Kazufumi Ito

发表

Minimal Effort Problems and Their Treatment by Semismooth Newton Methods

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2011, SIAM J. Control. Optim..

Augmented Lagrangian-SQP-Methods in Hilbert Spaces and Application to Control in the Coefficients Problems

Kazufumi Ito, Karl Kunisch, K. Kunisch, 1996, SIAM J. Optim..

The augmented lagrangian method for equality and inequality constraints in hilbert spaces

Kazufumi Ito, Karl Kunisch, K. Kunisch, 1990, Math. Program..

7. The Primal-Dual Active Set Method

Kazufumi Ito, Karl Kunisch, 2008 .

Higher-Order, Cartesian Grid Based Finite Difference Schemes for Elliptic Equations on Irregular Domains

Kazufumi Ito, Zhilin Li, Yaw Kyei, 2005, SIAM J. Sci. Comput..

Parameter Identification for Semiconductor Diodes by LBIC Imaging

Kazufumi Ito, David A. Redfern, Weifu Fang, 2002, SIAM J. Appl. Math..

A Time-Dependent Direct Sampling Method for Recovering Moving Potentials in a Heat Equation

Kazufumi Ito, Jun Zou, Yat Tin Chow, 2018, SIAM J. Sci. Comput..

Optimal Bilinear Control of an Abstract Schrödinger Equation

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2007, SIAM J. Control. Optim..

Regularized Linear Inversion with Randomized Singular Value Decomposition pdf

Kazufumi Ito, Bangti Jin, K. Ito, 2019, Mathematical and Numerical Approaches for Multi-Wave Inverse Problems.

Optimal Control with Lp(Ω), $p\in [0, 1)$, Control Cost

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2014, SIAM J. Control. Optim..

PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14

Kazufumi Ito, Rf Curtain, Ma Demetriou, 1990 .

Asymptotic Properties of Receding Horizon Optimal Control Problems

Kazufumi Ito, Karl Kunisch, 2002, SIAM J. Control. Optim..

On-line actuator fault detection and accommodation scheme for positive real infinite dimensional systems

Michael A. Demetriou, Kazufumi Ito, 2003 .

A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach

Kazufumi Ito, Zhonghua Qiao, K. Ito, 2008, J. Comput. Phys..

Optimum damping design for an abstract wave equation

Kazufumi Ito, Fariba Fahroo, K. Ito, 1996, Kybernetika.

Interface conditions for Stokes equations with a discontinuous viscosity and surface sources

Kazufumi Ito, Zhilin Li, 2006, Appl. Math. Lett..

A Note on the Existence of Nonsmooth Nonconvex Optimization Problems

Kazufumi Ito, Karl Kunisch, 2014, J. Optim. Theory Appl..

Development Of High Resolution And Low Noise Single-layered Perpendicular Recording Meidia For High Density Recording

Kazufumi Ito, Yoshiro Hirayama, Masaaki Futamoto, 1996, Digests of the Magnetic Recording Conference 'Magnetic Recording Media'..

Multi-Parameter Tikhonov Regularization pdf

Bangti Jin, Kazufumi Ito, Tomoya Takeuchi, 2011, ArXiv.

Theoretical and Computational Aspects of Feedback in Structural Systems with Piezoceramic Controllers

Kazufumi Ito, H. T. Banks, Belinda B. King, 1993 .

Modeling and Analysis of Laser-Beam-Induced Current Images in Semiconductors

Kazufumi Ito, Weifu Fang, Stavros Busenberg, 1993, SIAM J. Appl. Math..

The Nonnegative Matrix Factorization and atomic deconvolution

Kazufumi Ito, Amanda K. Landi, 2015, 2015 IEEE International Conference on Bioinformatics and Biomedicine (BIBM).

Approximate Nullspace Iterations for KKT Systems

Kazufumi Ito, Karl Kunisch, Volker Schulz, 2010, SIAM J. Matrix Anal. Appl..

