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1. A Mach-Zehnder Fabry-Perot hybrid fiber-optic interferometer operating at the thermal noise limit

   https://doi.org/10.1038/s41598-022-16474-y  

   Hoque, Nabil Md Rakinul ; Duan, Lingze ( July 2022 , Scientific Reports)

   A new type of interferometric fiber sensor based on a Mach-Zehnder Fabry-Perot hybrid scheme has been experimentally demonstrated. The interferometer combines the benefits of both a double-path configuration and an optical resonator, leading to record-high strain and phase resolutions limited only by the intrinsic thermal noise in optical fibers across a broad frequency range. Using only off-the-shelf components, the sensor is able to achieve noise-limited strain resolutions of 40 f$$\varepsilon $$$\epsilon$/$$\sqrt{(}Hz)$$$\sqrt{(}Hz)$at 10 Hz and 1 f$$\varepsilon $$$\epsilon$/$$\sqrt{(}Hz)$$$\sqrt{(}Hz)$at 100 kHz. With a proper scale-up, atto-strain resolutions are believed to be within reach in the ultrasonic frequency range with such interferometers.

    

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2. Search for dark matter produced in association with a single top quark and an energetic W boson in $$\sqrt{s}=$$ 13 TeV $$pp$$ collisions with the ATLAS detector

   https://doi.org/10.1140/epjc/s10052-023-11582-z  

   Aad, G. ; Abbott, B. ; Abbott, D. C. ; Abeling, K. ; Abidi, S. H. ; Aboulhorma, A. ; Abramowicz, H. ; Abreu, H. ; Abulaiti, Y. ; Hoffman, A. C. ; et al ( July 2023 , The European Physical Journal C)

   This paper presents a search for dark matter,$$\chi $$$\chi$, using events with a single top quark and an energeticWboson. The analysis is based on proton–proton collision data collected with the ATLAS experiment at$$\sqrt{s}=$$$\sqrt{s}=$13 TeV during LHC Run 2 (2015–2018), corresponding to an integrated luminosity of 139 fb$$^{-1}$$${}^{-1}$. The search considers final states with zero or one charged lepton (electron or muon), at least oneb-jet and large missing transverse momentum. In addition, a result from a previous search considering two-charged-lepton final states is included in the interpretation of the results. The data are found to be in good agreement with the Standard Model predictions and the results are interpreted in terms of 95% confidence-level exclusion limits in the context of a class of dark matter models involving an extended two-Higgs-doublet sector together with a pseudoscalar mediator particle. The search is particularly sensitive to on-shell production of the charged Higgs boson state,$$H^{\pm }$$$H^{\pm }$, arising from the two-Higgs-doublet mixing, and its semi-invisible decays via the mediator particle,a:$$H^{\pm } \rightarrow W^\pm a (\rightarrow \chi \chi )$$$H^{\pm }\to W^{\pm }a(\to \chi \chi )$. Signal models with$$H^{\pm }$$$H^{\pm }$masses up to 1.5 TeV andamasses up to 350 GeV are excluded assuming a$$\tan \beta $$$tan\beta$value of 1. For masses ofaof 150 (250) GeV,$$\tan \beta $$$tan\beta$values up to 2 are excluded for$$H^{\pm }$$$H^{\pm }$masses between 200 (400) GeV and 1.5 TeV. Signals with$$\tan \beta $$$tan\beta$values between 20 and 30 are excluded for$$H^{\pm }$$$H^{\pm }$masses between 500 and 800 GeV.

    

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3. Searching for dark photon dark matter in LIGO O1 data

   https://doi.org/10.1038/s42005-019-0255-0  

   Guo, Huai-Ke ; Riles, Keith ; Yang, Feng-Wei ; Zhao, Yue ( December 2019 , Communications Physics)

   Dark matter exists in our Universe, but its nature remains mysterious. The remarkable sensitivity of the Laser Interferometer Gravitational-Wave Observatory (LIGO) may be able to solve this mystery. A good dark matter candidate is the ultralight dark photon. Because of its interaction with ordinary matter, it induces displacements on LIGO mirrors that can lead to an observable signal. In a study that bridges gravitational wave science and particle physics, we perform a direct dark matter search using data from LIGO’s first (O1) data run, as opposed to an indirect search for dark matter via its production of gravitational waves. We demonstrate an achieved sensitivity on squared coupling as$$\sim\! 4\times 1{0}^{-45}$$$~4\times 10^{-45}$, in a$$U{(1)}_{{\rm{B}}}$$$U{\left(1\right)}_B$dark photon dark matter mass band around$${m}_{{\rm{A}}} \sim 4\,\times 1{0}^{-13}$$$m_A~4\times 10^{-13}$eV. Substantially improved search sensitivity is expected during the coming years of continued data taking by LIGO and other gravitational wave detectors in a growing global network.

