## PUBLICATIONS

### MI Preprint Series

Title：Moment convergence of regularized least-squares estimator for linear regression model

Author : Yusuke Shimizu

Abstract: In this paper we study the uniform tail-probability estimates of a regularized least-squares estimator for the linear regression model, by making use of the polynomial type large deviation inequality for the associated statistical random fields, which may not be locally asymptotically quadratic. Our results provide a measure of rate of consistency in variable selection in sparse estimation, which in particular enable us to verify various arguments requiring convergence of moments of estimator-dependent statistics, such as the expected maximum-likelihood for AIC-type and many other moment based model assessment procedure including the $C_{p}$-type.

#### 2014-12

Title：Exact and approximation algorithms for weighted matroid intersection

Author : Chien-Chung Huang, Naonori Kakimura & Naoyuki Kamiyama

Abstract: We present exact and approximation algorithms for the weighted matroid intersection problems. Our exact algorithms are faster than previous algorithms when the largest weight is relatively small. Our approximation algorithms deliver a (1 - ¥epsilon)-approximate solution with running times significantly faster than known exact algorithms. The core of our algorithms is a decomposition technique: we decompose the weighted version of the problem into a set of unweighted matroid intersection problems. The computational advantage of this approach is that we can then make use of fast unweighted matroid intersection algorithms as a black box for designing algorithms. To be precise, we show that we can find an exact solution via solving W unweighted matroid intersections problems, where W is the largest given weight. Furthermore, we can find a (1 - ¥epsilon)-approximate solution via solving O(¥epsilon^{-1} log r) unweighted matroid intersection problems, where r is the smallest rank of the given two matroids.

#### 2014-11(Published)

Title：Instability of plane Poiseuille flow in viscous compressible gas

Author : Yoshiyuki Kagei & Takaaki Nishida

Abstract: Instability of plane Poiseuille flow in viscous compressible gas is investigated. A condition for the Reynolds and Mach numbers is given in order for plane Poiseuille flow to be unstable. It turns out that plane Poiseuille flow is unstable for Reynolds numbers much less than the critical Reynolds number for the incompressible flow when the Mach number is suitably large. It is proved by the analytic perturbation theory that the linearized operator around plane Poiseuille flow has eigenvalues with positive real part when the instability condition for the Reynolds and Mach numbers is satisfied.

J. Math. Fluid Mech., vol. 17 (2015), pp. 129--143

DOI: 10.1007/s00021-014-0191-4

#### 2014-10

Title：On the existence and stability of time periodic solution to the compressible Navier-Stokes equation on the whole space

Author : Kazuyuki Tsuda

Abstract: The existence of a time periodic solution of the compressible Navier-Stokes equation on the whole space is proved for sufficiently small time periodic external force when the space dimension is greater than or equal to $3$. The proof is based on the spectral properties of the time-$T$-map associated with the linearized problem around the motionless state with constant density in some weighted $L^\infty$ and Sobolev spaces. The time periodic solution is shown to be asymptotically stable under sufficiently small initial perturbations and the $L^\infty$ norm of the perturbation decays as time goes to infinity.

#### 2014-9(Published)

Title：Spectral properties of the linearized semigroup of the compressible Navier-Stokes equation on a periodic layer

Author : Yoshiyuki Kagei & Naoki Makio

Abstract: The linearized problem for the compressible Navier-Stokes equation around a given constant state is considered in a periodic layer of $\mathbb{R}^{n}$ with $n\geq2$, and spectral properties of the linearized semigroup is investigated. It is shown that the linearized operator generates a $C_0$-semigroup in $L^2$ over the periodic layer and the time-asymptotic leading part of the semigroup is given by a $C_0$-semigroup generated by an $n-1$ dimensional elliptic operator with constant coefficients that are determined by solutions of a Stokes system over the basic period domain.

Publ. Res. Inst. Math. Sci., Vol.51, no. 2 (2015), pp. 337--372.

