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Masato Hoshino

Publications and source records attributed to Masato Hoshino.

17 recordsLinked to original sources
arXiv2025

In vivo imaging of central nervous system fluid spaces using synchrotron radiation-based micro computed tomography

Current approaches to in vivo imaging of the mouse central nervous system (CNS) do not offer a combination of micrometer resolution and a whole-brain field of view. To address this limitation, we introduce an approach based on synchrotron radiation-based hard X-ray micro computed tomography (SR$\mu$CT). We performed intravital SR$\mu$CT acquisitions of mouse CNS fluid spaces at three synchrotron radiation facilities. Imaging was conducted on both anesthetized free-breathing and ventilated animals, with and without retrospective cardiac gating. We achieved whole-brain imaging at 6.3 $\mu$m uniform voxel size, observed the distribution of cerebrospinal fluid (CSF) contrast agent over time and quantified choroid plexus movement. SR$\mu$CT bridges the gap between multiphoton microscopy and magnetic resonance imaging, offering dynamic imaging with micrometer-scale resolution and whole-organ field of view. Intravital SR$\mu$CT will play a crucial role in validating and integrating hypotheses on CSF dynamics and solute transport by providing unique data that cannot be acquired otherwise.

physics.med-ph↗
arXiv2024

A note on the Taylor estimates of iterated paraproducts

Bony's paraproduct is one of the main tools in the theory of paracontrolled calculus. The paraproduct is usually defined via Fourier analysis, so it is not a local operator. In the previous researches [7, 8], however, the author proved that the pointwise estimate like (1.2) holds for the paraproduct and its iterated versions when the sum of the regularities is smaller than 1. The aim of this article is to extend these results for higher regularities.

math.AP↗
arXiv2023

A semigroup approach to the reconstruction theorem and the multilevel Schauder estimate

The reconstruction theorem and the multilevel Schauder estimate have central roles in the analytic theory of regularity structures [17]. Inspired by [26], we provide elementary proofs for them by using the semigroup of operators. Essentially, we use only the semigroup property and the upper estimates of kernels. Moreover, we refine the several types of Besov reconstruction theorems [18, 7] and introduce the new framework "regularity-integrability structures". The analytic theorems in this paper are applied to the study of quasilinear SPDEs [5] and an inductive proof of the convergence of random models [4].

math.AP↗
arXiv2022

Non relativistic and ultra relativistic limits in 2d stochastic nonlinear damped Klein-Gordon equation

We study the non relativistic and ultra relativistic limits in the two-dimensional nonlinear damped Klein-Gordon equation driven by a space-time white noise on the torus. In order to take the limits, it is crucial to clarify the parameter dependence in the estimates of solution. In this paper we present two methods to confirm this parameter dependence. One is the classical, simple energy method. Another is the method via Strichartz estimates.

math.AP↗
arXiv2022

Stochastic quantization associated with the $\exp(Φ)_2$-quantum field model driven by space-time white noise on the torus in the full $L^1$-regime

The present paper is a continuation of our previous work on the stochastic quantization of the $\exp(Φ)_2$-quantum field model on the two-dimensional torus. Making use of key properties of Gaussian multiplicative chaos and refining the method for singular SPDEs introduced in the previous work, we construct a unique time-global solution to the corresponding parabolic stochastic quantization equation in the full "$L^{1}$-regime" $\vertα\vert<\sqrt{8π}$ of the charge parameter $α$. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.

math.PR↗
arXiv2020

Asymptotics of PDE in random environment by paracontrolled calculus

We apply the paracontrolled calculus to study the asymptotic behavior of a certain quasilinear PDE with smeared mild noise, which originally appears as the space-time scaling limit of a particle system in random environment on one dimensional discrete lattice. We establish the convergence result and show a local in time well-posedness of the limit stochastic PDE with spatial white noise. It turns out that our limit stochastic PDE does not require any renormalization. We also show a comparison theorem for the limit equation.

math.PR↗
arXiv2019

Stochastic quantization associated with the $\exp(\Phi)_2$-quantum field model driven by space-time white noise on the torus

We consider a quantum field model with exponential interactions on the two-dimensional torus, which is called the $\exp (\Phi)_{2}$-quantum field model or H{\o}egh-Krohn's model. In the present paper, we study the stochastic quantization of this model by singular stochastic partial differential equations, which is recently developed. By the method, we construct a unique time-global solution and the invariant probability measure of the corresponding stochastic quantization equation, and identify with an infinite-dimensional diffusion process, which has been constructed by the Dirichlet form approach.

math.PR↗
arXiv2019

Commutator estimates from a viewpoint of regularity structures

First we introduce the Bailleul-Hoshino's result [4], which links the theory of regularity structures and the paracontrolled calculus. As an application of their result, we give another algebraic proof of the multicomponent commutator estimate [3], which is a generalized version of the Gubinelli-Imkeller-Perkowski's commutator estimate [11, Lemma 2.4].

math.AP↗
arXiv2018

Synchrotron radiation microtomography of brain hemisphere and spinal cord of a mouse model of multiple sclerosis revealed a correlation between capillary dilation and clinical score

