Monge
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Cone-Compatible Monge Geometry for High-Dimensional Ordered Optimal Transport
Announce Type: new Abstract: High-dimensional optimal transport is seldom available in closed form. The one-dimensional case is exceptional because the order of the real line is compatible with convex transport costs, making monotone rearrangement optimal. This paper studies when an analogous Monge structure can be recovered in higher dimensions from a partial order.
The Semigeostrophic--Euler Limit via Perturbative Monge--Amp\`ere Estimates
arXiv:2601.04797v3 Announce Type: replace-cross Abstract: We study the two-dimensional semigeostrophic system on the flat torus in the small-amplitude regime. We formulate the rescaled dynamics as the Lie--Poisson flow of a renormalized optimal-transport energy and expand this Hamiltonian in \(C^1\). The leading term is the Euler Hamiltonian, while the first correction is an explicit cubic Monge--Amp\`ere functional.
Hong Kong man arrested for allegedly groping schoolgirl on bus
Hong Kong police have arrested a 65-year-old man in connection with a suspected indecent assault case in Mong Kok hours after footage appeared online showing a passenger harassing a schoolgirl sitting in front of him on a bus. Police said officers intercepted the suspect at the boundary checkpoint of the Hong Kong-Zhuhai-Macau Bridge. The victim, 17, is understood to be a Form Three student.
Mpox in Hong Kong: what to know about the virus and sauna-linked outbreak
Mpox in Hong Kong: what to know about the virus and sauna-linked outbreak The SCMP sheds light on the situation in the city and globally, including how to prevent infection Hong Kong has recorded a surge in Mpox cases linked to a gay-friendly sauna and fitness club in Mong Kok, prompting health authorities to launch a targeted vaccination outreach programme for high-risk groups. The Centre for Health Protection has contacted more than 300 people who visited the venue since May for medical...
5 Mpox cases linked to Hong Kong ‘premier’ gay sauna, contact tracing under way
5 Mpox cases linked to Hong Kong ‘premier’ gay sauna, contact tracing under way Health officials say all five patients engaged in ‘high-risk activities’ at Hutong sauna on Shanghai Street, including two cases previously reported by mainland authorities Hong Kong health authorities have identified at least five Mpox cases linked to a club offering “premier” gay sauna services in Mong Kok, with the venue temporarily closed amid ongoing epidemiological investigations. The Centre for Health...
Taxi driver, 69, arrested after woman killed in Tsim Sha Tsui collision
Hong Kong police have arrested a 69-year-old taxi driver after he allegedly knocked down and killed a 34-year-old woman in a shopping district in the early hours of Saturday. The incident happened at around 2.12am near Park Lane Shopper’s Boulevard in Tsim Sha Tsui. The taxi driver was travelling along Nathan Road towards Mong Kok when he struck the 34-year-old woman as she was crossing Granville Road.
Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds
Announce Type: cross Abstract: Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps. In Euclidean space, barycentric projection converts a coupling into a map by taking conditional expectations, but on a Riemannian manifold curvature and cut loci make this operation nontrivial. We develop a framework for barycentric projections of transport couplings on Riemannian manifolds.
Hessian-recovery-based C0 finite element methods for non-divergence form elliptic equations
arXiv:2606.03276v1 Announce Type: new Abstract: A Hessian-recovery-based C0 finite element framework is proposed for second-order elliptic equations in non-divergence form. The construction is based on a direct approximation of the strong non-divergence operator: the Hessian D2u is replaced by a recovered Hessian Hhuh, so that A : D2u is approximated by A : Hhuh. The resulting discretizations include a nodal formulation and a Galerkin-type formulation for general Lagrange finite element...