Showing 1–50 of 68 results for author: Ku, C

Mind the Gap: A Dual Knowledge Graph Framework for Unified Multi-task User Intent Inference

Authors: Tzu-Cheng Peng, Chien Chin Chen, Chih-Hao Ku, Yung-Chun Chang

Abstract: This paper proposes DKG-MTI, a dual knowledge graph framework for unified multi-task user intent inference from online travel reviews. Existing approaches often rely on hierarchical pipelines that suffer from error propagation or retrieval methods that ignore structural relationships in domain knowledge. To address these limitations, we introduce an inference-only knowledge augmentation framework… ▽ More This paper proposes DKG-MTI, a dual knowledge graph framework for unified multi-task user intent inference from online travel reviews. Existing approaches often rely on hierarchical pipelines that suffer from error propagation or retrieval methods that ignore structural relationships in domain knowledge. To address these limitations, we introduce an inference-only knowledge augmentation framework that dynamically constructs a User-Specific Intent Knowledge Graph from each review and aligns it with a Global Hotel Knowledge Graph through structure-aware semantic smoothing. The aligned knowledge is combined with the original review and processed by a large language model to simultaneously predict aspect ratings and generate reverse user intent statements. Experiments on TripAdvisor reviews show that DKG-MTI consistently outperforms strong LLM and retrieval-based baselines in both classification and intent generation tasks, demonstrating the effectiveness of structure-aware knowledge alignment for scalable and explainable intent inference. △ Less

Submitted 6 August, 2026; originally announced August 2026.

Comments: Published in the PACIS 2026 Proceedings as a Completed Research Paper. AIS eLibrary: https://aisel.aisnet.org/pacis2026/ai_ml/ai_ml/12/ 17 pages, 5 figures

Journal ref: Proceedings of the Pacific Asia Conference on Information Systems (PACIS 2026), Paper 12, 2026

Silicon Sampling via Cross-Survey Transfer

Authors: Chan-Tung Ku, Chan Hsu, Pei-Cing Huang, Frank Cheng-shan Liu, I-Ling Cheng, Yihuang Kang

Abstract: Silicon sampling-using large language models (LLMs) to simulate human survey respondents-has emerged as a promising approach for augmenting traditional survey research. However, most evaluations rely on distributional comparisons rather than individual-level prediction, which risks conflating pattern matching with coherent respondent-level prediction. We propose cross-survey transfer, a more rigor… ▽ More Silicon sampling-using large language models (LLMs) to simulate human survey respondents-has emerged as a promising approach for augmenting traditional survey research. However, most evaluations rely on distributional comparisons rather than individual-level prediction, which risks conflating pattern matching with coherent respondent-level prediction. We propose cross-survey transfer, a more rigorous evaluation framework in which an LLM is given a respondent's answers to one set of questions and must predict their answers to entirely different questions from the same survey. Using data from the Taiwan Election and Democratization Study (TEDS) 2024, three open-weight LLMs (27B-120B parameters), and supervised machine learning baselines, we find that: (1) zero-shot LLMs achieve 52% accuracy on genuinely unseen items, closing to within 6 percentage points (pp) of a supervised random forest trained on same-population data; (2) a stable construct predictability hierarchy emerges, from 67% for partisan attitudes to 23% for sovereignty; and (3) variance collapse and safety alignment effects-two commonly cited LLM limitations-turn out to be more nuanced than previously reported, with variance collapse affecting supervised models as well and alignment effects varying dramatically across model families. These findings clarify both the promise and boundaries of silicon sampling. △ Less

Submitted 3 July, 2026; originally announced July 2026.

ADVENT: LLM-Driven Automatic Predicate Invention for ILP

Authors: Tingting Yu, Pei-Cing Huang, Chan Hsu, Chan-Tung Ku, Yihuang Kang

Abstract: Predicate invention (PI), the creation of new predicates to extend the hypothesis space, remains a critical bottleneck in Inductive Logic Programming (ILP). Existing methods rely on domain expertise and produce semantically opaque predicates, hindering adaptation to unfamiliar domains and cross-task reuse. We present ADVENT, an LLM-driven PI mechanism for ILP. ADVENT pairs LLM abductive generation… ▽ More Predicate invention (PI), the creation of new predicates to extend the hypothesis space, remains a critical bottleneck in Inductive Logic Programming (ILP). Existing methods rely on domain expertise and produce semantically opaque predicates, hindering adaptation to unfamiliar domains and cross-task reuse. We present ADVENT, an LLM-driven PI mechanism for ILP. ADVENT pairs LLM abductive generation with Prolog deductive verification, forming an iterative loop in which concrete execution results guide the LLM to refine candidate predicates. The mechanism leverages Large Language Models to identify implicit patterns in structured relational data and invent auxiliary predicates with meaningful names and definitions. Invented predicates and learned rules accumulate in a knowledge pool for cross-task reuse. Experiments on nine poker-hand concepts across seven LLMs show that LLM-driven PI achieves 58% success rate where ILP alone fails entirely, formal verification raises this to 80%, and the knowledge pool yields gains up to +31 percentage points, while producing human-interpretable rules. These results suggest that ADVENT offers a promising direction for automating predicate invention and enabling cross-task knowledge reuse in ILP. △ Less

Submitted 1 July, 2026; originally announced July 2026.

Correlation-Converged Virtual Orbitals for Accurate and Efficient Quantum Molecular Simulations

Authors: Qian Wang, Calvin Ku, Jyh-Pin Chou, Peng-Jen Chen, Alice Hu, Min-Hsiu Hsieh

Abstract: Density functional theory with plane-wave basis sets is widely employed in computational materials science, including applications to isolated molecular systems. However, the inadequate description of electron correlation remains a fundamental limitation. Accurate correlation treatments based on many-body Hamiltonians require reliable representations of both occupied and virtual orbitals, yet virt… ▽ More Density functional theory with plane-wave basis sets is widely employed in computational materials science, including applications to isolated molecular systems. However, the inadequate description of electron correlation remains a fundamental limitation. Accurate correlation treatments based on many-body Hamiltonians require reliable representations of both occupied and virtual orbitals, yet virtual orbitals are often poorly described in conventional computational schemes, resulting in reduced accuracy. In this work, we introduce localized correlation-converged virtual orbitals (LCCVOs) as an efficient basis for constructing accurate many-body Hamiltonians in molecular systems. Using a substantially reduced number of orbitals, the LCCVO framework yields dissociation energies for singlet, doublet, and triplet molecules that are comparable to, and in many cases exceed, those obtained with high-level correlation-consistent basis sets such as cc-pVXZ (X = D, T, Q, 5). These results demonstrate the efficiency, scalability, and robustness of the LCCVO approach for high-accuracy quantum chemical calculations. △ Less

Submitted 18 April, 2026; originally announced April 2026.

Structure-Preserving Graph Contrastive Learning for Mathematical Information Retrieval

Authors: Chun-Hsi Ku, Hung-Hsuan Chen

Abstract: This paper introduces Variable Substitution as a domain-specific graph augmentation technique for graph contrastive learning (GCL) in the context of searching for mathematical formulas. Standard GCL augmentation techniques often distort the semantic meaning of mathematical formulas, particularly for small and highly structured graphs. Variable Substitution, on the other hand, preserves the core al… ▽ More This paper introduces Variable Substitution as a domain-specific graph augmentation technique for graph contrastive learning (GCL) in the context of searching for mathematical formulas. Standard GCL augmentation techniques often distort the semantic meaning of mathematical formulas, particularly for small and highly structured graphs. Variable Substitution, on the other hand, preserves the core algebraic relationships and formula structure. To demonstrate the effectiveness of our technique, we apply it to a classic GCL-based retrieval model. Experiments show that this straightforward approach significantly improves retrieval performance compared to generic augmentation strategies. We release the code on GitHub.\footnote{https://github.com/lazywulf/formula_ret_aug}. △ Less

Submitted 9 March, 2026; originally announced March 2026.

