New bijective proofs pertaining to alternating sign matrices

The alternating sign matrices-descending plane partitions (ASM-DPP) bijection problem is one of the most intriguing open problems in bijective combinatorics, which is also relevant to integrable combinatorics. The notion of a signed set and a signed bijection is used in [Fischer, I. \& Konvalinka, M., Electron. J. Comb., 27 (2020) 3-35.] to construct a bijection between $\text{ASM}_n \times \text{DPP}_{n-1}$ and $\text{DPP}_n \times \text{ASM}_{n-1}$. Here, we shall construct a more natural alternative to a signed bijection between alternating sign matrices and shifted Gelfand-Tsetlin patterns which is presented in that paper, based on the notion of compatibility which we introduce to measure the naturalness of a signed bijection. In addition, we give a bijective proof for the refined enumeration of an extension of alternating sign matrices with $n+3$ statistics, first proved in [Fischer, I. \& Schreier-Aigner, F., Advances in Mathematics 413 (2023) 108831.].Comment: 50 page

Stratified Ehrhart ring theory on periodic graphs

We investigate the "stratified Ehrhart ring theory" for periodic graphs, which gives an algorithm for determining the growth sequences of periodic graphs. The growth sequence $(s_{\Gamma, x_0, i})_{i \ge 0}$ is defined for a graph $\Gamma$ and its fixed vertex $x_0$, where $s_{\Gamma, x_0, i}$ is defined as the number of vertices of $\Gamma$ at distance $i$ from $x_0$. Although the sequences $(s_{\Gamma, x_0, i})_{i \ge 0}$ for periodic graphs are known to be of quasi-polynomial type, their determination had not been established, even in dimension two. Our algorithm and the proofs are based on algebraic combinatorics, analogous to the Ehrhart theory. As an application of the algorithm, we determine the growth sequences in several new examples.Comment: 46 pages. arXiv admin note: text overlap with arXiv:2305.0817

Suzaku X-Ray Observations of the Accreting NGC 4839 Group of Galaxies and the Radio Relic in the Coma Cluster

Based on Suzaku X-ray observations, we study the hot gas around the NGC4839 group of galaxies and the radio relic in the outskirts of the Coma cluster. We find a gradual decline in the gas temperature from 5 keV around NGC4839 to 3.6 keV at the radio relic, across which there is a further, steeper drop down to 1.5 keV. This drop as well as the observed surface brightness profile are consistent with a shock with Mach number M = 2.2 pm 0.5 and velocity vs = (1410 pm 110) km s^-1. A lower limit of B > 0.33 mu G is derived on the magnetic field strength around the relic from upper limits to inverse Compton X-ray emission. Although this suggests that the non-thermal electrons responsible for the relic are generated by diffusive shock acceleration (DSA), the relation between the measured Mach number and the electron spectrum inferred from radio observations are inconsistent with that expected from the simplest, test-particle theory of DSA. Nevertheless, DSA is still viable if it is initiated by the injection of a pre-existing population of non-thermal electrons. Combined with previous measurements, the temperature profile of Coma in the southwest direction is shallower outside NGC4839 and also slightly shallower in the outermost region. The metal abundance around NGC4839 is confirmed to be higher than in its vicinity, implying a significant peak in the abundance profile that decreases to 0.2 solar toward the outskirts. We interpret these facts as due to ram pressure stripping of metal-enriched gas from NGC4839 as it falls into Coma. The relic shock may result from the combined interaction of pre-existing intracluster gas, gas associated with NGC 4839, and cooler gas flowing in from the large-scale structure filament in the southwest.Comment: 13 page, accepted for publication in Publications of the Astronomical Society of Japa

Oral Tacrolimus in Patients with Ulcerative Colitis

Tacrolimus is a macrolide immunosuppressant that is structurally similar to rapamycin and has been found to have potent immunosuppressive properties, showing 10- to 100-fold higher potency for inhibiting lymphocyte activation than cyclosporine A (CsA). Because less variability in absorption and serum levels is observed among patients treated with tacrolimus compared with those who receive oral CsA, tacrolimus has been suggested to be more easily and safely administered to patients with refractory ulcerative colitis (UC) than CsA. However, because oral tacrolimus has a slower onset of action than intravenous CsA and food intake is known to reduce tacrolimus serum trough levels due to its low absorption rate, the proper method for administration of oral tacrolimus has not been determined. Moreover, the long-term effects of oral tacrolimus also remain unclear. In this chapter, key issues regarding the use of oral tacrolimus in patients with UC are reviewed

Topological unidirectional guided resonances emerged from interband coupling

Unidirectional guided resonances (UGRs) are optical modes in photonic crystal (PhC) slabs that radiate towards one side without the need for mirrors on the other, represented from a topological perspective by the merged points of paired, single-sided, half-integer topological charges. In this work, we report a mechanism to realize UGRs by tuning the interband coupling effect originating from up-down symmetry breaking. We theoretically demonstrate that a type of polarization singularity, the circular-polarized states (CPs), emerge from trivial polarization fields owing to the hybridization of two unperturbed states. By tuning structural parameters, two half-charges carried by CPs evolve in momentum space and merge to create UGRs. Our findings show that UGRs are ubiquitous in PhC slabs, and can systematically be found from our method, thus paving the way to new possibilities of light manipulation

Origins and conservation of topological polarization defects in resonant photonic-crystal diffraction

We present a continuative definition of topological charge to depict the polarization defects on any resonant diffraction orders in photonic crystal slab regardless they are radiative or evanescent. By using such a generalized definition, we investigate the origins and conservation of integer polarization defects across the whole Brollouin zone. We found that these polarization defects eventually originate from the mode degeneracy that is induced by lattice coupling as a consequence of momentum space folding, or inter-band coupling that can be either Hermitian or Non-hermitian. By counting all types of polarization defects, the total topological charge numbers in a given diffraction order is a conserved quantity across the whole Brillouin zone that is determined by lattice geometry only