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The tuning of magnetic phase, chemical potential, and structure is crucial to observe diverse exotic topological quantum states in $MnBi_2Te_4(Bi_2Te_3)_m$ (m = 0, 1, 2, & 3). Here we show a ferromagnetic (FM) phase with a chiral crystal structure in $Mn(Bi_{1-x}Sb_x)_4Te_7$, obtained via tuning the growth conditions and Sb concentration. Unlike previously reported $Mn(Bi_{1-x}Sb_x)_4Te_7$, which exhibits FM transitions only at high Sb doping levels, our samples show FM transitions ($T_C$ = 13.5 K) at 15%-27% doping levels. Furthermore, our single crystal x-ray diffraction structure refinements find Sb doping leads to a chiral structure with the space group of P3, contrasted with the centrosymmetric P-3m1 crystal structure of the parent compound $MnBi_4Te_7$. Through ARPES measurements, we also demonstrated that the non-trivial band topology is preserved in the Sb-doped FM samples. Given that the non-trivial band topology of this system remains robust for low Sb doping levels, our success in making FM $Mn(Bi_{1-x}Sb_x)_4Te_7$ with $x$ = 0.15, 0.175, 0.2 & 0.27 paves the way for realizing the predicted topological quantum states such as axion insulator and Weyl semimetals. Additionally, we also observed magnetic glassy behavior in both antiferromagnetic $MnBi_4Te_7$ and FM $Mn(Bi_{1-x}Sb_x)_4Te_7$ samples, which we believe originates from cluster spin glass phases coexisting with long-range AFM/FM orders. We have also discussed how the antisite Mn ions impact the interlayer magnetic coupling and how FM interlayer coupling is stabilized in this system., Comment: 37 Pages, 7 Figures and 2 Tables. Supplementary Materials is included

The latest generation of Galactic-plane surveys is enhancing our ability to study the effects of galactic environment upon the process of star formation. We present the first data from CO Heterodyne Inner Milky Way Plane Survey 2 (CHIMPS2). CHIMPS2 is a survey that will observe the Inner Galaxy, the Central Molecular Zone (CMZ), and a section of the Outer Galaxy in $^{12}$CO, $^{13}$CO, and C$^{18}$O $(J = 3\rightarrow2)$ emission with the Heterodyne Array Receiver Program on the James Clerk Maxwell Telescope (JCMT). The first CHIMPS2 data presented here are a first look towards the CMZ in $^{12}$CO J = 3$\rightarrow$2 and cover $-3^{\circ}\leq\,\ell\,\leq\,5^{\circ}$ and $\mid$b$\mid \leq 0.5^{\circ}$ with angular resolution of 15 arcsec, velocity resolution of 1 km s$^{-1}$, and rms $\Delta T_A ^\ast =$ 0.58 K at these resolutions. Such high-resolution observations of the CMZ will be a valuable data set for future studies, whilst complementing the existing Galactic Plane surveys, such as SEDIGISM, the Herschel infrared Galactic Plane Survey, and ATLASGAL. In this paper, we discuss the survey plan, the current observations and data, as well as presenting position-position maps of the region. The position-velocity maps detect foreground spiral arms in both absorption and emission., Comment: 18 pages, 14 figures, accepted for publication in MNRAS

This paper presents an overview of SPIRou, the new-generation near-infrared spectropolarimeter / precision velocimeter recently installed on the 3.6-m Canada-France-Hawaii Telescope (CFHT). Starting from the two main science goals, namely the quest for planetary systems around nearby M dwarfs and the study of magnetized star / planet formation, we outline the instrument concept that was designed to efficiently address these forefront topics, and detail the in-lab and on-sky instrument performances measured throughout the intensive testing phase that SPIRou was submitted to before passing the final acceptance review in early 2019 and initiating science observations. With a central position among the newly started programmes, the SPIRou Legacy Survey (SLS) Large Programme was allocated 300 CFHT nights until at least mid 2022. We also briefly describe a few of the first results obtained in the various science topics that SPIRou started investigating, focusing in particular on planetary systems of nearby M dwarfs, transiting exoplanets and their atmospheres, magnetic fields of young stars, but also on alternate science goals like the atmospheres of M dwarfs and the Earth's atmosphere. We finally conclude on the essential role that SPIRou and the CFHT can play in coordination with forthcoming major facilities like the JWST, the ELTs, PLATO and ARIEL over the decade., Comment: MNRAS, in press (20 pages, 18 figures, 1 table)