Direct Evidence of a Near-Ideal Jeff = 1/2 Ground State in Triangular-Lattice Na2BaCo(PO4)2

Authors: M. M. Ferreira-Carvalho, S. H. Chen, Y. C. Ku, Anagha Jose, Ryan Morrow, C. Y. Kuo, C. F. Chang, Z. Hu, M. W. Haverkort, L. H. Tjeng

Abstract: We investigated the local Co 3d electronic structure of Na2BaCo(PO4)2 using polarization-dependent X-ray absorption spectroscopy (XAS) in combination with full multiplet cluster calculations. We employed the line-fitting inverse partial fluorescence yield (IPFY) technique to obtain accurate XAS spectra from strong insulating materials. Our combined experimental and theoretical analysis reveals a v… ▽ More We investigated the local Co 3d electronic structure of Na2BaCo(PO4)2 using polarization-dependent X-ray absorption spectroscopy (XAS) in combination with full multiplet cluster calculations. We employed the line-fitting inverse partial fluorescence yield (IPFY) technique to obtain accurate XAS spectra from strong insulating materials. Our combined experimental and theoretical analysis reveals a very small effective trigonal distortion of only 11 meV in the CoO6 octahedra, indicating a close to ideal condition to render a ground state with the Jeff = 1/2 character. With our cluster model we were also able to simulate magnetic susceptibility measurements along different directions in the crystal. These findings highlight Na2BaCo(PO4)2 as a promising platform for exploring exotic magnetic phenomena associated with Jeff = 1/2 ground states on triangular lattices. △ Less

Submitted 9 February, 2026; originally announced February 2026.

PhysSFI-Net: Physics-informed Geometric Learning of Skeletal and Facial Interactions for Orthognathic Surgical Outcome Prediction

Authors: Jiahao Bao, Huazhen Liu, Yu Zhuang, Leran Tao, Xinyu Xu, Yongtao Shi, Mengjia Cheng, Yiming Wang, Congshuang Ku, Ting Zeng, Yilang Du, Siyi Chen, Shunyao Shen, Suncheng Xiang, Hongbo Yu

Abstract: Orthognathic surgery repositions jaw bones to restore occlusion and enhance facial aesthetics. Accurate simulation of postoperative facial morphology is essential for preoperative planning. This study aims to develop and validate a physics-informed geometric deep learning framework named PhysSFI-Net for precise prediction of soft tissue deformation following orthognathic surgery. The model integra… ▽ More Orthognathic surgery repositions jaw bones to restore occlusion and enhance facial aesthetics. Accurate simulation of postoperative facial morphology is essential for preoperative planning. This study aims to develop and validate a physics-informed geometric deep learning framework named PhysSFI-Net for precise prediction of soft tissue deformation following orthognathic surgery. The model integrates a hierarchical feature extraction module with attention mechanisms to capture skeletal-facial interactions, an LSTM-based sequential predictor for incremental deformation, and a biomechanics-inspired reconstruction module for high-resolution facial modeling. The model was trained on 135 patients and externally validated on an independent cohort of 33 patients. Model performance was assessed using point cloud shape error, surface deviation error and landmark error between predicted facial shapes with corresponding ground truths. Quantitative analysis demonstrated that PhysSFI-Net achieved a global shape error of 1.070 +/- 0.088 mm, a surface deviation error of 1.296 +/- 0.349 mm and a landmark error of 2.445 +/- 1.326 mm. Comparative experiments indicated that PhysSFI-Net outperformed the state-of-the-art method ACMT-Net and baseline models. External validation further confirmed its robustness with a global HD of 1.431 +/- 0.087 mm and consistently lower subregional and mesh-based errors. In conclusion, PhysSFI-Net enables interpretable, high-resolution prediction of postoperative facial morphology, showing strong potential for clinical application in orthognathic surgical planning. △ Less

Submitted 19 August, 2026; v1 submitted 5 January, 2026; originally announced January 2026.

Comments: 16 pages, 9 figures

Journal ref: Bao, J., Liu, H., Zhuang, Y. et al. PhysSFI-Net: physics-informed geometric learning of skeletal and facial interactions for orthognathic surgical outcome prediction. npj Digit. Med. (2026)

Point-contact Andreev reflection spectroscopy of layered superconductors with device-integrated diamond anvil cells

Authors: Che-hsuan Ku, Omargeldi Atanov, King Yau Yip, Wenyan Wang, Siu Tung Lam, Jiayu Zeng, Wei Zhang, Zheyu Wang, Lingfei Wang, Tsz Fung Poon, Rolf Lortz, Swee K. Goh

Abstract: Superconductors that can be mechanically exfoliated are an interesting platform for exploring superconducting properties tuned by layer thickness. These layered superconductors are also expected to exhibit sensitivity to applied pressure. While pressure has been demonstrated to be an effective way of tuning bulk superconductors, analogous studies on superconducting thin flakes have been limited du… ▽ More Superconductors that can be mechanically exfoliated are an interesting platform for exploring superconducting properties tuned by layer thickness. These layered superconductors are also expected to exhibit sensitivity to applied pressure. While pressure has been demonstrated to be an effective way of tuning bulk superconductors, analogous studies on superconducting thin flakes have been limited due to technical challenges. In particular, spectroscopic measurements under pressure remain insufficiently explored. In this work, we functionalized the diamond anvil cell technique for point-contact Andreev reflection spectroscopy (PCAR) measurement on thin-flake materials under pressure, offering the opportunity to obtain spectroscopic information on superconductivity. To validate the feasibility of this method, we have conducted PCAR measurements on iron-selenide thin flakes to extract temperature-dependent superconducting gap values under ambient and high pressure. Combine with the proven magnetotransport capability, our method provides a conceptually simple tool for a detailed examination of thin-flake superconductors under pressure. △ Less

Submitted 22 October, 2025; originally announced October 2025.

Comments: 8 pages, 7 figures, Editor's Pick

Journal ref: Rev. Sci. Instrum. 96, 103902 (2025)

Benchmarking Quantum Simulation of Chemical Hamiltonians using the Sorted-List Encoding

Authors: Calvin Ku, Yu-Cheng Chen, Alice Hu, Min-Hsiu Hsieh

Abstract: Quantum Phase Estimation (QPE) is a cornerstone algorithm for fault-tolerant quantum computation, especially for electronic structure calculations of chemical systems. Optimal simulation relies on a complex trade-offs across many parameters including Hamiltonian simulation techniques, basis sets, and the fermion-to-qubit encodings. Here, we characterize the trade-offs and quantify the quantum reso… ▽ More Quantum Phase Estimation (QPE) is a cornerstone algorithm for fault-tolerant quantum computation, especially for electronic structure calculations of chemical systems. Optimal simulation relies on a complex trade-offs across many parameters including Hamiltonian simulation techniques, basis sets, and the fermion-to-qubit encodings. Here, we characterize the trade-offs and quantify the quantum resource costs of the sorted-list encoding as a particle-conserving, low-qubit alternative to the Jordan-Wigner encoding. We identify specific regimes, across different simulation techniques and basis sets, where the sorted-list encoding would be favorable compared to existing methods. Our findings are further supported through numerical benchmarks of real-world chemical systems. We found the sorted-list encoding to be a viable alternative to the Jordan-Wigner encoding for the compact molecular orbital basis when the electron-filling ratio is low, which typically occurs when high-precision results are required. In the plane-wave basis, we found similar asymptotic gate and qubit scaling between the sorted-list and the first-quantized encoding, although the first-quantized encoding still retains lower constant factors. △ Less

Submitted 24 July, 2026; v1 submitted 2 October, 2025; originally announced October 2025.