Analysis on a Nonnegative Matrix Factorization and Its Applications

Kazufumi Ito, Jun Zou, Yat Tin Chow, 2016, SIAM J. Sci. Comput..

Feedback Solution and Receding Horizon Control Synthesis for a Class of Quantum Control Problems

Qin Zhang, Kazufumi Ito, 2010 .

The Primal-Dual Active Set Method for Nonlinear Optimal Control Problems with Bilateral Constraints

Kazufumi Ito, Karl Kunisch, 2004, SIAM J. Control. Optim..

Asymptotic Properties of Feedback Solutions for a Class of Quantum Control Problems

Kazufumi Ito, Karl Kunisch, 2009, SIAM J. Control. Optim..

Gaussian filters for nonlinear filtering problems

Kazufumi Ito, Kaiqi Xiong, K. Ito, 2000, IEEE Trans. Autom. Control..

A class of robust adaptive controllers for infinite dimensional dynamical systems

Kazufumi Ito, M. A. Demetriou, 1996 .

A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains

Kazufumi Ito, Zhilin Li, Ming-Chih Lai, 2009, J. Comput. Phys..

A fast algorithm for determining optimal feedback gain

Kazufumi Ito, Jari Toivanen, 2008 .

Immersed finite elements for optimal control problems of elliptic PDEs with interfaces

Qian Zhang, Kazufumi Ito, Zhilin Li, 2015, J. Comput. Phys..

Subspace Iteration and Immersed Interface Methods: Theory, Algorithm, and Applications

Kazufumi Ito, Zhilin Li, 2010 .

Evolution Equations And Approximations

Kazufumi Ito, Franz Kappel, K. Ito, 2002, Series on Advances in Mathematics for Applied Sciences.

On the Choice of the Regularization Parameter in Nonlinear Inverse Problems

Kazufumi Ito, Karl Kunisch, K. Kunisch, 1992, SIAM J. Optim..

Direct Sampling Method for Diffusive Optical Tomography

Kazufumi Ito, Jun Zou, Yat Tin Chow, 2014, SIAM J. Sci. Comput..

4. The IIM for Three-Dimensional Elliptic Interface Problems

Kazufumi Ito, Zhilin Li, 2006 .

Feedback stabilization and control of linear neutral systems

Mark W. Spong, Kazufumi Ito, Mark W. Spong, 1982 .

A Numerical Study of an Augmented Lagrangian Method for the Estimation of Parameters in Elliptic Systems

Kazufumi Ito, Karl Kunisch, M. Kroller, 1991, SIAM J. Sci. Comput..

A neural network based policy iteration algorithm with global H2-superlinear convergence for stochastic games on domains pdf

Kazufumi Ito, Christoph Reisinger, Yufei Zhang, 2019, Found. Comput. Math..

The Primal-Dual Active Set Strategy as a Semismooth Newton Method

Kazufumi Ito, Karl Kunisch, Michael Hintermüller, 2002, SIAM J. Optim..

Convergence of the Primal-Dual Active Set Strategy for Diagonally Dominant Systems

Kazufumi Ito, Karl Kunisch, 2007, SIAM J. Control. Optim..

Solving a Nonlinear Problem in Magneto-Rheological Fluids Using the Immersed Interface Method

Kazufumi Ito, Zhilin Li, Zhilin Li, 2003, J. Sci. Comput..

9. Semismooth Newton Methods II: Applications

Kazufumi Ito, Karl Kunisch, 2008 .

Lagrange multiplier approach to variational problems and applications

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2008, Advances in design and control.

Inverse Problems

Bangti Jin, Kazufumi Ito, K. Ito, 2014, Series on Applied Mathematics.

On the sectorial property of the Caputo derivative operator

Bangti Jin, Kazufumi Ito, Tomoya Takeuchi, 2015, Appl. Math. Lett..

Lagrange Multiplier Approach with Optimized Finite Difference Stencils for Pricing American Options under Stochastic Volatility

Kazufumi Ito, Jari Toivanen, K. Ito, 2009, SIAM J. Sci. Comput..

