A huge amount of data on cells has been accumulated due to rapid advances in collection techniques for cellular genomic data. In recent years, mathematical analysis based on data-driven and mathematical approaches to such big data has attracted a great deal of attention.
The purpose of this research is to elucidate the dynamics of cell differentiation by using such mathematical analysis. In particular, by applying mathematical theories such as optimal transport theory and topological data analysis, I will establish methods for tracking the cell differentiation process, estimating its origin, and so on.
Toshiaki Yachimura obtained his PhD from Tohoku University (2020). He was a recipient of a JSPS Research Fellowship for Young Scientist (DC2) from 2019 to 2020. He was appointed as a program-specific researcher in 2020 in ASHBi of Kyoto University.
M.Santacesaria, T.Yachimura, On an inverse Robin spectral problem, Inverse Problems, 36(7), (2020), 075004
L.Cavallina, T.Yachimura, Symmetry breaking solutions for a two-phase overdetermined problem of Serrin-type, to appear in the volume Trends in Mathematics, Research Perspectives.
G.Allaire, L.Cavallina, N.Miyake, T.Oka, T.Yachimura, The Homogenization Method for Topology Optimization of Structures: Old and New, Interdisciplinary Information Sciences, 25(2), (2019), pp. 75-146.
L.Cavallina, T.Yachimura, On a two-phase Serrin-type problem and its numerical computation, ESAIM: Control, Optimisation and Calculus of Variations, (2019), in press.
T.Yachimura, Asymptotic behavior for the principal eigenvalue of a reinforcement problem, Applicable Analysis, 98 (2019), pp. 1946-1958.
T.Yachimura, Two-phase eigenvalue problem on thin domains with Neumann boundary condition, Differential and Integral Equations, 31 (2018), pp.735-760.
Best paper award, The 18th Northeastern Symposium on Mathematical Analysis (2017)