Maximum Score Estimation of Preference Parameters for a Binary Choice Model under Uncertainty

This paper develops maximum score estimation of preference parameters in the binary choice model under uncertainty in which the decision rule is affected by conditional expectations. The preference parameters are estimated in two stages: we estimate conditional expectations nonparametrically in the first stage and then the preference parameters in the second stage based on Manski (1975, 1985)'s maximum score estimator using the choice data and first stage estimates. The paper establishes consistency and derives rate of convergence of the two-stage maximum score estimator. Moreover, the paper also provides sufficient conditions under which the two-stage estimator is asymptotically equivalent in distribution to the corresponding single-stage estimator that assumes the first stage input is known. These results are of independent interest for maximum score estimation with nonparametrically generated regressors. The paper also presents some Monte Carlo simulation results for finite-sample behavior of the two-stage estimator

Heating-compensated constant-temperature tunneling measurements on stacks of Bi2_2Sr2_2CaCu2_2O8+x_{8+x} intrinsic junctions

In highly anisotropic layered cuprates such as Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ tunneling measurements on a stack of intrinsic junctions in a high-bias range are often susceptible to self-heating. In this study we monitored the temperature variation of a stack ("sample stack") of intrinsic junctions by measuring the resistance change of a nearby stack ("thermometer stack") of intrinsic junctions, which was strongly thermal-coupled to the sample stack through a common Au electrode. We then adopted a proportional-integral-derivative scheme incorporated with a substrate-holder heater to compensate the temperature variation. This in-situ temperature monitoring and controlling technique allows one to get rid of spurious tunneling effects arising from the self-heating in a high bias range.Comment: 3 pages, 3 figure

Collective Josephson vortex dynamics in a finite number of intrinsic Josephson junctions

We report the experimental confirmation of the collective transverse plasma modes excited by the Josephson vortex lattice in stacks of intrinsic Josephson junctions in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ single crystals. The excitation was confirmed by analyzing the temperature ($T$) and magnetic field ($H$) dependencies of the multiple sub-branches in the Josephson-vortex-flow region of the current-voltage characteristics of the system. In the near-static Josephson vortex state for a low tunneling bias current, pronounced magnetoresistance oscillations were observed, which represented a triangular-lattice vortex configuration along the c axis. In the dynamic vortex state in a sufficiently high magnetic field and for a high bias current, splitting of a single Josephson vortex-flow branch into multiple sub-branches was observed. Detailed examination of the sub-branches for varying $H$ field reveals that sub-branches represent the different modes of the Josephson-vortex lattice along the c axis, with varied configuration from a triangular to a rectangular lattices. These multiple sub-branches merge to a single curve at a characteristic temperature, above which no dynamical structural transitions of the Josephson vortex lattice is expected

RECENT RESULTS ON SEQUENTIAL OPTIMALITY THEOREMS FOR CONVEX OPTIMIZATION PROBLEMS (Nonlinear Analysis and Convex Analysis)

In this brief note, we review sequential optimality theorems in [5]. We give two kinds of sequential optimality theorems for a convex optimization problem, which are expressed in terms of sequences of epsilon-subgradients and subgradients of involved functions

Competition between structural distortion and magnetic moment formation in fullerene C20_{20}

We investigated the effect of on-site Coulomb interactions on the structural and magnetic ground state of the fullerene C$_{20}$ based on density-functional-theory calculations within the local density approximation plus on-site Coulomb corrections (LDA+$U$). The total energies of the high symmetry ($I_{h}$) and distorted ($D_{3d}$) structures of C$_{20}$ were calculated for different spin configurations. The ground state configurations were found to depend on the forms of exchange-correlation potentials and the on-site Coulomb interaction parameter $U$, reflecting the subtle nature of the competition between Jahn-Teller distortion and magnetic instability in fullerene C$_{20}$. While the non-magnetic state of the distorted $D_{3d}$ structure is robust for small $U$, a magnetic ground state of the undistorted $I_{h}$ structure emerges for $U$ larger than 4 eV when the LDA exchange-correlation potential is employed.Comment: 4 figures, 1 tabl

Affinization of qq-oscillator representations of Uq(gln)U_q(\mathfrak{gl}_n)

We introduce a category $\widehat{\mathcal{O}}_{\rm osc}$ of $q$-oscillator representations of the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_n)$. We show that $\widehat{\mathcal{O}}_{\rm osc}$ has a family of irreducible representations, which naturally corresponds to finite-dimensional irreducible representations of quantum affine algebra of untwisted affine type $A$. It is done by constructing a category of $q$-oscillator representations of the quantum affine superalgebra of type $A$, which interpolates these two family of irreducible representations. The category $\widehat{\mathcal{O}}_{\rm osc}$ can be viewed as a quantum affine analogue of the semisimple tensor category generated by unitarizable highest weight representations of $\mathfrak{gl}_{u+v}$ ($n=u+v$) appearing in the $(\mathfrak{gl}_{u+v},\mathfrak{gl}_\ell)$-duality on a bosonic Fock space.Comment: 41 pages, Abstract and Introduction revised, together with minor correction