11 research outputs found
Effects of randomization on asymptotic periodicity of nonsingular transformations
It is known that the Perron--Frobenius operators of piecewise expanding
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