Effects of randomization on asymptotic periodicity of nonsingular transformations

It is known that the Perron--Frobenius operators of piecewise expanding $\mathcal{C}^2$ transformations possess an asymptotic periodicity of densities. On the other hand, external noise or measurement errors are unavoidable in practical systems; therefore, all realistic mathematical models should be regarded as random iterations of transformations. This paper aims to discuss the effects of randomization on the asymptotic periodicity of densities.Comment: 20 pages, 10 figure

Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact

We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a deterministic part increasing with execution volume and a positive stochastic noise part. Then, we derive a continuous-time model as a limit of a discrete-time value function. We find that the continuous-time value function is characterized by a stochastic control problem with a Levy process.Comment: 17 pages. Forthcoming in "Communications on Stochastic Analysis.

On the construction of Brownian house-moving and its properties

The purpose of this paper is to construct a new stochastic process "Brownian house-moving," which is a Brownian bridge that stays between its starting point and its terminal point. To construct this process, statements are prepared on the weak convergence of conditioned Brownian motion, a conditioned Brownian bridge, a conditioned Brownian meander, and a conditioned three-dimensional Bessel bridge. Also studied are the sample path properties of Brownian house-moving and the decomposition formula for its distribution.Comment: 78 page

Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648

Time-resolved serial femtosecond crystallography reveals early structural changes in channelrhodopsin

X線自由電子レーザーを用いて、光照射によるチャネルロドプシンの構造変化の過程を捉えることに成功. 京都大学プレスリリース. 2021-03-26.Channelrhodopsins (ChRs) are microbial light-gated ion channels utilized in optogenetics to control neural activity with light . Light absorption causes retinal chromophore isomerization and subsequent protein conformational changes visualized as optically distinguished intermediates, coupled with channel opening and closing. However, the detailed molecular events underlying channel gating remain unknown. We performed time-resolved serial femtosecond crystallographic analyses of ChR by using an X-ray free electron laser, which revealed conformational changes following photoactivation. The isomerized retinal adopts a twisted conformation and shifts toward the putative internal proton donor residues, consequently inducing an outward shift of TM3, as well as a local deformation in TM7. These early conformational changes in the pore-forming helices should be the triggers that lead to opening of the ion conducting pore