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1. High pressure raman spectroscopy and X-ray diffraction of K2Ca(CO3)2 bütschliite: multiple pressure-induced phase transitions in a double carbonate

   https://doi.org/10.1007/s00269-023-01262-5  

   Zeff, G. ; Kalkan, B. ; Armstrong, K. ; Kunz, M. ; Williams, Q. ( January 2024 , Physics and Chemistry of Minerals)

   The crystal structure and bonding environment of K₂Ca(CO₃)₂bütschliite were probed under isothermal compression via Raman spectroscopy to 95 GPa and single crystal and powder X-ray diffraction to 12 and 68 GPa, respectively. A second order Birch-Murnaghan equation of state fit to the X-ray data yields a bulk modulus,$${K}_{0}=46.9$$$K_0=46.9$GPa with an imposed value of$${K}_{0}^{\prime}= 4$$$K_0^{\prime }=4$for the ambient pressure phase. Compression of bütschliite is highly anisotropic, with contraction along thec-axis accounting for most of the volume change. Bütschliite undergoes a phase transition to a monoclinicC2/mstructure at around 6 GPa, mirroring polymorphism within isostructural borates. A fit to the compression data of the monoclinic phase yields$${V}_{0}=322.2$$$V_0=322.2$ Å³$$,$$$,$$${K}_{0}=24.8$$$K_0=24.8$GPa and$${K}_{0}^{\prime}=4.0$$$K_0^{\prime }=4.0$using a third order fit; the ability to access different compression mechanisms gives rise to a more compressible material than the low-pressure phase. In particular, compression of theC2/mphase involves interlayer displacement and twisting of the [CO₃] units, and an increase in coordination number of the K⁺ion. Three more phase transitions, at ~ 28, 34, and 37 GPa occur based on the Raman spectra and powder diffraction data: these give rise to new [CO₃] bonding environments within the structure.

    

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2. Evidence for AGN-regulated Cooling in Clusters at z ∼ 1.4: A Multiwavelength View of SPT-CL J0607-4448

   https://doi.org/10.3847/1538-4357/acae9e  

   Masterson, Megan ; McDonald, Michael ; Ansarinejad, Behzad ; Bayliss, Matthew ; Benson, Bradford A. ; Bleem, Lindsey E. ; Calzadilla, Michael S. ; Edge, Alastair C. ; Floyd, Benjamin ; Kim, Keunho J. ; et al ( February 2023 , The Astrophysical Journal)

   We present a multiwavelength analysis of the galaxy cluster SPT-CL J0607-4448 (SPT0607), which is one of the most distant clusters discovered by the South Pole Telescope atz= 1.4010 ± 0.0028. The high-redshift cluster shows clear signs of being relaxed with well-regulated feedback from the active galactic nucleus (AGN) in the brightest cluster galaxy (BCG). Using Chandra X-ray data, we construct thermodynamic profiles and determine the properties of the intracluster medium. The cool-core nature of the cluster is supported by a centrally peaked density profile and low central entropy ($K_0={18}_{-9}^{+11}$keV cm²), which we estimate assuming an isothermal temperature profile due to the limited spectral information given the distance to the cluster. Using the density profile and gas cooling time inferred from the X-ray data, we find a mass-cooling rate${\dot{M}}_{\mathrm{cool}}={100}_{-60}^{+90}{M}_{\odot }$yr⁻¹. From optical spectroscopy and photometry around the [Oii] emission line, we estimate that the BCG star formation rate is${\mathrm{SFR}}_{[\mathrm{O}\mathrm{II}]}={1.7}_{-0.6}^{+1.0}{M}_{\odot }$yr⁻¹, roughly two orders of magnitude lower than the predicted mass-cooling rate. In addition, using ATCA radio data at 2.1 GHz, we measure a radio jet power$P_{\mathrm{cav}}={3.2}_{-1.3}^{+2.1}\times {10}^{44}$erg s⁻¹, which is consistent with the X-ray cooling luminosity ($L_{\mathrm{cool}}={1.9}_{-0.5}^{+0.2}\times {10}^{44}$erg s⁻¹withinr_cool= 43 kpc). These findings suggest that SPT0607 is a relaxed, cool-core cluster with AGN-regulated cooling at an epoch shortly after cluster formation, implying that the balance between cooling and feedback can be reached quickly. We discuss the implications for these findings on the evolution of AGN feedback in galaxy clusters.

    

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3. Rates of convergence for regression with the graph poly-Laplacian

   https://doi.org/10.1007/s43670-023-00075-5  

   Trillos, Nicolás García ; Murray, Ryan ; Thorpe, Matthew ( November 2023 , Sampling Theory, Signal Processing, and Data Analysis)

   In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularization. Higher order regularity can be obtained via replacing the Laplacian regulariser with a poly-Laplacian regulariser. The methodology is readily adapted to graphs and here we consider graph poly-Laplacian regularization in a fully supervised, non-parametric, noise corrupted, regression problem. In particular, given a dataset$$\{x_i\}_{i=1}^n$$${\left\{x_i\right\}}_{i=1}^n$and a set of noisy labels$$\{y_i\}_{i=1}^n\subset \mathbb {R}$$${\left\{y_i\right\}}_{i=1}^n\subset R$we let$$u_n{:}\{x_i\}_{i=1}^n\rightarrow \mathbb {R}$$$u_n:{\left\{x_i\right\}}_{i=1}^n\to R$be the minimizer of an energy which consists of a data fidelity term and an appropriately scaled graph poly-Laplacian term. When$$y_i = g(x_i)+\xi _i$$$y_i=g\left(x_i\right)+{\xi }_i$, for iid noise$$\xi _i$$${\xi }_i$, and using the geometric random graph, we identify (with high probability) the rate of convergence of$$u_n$$$u_n$togin the large data limit$$n\rightarrow \infty $$$n\to \infty$. Furthermore, our rate is close to the known rate of convergence in the usual smoothing spline model.