Comments: 36 pages, 25 figures, updated results

Journal ref: Phys. Rev. Research 8, 033091 (2026)

HELIOS: Hierarchical Exploration for Language-Grounded Interaction in Open Scenes

Authors: Katrina Ashton, Chahyon Ku, Shrey Shah, Saumit Vedula, Tingrui Zhang, Wen Jiang, Kostas Daniilidis, Bernadette Bucher

Abstract: Language-specified mobile manipulation tasks in novel environments simultaneously face challenges interacting with a scene which is only partially observed, grounding semantic information from language instructions to the partially observed scene, and actively updating knowledge of the scene with new observations. To address these challenges, we propose HELIOS, a hierarchical scene representation… ▽ More Language-specified mobile manipulation tasks in novel environments simultaneously face challenges interacting with a scene which is only partially observed, grounding semantic information from language instructions to the partially observed scene, and actively updating knowledge of the scene with new observations. To address these challenges, we propose HELIOS, a hierarchical scene representation and associated search objective. We construct 2D maps containing the relevant semantic and occupancy information for navigation while simultaneously actively constructing 3D Gaussian representations of task-relevant objects. We fuse observations across this multi-layered representation while explicitly modeling the multi-view consistency of the detections of each object using the Dirichlet distribution. Planning is formulated as a search problem over our hierarchical representation. We formulate an objective that jointly considers (i) exploration of unobserved or uncertain regions of the environment and (ii) information gathering from additional observations of candidate objects. This objective integrates frontier-based exploration with the expected information gain associated with improving semantic consistency of object detections. We evaluate HELIOS on the OVMM benchmark in the Habitat simulator, a pick and place benchmark in which perception is challenging due to large and complex scenes with comparatively small target objects. HELIOS achieves state-of-the-art results on OVMM. We demonstrate HELIOS performing language specified pick and place in a real world office environment on a Spot robot. Our method leverages pretrained VLMs to achieve these results in simulation and the real world without any task specific training. △ Less

Submitted 26 March, 2026; v1 submitted 26 September, 2025; originally announced September 2025.

CoachMe: Decoding Sport Elements with a Reference-Based Coaching Instruction Generation Model

Authors: Wei-Hsin Yeh, Yu-An Su, Chih-Ning Chen, Yi-Hsueh Lin, Calvin Ku, Wen-Hsin Chiu, Min-Chun Hu, Lun-Wei Ku

Abstract: Motion instruction is a crucial task that helps athletes refine their technique by analyzing movements and providing corrective guidance. Although recent advances in multimodal models have improved motion understanding, generating precise and sport-specific instruction remains challenging due to the highly domain-specific nature of sports and the need for informative guidance. We propose CoachMe,… ▽ More Motion instruction is a crucial task that helps athletes refine their technique by analyzing movements and providing corrective guidance. Although recent advances in multimodal models have improved motion understanding, generating precise and sport-specific instruction remains challenging due to the highly domain-specific nature of sports and the need for informative guidance. We propose CoachMe, a reference-based model that analyzes the differences between a learner's motion and a reference under temporal and physical aspects. This approach enables both domain-knowledge learning and the acquisition of a coach-like thinking process that identifies movement errors effectively and provides feedback to explain how to improve. In this paper, we illustrate how CoachMe adapts well to specific sports such as skating and boxing by learning from general movements and then leveraging limited data. Experiments show that CoachMe provides high-quality instructions instead of directions merely in the tone of a coach but without critical information. CoachMe outperforms GPT-4o by 31.6% in G-Eval on figure skating and by 58.3% on boxing. Analysis further confirms that it elaborates on errors and their corresponding improvement methods in the generated instructions. You can find CoachMe here: https://motionxperts.github.io/ △ Less

Submitted 15 September, 2025; originally announced September 2025.

Comments: Published in Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), ACL 2025. Official version: https://doi.org/10.18653/v1/2025.acl-long.1413

ACM Class: I.2.7; I.2.10

Journal ref: Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics Volume 1: Long Papers (2025) 29126-29151

An analogue of the Erd{\H o}s Matching Conjecture for permutations with fixed number of cycles

Authors: Cheng Yeaw Ku, Kok Bin Wong

Abstract: Let $S_{n}$ denote the set of permutations of $[n]=\{1,2,\dots, n\}$. For each integer $k\geq 1$, let $S_{n,k}$ be the set of all permutations of $[n]$ with exactly $k$ disjoint cycles. A subset $H\subseteq S_{n,k}$ is to be a matching if $π_1$ and $π_2$ do not have any common cycles for all distinct $π_1,π_2\in H$. The matching number of a family $\mathcal A\subseteq S_{n,k}$ is denoted by… ▽ More Let $S_{n}$ denote the set of permutations of $[n]=\{1,2,\dots, n\}$. For each integer $k\geq 1$, let $S_{n,k}$ be the set of all permutations of $[n]$ with exactly $k$ disjoint cycles. A subset $H\subseteq S_{n,k}$ is to be a matching if $π_1$ and $π_2$ do not have any common cycles for all distinct $π_1,π_2\in H$. The matching number of a family $\mathcal A\subseteq S_{n,k}$ is denoted by $ν_{p}(\mathcal A)$ and is defined to be the size of the largest matching in $\mathcal A$. In this paper, we determine the maximum size of a family $\mathcal A\subseteq S_{n,k}$ subject to the condition $ν_p(\mathcal A)\leq s$. △ Less

Submitted 25 August, 2025; originally announced August 2025.

From Screen to Stage: Kid Cosmo, A Life-Like, Torque-Controlled Humanoid for Entertainment Robotics

Authors: Havel Liu, Mingzhang Zhu, Arturo Moises Flores Alvarez, Yuan Hung Lo, Conrad Ku, Federico Parres, Justin Quan, Colin Togashi, Aditya Navghare, Quanyou Wang, Dennis W. Hong

Abstract: Humanoid robots represent the cutting edge of robotics research, yet their potential in entertainment remains largely unexplored. Entertainment as a field prioritizes visuals and form, a principle that contrasts with the purely functional designs of most contemporary humanoid robots. Designing entertainment humanoid robots capable of fluid movement presents a number of unique challenges. In this p… ▽ More Humanoid robots represent the cutting edge of robotics research, yet their potential in entertainment remains largely unexplored. Entertainment as a field prioritizes visuals and form, a principle that contrasts with the purely functional designs of most contemporary humanoid robots. Designing entertainment humanoid robots capable of fluid movement presents a number of unique challenges. In this paper, we present Kid Cosmo, a research platform designed for robust locomotion and life-like motion generation while imitating the look and mannerisms of its namesake character from Netflix's movie The Electric State. Kid Cosmo is a child-sized humanoid robot, standing 1.45 m tall and weighing 25 kg. It contains 28 degrees of freedom and primarily uses proprioceptive actuators, enabling torque-control walking and lifelike motion generation. Following worldwide showcases as part of the movie's press tour, we present the system architecture, challenges of a functional entertainment robot and unique solutions, and our initial findings on stability during simultaneous upper and lower body movement. We demonstrate the viability of performance-oriented humanoid robots that prioritize both character embodiment and technical functionality. △ Less

Submitted 15 August, 2025; originally announced August 2025.

Comments: 8 pages, 14 figures, accepted by IEEE Humanoids 2025

LLM-based Agents for Automated Confounder Discovery and Subgroup Analysis in Causal Inference

Authors: Po-Han Lee, Yu-Cheng Lin, Chan-Tung Ku, Chan Hsu, Pei-Cing Huang, Ping-Hsun Wu, Yihuang Kang

Abstract: Estimating individualized treatment effects from observational data presents a persistent challenge due to unmeasured confounding and structural bias. Causal Machine Learning (causal ML) methods, such as causal trees and doubly robust estimators, provide tools for estimating conditional average treatment effects. These methods have limited effectiveness in complex real-world environments due to th… ▽ More Estimating individualized treatment effects from observational data presents a persistent challenge due to unmeasured confounding and structural bias. Causal Machine Learning (causal ML) methods, such as causal trees and doubly robust estimators, provide tools for estimating conditional average treatment effects. These methods have limited effectiveness in complex real-world environments due to the presence of latent confounders or those described in unstructured formats. Moreover, reliance on domain experts for confounder identification and rule interpretation introduces high annotation cost and scalability concerns. In this work, we proposed Large Language Model-based agents for automated confounder discovery and subgroup analysis that integrate agents into the causal ML pipeline to simulate domain expertise. Our framework systematically performs subgroup identification and confounding structure discovery by leveraging the reasoning capabilities of LLM-based agents, which reduces human dependency while preserving interpretability. Experiments on real-world medical datasets show that our proposed approach enhances treatment effect estimation robustness by narrowing confidence intervals and uncovering unrecognized confounding biases. Our findings suggest that LLM-based agents offer a promising path toward scalable, trustworthy, and semantically aware causal inference. △ Less

Submitted 10 August, 2025; originally announced August 2025.