DOI: 10.4171/PRIMS/158

#### 2014-8

Title：Local stability analysis of azimuthal magnetorotational instability of ideal MHD flows

Author : Rong Zou & Yasuhide Fukumoto

Abstract: Short-wavelength stability analysis is made of axisymmetric rotating flows of a perfectly conducting fluid, subjected to external azimuthal magnetic field to non-axisymmetric as well as axisymmetric perturbations. When the magnetic field is sufficiently weak, the instability occurs for Rossby number smaller than the critical value near zero and the maximum growth rate is close to the Oort A-value. As the magnetic field is increased, the flow becomes unstable to waves of very short axial wavelengths for the whole range of Rossby number and for magnetic Rossby number greater than -3/4 and to waves of very long axial wavelengths for a finite range of Rossby number and for magnetic Rossby number smaller than -1/2. For the both waves, the maximum growth rate increases, beyond the Oort A-value, without bound in proportion to magnetic field strength.

Progress of Theoretical and Experimental Physics (PTEP),2014,113J01 (18pages),2014.11.

#### 2014-7

Title：On decay estimate of strong solutions in critical spaces for the compressible Navier-Stokes equations

Author : Masatoshi Okita

Abstract: This paper is concerned with the convergence rates of the global strong solutions to the motionless state with constant density of the compressible

Navier-Stokes equations in the whole space. The optimal decay estimates in critical spaces are established if the initial perturbations are small in critical regularity Besov spaces.

#### 2014-6

Title：*****

This paper was withdrawn by the authors.

#### 2014-5(Published)

Title：Existence and stability of time periodic solution to the compressible Navier-Stokes equation for time periodic external force with symmetry

Author : Yoshiyuki Kagei & Kazuyuki Tsuda

Abstruct: Time periodic problem for the compressible Navier-Stokes equation on the whole space is studied. The existence of a time periodic solution is proved for sufficiently small time periodic external force with some symmetry when the space dimension is greater than or equal to 3. The proof is based on the spectral properties of the time-T map associated with the linearized problem around the motionless state with constant density in some weighted Sobolev space. The stability of the time periodic solution is also proved and the decay estimate of the perturbation is established.

J. Differential Equations, vol. 158 (2015), pp. 399--444

doi:10.1016/j.jde.2014.09.016

#### 2014-4(Published)

Title：The Popular Condensation Problem under Matroid Constraints

Author : Naoyuki Kamiyama

Abstract: The popular matching problem introduced by Abraham, Irving, Kavitha, and Mehlhorn is one of assignment problems in strategic situation. It is known that a given instance of this problem may admit no popular matching. For coping with such instances, Wu, Lin, Wang, and Chao introduced the popular condensation problem whose goal is to transform a given instance so that it has popular matching by deleting a minimum number of agents. In this paper, we consider a matroid generalization of the popular condensation problem, and give a polynomial-time algorithm for this problem.

Lecture Notes in Computer Science

#### 2014-3

Title：Decay estimates on solutions of the linearized compressible Navier-Stokes equation around a Parallel flow in a cylindrical domain

Author : Reika Aoyama

Abstract: This paper is concerned with the stability of a parallel flow of the compressible Navier-Stokes equation in a cylindrical domain. Decay estimates on the linearized semigroup is established. It is shown that if the Reynolds and Mach numbers are sufficiently small, then solutions of the linearized problem decay in the L^2-norm as a one dimensional heat kernel. The proof is given by a variant of the Matsumura-Nishida energy method.

#### 2014-2

Title：Lagrangian approach to weakly nonlinear interaction of Kelvin waves and a symmetry-breaking bifurcation of a rotating flow

Author : Yasuhide Fukumoto & Youichi Mie

Abstract: We develop a general framework of using the Lagrangian variables for calculating the energy of waves on a steady Euler flow and the mean flow induced by their nonlinear interaction. With the mean flow at hand, we can determine, without ambiguity, all the coefficients of the amplitude equations to third order in amplitude, for a rotating flow subject to a steady perturbation breaking the circular symmetry of the streamlines. Moreover, a resonant triad of waves is identified, which brings in the secondary instability of the Moore-Saffman-Tsai-Widnall instability, and, with the aid of the energetic viewpoint, resonant amplification of the waves without bound is numerically confirmed.

Fluid Dynamics Research,47,1,015509 (15pp),2015.02.

#### 2014-1(Published)

Title：Popular Matchings under Matroid Constraints

Author : Naoyuki Kamiyama

Abstract: In this paper, we consider a matroid generalization of the popular matching problem introduced by Abraham, Irving, Kavitha and Mehlhorn, and present a polynomial-time algorithm for this problem.

Lecture Notes in Computer Science

## 2014-13