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1. Infernal and exceptional edge modes: non-Hermitian topology beyond the skin effect

   https://doi.org/10.1088/2515-7639/acf2ca  

   Denner, M. Michael ; Neupert, Titus ; Schindler, Frank ( August 2023 , Journal of Physics: Materials)

   The classification of point gap topology in all local non-Hermitian (NH) symmetry classes has been recently established. However, many entries in the resulting periodic table have only been discussed in a formal setting and still lack a physical interpretation in terms of their bulk-boundary correspondence. Here, we derive the edge signatures of all two-dimensional phases with intrinsic point gap topology. While in one dimension point gap topology invariably leads to the NH skin effect, NH boundary physics is significantly richer in two dimensions. We find two broad classes of non-Hermitian edge states: (1)infernal points, where a skin effect occurs only at a single edge momentum, while all other edge momenta are devoid of edge states. Under semi-infinite boundary conditions, the point gap thereby closes completely, but only at a single edge momentum. (2) NH exceptional pointdispersions, where edge states persist at all edge momenta and furnish an anomalous number of symmetry-protected exceptional points. Surprisingly, the latter class of systems allows for a finite, non-extensive number of edge states with a well defined dispersion along all generic edge terminations. Concomitantly, the point gap only closes along the real and imaginary eigenvalue axes, realizing a novel form of NH spectral flow.

    

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2. Individually tailored spatial–spectral pulsed CEST MRI for ratiometric mapping of myocardial energetic species at 3T

   https://doi.org/10.1002/mrm.29801  

   Ayala, Cindy ; Luo, Huiwen ; Godines, Kevin ; Alghuraibawi, Wissam ; Ahn, Sinyeob ; Rehwald, Wolfgang ; Grissom, William A. ; Vandsburger, Moriel H. ( August 2023 , Magnetic Resonance in Medicine)

   CEST MRI has been used to probe changes in cardiac metabolism via assessment of CEST contrast from Cr. However, B₁variation across the myocardium leads to spatially variable Cr CEST contrast in healthy myocardium.

   We developed a spatial–spectral (SPSP) saturation pulsed CEST protocol to compensate for B₁variation. Flip angle maps were used to individually tailor SPSP pulses comprised of a train of one‐dimensional spatially selective subpulses selective along the principal B₁gradient dimension. Complete Z‐spectra in the hearts of (n = 10) healthy individuals were acquired using conventional Gaussian saturation and SPSP schemes and supported by phantom studies.

   In simulations, the use of SPSP pulses reduced the average SD of the effective saturation B₁values within the myocardium (n = 10) from 0.12 ± 0.02 μT to 0.05 ± 0.01 μT (p < 0.01) and reduced the average SD of Cr CEST contrast in vivo from 10.0 ± 4.3% to 6.1 ± 3.5% (p < 0.05). Results from the hearts of human subjects showed a significant reduction of CEST contrast distribution at 2 ppm, as well as amplitude, when using SPSP saturation. Corresponding phantom experiments revealed PCr‐specific contrast generation at body temperature when SPSP saturation was used but combined PCr and Cr contrast generation when Gaussian saturation was used.

   The use of SPSP saturation pulsed CEST resulted in PCr‐specific contrast generation and enabled ratiometric mapping of PCr to total Cr CEST contrast in the human heart at 3T.

    

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3. Asymptotics of Selective Inference

   https://doi.org/10.1111/sjos.12261  

   Tian, Xiaoying ; Taylor, Jonathan ( March 2017 , Scandinavian Journal of Statistics)

   In this paper, we seek to establish asymptotic results for selective inference procedures removing the assumption of Gaussianity. The class of selection procedures we consider are determined by affine inequalities, which we refer to as affine selection procedures. Examples of affine selection procedures include selective inference along the solution path of the least absolute shrinkage and selection operator (LASSO), as well as selective inference after fitting the least absolute shrinkage and selection operator at a fixed value of the regularization parameter. We also consider some tests in penalized generalized linear models. Our result proves asymptotic convergence in the high‐dimensional setting wheren<p, andncan be of a logarithmic factor of the dimensionpfor some procedures.

    

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4. Anomalous high-field magnetotransport in CaFeAsF due to the quantum Hall effect

   https://doi.org/10.1038/s41535-022-00470-6  

   Terashima, Taichi ; Hirose, Hishiro T. ; Kikugawa, Naoki ; Uji, Shinya ; Graf, David ; Morinari, Takao ; Wang, Teng ; Mu, Gang ( June 2022 , npj Quantum Materials)

   CaFeAsF is an iron-based superconductor parent compound whose Fermi surface is quasi-two dimensional, composed of Dirac-electron and Schrödinger-hole cylinders elongated along thecaxis. We measured the longitudinal and Hall resistivities in CaFeAsF with the electrical current in theabplane in magnetic fields up to 45 T applied along thecaxis and obtained the corresponding conductivities via tensor inversion. We found that both the longitudinal and Hall conductivities approached zero above ~40 T as the temperature was lowered to 0.4 K. Our analysis indicates that the Landau-level filling factor isν = 2 for both electrons and holes at these high field strengths, resulting in a total filling factorν = ν_hole − ν_electron = 0. We therefore argue that theν = 0 quantum Hall state emerges under these conditions.

    

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5. Homotopy equivalent boundaries of cube complexes

   https://doi.org/10.1007/s10711-023-00877-w  

   Fernós, Talia ; Futer, David ; Hagen, Mark ( January 2024 , Geometriae Dedicata)

   A finite-dimensional CAT(0) cube complexXis equipped with several well-studied boundaries. These include theTits boundary$$\partial _TX$$${\partial }_{T}X$(which depends on the CAT(0) metric), theRoller boundary$${\partial _R}X$$${\partial }_{R}X$(which depends only on the combinatorial structure), and thesimplicial boundary$$\partial _\triangle X$$${\partial }_{▵}X$(which also depends only on the combinatorial structure). We use a partial order on a certain quotient of$${\partial _R}X$$${\partial }_{R}X$to define a simplicial Roller boundary$${\mathfrak {R}}_\triangle X$$$R_{▵}X$. Then, we show that$$\partial _TX$$${\partial }_{T}X$,$$\partial _\triangle X$$${\partial }_{▵}X$, and$${\mathfrak {R}}_\triangle X$$$R_{▵}X$are all homotopy equivalent,$$\text {Aut}(X)$$$\text{Aut}\left(X\right)$-equivariantly up to homotopy. As an application, we deduce that the perturbations of the CAT(0) metric introduced by Qing do not affect the equivariant homotopy type of the Tits boundary. Along the way, we develop a self-contained exposition providing a dictionary among different perspectives on cube complexes.

    

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