A feedback control law for systems arising in fluid dynamics

Kazufumi Ito, S. Kang, 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

Multi)fractality of Earthquakes by use of Wavelet Analysis

Kazufumi Ito, Zbigniew R. Struzik, Bogdan Enescu, 2002 .

Novel Concepts for Nonsmooth Optimization and their Impact on Science and Technology

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2011 .

A numerical integration-based Kalman filter for moderately nonlinear systems

Kazufumi Ito, Daniel Hodyss, Sarah A. King, 2020 .

A domain decomposition solver for acoustic scattering by elastic objects in layered media

Kazufumi Ito, Zhonghua Qiao, Jari Toivanen, 2008, J. Comput. Phys..

Semismooth Newton Methods for Time-Optimal Control for a Class of ODEs

Kazufumi Ito, Karl Kunisch, 2010, SIAM J. Control. Optim..

Optimal Control of Thermally Convected Fluid Flows

Kazufumi Ito, S. S. Ravindran, S. Ravindran, 1998, SIAM J. Sci. Comput..

Semi-smooth Newton methods for state-constrained optimal control problems

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2003, Syst. Control. Lett..

Optimal Control of the Solid Fuel Ignition Model with H[sup 1]-Cost

Kazufumi Ito, Karl Kunisch, 2002, SIAM J. Control. Optim..

Receding Horizon Control with Incomplete Observations

Kazufumi Ito, Karl Kunisch, 2006, SIAM J. Control. Optim..

A two-stage method for inverse medium scattering

Bangti Jin, Kazufumi Ito, Jun Zou, 2012, J. Comput. Phys..

On a semi-smooth Newton method and its globalization

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2009, Math. Program..

Nonsmooth Formulation of the Support Vector Machine for a Neural Decoding Problem

Kazufumi Ito, Chad Bouton, Cary Humber, 2010, 1012.0958.

LBIC imaging of semiconductor arrays: the cross-sectional model

Kazufumi Ito, Weifu Fang, D. A. Redfern, 2004, Math. Comput. Model..

A Parallel Domain Decomposition Method for the Helmholtz Equation in Layered Media

Kazufumi Ito, Jari Toivanen, Erkki Heikkola, 2019, SIAM J. Sci. Comput..

Applications to Concrete Systems

Kazufumi Ito, Franz Kappel, 2002 .

Newton's Method for a Class of Weakly Singular Optimal Control Problems

Kazufumi Ito, Karl Kunisch, 2000, SIAM J. Optim..

Reduced-Order Optimal Control Based on Approximate Inertial Manifolds for Nonlinear Dynamical Systems

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2008, SIAM J. Numer. Anal..

An Optimal Optical Flow

Kazufumi Ito, Kazufumi Ito, 2005, SIAM J. Control. Optim..

Material Surface Design to Counter Electromagnetic Interrogation of Targets

Kazufumi Ito, H. T. Banks, Grace M. Kepler, 2006, SIAM J. Appl. Math..

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

Kazufumi Ito, 1983, The 22nd IEEE Conference on Decision and Control.

The Trotter-Kato theorem and approximation of PDEs

Kazufumi Ito, Franz Kappel, F. Kappel, 1998, Math. Comput..

Optimal control laws for traffic flow

Kazufumi Ito, Kazuyuki Aihara, Junichi Nakagawa, 2013, Appl. Math. Lett..

Reconstruction of Semiconductor Doping Profile from Laser-Beam-Induced Current Image

Kazufumi Ito, Weifu Fang, W. Fang, 1994, SIAM J. Appl. Math..

Approximation of the Kushner Equation for Nonlinear Filtering

Kazufumi Ito, Boris Rozovskii, 2000, SIAM J. Control. Optim..

Nonsmooth Optimization Method and Sparsity

Kazufumi Ito, Kazufumi Ito, 2013, Control and Optimization with PDE Constraints.