This paper gives $n$-dimensional analogues of the Apollonian circle packings in parts I and II. We work in the space $\sM_{\dd}^n$ of all $n$-dimensional oriented Descartes configurations parametrized in a coordinate system, ACC-coordinates, as those $(n+2) \times (n+2)$ real matrices $\bW$ with $\bW^T \bQ_{D,n} \bW = \bQ_{W,n}$ where $Q_{D,n} = x_1^2 +... + x_{n+2}^2 - \frac{1}{n}(x_1 +... + x_{n+2})^2$ is the $n$-dimensional Descartes quadratic form, $Q_{W,n} = -8x_1x_2 + 2x_3^2 + ... + 2x_{n+2}^2$, and $\bQ_{D,n}$ and $\bQ_{W,n}$ are their corresponding symmetric matrices. There are natural actions on the parameter space $\sM_{\dd}^n$. We introduce $n$-dimensional analogues of the Apollonian group, the dual Apollonian group and the super-Apollonian group. These are finitely generated groups with the following integrality properties: the dual Apollonian group consists of integral matrices in all dimensions, while the other two consist of rational matrices, with denominators having prime divisors drawn from a finite set $S$ depending on the dimension. We show that the the Apollonian group and the dual Apollonian group are finitely presented, and are Coxeter groups. We define an Apollonian cluster ensemble to be any orbit under the Apollonian group, with similar notions for the other two groups. We determine in which dimensions one can find rational Apollonian cluster ensembles (all curvatures rational) and strongly rational Apollonian sphere ensembles (all ACC-coordinates rational)., Comment: 37 pages. The third in a series on Apollonian circle packings beginning with math.MG/0010298. Revised and extended. Added: Apollonian groups and Apollonian Cluster Ensembles (Section 4),and Presentation for n-dimensional Apollonian Group (Section 5). Slight revision on March 10, 2005

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes configurations they contain. It observed there exist infinitely many types of integral Apollonian packings in which all circles had integer curvatures, with the integral structure being related to the integral nature of the Apollonian group. Here we consider the action of a larger discrete group, the super-Apollonian group, also having an integral structure, whose orbits describe the Descartes quadruples of a geometric object we call a super-packing. The circles in a super-packing never cross each other but are nested to an arbitrary depth. Certain Apollonian packings and super-packings are strongly integral in the sense that the curvatures of all circles are integral and the curvature$\times$centers of all circles are integral. We show that (up to scale) there are exactly 8 different (geometric) strongly integral super-packings, and that each contains a copy of every integral Apollonian circle packing (also up to scale). We show that the super-Apollonian group has finite volume in the group of all automorphisms of the parameter space of Descartes configurations, which is isomorphic to the Lorentz group $O(3, 1)$., Comment: 37 Pages, 11 figures. The second in a series on Apollonian circle packings beginning with math.MG/0010298. Extensively revised in June, 2004. More integral properties are discussed. More revision in July, 2004: interchange sections 7 and 8, revised sections 1 and 2 to match, and added matrix formulations for super-Apollonian group and its Lorentz version. Slight revision in March 10, 2005

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)$\times$(center) is an integer vector. This series of papers explain such properties. A {\em Descartes configuration} is a set of four mutually tangent circles with disjoint interiors. We describe the space of all Descartes configurations using a coordinate system $\sM_\DD$ consisting of those $4 \times 4$ real matrices $\bW$ with $\bW^T \bQ_{D} \bW = \bQ_{W}$ where $\bQ_D$ is the matrix of the Descartes quadratic form $Q_D= x_1^2 + x_2^2+ x_3^2 + x_4^2 -{1/2}(x_1 +x_2 +x_3 + x_4)^2$ and $\bQ_W$ of the quadratic form $Q_W = -8x_1x_2 + 2x_3^2 + 2x_4^2$. There are natural group actions on the parameter space $\sM_\DD$. We observe that the Descartes configurations in each Apollonian packing form an orbit under a certain finitely generated discrete group, the {\em Apollonian group}. This group consists of $4 \times 4$ integer matrices, and its integrality properties lead to the integrality properties observed in some Apollonian circle packings. We introduce two more related finitely generated groups, the dual Apollonian group and the super-Apollonian group, which have nice geometrically interpretations. We show these groups are hyperbolic Coxeter groups., Comment: 42 pages, 11 figures. Extensively revised version on June 14, 2004. Revised Appendix B and a few changes on July, 2004. Slight revision on March 10, 2005

Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. It is possible for every circle in such a packing to have integer radius of curvature, and we call such a packing an {\em integral Apollonian circle packing.} This paper studies number-theoretic properties of the set of integer curvatures appearing in such packings. Each Descartes quadruple of four tangent circles in the packing gives an integer solution to the {\em Descartes equation}, which relates the radii of curvature of four mutually tangent circles: $2 (x^2 + y^2 + z^2 + w^2) - (x + y + z + w)^2 = 0.$ Each integral Apollonian circle packing is classified by a certain {\em root quadruple} of integers that satisfies the Descartes equation, and that corresponds to a particular quadruple of circles appearing in the packing. We determine asymptotics for the number of root quadruples of size below $T$. We study which integers occur in a given integer packing, and determine congruence restrictions which sometimes apply. Finally, we present evidence suggesting that the set of integer radii of curvatures that appear in an integral Apollonian circle packing has positive density, and in fact represents all sufficiently large integers not excluded by congruence conditions. In a series of companion papersr ``Apollonian Circle Packings: Geometry and Group Theory,'' we investigate a variety of group-theoretic properties of these configurations, as well as various extensions to higher dimensions and other spaces, such as hyperbolic space., Comment: 53 pages, 4 figures

