Clustering with diversity

We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a 2-approximation to this problem for any $\ell$ when the objective is to minimize the maximum radius of any cluster. We show that the approximation ratio is optimal unless $\mathbf{P=NP}$, by providing a matching lower bound. Several extensions to our algorithm have also been developed for handling outliers. This problem is mainly motivated by applications in privacy-preserving data publication.Comment: Extended abstract accepted in ICALP 2010. Keywords: Approximation algorithm, k-center, k-anonymity, l-diversit

FSDiffReg: Feature-wise and Score-wise Diffusion-guided Unsupervised Deformable Image Registration for Cardiac Images

Unsupervised deformable image registration is one of the challenging tasks in medical imaging. Obtaining a high-quality deformation field while preserving deformation topology remains demanding amid a series of deep-learning-based solutions. Meanwhile, the diffusion model's latent feature space shows potential in modeling the deformation semantics. To fully exploit the diffusion model's ability to guide the registration task, we present two modules: Feature-wise Diffusion-Guided Module (FDG) and Score-wise Diffusion-Guided Module (SDG). Specifically, FDG uses the diffusion model's multi-scale semantic features to guide the generation of the deformation field. SDG uses the diffusion score to guide the optimization process for preserving deformation topology with barely any additional computation. Experiment results on the 3D medical cardiac image registration task validate our model's ability to provide refined deformation fields with preserved topology effectively. Code is available at: https://github.com/xmed-lab/FSDiffReg.git.Comment: Accepted as a conference paper at Medical Image Computing and Computer-Assisted Intervention (MICCAI) conference 202

Occupation-dependent particle separation in one-dimensional non-Hermitian lattices

We unveil an exotic phenomenon arising from the intricate interplay between non-Hermiticity and many-body physics, namely an occupation-dependent particle separation for hardcore bosons in a one-dimensional lattice driven by uni-directional non-Hermitian pumping. Taking hardcore bosons as an example, we find that a pair of particles occupying the same unit cell exhibit an opposite non-Hermitian pumping direction to that of unpaired ones occupying different unit cells. By turning on an intracell interaction, many-body eigenstates split in their real energies, forming separable clusters in the complex energy plane with either left-, right-, or bipolar-types of non-Hermitian skin effect (NHSE). The dependency of skin accumulating directions on particle occupation is further justified with local sublattice correlation and entanglement entropy of many-body eigenstates. Dynamically, this occupation-dependent NHSE manifests as uni- or bi-directional pumping for many-body initial states, allowing for spatially separating paired and unpaired particles. Similar phenomena also apply to fermionic systems, unveiling the possibility of designing and exploring novel non-Hermitian phases originated from particle non-conservation in subsystems (e.g., orbitals, sublattices, or spin species) and their spatial configurations.Comment: 18pages, 14 fiugre

Low magnetic field reversal of electric polarization in a Y-type hexaferrite

Magnetoelectric multiferroics in which ferroelectricity and magnetism coexist have attracted extensive attention because they provide great opportunities for the mutual control of electric polarization by magnetic fields and magnetization by electric fields. From a practical point view, the main challenge in this field is to find proper multiferroic materials with a high operating temperature and great magnetoelectric sensitivity. Here we report on the magnetically tunable ferroelectricity and the giant magnetoelectric sensitivity up to 250 K in a Y-type hexaferrite, BaSrCoZnFe11AlO22. Not only the magnitude but also the sign of electric polarization can be effectively controlled by applying low magnetic fields (a few hundreds of Oe) that modifies the spiral magnetic structures. The magnetically induced ferroelectricity is stabilized even in zero magnetic field. Decayless reproducible flipping of electric polarization by oscillating low magnetic fields is shown. The maximum linear magnetoelectric coefficient reaches a high value of ~ 3.0\times10^3 ps/m at 200 K.Comment: 9 pages, 5 figures, a couple of errors are correcte

Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice

The interplay between the non-Hermiticity and dimensionality gives rise to exotic characteristics in higher dimensions, with one representative phenomenon known as the geometry-dependent skin effect (GDSE), which refers to that the localization of extensive eigenstates depends on the system's geometry under open boundary conditions. In this paper, we demonstrate the emergence of GDSE in a two-dimensional $sp$ optical ladder lattice with on-site atom loss, which can be manifested by anisotropic dynamics of Bloch oscillations in the bulk of the system. By applying a static force in different directions, the wave-packet dynamics retrieve the complex energy spectra with either nonzero or zero spectral winding number, indicating the presence or absence of skin accumulation in the corresponding directions, respectively. Our results reveal that the GDSE has an intrinsic anisotropic bulk dynamics independent of boundary conditions, and offer its realization and detection in quantum systems.Comment: 16 pages, 13 figure