Multiple sclerosis is a neurological disorder in which the myelin sheaths of axons are damaged by the immune response. We report here a three-dimensional structural analysis of brain and spinal cord tissues of a mouse model of multiple sclerosis, known as experimental autoimmune encephalomyelitis (EAE). EAE-induced mice were raised with or without administration of fingolimod, which is used in the treatment of multiple sclerosis. Brains and spinal cords dissected from the EAE mice were lyophilized so as to reconstitute the intrinsic contrast of tissue elements, such as axons, in X-ray images. Three-dimensional structures of the brain hemispheres and spinal cords of the EAE mice were visualized with synchrotron radiation microtomography. Microtomographic cross sections reconstructed from the X-ray images revealed dilation of capillary vessels and vacuolation in the spinal cord of the EAE mice. Vacuolation was also observed in the cerebellum, suggesting that the neuroinflammatory response progressed in the brain. The vessel networks and vacuolation lesions in the spinal cords were modelled by automatically tracing the three-dimensional image in order to analyze the tissue structures quantitatively. The results of the analysis indicated that the distribution of vacuolations was not uniform but three-dimensionally localized. The mean vessel diameter showed a linear correlation with the clinical score, indicating that vasodilation is relevant to paralysis severity in the disease model. We suggest that vasodilation and vacuolation are related with neurological symptoms of multiple sclerosis.

physics.bio-ph↗
arXiv2017

Stochastic complex Ginzburg-Landau equation with space-time white noise

We study the stochastic cubic complex Ginzburg-Landau equation with complex-valued space-time white noise on the three dimensional torus. This nonlinear equation is so singular that it can only be under- stood in a renormalized sense. In the first half of this paper we prove local well-posedness of this equation in the framework of regularity structure theory. In the latter half we prove local well-posedness in the framework of paracontrolled distribution theory.

math.PR↗
arXiv2017

Global well-posedness of complex Ginzburg-Landau equation with a space-time white noise

We show the global-in-time well-posedness of the complex Ginzburg-Landau (CGL) equation with a space-time white noise on the 3-dimensional torus. Our method is based on [14], where Mourrat and Weber showed the global well-posedness for the dynamical $Φ_3^4$ model. We prove a priori $L^{2p}$ estimate for the paracontrolled solution as in the deterministic case [5].

math.PR↗
arXiv2017

A coupled KPZ equation, its two types of approximations and existence of global solutions

This paper concerns the multi-component coupled Kardar-Parisi-Zhang (KPZ) equation and its two types of approximations. One approximation is obtained as a simple replacement of the noise term by a smeared noise with a proper renormalization, while the other one introduced in [6] is suitable for studying the invariant measures. By applying the paracontrolled calculus introduced by Gubinelli et al. [8, 9], we show that two approximations have the common limit under the properly adjusted choice of renormalization factors for each of these approximations. In particular, if the coupling constants of the nonlinear term of the coupled KPZ equation satisfy the so-called "trilinear" condition, the renormalization factors can be taken the same in two approximations and the difference of the limits of two approximations are explicitly computed. Moreover, under the trilinear condition, the Wiener measure twisted by the diffusion matrix becomes stationary for the limit and we show that the solution of the limit equation exists globally in time when the initial value is sampled from the stationary measure. This is shown for the associated tilt process. Combined with the strong Feller property shown by Hairer and Mattingly [12], this result can be extended for all initial values.

math.PR↗
arXiv2017

Paracontrolled calculus and Funaki-Quastel approximation for the KPZ equation

In this paper, we consider the approximating KPZ equation introduced by Funaki and Quastel [2], which is suitable for studying invariant measures. They showed that the stationary solution of the approximating equation converges to the Cole-Hopf solution of the KPZ equation with extra term $(1/24)t$. On the other hand, Gubinelli and Perkowski [5] gave a pathwise meaning to the KPZ equation as an application of the paracontrolled calculus. We show that Funaki and Quastel's result is extended to nonstationary solutions by using the paracontrolled calculus.

math.PR↗
arXiv2016

Three-dimensional X-ray visualization of axonal tracts in mouse brain hemisphere

Neurons transmit active potentials through axons, which are essential for the brain to function. In this study, the axonal networks of the murine brain were visualized with X-ray tomographic microscopy, also known as X-ray microtomography or micro-CT. Murine brain samples were freeze-dried to reconstitute the intrinsic contrast of tissue constituents and subjected to X-ray visualization. A whole brain hemisphere visualized by absorption contrast illustrated three-dimensional structures including those of the striatum, corpus callosum, and anterior commissure. Axonal tracts observed in the striatum start from the basal surface of the cerebral cortex and end at various positions in the basal ganglia. The distribution of X-ray attenuation coefficients indicated that differences in water and phospholipid content between the myelin sheath and surrounding tissue constituents account for the observed contrast. A rod-shaped cutout of brain tissue was also analyzed with a phase retrieval method, wherein tissue microstructures could be resolved with up to 2.7 μm resolution. Structures of axonal networks of the striatum were reconstructed by tracing axonal tracts. Such an analysis should be able to delineate the functional relationships of the brain regions involved in the observed network.

physics.bio-ph↗
arXiv2016

KPZ equation with fractional derivatives of white noise

In this paper, we consider the KPZ equation driven by space-time white noise replaced with its fractional derivatives of order $γ>0$ in spatial variable. A well-posedness theory for the KPZ equation is established by Hairer [3] as an application of the theory of regularity structures. Our aim is to see to what extent his theory works if noises become rougher. We can expect that his theory works if and only if $γ<1/2$. However, we show that the renormalization like "$(\partial_x h)^2-\infty$" is well-posed only if $γ<1/4$.

math.PR↗