In this talk we will present an example of topological fiber bundles whose base, fiber and total manifolds are all smoothable, but they are not smoothable as fiber bundles.
As three basic tools, we use a family Seiberg-Witten theory developed by Baraglia-Konno, Kirby-Siebenmann theory and topological invariance of rational Pontryagin classes by Novikov.
This is a joint work with H.Konno and N.Nakamura.
Generalizing the concept of an expected value to metric spaces, Fréchet (1948) introduced means as minimizers of expected squared distance. Bhattacharya and Patrangenaru (2005) derived a central limit theorem (CLT) for such Fréchet means on manifolds under rather obscure conditions. We generalize their CLT and shed some light on these obscure conditions. It turns out that the CLT may have...
In this talk we introduce a distance between two spaces, so-called Gromov-Hausdorff distance, and discuss a question how geometric/analytic quantities are close if the distance is small.
Time-variant fractional models are used to describe many applications, e.g. lithium-ion batteries. For such models, neither a controllability criterion for state space equations nor the energy-optimal control function are available so far. To overcome this limitation, in this talk a reachability and controllability definition for time-variant fractional state space systems is formulated and...
Statistics on Riemannian manifolds has attracted much interest, it being the natural setting for considering data on smooth curved spaces. I will discuss a Central Limit Theorem for closed Riemannian manifolds, assuming certain stability hypothesis for the cut locus, which always holds when the manifold is compact but may not be satisfied in the non-compact case. This is joint work with...
Aortic aneurysm and aortic dissections persist as life-threatening hazards. Although patient-specific simulations are common in biomedical engineering and extremely useful for a surgical planning etc., they remain insufficient to elucidate the general characteristics of targeted diseases. We introduce a geometrical characterization of blood vessels, which vary widely among individuals. Through...
Mechanochemical models present a new paradigm for biological pattern formation, where the interaction between domain curvature and pattern shape replaces the activator-inhibitor mechanism. Numerical simulations of a mechanochemical model formulated by M. Mercker & A. Marciniak-Czochra reveal a wide spectrum of novel patterning phenomena, which are as yet poorly understood from an analytical...
In this presentation, the author suggests shape optimization problem based on Model-based and Data-Drive Approach, for controlling transient flows effectively.
The central limit theorem (CLT) for the mean in Euclidean space features a normal limiting distribution and an asymptotic rate of $n^{-1/2}$ for all probability measures it applies to. We revisit the generalized CLT for the Fréchet mean on hyperspheres. For some probability measures,
the sample mean fluctuates around the population mean asymptotically at a scale $n^{-\alpha}$ with exponent...
The box-ball system(BBS), introduced by Takahashi and Satsuma, is a cellular automaton that exhibits solitonic behaviour. We show that the BBS dynamics can be described by using the transformation of a nearest neighbour path encoding of the particle configuration given by ‘reflection in the past maximum’, which is known as Pitman's transformation. The techniques developed to understand the...
Medical Robots are gaining interest in the field of healthcare due to their manifold advantages, such as enabling minimally-invasive surgical procedures with high precision, reduced tremor, and direct feedback from various sensors to the surgeon. In this talk, I will outline several medical robots, which are commercially available or focused on in current research. Additionally, I will stress...