A Sequential Method for a Class of Stable Mathematical Programming Problems

Kazufumi Ito, Karl Kunisch, 2016, SIAM J. Optim..

Optimal Control Formulation for Determining Optical Flow

Kazufumi Ito, Karl Kunisch, Alfio Borzì, 2002, SIAM J. Sci. Comput..

Multi-parameter Tikhonov regularization — An augmented approach

Bangti Jin, Kazufumi Ito, Tomoya Takeuchi, 2013 .

The Nonnegative Matrix Factorization: Regularization and Complexity

Kazufumi Ito, A. K. Landi, 2016, SIAM J. Sci. Comput..

11. Shape Optimization

Kazufumi Ito, Karl Kunisch, 2008 .

Adaptive monitoring and accommodation of nonlinear actuator faults in positive real infinite dimensional systems

Michael A. Demetriou, Kazufumi Ito, Ralph C. Smith, 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

Preconditioned iterative methods on sparse subspaces

Kazufumi Ito, Jari Toivanen, J. Toivanen, 2006, Appl. Math. Lett..

A method for determination of optimal gaits with application to a snake-like serial-link structure

Kazufumi Ito, Gregory Hicks, G. Hicks, 2005, IEEE Transactions on Automatic Control.

A Regularization Parameter for Nonsmooth Tikhonov Regularization

Kazufumi Ito, Bangti Jin, Tomoya Takeuchi, 2011, SIAM J. Sci. Comput..

Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients

Kazufumi Ito, Zhilin Li, K. Ito, 2001, SIAM J. Sci. Comput..

Karush-Kuhn-Tucker Conditions for Nonsmooth Mathematical Programming Problems in Function Spaces

Kazufumi Ito, Karl Kunisch, 2011, SIAM J. Control. Optim..

Least squares formulation for ill-posed inverse problems and applications

Kazufumi Ito, Eric T. Chung, Masahiro Yamamoto, 2021, Applicable Analysis.

Least-Squares Method for Inverse Medium Problems

Kazufumi Ito, Jun Zou, Ying Liang, 2022 .

Semi-decoupling hybrid asymptotic and augmented finite volume method for nonlinear singular interface problems

Kazufumi Ito, Tengjin Zhao, Zhiyue Zhang, 2021, J. Comput. Appl. Math..

APPROXIMATE NULLSPACE ITERATIONS FOR KKT SYSTEMS IN MODEL BASED OPTIMIZATION

Kazufumi Ito, Karl Kunisch, Ilia Gherman, 2006 .

Legendre-Tau approximations for functional differential equations

Kazufumi Ito, K. Ito, Russell Teglas, 1986 .

A linear quadratic optimal control for neutral systems

Kazufumi Ito, T. J. Tarn, 1985 .

A Dissipative Feedback Control Synthesis for Systems Arising in Fluid Dynamics

Kazufumi Ito, Sungkwon Kang, 1994 .

Adaptive observers for slowly time varying infinite dimensional systems

Ruth F. Curtain, Michael A. Demetriou, Kazufumi Ito, 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

The primal-dual active set strategy as a semi-smooth Newton method for quadratic problems with affine constraints

Kazufumi Ito, K. Kunisch, M. Hintermüller, 2002 .

Piecewise linear model for field-responsive fluids

Kazufumi Ito, Harvey Thomas Banks, Fernando Reitich, 2001 .

Variational approach to shape derivatives

Kazufumi Ito, Karl Kunisch, Gunther H. Peichl, 2008 .

Sensitivity analysis of solutions to optimization problems in Hilbert spaces with applications to optimal control and estimation

Kazufumi Ito, Karl Kunisch, K. Kunisch, 1992 .

A direct sampling method to an inverse medium scattering problem

Bangti Jin, Kazufumi Ito, Jun Zou, 2012 .

A reduced order method for control of fluid flows

Kazufumi Ito, Sivaguru S. Ravindran, 1996, Proceedings of 35th IEEE Conference on Decision and Control.

