm. This study designs preference-aware datasets incorporating eight personas and five contexts to establish scoring standards for both fine-tuning and RAG. This work conducted four experiments to validate the solutions’ feasibility, extraction of routing information and preferences, solution set quality and completeness, and latency and computational tractability. Results demonstrate that ChatPlanner generates feasible solutions reliably. Fine-tuning enforces the required output structure and learns general preference patterns, while RAG provides query-specific context to resolve imprecise or conversational expressions and calibrate continuous scores. The combination of both achieves the highest accuracy in routing information extraction and rubric-consistent user preference interpretation. Results based on selected case studies show that by capturing user conversationally expressed preferences, ChatPlanner identifies preference-relevant solutions across different dimensions that existing route planners overlook, generating more route alternatives. The latency evaluation confirms that the framework is computationally tractable. This research establishes a new paradigm for integrating natural language understanding into transportation optimization.
