Comment on "Vortex Liquid Crystal in Anisotropic Type II Superconductors"

This is a Comment on "Vortex Liquid Crystal in Anisotropic Type II Superconductors" by E. W. Carlson et al. in PRL, vol.90, 087001 (2003) [cond-mat/0209175].Comment: 2 pages, 1 figure, revised versio

Collective modes of a harmonically trapped one-dimensional Bose gas: the effects of finite particle number and nonzero temperature

Following the idea of the density functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap, by using a local chemical potential - calculated with the Lieb-Liniger exact solution - as the exchange energy. At zero temperature, we use the theory to describe collective modes of a finite-particle system in all interaction regimes from the ideal gas limit, to the mean-field Thomas-Fermi regime, and to the strongly interacting Tonks-Girardeau regime. At finite temperature, we investigate the temperature dependence of collective modes in the weak-coupling regime by means of a Hartree-Fock-Bogoliubov theory with Popov approximation. By emphasizing the effects of finite particle number and nonzero temperature on collective mode frequencies, we make comparisons of our results with the recent experimental measurement [E. Haller et al., Science 325, 1224 (2009)] and some previous theoretical predictions. We show that the experimental data are still not fully explained within current theoretical framework.Comment: 10 pages, 8 figure

A generalized exchange-correlation functional: the Neural-Networks approach

A Neural-Networks-based approach is proposed to construct a new type of exchange-correlation functional for density functional theory. It is applied to improve B3LYP functional by taking into account of high-order contributions to the exchange-correlation functional. The improved B3LYP functional is based on a neural network whose structure and synaptic weights are determined from 116 known experimental atomization energies, ionization potentials, proton affinities or total atomic energies which were used by Becke in his pioneer work on the hybrid functionals [J. Chem. Phys. ${\bf 98}$, 5648 (1993)]. It leads to better agreement between the first-principles calculation results and these 116 experimental data. The new B3LYP functional is further tested by applying it to calculate the ionization potentials of 24 molecules of the G2 test set. The 6-311+G(3{\it df},2{\it p}) basis set is employed in the calculation, and the resulting root-mean-square error is reduced to 2.2 kcal$\cdot$mol$^{-1}$ in comparison to 3.6 kcal$\cdot$mol$^{-1}$ of conventional B3LYP/6-311+G(3{\it df},2{\it p}) calculation.Comment: 10 pages, 1figur

Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants

For the first two equations of the Volterra lattice hierarchy and the first two equations of its non-autonomous (non-isospectral) extension, we present Riccati systems for functions c_j(t), j=0,1,..., such that an expression in terms of Hankel determinants built from them solves these equations on the right half of the lattice. This actually achieves a complete linearization of these equations of the extended Volterra lattice hierarchy.Comment: 31 pages, 3rd version: introduction extended, part of Section 2 moved there, Appendix D added, additional references, to appear in Nonlinearit

Enhancing Grasping Performance of Novel Objects through an Improved Fine-Tuning Process

Grasping algorithms have evolved from planar depth grasping to utilizing point cloud information, allowing for application in a wider range of scenarios. However, data-driven grasps based on models trained on basic open-source datasets may not perform well on novel objects, which are often required in different scenarios, necessitating fine-tuning using new objects. The data driving these algorithms essentially corresponds to the closing region of the hand in 6D pose, and due to the uniqueness of 6D pose, synthetic annotation or real-machine annotation methods are typically employed. Acquiring large amounts of data with real-machine annotation is challenging, making synthetic annotation a common practice. However, obtaining annotated 6D pose data using conventional methods is extremely time-consuming. Therefore, we propose a method to quickly acquire data for novel objects, enabling more efficient fine-tuning. Our method primarily samples grasp orientations to generate and annotate grasps. Experimental results demonstrate that our fine-tuning process for a new object is 400 \% faster than other methods. Furthermore, we propose an optimized grasp annotation framework that accounts for the effects of the gripper closing, making the annotations more reasonable. Upon acceptance of this paper, we will release our algorithm as open-source