    

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4. Atmospheric Metallicity and C/O of HD 189733 b from High-resolution Spectroscopy

   https://doi.org/10.3847/1538-3881/ad1180  

   Finnerty, Luke ; Xuan, Jerry W. ; Xin, Yinzi ; Liberman, Joshua ; Schofield, Tobias ; Fitzgerald, Michael P. ; Agrawal, Shubh ; Baker, Ashley ; Bartos, Randall ; Blake, Geoffrey A. ; et al ( January 2024 , The Astronomical Journal)

   We present high-resolutionK-band emission spectra of the quintessential hot Jupiter HD 189733 b from the Keck Planet Imager and Characterizer. Using a Bayesian retrieval framework, we fit the dayside pressure–temperature profile, orbital kinematics, mass-mixing ratios of H₂O, CO, CH₄, NH₃, HCN, and H₂S, and the¹³CO/¹²CO ratio. We measure mass fractions of${\mathrm{logH}}_2\mathrm{O}=-{2.0}_{-0.4}^{+0.4}$and$\mathrm{logCO}=-{2.2}_{-0.5}^{+0.5}$, and place upper limits on the remaining species. Notably, we find logCH₄< −4.5 at 99% confidence, despite its anticipated presence at the equilibrium temperature of HD 189733 b assuming local thermal equilibrium. We make a tentative (∼3σ) detection of¹³CO, and the retrieved posteriors suggest a¹²C/¹³C ratio similar to or substantially less than the local interstellar value. The possible¹³C enrichment would be consistent with accretion of fractionated material in ices or in the protoplanetary disk midplane. The retrieved abundances correspond to a substantially substellar atmospheric C/O = 0.3 ± 0.1, while the carbon and oxygen abundances are stellar to slightly superstellar, consistent with core-accretion models which predict an inverse correlation between C/O and metallicity. The specific combination of low C/O and high metallicity suggests significant accretion of solid material may have occurred late in the formation process of HD 189733 b.

    

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5. Finding solutions with distinct variables to systems of linear equations over $$\mathbb {F}_p$$

   https://doi.org/10.1007/s00208-022-02391-y  

   Sauermann, Lisa ( April 2022 , Mathematische Annalen)

   Let us fix a primepand a homogeneous system ofmlinear equations$$a_{j,1}x_1+\dots +a_{j,k}x_k=0$$$a_{j,1}{x}_1+\cdots +a_{j,k}{x}_k=0$for$$j=1,\dots ,m$$$j=1,\cdots ,m$with coefficients$$a_{j,i}\in \mathbb {F}_p$$$a_{j,i}\in F_p$. Suppose that$$k\ge 3m$$$k\ge 3m$, that$$a_{j,1}+\dots +a_{j,k}=0$$$a_{j,1}+\cdots +a_{j,k}=0$for$$j=1,\dots ,m$$$j=1,\cdots ,m$and that every$$m\times m$$$m\times m$minor of the$$m\times k$$$m\times k$matrix$$(a_{j,i})_{j,i}$$${\left(a_{j,i}\right)}_{j,i}$is non-singular. Then we prove that for any (large)n, any subset$$A\subseteq \mathbb {F}_p^n$$$A\subseteq F_p^n$of size$$|A|> C\cdot \Gamma ^n$$$\left|A\right|>C·{\Gamma }^n$contains a solution$$(x_1,\dots ,x_k)\in A^k$$$(x_1,\cdots ,x_k)\in A^k$to the given system of equations such that the vectors$$x_1,\dots ,x_k\in A$$$x_1,\cdots ,x_k\in A$are all distinct. Here,Cand$$\Gamma $$$\Gamma$are constants only depending onp,mandksuch that$$\Gamma $\Gamma <p$. The crucial point here is the condition for the vectors$$x_1,\dots ,x_k$$$x_1,\cdots ,x_k$in the solution$$(x_1,\dots ,x_k)\in A^k$$$(x_1,\cdots ,x_k)\in A^k$to be distinct. If we relax this condition and only demand that$$x_1,\dots ,x_k$$$x_1,\cdots ,x_k$are not all equal, then the statement would follow easily from Tao’s slice rank polynomial method. However, handling the distinctness condition is much harder, and requires a new approach. While all previous combinatorial applications of the slice rank polynomial method have relied on the slice rank of diagonal tensors, we use a slice rank argument for a non-diagonal tensor in combination with combinatorial and probabilistic arguments.

    

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