Towards Simulating Social Influence Dynamics with LLM-based Multi-agents

Authors: Hsien-Tsung Lin, Pei-Cing Huang, Chan-Tung Ku, Chan Hsu, Pei-Xuan Shieh, Yihuang Kang

Abstract: Recent advancements in Large Language Models offer promising capabilities to simulate complex human social interactions. We investigate whether LLM-based multi-agent simulations can reproduce core human social dynamics observed in online forums. We evaluate conformity dynamics, group polarization, and fragmentation across different model scales and reasoning capabilities using a structured simulat… ▽ More Recent advancements in Large Language Models offer promising capabilities to simulate complex human social interactions. We investigate whether LLM-based multi-agent simulations can reproduce core human social dynamics observed in online forums. We evaluate conformity dynamics, group polarization, and fragmentation across different model scales and reasoning capabilities using a structured simulation framework. Our findings indicate that smaller models exhibit higher conformity rates, whereas models optimized for reasoning are more resistant to social influence. △ Less

Submitted 30 July, 2025; originally announced July 2025.

Towards Interpretable Renal Health Decline Forecasting via Multi-LMM Collaborative Reasoning Framework

Authors: Peng-Yi Wu, Pei-Cing Huang, Ting-Yu Chen, Chantung Ku, Ming-Yen Lin, Yihuang Kang

Abstract: Accurate and interpretable prediction of estimated glomerular filtration rate (eGFR) is essential for managing chronic kidney disease (CKD) and supporting clinical decisions. Recent advances in Large Multimodal Models (LMMs) have shown strong potential in clinical prediction tasks due to their ability to process visual and textual information. However, challenges related to deployment cost, data p… ▽ More Accurate and interpretable prediction of estimated glomerular filtration rate (eGFR) is essential for managing chronic kidney disease (CKD) and supporting clinical decisions. Recent advances in Large Multimodal Models (LMMs) have shown strong potential in clinical prediction tasks due to their ability to process visual and textual information. However, challenges related to deployment cost, data privacy, and model reliability hinder their adoption. In this study, we propose a collaborative framework that enhances the performance of open-source LMMs for eGFR forecasting while generating clinically meaningful explanations. The framework incorporates visual knowledge transfer, abductive reasoning, and a short-term memory mechanism to enhance prediction accuracy and interpretability. Experimental results show that the proposed framework achieves predictive performance and interpretability comparable to proprietary models. It also provides plausible clinical reasoning processes behind each prediction. Our method sheds new light on building AI systems for healthcare that combine predictive accuracy with clinically grounded interpretability. △ Less

Submitted 30 July, 2025; originally announced July 2025.

Optimizing Quantum Chemistry Simulations with a Hybrid Quantization Scheme

Authors: Calvin Ku, Yu-Cheng Chen, Alice Hu, Min-Hsiu Hsieh

Abstract: Complex quantum simulation workflows are often hindered by incompatible wavefunction representations adopted across different algorithmic frameworks. In particular, the mismatch between the first- and second-quantization formalisms prevents algorithms specialized for their respective quantizations from being integrated within a single circuit, thereby forcing practitioners to rely on suboptimal me… ▽ More Complex quantum simulation workflows are often hindered by incompatible wavefunction representations adopted across different algorithmic frameworks. In particular, the mismatch between the first- and second-quantization formalisms prevents algorithms specialized for their respective quantizations from being integrated within a single circuit, thereby forcing practitioners to rely on suboptimal methods simply to maintain a consistent representation. To address this challenge, we propose a hybrid quantization scheme that employs a conversion circuit to switch between the two, requiring $\mathcal{O}(N\log N\log M)$ gates for a system of N electrons and M orbitals. This capability is critical for constructing complex quantum simulation workflows, allowing us to use the most efficient quantization for each individual step. We discuss its applications to bring polynomial improvements in the characterization of ground-state, ab-initio molecular dynamics, and characterization of spectroscopic properties. Quantitative estimations of such applications found up to three orders of magnitude fewer ground-state preparations when measuring the 2-reduced density matrix of molecular systems. △ Less

Submitted 30 April, 2026; v1 submitted 6 July, 2025; originally announced July 2025.

Comments: 21 pages, 14 figures, reordered and rewritten applications, added numerical estimations

Journal ref: Commun Phys 9, 148 (2026)

Proof of a conjecture on eigenvalues of transposition graph

Authors: Cheng Yeaw Ku, Leyou Xu

Abstract: The transposition graph $Cay(S_n,T_n)$ is the Cayley graph on the symmetric group $S_n$ generated by the set $T_n$ of all transpositions. In this paper, we show that each integer in the interval $\left[-{\lfloor(2n+1)/3 \rfloor\choose 2}, {\lfloor(2n+1)/3 \rfloor\choose 2}\right]$ is an eigenvalue of $Cay(S_n,T_n)$. This proves a recent conjecture by Kravchuk \cite{Kravchuk}. The transposition graph $Cay(S_n,T_n)$ is the Cayley graph on the symmetric group $S_n$ generated by the set $T_n$ of all transpositions. In this paper, we show that each integer in the interval $\left[-{\lfloor(2n+1)/3 \rfloor\choose 2}, {\lfloor(2n+1)/3 \rfloor\choose 2}\right]$ is an eigenvalue of $Cay(S_n,T_n)$. This proves a recent conjecture by Kravchuk \cite{Kravchuk}. △ Less

Submitted 17 June, 2025; originally announced June 2025.

CodEv: An Automated Grading Framework Leveraging Large Language Models for Consistent and Constructive Feedback

Authors: En-Qi Tseng, Pei-Cing Huang, Chan Hsu, Peng-Yi Wu, Chan-Tung Ku, Yihuang Kang

Abstract: Grading programming assignments is crucial for guiding students to improve their programming skills and coding styles. This study presents an automated grading framework, CodEv, which leverages Large Language Models (LLMs) to provide consistent and constructive feedback. We incorporate Chain of Thought (CoT) prompting techniques to enhance the reasoning capabilities of LLMs and ensure that the gra… ▽ More Grading programming assignments is crucial for guiding students to improve their programming skills and coding styles. This study presents an automated grading framework, CodEv, which leverages Large Language Models (LLMs) to provide consistent and constructive feedback. We incorporate Chain of Thought (CoT) prompting techniques to enhance the reasoning capabilities of LLMs and ensure that the grading is aligned with human evaluation. Our framework also integrates LLM ensembles to improve the accuracy and consistency of scores, along with agreement tests to deliver reliable feedback and code review comments. The results demonstrate that the framework can yield grading results comparable to human evaluators, by using smaller LLMs. Evaluation and consistency tests of the LLMs further validate our approach, confirming the reliability of the generated scores and feedback. △ Less

Submitted 9 January, 2025; originally announced January 2025.

Generalization Analysis for Deep Contrastive Representation Learning

Authors: Nong Minh Hieu, Antoine Ledent, Yunwen Lei, Cheng Yeaw Ku

Abstract: In this paper, we present generalization bounds for the unsupervised risk in the Deep Contrastive Representation Learning framework, which employs deep neural networks as representation functions. We approach this problem from two angles. On the one hand, we derive a parameter-counting bound that scales with the overall size of the neural networks. On the other hand, we provide a norm-based bound… ▽ More In this paper, we present generalization bounds for the unsupervised risk in the Deep Contrastive Representation Learning framework, which employs deep neural networks as representation functions. We approach this problem from two angles. On the one hand, we derive a parameter-counting bound that scales with the overall size of the neural networks. On the other hand, we provide a norm-based bound that scales with the norms of neural networks' weight matrices. Ignoring logarithmic factors, the bounds are independent of $k$, the size of the tuples provided for contrastive learning. To the best of our knowledge, this property is only shared by one other work, which employed a different proof strategy and suffers from very strong exponential dependence on the depth of the network which is due to a use of the peeling technique. Our results circumvent this by leveraging powerful results on covering numbers with respect to uniform norms over samples. In addition, we utilize loss augmentation techniques to further reduce the dependency on matrix norms and the implicit dependence on network depth. In fact, our techniques allow us to produce many bounds for the contrastive learning setting with similar architectural dependencies as in the study of the sample complexity of ordinary loss functions, thereby bridging the gap between the learning theories of contrastive learning and DNNs. △ Less

Submitted 19 December, 2024; v1 submitted 16 December, 2024; originally announced December 2024.

