We investigate mappings $F = (f_1, f_2) \colon \mathbb{R}^2 \to \mathbb{R}^2
$ where $ f_1, f_2 $ are bivariate normal densities from the perspective of
singularity theory of mappings, motivated by the need to understand properties
of two-component bivariate normal mixtures. We show a classification of
mappings $ F = (f_1, f_2) $ via $\mathcal{A}$-equivalence and characterize them
using statistical notions. Our analysis reveals three distinct types, each with
specific geometric properties. Furthermore, we determine the upper bounds for
the number of modes in the mixture for each type.

arXiv

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その他リンク： http://arxiv.org/pdf/2410.00415v2

掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

We investigate differential geometric properties of a parabolic point of a
surface in the Euclidean three space. We introduce the contact cylindrical
surface which is a cylindrical surface having a degenerate contact type with
the original surface at a parabolic point. Furthermore, we show that such a
contact property gives a characterization to the $\mathcal{A}$-singularity of
the orthogonal projection of a surface from the asymptotic direction.

DOI： 10.1007/s40598-024-00251-y

arXiv

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その他リンク： https://link.springer.com/article/10.1007/s40598-024-00251-y/fulltext.html

掲載種別：研究論文（学術雑誌）   出版者・発行元：Elsevier BV  

DOI： 10.1016/j.cagd.2024.102289

Scopus

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掲載種別：研究論文（学術雑誌）   出版者・発行元：Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences)  

Since the first-principles calculations in quantum chemistry precisely
provide possible configurations of carbon atoms in nanocarbons, we have
analyzed the geometrical structure of the possible carbon configurations and
found that there exists a novel symmetry in the nanocarbons, i.e., the
pre-constant discrete principal curvature (pCDPC) structure. In terms of the
discrete principal curvature based on the discrete geometry for trivalent
oriented graphs developed by Kotani, Naito, and Omori (Comput. Aided Geom.
Design, $\bf{58}$, (2017), 24-54), we numerically investigated discrete
principal curvature distribution of the nanocarbons, C$_{60}$, carbon
nanotubes, C$_{120}$ (C$_{60}$ dimer), and C$_{60}$-polymers (peanut-shaped
fullerene polymers). While the C$_{60}$ and nanotubes have the constant
discrete principal curvature (CDPC) as we expected, it is interesting to note
that the C$_{60}$-polymers and C$_{60}$ dimer also have the almost constant
discrete principal curvature, i.e., pCDPC, which is surprising. A nontrivial
pCDPC structure with revolutionary symmetry is available due to discreteness,
though it has been overlooked in geometry. In discrete geometry, there appears
a center axisoid which is the discrete analogue of the center axis in the
continuum differential geometry but has three-dimensional structure rather than
a one-dimensional curve due to its discrete nature. We demonstrated that such
pCDPC structure exists in nature, namely in the C$_{60}$-polymers. Furthermore,
since we found that there is a positive correlation between the degree of the
CDPC structure and stability of the configurations for certain class of the
C$_{60}$-polymers, we also revealed the origin of the pCDPC structure from an
aspect of materials science.

DOI： 10.7546/giq-27-2024-25-44

arXiv

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その他リンク： http://arxiv.org/pdf/2306.15839v2

記述言語：日本語   出版者・発行元：(一社)日本医用画像工学会  

本研究の目的は,上皮成長因子受容体(EGFR)のチロシンキナーゼ阻害剤(TKI)治療を行う非小細胞肺がん(NSCLC)患者における腫瘍成長の経時変化予測モデルを構築することである.TKI治療を受けたEGFR陽性NSCLC患者26名を選択し,治療前後のCT画像における肉眼的腫瘍体積の輪郭を抽出した.各患者の腫瘍細胞数は輪郭抽出を行ったCT画像から求めた腫瘍体積に腫瘍細胞密度を乗じることで算出し,参考値として使用した.最後に,TKIに対する腫瘍の増減を表現する微分方程式モデルを構築し,パラメータを最適化することで腫瘍の経時変化の軌跡を推定した.本研究で構築したモデルは,平均絶対パーセント誤差(MAPE)とスピアマンの相関係数(SCC)で評価し平均値はそれぞれ7.50%,0.918であった.先行研究のモデルの結果(MAPE:11.1%,SCC:0.913)と比較してより腫瘍の経時変化を表現できる可能性がある.本研究のモデルは,EGFR-TKIを受けているNSCLC患者に対する治療効果予測法の基礎モデルとなりうると考える.(著者抄録)

掲載種別：研究論文（学術雑誌）   出版者・発行元：Elsevier BV  

DOI： 10.1016/j.cmpb.2023.107544

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1002/mana.201900327

Web of Science

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s13366-021-00606-y

Web of Science

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記述言語：英語   会議種別：ポスター発表  

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会議種別：口頭発表（一般）  

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記述言語：日本語  

記述言語：英語  

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会議種別：ポスター発表  

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会議種別：口頭発表（招待・特別）  

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会議種別：口頭発表（招待・特別）  

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記述言語：日本語   会議種別：口頭発表（招待・特別）  

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会議種別：口頭発表（一般）  

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会議種別：ポスター発表  

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会議種別：公開講演，セミナー，チュートリアル，講習，講義等  

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会議種別：公開講演，セミナー，チュートリアル，講習，講義等  

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