arXiv subjects

Min Kang

Publications and source records attributed to Min Kang.

8 recordsLinked to original sources

arXiv2026

Phase Matching for a Generalized Grover's Algorithm

We study the fully generalized Grover's algorithm to find the optimal phase changes for each step of the iteration to maximize gain in probability of observation of the target, and when phase matching is required. We find that classical Grover's algorithm and phase matching remains to be optimal till the target probability gets close 1. However, as the probability of observation approaches 1, the optimal phase changes differ from $\pi$ and no longer observe phase matching. We provide the optimization statement to find the optimal phase changes given the current amplitude vector and the size of the set. To analyze this formula, we approach it from a numerical and analytical perspective, with the analytical perspective focusing on special cases that simplify the optimization and allow for general statements about its behavior. Finally, we provide an example of a 5 qubit system and show that for the final iteration the optimal phase changes differ from traditional Grover's algorithm and do not observe phase matching, but lead to an increase in the probability of the target.

quant-ph↗

arXiv2026

Annotation-free deep learning for detection and segmentation of fetal germinal matrix-intraventricular hemorrhage in brain MRI

Prenatal germinal matrix-intraventricular hemorrhage (GMH-IVH) is a leading cause of infant mortality and neurodevelopmental impairment, yet its manual diagnosis and lesion segmentation on fetal brain MRI are labor-intensive and error-prone. Although supervised deep learning offers potential for automation, it typically requires large amounts of annotated GMH-IVH data, which are challenging to obtain for such a rare condition (0.5-0.9 per 1000 pregnancies). To address these problems, an annotation-free deep learning framework, FreeHemoSeg, was developed for automated detection and segmentation of GMH-IVH without any real patient annotations. Instead of learning from expert labels, FreeHemoSeg was trained on pseudo GMH-IVH images synthesized from normal fetal data guided by medical priors. The framework was evaluated in a retrospective multicentre study of 1,674 stacks of 2D T2-weighted MRI from 558 pregnant women, using data from one hospital for internal training and validation and two hospitals for external validation. FreeHemoSeg achieved the highest diagnostic and segmentation performance in both internal validation (AUROC: 0.959; AUPR: 0.928; sensitivity: 0.914; specificity: 0.966; DSC: 0.559) and external validation (AUROC: 0.930; AUPR: 0.884; sensitivity: 0.824; specificity: 0.943; DSC: 0.512), outperforming a supervised model trained on limited empirical data and unsupervised anomaly detection methods. Moreover, FreeHemoSeg assistance improved radiologists' sensitivity (from 0.882 to 0.941-1.000) and diagnostic confidence, while reducing interpretation time by 16.0-52.7%. We anticipate its immediate utility in supporting earlier diagnosis, prognostic counselling, and perinatal planning for fetal GMH-IVH. Code: https://github.com/Arktis2022/FreeHemoSeg.

eess.IV↗

arXiv2026

Full-channel wavefront manipulation of surface waves with chirality-assisted geometric-phase metasurface

Owing to their localized field enhancement and subwavelength resolution, surface waves (SWs) offer broad application potential in communications, sensing, and photonics via on-chip wavefront manipulation. This makes multi-channel SW wavefront manipulation highly desirable. However, conventional metasurfaces for SW wavefront shaping, relying on geometric and propagation phase mechanisms, typically exhibit similar functionalities for co- or cross-polarized output channels under different circularly polarized (CP) incidences, thereby limiting the development of high-capacity on-chip integrated devices. Here, by introducing the chirality-assisted phase as an additional phase control mechanism, we effectively decouple both co- and cross-polarized output channels, enabling independent SW wavefront shaping in four distinct channels. We numerically and experimentally demonstrate two metasurfaces in the microwave range: a four-channel SW meta-deflector and a four-channel SW metadevice that simultaneously produces a focused SW beam, a SW Bessel beam, and two deflected SW beams in different directions. Therefore, chirality-assisted geometric-phase metasurfaces provide a versatile platform for multi-channel SW wavefront engineering, offering significant potential for high-capacity on-chip communication and integrated photonic systems.

physics.optics↗

arXiv2025

Optimal phase change for a generalized Grover's algorithm

We study the generalized Grover's algorithm with an arbitrary amplitude vector to find the optimal phase change for maximizing the gain in probability for the target of each iteration. In the classic setting of Grover's algorithm with a real initial amplitude vector, we find that a phase change of $\pi$ stays optimal until the probability of observing the target is quite close to 1. We provide a formula for identifying this cut-off point based on the size of the data set. When the amplitude is truly complex, we find that the optimal phase change depends non-trivially on the complexity of the amplitude vector. We provide an optimization formula to identify the required optimal phase change.