Comments: Accepted at AAAI 2025

Subgroup Analysis via Model-based Rule Forest

Authors: I-Ling Cheng, Chan Hsu, Chantung Ku, Pei-Ju Lee, Yihuang Kang

Abstract: Machine learning models are often criticized for their black-box nature, raising concerns about their applicability in critical decision-making scenarios. Consequently, there is a growing demand for interpretable models in such contexts. In this study, we introduce Model-based Deep Rule Forests (mobDRF), an interpretable representation learning algorithm designed to extract transparent models from… ▽ More Machine learning models are often criticized for their black-box nature, raising concerns about their applicability in critical decision-making scenarios. Consequently, there is a growing demand for interpretable models in such contexts. In this study, we introduce Model-based Deep Rule Forests (mobDRF), an interpretable representation learning algorithm designed to extract transparent models from data. By leveraging IF-THEN rules with multi-level logic expressions, mobDRF enhances the interpretability of existing models without compromising accuracy. We apply mobDRF to identify key risk factors for cognitive decline in an elderly population, demonstrating its effectiveness in subgroup analysis and local model optimization. Our method offers a promising solution for developing trustworthy and interpretable machine learning models, particularly valuable in fields like healthcare, where understanding differential effects across patient subgroups can lead to more personalized and effective treatments. △ Less

Submitted 27 August, 2024; originally announced August 2024.

Molecular Ground State Simulation by Subspace Restriction and Hund's Rule

Authors: Tsung-Chi Chiang, Calvin Ku, Jyh-Pin Chou, Alice Hu, Peng-Jen Chen, Ching-Jui Lai

Abstract: Simulation of molecular ground states on near-term quantum hardware is constrained by qubit availability and the cost of variational optimization. To address these challenges, the Subspace Restriction Scheme (SRS) is introduced as a mathematical framework that projects the molecular Hamiltonian onto a selected Fock subspace prior to qubit encoding. By enforcing molecular multiplicity and a general… ▽ More Simulation of molecular ground states on near-term quantum hardware is constrained by qubit availability and the cost of variational optimization. To address these challenges, the Subspace Restriction Scheme (SRS) is introduced as a mathematical framework that projects the molecular Hamiltonian onto a selected Fock subspace prior to qubit encoding. By enforcing molecular multiplicity and a generalized Hund's rule, the Multi-Hund Subspace (MHS) is constructed. This physically motivated restriction significantly reduces the effective Fock-space dimension, asymptotically saving $N$ qubits for a Hamiltonian of $M$ spatial orbitals and $N$ electrons. As a result, we successfully overcome classical memory bottlenecks and enable simulations of large systems, such as the $H_{22}$ chain, which requires 44 qubits under standard Jordan-Wigner (JW) encoding. While the strict pairing structure may limit accuracy in strongly correlated dissociation regimes, MHS effectively captures the essential low-energy physics of closed-shell molecules near equilibrium. In Variational Quantum Eigensolver (VQE) benchmarks, MHS enhances optimization behaviour and achieves high accuracy with a shallow ansatz. These findings demonstrate that physically motivated subspace restriction offers an effective approach to more resource-efficient quantum-chemistry simulations. △ Less

Submitted 31 May, 2026; v1 submitted 4 April, 2024; originally announced April 2024.

BlenDA: Domain Adaptive Object Detection through diffusion-based blending

Authors: Tzuhsuan Huang, Chen-Che Huang, Chung-Hao Ku, Jun-Cheng Chen

Abstract: Unsupervised domain adaptation (UDA) aims to transfer a model learned using labeled data from the source domain to unlabeled data in the target domain. To address the large domain gap issue between the source and target domains, we propose a novel regularization method for domain adaptive object detection, BlenDA, by generating the pseudo samples of the intermediate domains and their corresponding… ▽ More Unsupervised domain adaptation (UDA) aims to transfer a model learned using labeled data from the source domain to unlabeled data in the target domain. To address the large domain gap issue between the source and target domains, we propose a novel regularization method for domain adaptive object detection, BlenDA, by generating the pseudo samples of the intermediate domains and their corresponding soft domain labels for adaptation training. The intermediate samples are generated by dynamically blending the source images with their corresponding translated images using an off-the-shelf pre-trained text-to-image diffusion model which takes the text label of the target domain as input and has demonstrated superior image-to-image translation quality. Based on experimental results from two adaptation benchmarks, our proposed approach can significantly enhance the performance of the state-of-the-art domain adaptive object detector, Adversarial Query Transformer (AQT). Particularly, in the Cityscapes to Foggy Cityscapes adaptation, we achieve an impressive 53.4% mAP on the Foggy Cityscapes dataset, surpassing the previous state-of-the-art by 1.5%. It is worth noting that our proposed method is also applicable to various paradigms of domain adaptive object detection. The code is available at:https://github.com/aiiu-lab/BlenDA △ Less

Submitted 18 January, 2024; originally announced January 2024.

Comments: ICASSP(2024):2024 IEEE International Conference on Acoustics, Speech and Signal Processing

Downlink Rate Maximization with Reconfigurable Intelligent Surface Assisted Full-Duplex Transmissions

Authors: Li-Hsiang Shen, Chia-Jou Ku, Kai-Ten Feng

Abstract: Reconfigurable intelligent surfaces (RIS) as an effective technique for intelligently manipulating channel paths through reflection to serve desired users. Full-duplex (FD) systems, enabling simultaneous transmission and reception from a base station (BS), offer the theoretical advantage of doubled spectrum efficiency. However, the presence of strong self-interference (SI) in FD systems significan… ▽ More Reconfigurable intelligent surfaces (RIS) as an effective technique for intelligently manipulating channel paths through reflection to serve desired users. Full-duplex (FD) systems, enabling simultaneous transmission and reception from a base station (BS), offer the theoretical advantage of doubled spectrum efficiency. However, the presence of strong self-interference (SI) in FD systems significantly degrades performance, which can be mitigated by leveraging the capabilities of RIS. In this work, we consider joint BS and RIS beamforming for maximizing the downlink (DL) transmission rate while guaranteeing uplink (UL) rate requirement. We propose an FD-RIS beamforming (FRIS) scheme by adopting penalty convex-concave programming. Simulation results demonstrate the UL/DL rate improvements achieved by considering various levels of imperfect CSI. The proposed FRIS scheme validates their effectiveness across different RIS deployments and RIS/BS configurations. FRIS has achieved the highest rate compared to the other approximation method, conventional beamforming techniques, HD systems, and deployment without RIS. △ Less

Submitted 6 November, 2023; originally announced November 2023.

Comments: arXiv admin note: substantial text overlap with arXiv:2306.05693

Evaluating Robustness of Visual Representations for Object Assembly Task Requiring Spatio-Geometrical Reasoning

Authors: Chahyon Ku, Carl Winge, Ryan Diaz, Wentao Yuan, Karthik Desingh

Abstract: This paper primarily focuses on evaluating and benchmarking the robustness of visual representations in the context of object assembly tasks. Specifically, it investigates the alignment and insertion of objects with geometrical extrusions and intrusions, commonly referred to as a peg-in-hole task. The accuracy required to detect and orient the peg and the hole geometry in SE(3) space for successfu… ▽ More This paper primarily focuses on evaluating and benchmarking the robustness of visual representations in the context of object assembly tasks. Specifically, it investigates the alignment and insertion of objects with geometrical extrusions and intrusions, commonly referred to as a peg-in-hole task. The accuracy required to detect and orient the peg and the hole geometry in SE(3) space for successful assembly poses significant challenges. Addressing this, we employ a general framework in visuomotor policy learning that utilizes visual pretraining models as vision encoders. Our study investigates the robustness of this framework when applied to a dual-arm manipulation setup, specifically to the grasp variations. Our quantitative analysis shows that existing pretrained models fail to capture the essential visual features necessary for this task. However, a visual encoder trained from scratch consistently outperforms the frozen pretrained models. Moreover, we discuss rotation representations and associated loss functions that substantially improve policy learning. We present a novel task scenario designed to evaluate the progress in visuomotor policy learning, with a specific focus on improving the robustness of intricate assembly tasks that require both geometrical and spatial reasoning. Videos, additional experiments, dataset, and code are available at https://bit.ly/geometric-peg-in-hole . △ Less

Submitted 6 February, 2024; v1 submitted 15 October, 2023; originally announced October 2023.