Two Families of Approximation Schemes for Delay Systems

Kazufumi Ito, Franz Kappel, K. Ito, 1992 .

Semi-smooth Newton methods for the Signorini problem

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2008 .

Estimation of the Effective Permeability in Magnetorheological Fluids

Kazufumi Ito, Fernando Reitich, Mark R. Jolly, 1999 .

Adaptive observers for structurally perturbed positive real delay systems

Kazufumi Ito, R. F. Curtain, M. A. Demetriou, 1998 .

On-line monitoring and accommodation of nonlinear actuator faults in positive real infinite dimensional systems

Michael A. Demetriou, Kazufumi Ito, Ralph C. Smith, 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

Identifiability of stiffness and damping coefficients in euler-bernoulli beam equations with kelvin-voigt damping

Kazufumi Ito, Shin-ichi Nakagiri, K. Ito, 1997 .

Indentification of some source densities of the distribution type

Kazufumi Ito, Jun Zou, 2001 .

A uniformly differentiable approximation scheme for delay systems using splines

Kazufumi Ito, Franz Kappel, 1991 .

An augmented Lagrangian technique for variational inequalities

Kazufumi Ito, Karl Kunisch, K. Kunisch, 1990 .

Optimal control of parabolic variational inequalities

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2010 .

Approximation in LQR problems for infinite dimensional systems with unbounded input operators

Kazufumi Ito, Harvey Thomas Banks, H. Banks, 1994 .

Uniqueness for solutions of differential complementarity problems

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2009 .

A Fast Helmholtz Solver for Scattering by a Sound-soft Target in Sediment

Kazufumi Ito, Jari Toivanen, Quyen Huynh, 2007 .

On Convergence of A Fixed-Point Iterate for Quasilinear Elliptic Equations

Kazufumi Ito, 2009 .

Strong convergence and convergence rates of approximating solutions for algebraic riccati equations in Hilbert spaces

Kazufumi Ito, Kazufumi Ito, 1987 .

ADAPTIVE COMPENSATORS FOR PERTURBED POSITIVE REAL INFINITE-DIMENSIONAL SYSTEMS

Ruth F. Curtain, Michael A. Demetriou, Kazufumi Ito, 2003 .

On the shape derivative for problems of Bernoulli type

Kazufumi Ito, Karl Kunisch, Tomáš Kozubek, 2009 .

Three-dimensional elliptic solvers for interface problems and applications

Kazufumi Ito, Shaozhong Deng, Zhilin Li, 2003 .

Regular Article: Simulations of Particle Dynamics in Magnetorheological Fluids

Kazufumi Ito, Harvey Thomas Banks, Fernando Reitich, 1999 .

Level Set Methods for Variational Problems and Applications

Kazufumi Ito, K. Ito, 2003 .

Adaptive observers for structurally perturbed infinite dimensional systems

Ruth F. Curtain, Michael A. Demetriou, Kazufumi Ito, 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

A variational approach to approximation of delay systems

Kazufumi Ito, Franz Kappel, Dietmar Salamon, 1991 .

A variational approach to sparsity optimization based on Lagrange multiplier theory

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2013 .

Identifiability of semiconductor defects from LBIC images

Kazufumi Ito, Weifu Fang, K. Ito, 1992 .

Optimal Controls of Navier--Stokes Equations

Kazufumi Ito, Mihir Desai, K. Ito, 1994 .

Adaptive Observers for a Class of Infinite Dimensional Systems

Michael A. Demetriou, Kazufumi Ito, 1996 .

Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2000 .

Semigroup theory and numerical approximation for equations in linear viscoelasticity

Kazufumi Ito, R. H. Fabiano, 1990 .

A direct sampling method for inverse electromagnetic medium scattering

Bangti Jin, Kazufumi Ito, Jun Zou, 2012, 1212.5085.

Low temperature saturation of p–n junction laser beam induced current signals

Kazufumi Ito, Lorenzo Faraone, John Dell, 2004 .

A fully discretized approximation scheme for size-structured population models

Kazufumi Ito, Franz Kappel, Gunther H. Peichl, 1991 .

