Almost alternating diagrams and fibered links in S^3

Let $L$ be an oriented link with an alternating diagram $D$. It is known that $L$ is a fibered link if and only if the surface $R$ obtained by applying Seifert's algorithm to $D$ is a Hopf plumbing. Here, we call $R$ a Hopf plumbing if $R$ is obtained by successively plumbing finite number of Hopf bands to a disk. In this paper, we discuss its extension so that we show the following theorem. Let $R$ be a Seifert surface obtained by applying Seifert's algorithm to an almost alternating diagrams. Then $R$ is a fiber surface if and only if $R$ is a Hopf plumbing. We also show that the above theorem can not be extended to 2-almost alternating diagrams, that is, we give examples of 2-almost alternating diagrams for knots whose Seifert surface obtained by Seifert's algorithm are fiber surfaces that are not Hopf plumbing. This is shown by using a criterion of Melvin-Morton.Comment: 18 pages, 30 figure

Concentration-adjustable micromixer using droplet injection into a microchannel

A novel micromixing technique that exploit a thrust of droplets into the mixing interface is developed. The technique enhances the mixing by injecting immiscible droplets in a mixing channel and the methodology enables a control of the mixing level simply by changing the droplet injection frequency. We experimentally characterize the mixing performance with various droplet injection frequencies, channel geometries, and diffusion coefficients. Consequently, it is revealed that the mixing level increases with the injection frequency, the droplet-diameter-to-channel-width ratio, and the diffusion coefficient. Moreover, the mixing level is found to be a linear function of the droplet volume fraction in the mixing section. The results suggest that the developed technique can produce a large amount of sample solution whose concentration is arbitrary and precisely controllable with a simple and stable operation.Comment: 12 + 3 pages, 6 + 4 figure

A sharp sparse domination of pseudodifferential operators

In this paper, we give a sharp sparse domination of pseudodifferential operators associated with symbols belonging to the H\"{o}rmander class, and fundamental solutions of dispersive equations. Furthermore, we give boundedness results of these operators on weighted Besov spaces by using the sparse domination

In silico analysis of inner ear development using public whole embryonic body single-cell RNA-sequencing data

The inner ear comprises four epithelial domains: the cochlea, vestibule, semicircular canals, and endolymphatic duct/sac. These structures are segregated at embryonic day 13.5 (E13.5). However, these four anatomical structures remain undefined at E10.5. Here, we aimed to identify lineage-specific genes in the early developing inner ear using published data obtained from single-cell RNA-sequencing (scRNA-seq) of embryonic mice. We downloaded 5000 single-cell transcriptome data, named ‘auditory epithelial trajectory’, from the Mouse Organogenesis Cell Atlas. The dataset was supposed to include otic epithelial cells at E9.5–13.5. We projected the 5000 ​cells onto a two-dimensional space encoding the transcriptional state and visualised the pattern of otic epithelial cell differentiation. We identified 15 clusters, which were annotated as one of the four components of the inner ear epithelium using known genes that characterise the four different tissues. Additionally, we classified 15 clusters into sub-regions of the four inner ear components. By comparing transcriptomes between these 15 clusters, we identified several candidates of lineage-specific genes. Characterising these new candidate genes will help future studies about inner ear development

Verification of the relationship between full-body illusion indices

Full Body Illusion (FBI) is a phenomenon which changes over the sense of body ownership to other object and the illusion has been reported using various measurement indices (e.g., questionnaire , skin conductance response, and skin temperature). However, no studies have simultaneously measured these indices and it still remains unclear whether those indices capture the similar aspects of FBI. The present study investigate the relationship among those FBI indices. In this study, we presented an avatar to participants in a virtual room. We measured the questionnaires, skin conductance response, skin temperature, and drift as FBI indices. The result s showed that me asurement of the questionnaires and skin conductance response were reflected FBI, and the positive correlation was found between those two measurements questionnaire and skin conductance response ( rho = .5 5 , p < .05). Alternatively, no correlations were found among the other indices. Our results suggest that both the questionnaire and the skin conductance response reflect similar aspects of FBI

ファイバー曲面とホップバンドのプラミング

博士（理学）神戸大

都市および流域の植生把握に適した観測および解析手法に関する地理情報学的研究 : UAVによる超高解像度画像や360度画像およびオブジェクトベース解析手法の可能性

東京都立大