D-STAR: Dual Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surfaces for Joint Uplink/Downlink Transmission

Authors: Li-Hsiang Shen, Po-Chen Wu, Chia-Jou Ku, Yu-Ting Li, Kai-Ten Feng, Yuanwei Liu, Lajos Hanzo

Abstract: The joint uplink/downlink (JUD) design of simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) is conceived in support of both uplink (UL) and downlink (DL) users. Furthermore, the dual STAR-RISs (D-STAR) concept is conceived as a promising architecture for 360-degree full-plane service coverage, including UL/DL users located between the base station (BS) and t… ▽ More The joint uplink/downlink (JUD) design of simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) is conceived in support of both uplink (UL) and downlink (DL) users. Furthermore, the dual STAR-RISs (D-STAR) concept is conceived as a promising architecture for 360-degree full-plane service coverage, including UL/DL users located between the base station (BS) and the D-STAR as well as beyond. The corresponding regions are termed as primary (P) and secondary (S) regions. Both BS/users exist in the P-region, but only users are located in the S-region. The primary STAR-RIS (STAR-P) plays an important role in terms of tackling the P-region inter-user interference, the self-interference (SI) from the BS and from the reflective as well as refractive UL users imposed on the DL receiver. By contrast, the secondary STAR-RIS (STAR-S) aims for mitigating the S-region interferences. The non-linear and non-convex rate-maximization problem formulated is solved by alternating optimization amongst the decomposed convex sub-problems of the BS beamformer, and the D-STAR amplitude as well as phase shift configurations. We also propose a D-STAR based active beamforming and passive STAR-RIS amplitude/phase (DBAP) optimization scheme to solve the respective sub-problems by Lagrange dual with Dinkelbach's transformation, alternating direction method of multipliers (ADMM) with successive convex approximation (SCA), and penalty convex-concave procedure (PCCP). Our simulation results reveal that the proposed D-STAR architecture outperforms the conventional single RIS, single STAR-RIS, and half-duplex networks. The proposed DBAP of D-STAR outperforms the state-of-the-art solutions found in the open literature for different numbers of quantization levels, geographic deployment, transmit power and for diverse numbers of transmit antennas, patch partitions as well as D-STAR elements. △ Less

Submitted 8 February, 2024; v1 submitted 29 July, 2023; originally announced July 2023.

Comments: Accepted by IEEE TCOM

Robust Active and Passive Beamforming for RIS-Assisted Full-Duplex Systems under Imperfect CSI

Authors: Li-Hsiang Shen, Chia-Jou Ku, Kai-Ten Feng

Abstract: The sixth-generation (6G) wireless technology recognizes the potential of reconfigurable intelligent surfaces (RIS) as an effective technique for intelligently manipulating channel paths through reflection to serve desired users. Full-duplex (FD) systems, enabling simultaneous transmission and reception from a base station (BS), offer the theoretical advantage of doubled spectrum efficiency. Howev… ▽ More The sixth-generation (6G) wireless technology recognizes the potential of reconfigurable intelligent surfaces (RIS) as an effective technique for intelligently manipulating channel paths through reflection to serve desired users. Full-duplex (FD) systems, enabling simultaneous transmission and reception from a base station (BS), offer the theoretical advantage of doubled spectrum efficiency. However, the presence of strong self-interference (SI) in FD systems significantly degrades performance, which can be mitigated by leveraging the capabilities of RIS. Moreover, accurately obtaining channel state information (CSI) from RIS poses a critical challenge. Our objective is to maximize downlink (DL) user data rates while ensuring quality-of-service (QoS) for uplink (UL) users under imperfect CSI from reflected channels. To address this, we propose a robust active BS and passive RIS beamforming (RAPB) scheme for RIS-FD, accounting for both SI and imperfect CSI. RAPB incorporates distributionally robust design, conditional value-at-risk (CVaR), and penalty convex-concave programming (PCCP) techniques. Simulation results demonstrate the UL/DL rate improvement are achieved by considering different levels of imperfect CSI. The proposed RAPB schemes validate their effectiveness across different RIS deployments and RIS/BS configurations. Benefited from robust beamforming, RAPB outperforms the existing methods in terms of non-robustness, deployment without RIS, conventional approximation, and half-duplex systems. △ Less

Submitted 19 November, 2023; v1 submitted 9 June, 2023; originally announced June 2023.

Comments: some errors found

An emergent quasi-2D metallic state derived from the Mott insulator framework

Authors: P. -C. Chiang, S. C. Lin, C. -Y. Chiang, C. -S. Ku, S. W. Huang, J. M. Lee, Y. -D. Chuang, H. J. Lin, Y. F. Liao, C. -M. Cheng, S. C. Haw, J. M. Chen, Y. -H. Chu, T. H. Do, C. W. Luo, J. -Y. Juang, K. H. Wu, Y. -W. Chang, J. -C. Yang, J. -Y. Lin

Abstract: Recent quasi-2D systems with judicious exploitation of the atomic monolayer or few-layer architecture exhibit unprecedented physical properties that challenge the conventional wisdom on the condensed matter physics. Here we show that the infinite layer SrCuO2 (SCO), a topical cuprate Mott insulator in the bulk form, can manifest an unexpected metallic state in the quasi-2D limit when SCO is grown… ▽ More Recent quasi-2D systems with judicious exploitation of the atomic monolayer or few-layer architecture exhibit unprecedented physical properties that challenge the conventional wisdom on the condensed matter physics. Here we show that the infinite layer SrCuO2 (SCO), a topical cuprate Mott insulator in the bulk form, can manifest an unexpected metallic state in the quasi-2D limit when SCO is grown on TiO2-terminated SrTiO3 (STO) substrates. Hard x-ray core-level photoemission spectra demonstrate a definitive Fermi level that resembles the hole doped metal. Soft x-ray absorption spectroscopy also reveals features analogous to those of a hole doped Mott insulator. Based on these results, we conclude that the hole doping does not occur at the interfaces between SCO and STO; instead, it comes from the transient layers between the chain type and the planar type structures within the SCO slab. The present work reveals a novel metallic state in the infinite layer SCO and invites further examination to elucidate the spatial extent of this state. △ Less

Submitted 14 December, 2022; originally announced December 2022.

Comments: 31 pages, 11 figures. Physical Review B, in press

Journal ref: Physical Review B 107, 075104 (2023)

Reconfigurable Intelligent Surface-Empowered Self-Interference Cancellation for 6G Full-Duplex MIMO Communication Systems

Authors: Chia-Jou Ku, Li-Hsiang Shen, Kai-Ten Feng

Abstract: Substantially increasing wireless traffic and extending serving coverage is required with the advent of sixth-generation (6G) wireless communication networks. Reconfigurable intelligent surface (RIS) is widely considered as a promising technique which is capable of improving the system sum rate and energy efficiency. Moreover, full-duplex (FD) multi-input-multi-output (MIMO) transmission provides… ▽ More Substantially increasing wireless traffic and extending serving coverage is required with the advent of sixth-generation (6G) wireless communication networks. Reconfigurable intelligent surface (RIS) is widely considered as a promising technique which is capable of improving the system sum rate and energy efficiency. Moreover, full-duplex (FD) multi-input-multi-output (MIMO) transmission provides simultaneous transmit and received signals, which theoretically provides twice of spectrum efficiency. However, the self-interference (SI) in FD system is a challenging task requiring high-overhead cancellation, which can be resolved by configuring appropriate phase shifts of RIS. This paper has proposed an RIS-empowered full-duplex interference cancellation (RFIC) scheme in order to alleviate the severe interference in an RIS-FD system. We consider the interference minimization of RIS-FD MIMO while guaranteeing quality-of-service (QoS) of whole system. The closed-form solution of RIS phase shifts is theoretically derived with the discussion of different numbers of RIS elements and receiving antennas. Simulation results reveal that the proposed RFIC scheme outperforms existing benchmarks with more than 50% of performance gain of sum rate. △ Less

Submitted 29 March, 2023; v1 submitted 14 December, 2021; originally announced December 2021.