Well posedness for damped second-order systems with unbounded input operators

Kazufumi Ito, Harvey Thomas Banks, H. Banks, 1995, Differential and Integral Equations.

Adaptive techniques for the MRAC, adaptive parameter identification, and on‐line fault monitoring and accommodation for a class of positive real infinite dimensional systems

Michael A. Demetriou, Kazufumi Ito, Ralph C. Smith, 2009 .

A time reversal based algorithm for solving initial data inverse problems

Kazufumi Ito, Marius Tucsnak, Karim Ramdani, 2010 .

Optimal absorption design for damped elastic systems

Kazufumi Ito, Fariba Fahroo, K. Ito, 2006, 2006 American Control Conference.

Estimation of the convection coefficient in elliptic equations

Kazufumi Ito, Karl Kunisch, K. Kunisch, 1997 .

Recovery of inclusions in 2D and 3D domains for Poisson?s equation

Kazufumi Ito, Ji-Chuan Liu, 2013 .

A new choice rule for regularization parameters in Tikhonov regularization

Bangti Jin, Kazufumi Ito, Jun Zou, 2011 .

Semi–Smooth Newton Methods for Variational Inequalities of the First Kind

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2003 .

A high-order perturbation approach to profile reconstruction

Kazufumi Ito, Fernando Reitich, F. Reitich, 1999 .

Optimal Control of Elliptic Variational Inequalities

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2000 .

4. Augmented Lagrangian Methods for Nonsmooth, Convex Optimization

Kazufumi Ito, Karl Kunisch, 2008 .

EXISTENCE OF STATIONARY SOLUTIONS TO AN ENERGY DRIFT-DIFFUSION MODEL FOR SEMICONDUCTOR DEVICES

Kazufumi Ito, Weifu Fang, 2001 .

On nonconvergence of adjoint semigroups for control systems with delays

Kazufumi Ito, John A. Burns, Georg Propst, 1988 .

A new approach to nonlinear constrained Tikhonov regularization

Bangti Jin, Kazufumi Ito, K. Ito, 2011, 1109.0654.

The effective magnetic properties of magnetorheological fluids

Kazufumi Ito, Harvey Thomas Banks, Fernando Reitich, 2001 .

A minimum effort optimal control problem for elliptic PDEs

Kazufumi Ito, Karl Kunisch, Christian Clason, 2012 .

An Approximation Theory of Solutions to Operator Riccati Equations for $H^\infty$ Control

Kazufumi Ito, K. A. Morris, 1998 .

Real-Time Optical Control of Ga1-xInxP Film Growth by P-Polarized Reflectance

Kazufumi Ito, Vincent Woods, K. Ito, 1999 .

Numerical methods for a class of singular integro-differential equations based on semigroup approximation

Kazufumi Ito, Janos Turi, 1991 .

A direct sampling method for electrical impedance tomography

Kazufumi Ito, Jun Zou, Yat Tin Chow, 2014 .

Reduced basis method for flow control

Kazufumi Ito, Sivaguru S. Ravindran, 1996 .

Reduced order feedback synthesis for viscous incompressible flows

Kazufumi Ito, J. D. Schroeter, Kazufumi Ito, 2001 .

Unbounded observation and boundary control problems for Burgers equation

Kazufumi Ito, John A. Burns, J. Burns, 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

Reduced order control based on approximate inertial manifolds

Kazufumi Ito, Karl Kunisch, K. Kunisch, 2006 .

Steady-State Solutions of a One-Dimensional Hydrodynamic Model for Semiconductors

Kazufumi Ito, Weifu Fang, 1997 .

Identification of contact regions in semiconductor transistors by level-set methods

Kazufumi Ito, Weifu Fang, K. Ito, 2003 .

Dynamic Evasion-Interrogation Games with Uncertainty in the Context of Electromagetics

Kazufumi Ito, Harvey Thomas Banks, Shuhua Hu, 2011 .