Abstract. We give a definition of monoidal categorifications of quantum cluster algebras and provide a criterion for a monoidal category of finite-dimensional graded R-modules to become a monoidal categorification of a quantum cluster algebra, where R is a symmetric Khovanov-Lauda-Rouquier algebra. Roughly speaking, this criterion asserts that a quantum monoidal seed can be mutated successively in all the directions once the first-step mutations are possible. In the course of the study, we also give a proof of a conjecture of Leclerc on the product of upper global basis elements.

Tissue expansion techniques physically expand swellable gel‐embedded biological specimens to overcome the resolution limit of light microscopy. As the benefits of expansion come at the expense of signal concentration, imaging volume and time, and mechanical integrity of the sample, the optimal expansion ratio may widely differ depending on the experiment. However, existing expansion methods offer only fixed expansion ratios that cannot be easily adjusted to balance the gain and loss associated with expansion. Here, a hydrogel conversion‐based expansion method is presented, that enables easy adjustment of the expansion ratio for individual needs, simply by changing the duration of a heating step. This method, termed ZOOM, isotropically expands samples up to eightfold in a single expansion process. ZOOM preserves biomolecules for post‐processing labelings and supports multi‐round expansion for the imaging of a single sample at multiple zoom factors. ZOOM can be flexibly and scalably applied to nanoscale imaging of diverse samples, ranging from cultured cells to thick tissues, as well as bacteria, exoskeletal Caenorhabditis elegans, and human brain samples.

We prove that, for simple modules $M$ and $N$ over a quantum affine algebra, their tensor product $M \otimes N$ has a simple head and a simple socle if $M \otimes M$ is simple. A similar result is proved for the convolution product of simple modules over quiver Hecke algebras. In the second version, the statement (1.11) (in the revised version) is modified and its proof is given in Section 4.Comment: 21 pages (the first version), 23 pages (the second version

Fas (Apo-1/CD95) is a cell-surface receptor involved in cell death signaling. The key role of the Fas system in negative growth regulation has been studied mostly within the immune system, and somatic mutations of Fas gene in cancer patients have been described solely in lymphoid-lineage malignancies. However, many nonlymphoid tumor cells have been found to be resistant to Fas-mediated apoptosis, which suggests that Fas mutations, one of the possible mechanisms for Fas resistance, may be involved in the pathogenesis of nonlymphoid malignancies as well. In this study, we have analyzed the entire coding region and all splice sites of the Fas gene for the detection of the gene mutations in 44 human malignant melanomas in skin by polymerase chain reaction, single-strand conformation polymorphism, and DNA sequencing. Overall, 3 tumors (6.8%) were found to have the Fas mutations, which were all missense variants and identified in the cytoplasmic region (death domain) known to be involved in the transduction of an apoptotic signal. The data presented here suggest that somatic alterations of the Fas gene might lead to the loss of its apoptotic function and contribute to the pathogenesis of some human malignant melanomas.

The present study was conducted to apply an interspecies germ cell transfer technique to wild bird reproduction. Pheasant (Phasianus colchicus) primordial germ cells (PGCs) retrieved from the gonads of 7-day-old embryos were transferred to the bloodstream of 2.5-day-old chicken (Gallus gallus) embryos. Pheasant-to-chicken germline chimeras hatched from the recipient embryos, and 10 pheasants were derived from testcross reproduction of the male chimeras with female pheasants. Gonadal migration of the transferred PGCs, their involvement in spermatogenesis, and production of chimeric semen were confirmed. The phenotype of pheasant progenies derived from the interspecies transfer was identical to that of wild pheasants. The average efficiency of reproduction estimated from the percentage of pheasants to total progenies was 17.5%. In conclusion, interspecies germ cell transfer into a developing embryo can be used for wild bird reproduction, and this reproductive technology may be applicable in conserving endangered bird species.