Journal ref: IEEE 33rd Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), 2022

CAMEL: A Weakly Supervised Learning Framework for Histopathology Image Segmentation

Authors: Gang Xu, Zhigang Song, Zhuo Sun, Calvin Ku, Zhe Yang, Cancheng Liu, Shuhao Wang, Jianpeng Ma, Wei Xu

Abstract: Histopathology image analysis plays a critical role in cancer diagnosis and treatment. To automatically segment the cancerous regions, fully supervised segmentation algorithms require labor-intensive and time-consuming labeling at the pixel level. In this research, we propose CAMEL, a weakly supervised learning framework for histopathology image segmentation using only image-level labels. Using mu… ▽ More Histopathology image analysis plays a critical role in cancer diagnosis and treatment. To automatically segment the cancerous regions, fully supervised segmentation algorithms require labor-intensive and time-consuming labeling at the pixel level. In this research, we propose CAMEL, a weakly supervised learning framework for histopathology image segmentation using only image-level labels. Using multiple instance learning (MIL)-based label enrichment, CAMEL splits the image into latticed instances and automatically generates instance-level labels. After label enrichment, the instance-level labels are further assigned to the corresponding pixels, producing the approximate pixel-level labels and making fully supervised training of segmentation models possible. CAMEL achieves comparable performance with the fully supervised approaches in both instance-level classification and pixel-level segmentation on CAMELYON16 and a colorectal adenoma dataset. Moreover, the generality of the automatic labeling methodology may benefit future weakly supervised learning studies for histopathology image analysis. △ Less

Submitted 28 August, 2019; originally announced August 2019.

Comments: 10 pages, 9 figures, accepted by ICCV 2019

A simple INDIUM TIN OXIDE/glass DRA

Authors: Vivek Parimi, Chia Hao Ku, Abhirup Datta, Sajal Biring, Somaditya Sen

Abstract: A novel Dielectric Resonator Antenna, simply made of INDIUM TIN OXIDE coated glass slides placed on a microstrip transmission line, for communication applications is presented. Changes in the bandwidth and gain of the antenna are observed by modifying the dimensions of the INDIUM TIN OXIDE coated glass slides. Changes in gain, directivity and reflection coefficient are observed. A parametric study… ▽ More A novel Dielectric Resonator Antenna, simply made of INDIUM TIN OXIDE coated glass slides placed on a microstrip transmission line, for communication applications is presented. Changes in the bandwidth and gain of the antenna are observed by modifying the dimensions of the INDIUM TIN OXIDE coated glass slides. Changes in gain, directivity and reflection coefficient are observed. A parametric study is conducted on the size of the DRA to understand the effect on bandwidth, reflection coefficient and gain. △ Less

Submitted 27 January, 2019; originally announced January 2019.

Comments: INDIUM TIN OXIDE, DRA, directivity, gain, bandwidth, WLAN, WiMAX

Cayley Graph on Symmetric Group Generated by Elements Fixing $k$ Points

Authors: Kok Bin Wong, Terry Lau, Cheng Yeaw Ku

Abstract: Let $\mathcal{S}_{n}$ be the symmetric group on $[n]=\{1, \ldots, n\}$. The $k$-point fixing graph $\mathcal{F}(n,k)$ is defined to be the graph with vertex set $\mathcal{S}_{n}$ and two vertices $g$, $h$ of $\mathcal{F}(n,k)$ are joined if and only if $gh^{-1}$ fixes exactly $k$ points. In this paper, we derive a recurrence formula for the eigenvalues of $\mathcal{F}(n,k)$. Then we apply our resu… ▽ More Let $\mathcal{S}_{n}$ be the symmetric group on $[n]=\{1, \ldots, n\}$. The $k$-point fixing graph $\mathcal{F}(n,k)$ is defined to be the graph with vertex set $\mathcal{S}_{n}$ and two vertices $g$, $h$ of $\mathcal{F}(n,k)$ are joined if and only if $gh^{-1}$ fixes exactly $k$ points. In this paper, we derive a recurrence formula for the eigenvalues of $\mathcal{F}(n,k)$. Then we apply our result to determine the sign of the eigenvalues of $\mathcal{F}(n,1)$. △ Less

Submitted 26 May, 2014; originally announced May 2014.

Comments: 22 pages

An Erd{\H o}s-Ko-Rado theorem for permutations with fixed number of cycles

Authors: Cheng Yeaw Ku, Kok Bin Wong

Abstract: Let $S_{n}$ denote the set of permutations of $[n]=\{1,2,\dots, n\}$. For a positive integer $k$, define $S_{n,k}$ to be the set of all permutations of $[n]$ with exactly $k$ disjoint cycles, i.e., \[ S_{n,k} = \{π\in S_{n}: π= c_{1}c_{2} \cdots c_{k}\},\] where $c_1,c_2,\dots ,c_k$ are disjoint cycles. The size of $S_{n,k}$ is given by… ▽ More Let $S_{n}$ denote the set of permutations of $[n]=\{1,2,\dots, n\}$. For a positive integer $k$, define $S_{n,k}$ to be the set of all permutations of $[n]$ with exactly $k$ disjoint cycles, i.e., \[ S_{n,k} = \{π\in S_{n}: π= c_{1}c_{2} \cdots c_{k}\},\] where $c_1,c_2,\dots ,c_k$ are disjoint cycles. The size of $S_{n,k}$ is given by $\left [ \begin{matrix}n\\ k \end{matrix}\right]=(-1)^{n-k}s(n,k)$, where $s(n,k)$ is the Stirling number of the first kind. A family $\mathcal{A} \subseteq S_{n,k}$ is said to be $t$-{\em intersecting} if any two elements of $\mathcal{A}$ have at least $t$ common cycles. In this paper, we show that, given any positive integers $k,t$ with $k\geq t+1$, there exists an integer $n_0=n_0(k,t)$, such that for all $n\geq n_0$, if $\mathcal{A} \subseteq S_{n,k}$ is $t$-intersecting, then \[ |\mathcal{A}| \le \left [ \begin{matrix}n-t\\ k-t \end{matrix}\right],\] with equality if and only if $\mathcal{A}$ is the stabiliser of $t$ fixed points. △ Less

Submitted 4 February, 2014; originally announced February 2014.

Comments: 8 pages

On $r$-cross $t$-intersecting families for weak compositions

Authors: Kok Bin Wong, Cheng Yeaw Ku

Abstract: Let $\mathbb N_0$ be the set of non-negative integers, and let $P(n,l)$ denote the set of all weak compositions of $n$ with $l$ parts, i.e., $P(n,l)=\{ (x_1,x_2,\dots, x_l)\in\mathbb N_0^l\ :\ x_1+x_2+\cdots+x_l=n\}$. For any element $\mathbf u=(u_1,u_2,\dots, u_l)\in P(n,l)$, denote its $i$th-coordinate by $\mathbf u(i)$, i.e., $\mathbf u(i)=u_i$. Let $l=\min(l_1,l_2,\dots, l_r)$. Families… ▽ More Let $\mathbb N_0$ be the set of non-negative integers, and let $P(n,l)$ denote the set of all weak compositions of $n$ with $l$ parts, i.e., $P(n,l)=\{ (x_1,x_2,\dots, x_l)\in\mathbb N_0^l\ :\ x_1+x_2+\cdots+x_l=n\}$. For any element $\mathbf u=(u_1,u_2,\dots, u_l)\in P(n,l)$, denote its $i$th-coordinate by $\mathbf u(i)$, i.e., $\mathbf u(i)=u_i$. Let $l=\min(l_1,l_2,\dots, l_r)$. Families $\mathcal A_j\subseteq P(n_j,l_j)$ ($j=1,2,\dots, r$) are said to be $r$-cross $t$-intersecting if $\vert \{ i\in [l] \ :\ \mathbf u_1(i)=\mathbf u_2(i)=\cdots=\mathbf u_r(i)\} \vert\geq t$ for all $\mathbf u_j\in \mathcal A_j$. Suppose that $l\geq t+2$. We prove that there exists a constant $n_0=n_0(l_1,l_2,\dots,l_r,t)$ depending only on $l_j$'s and $t$, such that for all $n_j\geq n_0$, if the families $\mathcal A_j\subseteq P(n_j,l_j)$ ($j=1,2,\dots, r$) are $r$-cross $t$-intersecting, then \begin{equation} \prod_{j=1}^r \vert \mathcal{A}_j \vert\leq \prod_{j=1}^r {n_j+l_j-t-1 \choose l_j-t-1}.\notag \end{equation} Moreover, equality holds if and only if there is a $t$-set $T$ of $\{1,2,\dots,l\}$ such that $\mathcal{A}_j=\{\mathbf u\in P(n_j,l_j)\ :\ \mathbf u(i)=0\ {\rm for\ all}\ i\in T\}$ for $j=1,2,\dots, r$. △ Less

Submitted 7 November, 2013; originally announced November 2013.

