悉尼大学

We prove that for any knot K, there exists a decomposition of the 3-sphere into tetrahedra such that a representative of K is formed from one vertex and one edge of the decomposition. The proof is constructive, and based on fully augmented links. We use our method to produce a family of simplicial triangulations of the 3-sphere with a loop of four edges representing a t-fold connected sum of the trefoil, whose number of tetrahedra grows linearly in t. This is best possible up to a constant factor.

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.

Meeting points (MPs) consolidate passenger pick-up and drop-off (PUDO) in ridepooling at pre-designated locations, improving fleet efficiency while shifting part of the access and egress burden to passenger walking. This raises a question: who selects each trip’s PUDO MPs? In the operator-centric regime, the platform dynamically selects both MPs using vehicle schedules and fleet state to minimize a candidate vehicle’s remaining-schedule completion time. In the user-centric regime, each passenger selects an MP pair that minimizes weighted walking and estimated travel time, thereby controlling where they walk. These differing objectives and information create a trade-off between routing and service availability and the burden on served passengers. Although prior work establishes the operational benefits of MPs, it has not systematically quantified disagreement between operator- and user-preferred selections, its spatial distribution, or its cost consequences. We address this gap by formalizing party-specific cost functions and pick-up and drop-off disagreement, quantifying system-level trade-offs, and measuring cost discrepancies through counterfactual analysis that holds the realized vehicle schedule fixed while substituting one party’s preferred MPs with the other’s.We evaluate the framework across three structurally distinct cities under three MP placement strategies: grid-based, greedy coverage, and multi-objective optimization. Operator-centric selection improves service coverage, whereas user-centric selection reduces average walking distance per PUDO leg by roughly a factor of three. A decomposition of MP selection and the matching objective shows that who selects the MPs, rather than whose cost drives matching, primarily determines this trade-off. Across cities and placements, drop-off disagreement exceeds pick-up disagreement, disagreement is spatially associated with larger cost discrepancies, and replacing user-preferred MPs imposes a substantially larger relative burden on users than the converse imposes on operators. Low-willingness-to-walk passengers bear the largest user-side discrepancy. These findings establish a pervasive, spatially structured, and asymmetric conflict that supports zone-level regulatory screening and targeted service design.

The fast uptake of distributed energy resources (DERs) presents increasing challenges for managing hosting capacity in distribution networks. Existing solutions include direct load control, operating envelopes, and price-based control through dynamic energy prices. Despite their effectiveness, these methods often rely on assumed prosumer behavioural patterns and overlook prosumers' desire to retain control over their devices. Additionally, current fixed or Time-of-Use (ToU) prices are based on spatial and temporal averages, having limited impact on network conditions and DER operation. To address these limitations, this paper proposes a bilevel optimisation framework that explicitly models prosumer decision-making in the design of dynamic network prices. The upper level represents the distribution system operator (DSO), setting network prices under cost-recovery and network constraints, while the lower level models prosumers optimising DER operation in response. The proposed framework preserves customer prerogative, enhances DER flexibility, and offers actionable insights for network hosting capacity management and the evolution of network tariff structures under high DER penetration.

We study switching among multiple square selections of output functions (melds) drawn from a deck of candidate outputs for nonlinear systems that are static feedback linearizable via outputs. Fixing an operating point, each meld induces a distinct feedback-linearizing coordinate chart defined on a common neighborhood. Switching between melds therefore produces state-dependent coordinate mismatches that are not represented explicitly in standard fixed-coordinate dwell-time formulations. We quantify this effect through Lipschitz bounds on the cross-chart maps over a compact safe set and introduce a reference-compatibility constant that measures mismatch among reference families across melds. We derive an explicit dwell-time condition depending on the controller decay rates, the reference-compatibility constant, and a bound on the desired-jet resets. The resulting condition guarantees exponential decay of the active-output tracking errors between switches, conditional seamless tracking of shared outputs whose desired jets do not reset, and uniform boundedness of the state error within the safe set. Safe-set invariance follows under an explicit margin condition. A planar 3R manipulator illustrates the results.