quant-ph↗

arXiv2023

Ophtha-LLaMA2: A Large Language Model for Ophthalmology

In recent years, pre-trained large language models (LLMs) have achieved tremendous success in the field of Natural Language Processing (NLP). Prior studies have primarily focused on general and generic domains, with relatively less research on specialized LLMs in the medical field. The specialization and high accuracy requirements for diagnosis in the medical field, as well as the challenges in collecting large-scale data, have constrained the application and development of LLMs in medical scenarios. In the field of ophthalmology, clinical diagnosis mainly relies on doctors' interpretation of reports and making diagnostic decisions. In order to take advantage of LLMs to provide decision support for doctors, we collected three modalities of ophthalmic report data and fine-tuned the LLaMA2 model, successfully constructing an LLM termed the "Ophtha-LLaMA2" specifically tailored for ophthalmic disease diagnosis. Inference test results show that even with a smaller fine-tuning dataset, Ophtha-LLaMA2 performs significantly better in ophthalmic diagnosis compared to other LLMs. It demonstrates that the Ophtha-LLaMA2 exhibits satisfying accuracy and efficiency in ophthalmic disease diagnosis, making it a valuable tool for ophthalmologists to provide improved diagnostic support for patients. This research provides a useful reference for the application of LLMs in the field of ophthalmology, while showcasing the immense potential and prospects in this domain.

cs.CL↗

arXiv2020

Local Convergence of an AMP Variant to the LASSO Solution in Finite Dimensions

A common sparse linear regression formulation is the l1 regularized least squares, which is also known as least absolute shrinkage and selection operator (LASSO). Approximate message passing (AMP) has been proved to asymptotically achieve the LASSO solution when the regression matrix has independent and identically distributed (i.i.d.) Gaussian entries in the sense that the averaged per-coordinate l2 distance between the AMP iterates and the LASSO solution vanishes as the signal dimension goes to infinity before the iteration number. However, in finite dimensional settings, characterization of AMP iterates in the limit of large iteration number has not been established. In this work, we propose an AMP variant by including a parameter that depends on the largest singular value of the regression matrix. The proposed algorithm can also be considered as a primal dual hybrid gradient algorithm with adaptive stepsizes. We show that whenever the AMP variant converges, it converges to the LASSO solution for arbitrary finite dimensional regression matrices. Moreover, we show that the AMP variant is locally stable around the LASSO solution under the condition that the LASSO solution is unique and that the regression matrix is drawn from a continuous distribution. Our local stability result implies that in the special case where the regression matrix is large and has i.i.d. random entries, the original AMP, which is a special case of the proposed AMP variant, is locally stable around the LASSO solution.

cs.IT↗

arXiv2019

Non-Markovian Monte Carlo on Directed Graphs

Markov Chain Monte Carlo (MCMC) has been the de facto technique for sampling and inference of large graphs such as online social networks. At the heart of MCMC lies the ability to construct an ergodic Markov chain that attains any given stationary distribution $\boldsymbol{\pi}$, often in the form of random walks or crawling agents on the graph. Most of the works around MCMC, however, presume that the graph is undirected or has reciprocal edges, and become inapplicable when the graph is directed and non-reciprocal. Here we develop a similar framework for directed graphs, which we call Non-Markovian Monte Carlo (NMMC), by establishing a mapping to convert $\boldsymbol{\pi}$ into the quasi-stationary distribution of a carefully constructed transient Markov chain on an extended state space. As applications, we demonstrate how to achieve any given distribution $\boldsymbol{\pi}$ on a directed graph and estimate the eigenvector centrality using a set of non-Markovian, history-dependent random walks on the same graph in a distributed manner. We also provide numerical results on various real-world directed graphs to confirm our theoretical findings, and present several practical enhancements to make our NMMC method ready for practical use in most directed graphs. To the best of our knowledge, the proposed NMMC framework for directed graphs is the first of its kind, unlocking all the limitations set by the standard MCMC methods for undirected graphs.

math.ST↗

arXiv2003

Behavior dominated by slow particles in a disordered asymmetric exclusion process

We study the large space and time scale behavior of a totally asymmetric, nearest-neighbor exclusion process in one dimension with random jump rates attached to the particles. When slow particles are sufficiently rare the system has a phase transition. At low densities there are no equilibrium distributions, and on the hydrodynamic scale the initial profile is transported rigidly. We elaborate this situation further by finding the correct order of the correction from the hydrodynamic limit, together with distributional bounds averaged over the disorder. We consider two settings, a macroscopically constant low density profile and the outflow from a large jam.

math.PR↗