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🪙 Polymer-protected DNA sensors enable two-month storage for 50-cent disease diagnostics
#dna…

Polymer-protected DNA sensors enable two-month storage for 50-cent disease diagnostics
Using an inexpensive electrode coated with DNA, MIT researchers have designed disposable diagnostics that could be adapted to detect a variety of diseases, including cancer or infectious diseases such as influenza and HIV.

Maximal optical chirality via mode coupling in bilayer metasurfaces
Brijesh Kumar, Ivan Toftul, Anshuman Kumar, Maxim Gorkunov, Yuri Kivshar
https://arxiv.org/abs/2507.17428 htt…

Maximal optical chirality via mode coupling in bilayer metasurfaces
Recent advances in the physics of resonant optical metasurfaces allowed to realize the so-called {\it maximum chirality} of planar structures by engineering their geometric parameters. Here we employ bilayer membrane metasurfaces with a square lattice of rotated C$_4$-symmetric holes and uncover very different scenarios of chirality maximization by virtue of strong coupling of photonic eigenmodes of the membranes supplemented by smart engineering of dissipation losses. Our findings substantiall…

A Discrete Analog of Tutte's Barycentric Embeddings on Surfaces
\'Eric Colin de Verdi\`ere, Vincent Despr\'e, Lo\"ic Dubois
https://arxiv.org/abs/2507.13096

A Discrete Analog of Tutte's Barycentric Embeddings on Surfaces
Tutte's celebrated barycentric embedding theorem describes a natural way to build straight-line embeddings (crossing-free drawings) of a (3-connected) planar graph: map the vertices of the outer face to the vertices of a convex polygon, and ensure that each remaining vertex is in convex position, namely, a barycenter with positive coefficients of its neighbors. Actually computing an embedding then boils down to solving a system of linear equations. A particularly appealing feature of this metho…

Existence and Nonexistence of Extremals for Trudinger-Moser inequalities with $L^p$ type perturbation on any bounded planar domains
Lu Chen, Rou Jiang, Guozhen Lu, Maochun Zhu
https://arxiv.org/abs/2506.23076

Existence and Nonexistence of Extremals for Trudinger-Moser inequalities with $L^p$ type perturbation on any bounded planar domains
In this study, we investigate the perturbed Trudinger-Moser inequalities as follows:\[ S_Ω(λ,p)=\sup_{u\in H_{0}^{1}(Ω),\Vert\nabla u\Vert _{L^{2}\left( Ω\right) }\leq 1}\int_Ω\left( e^{4πu^{2}}-λ|u|^{p}\right) dx, \] where $1\leq p<\infty$ and $Ω$ is a bounded domain in $\mathbb{R}^2$. Our results demonstrate that there exists a threshold $λ^{\ast}(p)>0$ such that $S_Ω(λ,p)$ is attainable if $λ<λ^{\ast}(p)$, but unattainable if $λ>λ^{\ast}(p)$ when $p\in[1,2]$. For $p>…