Changes in the material characteristics of bone marrow with aging can be a significant source of error in measurements of bone density when using X-ray and ultrasound imaging modalities. In the context of computed tomography, dual-energy computed techniques have been used to correct for changes in marrow composition. However, dual-energy quantitative computed tomography (DE-QCT) protocols, while increasing the accuracy of the measurement, reduce the precision and increase the radiation dose to the patient in comparison to single-energy quantitative computed tomography (SE-QCT) protocols. If the attenuation properties of the marrow for a particular bone can be shown to be relatively constant with age, it should be possible to use single-energy techniques without experiencing errors caused by unknown marrow composition. Marrow was extracted by centrifugation from 10 mm thick frontal sections of 34 adult cadaver calcanei (28 males, 6 females, ages 17-65 years). The density and energy-dependent linear X-ray attenuation coefficient of each marrow sample were determined. For purposes of comparing our results, we then computed an effective CT number at two GE CT/i scan voltages (80 and 120 kVp) for each specimen. The coefficients of variation for the density, CT number at 80 kVp and CT number at 120 kVp were each less than 1%, and the parameters did not change significantly with age (p > 0.2, r2 < 0.02, power > 0.8 where the minimum acceptable r2 = 0.216). We could demonstrate no significant gender-associated differences in these relationships. These data suggest that calcaneal bone marrow X-ray attenuation properties and marrow density are essentially constant from the third through sixth decades of life.

This paper presents a new reconstruction algorithm for both single- and dual-energy computed tomography (CT) imaging. By incorporating the polychromatic characteristics of the X-ray beam into the reconstruction process, the algorithm is capable of eliminating beam hardening artifacts. The single energy version of the algorithm assumes that each voxel in the scan field can be expressed as a mixture of two known substances, for example, a mixture of trabecular bone and marrow, or a mixture of fat and flesh. These assumptions are easily satisfied in a quantitative computed tomography (QCT) setting. We have compared our algorithm to three commonly used single-energy correction techniques. Experimental results show that our algorithm is much more robust and accurate. We have also shown that QCT measurements obtained using our algorithm are five times more accurate than that from current QCT systems (using calibration). The dual-energy mode does not require any prior knowledge of the object in the scan field, and can be used to estimate the attenuation coefficient function of unknown materials. We have tested the dual-energy setup to obtain an accurate estimate for the attenuation coefficient function of K2 HPO4 solution.

This paper presents a procedure for estimating an accurate model of the CT imaging process including spectral effects. As raw projection data are typically unavailable to the end-user, we adopt a post-processing approach that utilizes the reconstructed images themselves. This approach includes errors from x-ray scatter and the nonidealities of the built-in soft tissue correction into the beam characteristics, which is crucial to beam hardening correction algorithms that are designed to be applied directly to CT reconstructed images. We formulate this approach as a quadratic programming problem and propose two different methods, dimension reduction and regularization, to overcome ill conditioning in the model. For the regularization method we use a statistical procedure, Cross Validation, to select the regularization parameter. We have constructed step-wedge phantoms to estimate the effective beam spectrum of a GE CT-I scanner. Using the derived spectrum, we computed the attenuation ratios for the wedge phantoms and found that the worst case modeling error is less than 3% of the corresponding attenuation ratio. We have also built two test (hybrid) phantoms to evaluate the effective spectrum. Based on these test phantoms, we have shown that the effective beam spectrum provides an accurate model for the CT imaging process. Last, we used a simple beam hardening correction experiment to demonstrate the effectiveness of the estimated beam profile for removing beam hardening artifacts. We hope that this estimation procedure will encourage more independent research on beam hardening corrections and will lead to the development of application-specific beam hardening correction algorithms.

This paper presents a new algorithm for frame registration. Our algorithm requires only that the frame be comprised of straight rods, as opposed to the N structures or an accurate frame model required by existing algorithms. The algorithm utilizes the full 3D information in the frame as well as a least squares weighting scheme to achieve highly accurate registration. We use simulated CT data to assess the accuracy of our algorithm. We compare the performance of the proposed algorithm to two commonly used algorithms. Simulation results show that the proposed algorithm is comparable to the best existing techniques with knowledge of the exact mathematical frame model. For CT data corrupted with an unknown in-plane rotation or translation, the proposed technique is also comparable to the best existing techniques. However, in situations where there is a discrepancy of more than 2 mm (0.7% of the frame dimension) between the frame and the mathematical model, the proposed technique is significantly better (p < or = 0.05) than the existing techniques. The proposed algorithm can be applied to any existing frame without modification. It provides better registration accuracy and is robust against model mis-match. It allows greater flexibility on the frame structure. Lastly, it reduces the frame construction cost as adherence to a concise model is not required.