    

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4. On a Traveling Salesman Problem for Points in the Unit Cube

   https://doi.org/10.1007/s00453-024-01257-w  

   Balogh, József ; Clemen, Felix Christian ; Dumitrescu, Adrian ( September 2024 , Algorithmica)

   LetXbe ann-element point set in thek-dimensional unit cube$$[0,1]^k$$${[0,1]}^k$where$$k \ge 2$$$k\ge 2$. According to an old result of Bollobás and Meir (Oper Res Lett 11:19–21, 1992) , there exists a cycle (tour)$$x_1, x_2, \ldots , x_n$$$x_1,x_2,\dots ,x_n$through thenpoints, such that$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} \le c_k$$${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^k\right)}^{1/k}\le c_k$, where$$|x-y|$$$|x-y|$is the Euclidean distance betweenxandy, and$$c_k$$$c_k$is an absolute constant that depends only onk, where$$x_{n+1} \equiv x_1$$$x_{n+1}\equiv x_1$. From the other direction, for every$$k \ge 2$$$k\ge 2$and$$n \ge 2$$$n\ge 2$, there existnpoints in$$[0,1]^k$$${[0,1]}^k$, such that their shortest tour satisfies$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} = 2^{1/k} \cdot \sqrt{k}$$${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^k\right)}^{1/k}=2^{1/k}·\sqrt{k}$. For the plane, the best constant is$$c_2=2$$$c_2=2$and this is the only exact value known. Bollobás and Meir showed that one can take$$c_k = 9 \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$$c_k=9{\left(\frac{2}{3}\right)}^{1/k}·\sqrt{k}$for every$$k \ge 3$$$k\ge 3$and conjectured that the best constant is$$c_k = 2^{1/k} \cdot \sqrt{k}$$$c_k=2^{1/k}·\sqrt{k}$, for every$$k \ge 2$$$k\ge 2$. Here we significantly improve the upper bound and show that one can take$$c_k = 3 \sqrt{5} \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$$c_k=3\sqrt{5}{\left(\frac{2}{3}\right)}^{1/k}·\sqrt{k}$or$$c_k = 2.91 \sqrt{k} \ (1+o_k(1))$$$c_k=2.91\sqrt{k}(1+o_k\left(1\right))$. Our bounds are constructive. We also show that$$c_3 \ge 2^{7/6}$$$c_3\ge 2^{7/6}$, which disproves the conjecture for$$k=3$$$k=3$. Connections to matching problems, power assignment problems, related problems, including algorithms, are discussed in this context. A slightly revised version of the Bollobás–Meir conjecture is proposed.

    

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5. Abelian varieties of prescribed order over finite fields

   https://doi.org/10.1007/s00208-024-03084-4  

   van_Bommel, Raymond ; Costa, Edgar ; Li, Wanlin ; Poonen, Bjorn ; Smith, Alexander ( March 2025 , Mathematische Annalen)

   Given a prime powerqand$$n \gg 1$$$n\gg 1$, we prove that every integer in a large subinterval of the Hasse–Weil interval$$[(\sqrt{q}-1)^{2n},(\sqrt{q}+1)^{2n}]$$$[{(\sqrt{q}-1)}^{2n},{(\sqrt{q}+1)}^{2n}]$is$$\#A({\mathbb {F}}_q)$$$\#A\left(F_q\right)$for some ordinary geometrically simple principally polarized abelian varietyAof dimensionnover$${\mathbb {F}}_q$$$F_q$. As a consequence, we generalize a result of Howe and Kedlaya for$${\mathbb {F}}_2$$$F_2$to show that for each prime powerq, every sufficiently large positive integer is realizable, i.e.,$$\#A({\mathbb {F}}_q)$$$\#A\left(F_q\right)$for some abelian varietyAover$${\mathbb {F}}_q$$$F_q$. Our result also improves upon the best known constructions of sequences of simple abelian varieties with point counts towards the extremes of the Hasse–Weil interval. A separate argument determines, for fixedn, the largest subinterval of the Hasse–Weil interval consisting of realizable integers, asymptotically as$$q \rightarrow \infty $$$q\to \infty$; this gives an asymptotically optimal improvement of a 1998 theorem of DiPippo and Howe. Our methods are effective: We prove that if$$q \le 5$$$q\le 5$, then every positive integer is realizable, and for arbitraryq, every positive integer$$\ge q^{3 \sqrt{q} \log q}$$$\ge q^{3\sqrt{q}logq}$is realizable.

    

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