Comments: 9 pages. arXiv admin note: text overlap with arXiv:1311.1592

A generalization of the extremal function of the Davenport-Schinzel sequences

Authors: Kok Bin Wong, Cheng Yeaw Ku

Abstract: Let $[n]=\{1, \ldots, n\}$. A sequence $u=a_1a_2\dots a_l$ over $[n]$ is called $k$-sparse if $a_i = a_j$, $i > j$ implies $i-j\geq k$. In other words, every consecutive subsequence of $u$ of length at most $k$ does not have letters in common. Let $u,v$ be two sequences. We say that $u$ is $v$-free, if $u$ does not contain a subsequence isomorphic to $v$. Suppose there are only $k$ letters appeari… ▽ More Let $[n]=\{1, \ldots, n\}$. A sequence $u=a_1a_2\dots a_l$ over $[n]$ is called $k$-sparse if $a_i = a_j$, $i > j$ implies $i-j\geq k$. In other words, every consecutive subsequence of $u$ of length at most $k$ does not have letters in common. Let $u,v$ be two sequences. We say that $u$ is $v$-free, if $u$ does not contain a subsequence isomorphic to $v$. Suppose there are only $k$ letters appearing in $v$. The extremal function Ex$(v,n)$ is defined as the maximum length of all the $v$-free and $k$-sparse sequences. In this paper, we study a generalization of the extremal function Ex$(v,n)$. △ Less

Submitted 7 November, 2013; originally announced November 2013.

Comments: 8 pages

An Analogue of the Hilton-Milner Theorem for weak compositions

Authors: Kok Bin Wong, Cheng Yeaw Ku

Abstract: Let $\mathbb N_0$ be the set of non-negative integers, and let $P(n,l)$ denote the set of all weak compositions of $n$ with $l$ parts, i.e., $P(n,l)=\{ (x_1,x_2,\dots, x_l)\in\mathbb N_0^l\ :\ x_1+x_2+\cdots+x_l=n\}$. For any element $\mathbf u=(u_1,u_2,\dots, u_l)\in P(n,l)$, denote its $i$th-coordinate by $\mathbf u(i)$, i.e., $\mathbf u(i)=u_i$. A family $\mathcal A\subseteq P(n,l)$ is said to… ▽ More Let $\mathbb N_0$ be the set of non-negative integers, and let $P(n,l)$ denote the set of all weak compositions of $n$ with $l$ parts, i.e., $P(n,l)=\{ (x_1,x_2,\dots, x_l)\in\mathbb N_0^l\ :\ x_1+x_2+\cdots+x_l=n\}$. For any element $\mathbf u=(u_1,u_2,\dots, u_l)\in P(n,l)$, denote its $i$th-coordinate by $\mathbf u(i)$, i.e., $\mathbf u(i)=u_i$. A family $\mathcal A\subseteq P(n,l)$ is said to be $t$-intersecting if $\vert \{ i \ :\ \mathbf u(i)=\mathbf v(i)\} \vert\geq t$ for all $\mathbf u,\mathbf v\in \mathcal A$. A family $\mathcal A\subseteq P(n,l)$ is said to be trivially $t$-intersecting if there is a $t$-set $T$ of $\{1,2,\dots,l\}$ and elements $y_s\in \mathbb N_0$ ($s\in T$) such that $\mathcal{A}= \{\mathbf u\in P(n,l)\ :\ \mathbf u(j)=y_j\ {\rm for all}\ j\in T\}$. We prove that given any positive integers $l,t$ with $l\geq 2t+3$, there exists a constant $n_0(l,t)$ depending only on $l$ and $t$, such that for all $n\geq n_0(l,t)$, if $\mathcal{A} \subseteq P(n,l)$ is non-trivially $t$-intersecting then \begin{equation} \vert \mathcal{A} \vert\leq {n+l-t-1 \choose l-t-1}-{n-1 \choose l-t-1}+t.\notag \end{equation} Moreover, equality holds if and only if there is a $t$-set $T$ of $\{1,2,\dots,l\}$ such that \begin{equation} \mathcal A=\bigcup_{s\in \{1,2,\dots, l\}\setminus T} \mathcal A_s\cup \left\{ \mathbf q_i\ :\ i\in T \right\},\notag \end{equation} where \begin{align} \mathcal{A}_s & =\{\mathbf u\in P(n,l)\ :\ \mathbf u(j)=0\ {\rm for all}\ j\in T\ {\rm and}\ \mathbf u(s)=0\}\notag \end{align} and $\mathbf q_i\in P(n,l)$ with $\mathbf q_i(j)=0$ for all $j\in \{1,2,\dots, l\}\setminus \{i\}$ and $\mathbf q_i(i)=n$. △ Less

Submitted 7 November, 2013; originally announced November 2013.

Comments: 19 pages

Solving the Ku-Wales conjecture on the eigenvalues of the derangement graph

Authors: Cheng Yeaw Ku, Kok Bin Wong

Abstract: We give a new recurrence formula for the eigenvalues of the derangement graph. Consequently, we provide a simpler proof of the Alternating Sign Property of the derangement graph. Moreover, we prove that the absolute value of the eigenvalue decreases whenever the corresponding partition decreases in the dominance order. In particular, this settles affirmatively a conjecture of Ku and Wales (J. of C… ▽ More We give a new recurrence formula for the eigenvalues of the derangement graph. Consequently, we provide a simpler proof of the Alternating Sign Property of the derangement graph. Moreover, we prove that the absolute value of the eigenvalue decreases whenever the corresponding partition decreases in the dominance order. In particular, this settles affirmatively a conjecture of Ku and Wales (J. of Combin. Theory, Series A 117 (2010) 289--312) regarding the lower and upper bound for the absolute values of these eigenvalues. △ Less

Submitted 17 July, 2012; originally announced July 2012.

An Analogue of Hilton-Milner Theorem for Set Partitions

Authors: Cheng Yeaw Ku, Kok Bin Wong

Abstract: Let $\mathcal{B}(n)$ denote the collection of all set partitions of $[n]$. Suppose $\mathcal{A} \subseteq \mathcal{B}(n)$ is a non-trivial $t$-intersecting family of set partitions i.e. any two members of $\A$ have at least $t$ blocks in common, but there is no fixed $t$ blocks of size one which belong to all of them. It is proved that for sufficiently large $n$ depending on $t$, \[ |\mathcal{A}|… ▽ More Let $\mathcal{B}(n)$ denote the collection of all set partitions of $[n]$. Suppose $\mathcal{A} \subseteq \mathcal{B}(n)$ is a non-trivial $t$-intersecting family of set partitions i.e. any two members of $\A$ have at least $t$ blocks in common, but there is no fixed $t$ blocks of size one which belong to all of them. It is proved that for sufficiently large $n$ depending on $t$, \[ |\mathcal{A}| \le B_{n-t}-\tilde{B}_{n-t}-\tilde{B}_{n-t-1}+t \] where $B_{n}$ is the $n$-th Bell number and $\tilde{B}_{n}$ is the number of set partitions of $[n]$ without blocks of size one. Moreover, equality holds if and only if $\mathcal{A}$ is equivalent to \[ \{P \in \mathcal{B}(n): \{1\}, \{2\},..., \{t\}, \{i\} \in P \textnormal{for some} i \not = 1,2,..., t,n \}\cup \{Q(i,n)\ :\ 1\leq i\leq t\} \] where $Q(i,n)=\{\{i,n\}\}\cup\{\{j\}\ :\ j\in [n]\setminus \{i,n\}\}$. This is an analogue of the Hilton-Milner theorem for set partitions. △ Less

Submitted 2 September, 2011; originally announced September 2011.

On AZ-style identity

Authors: Cheng Yeaw Ku, Kok Bin Wong

Abstract: The AZ identity is a generalization of the LYM-inequality. In this paper, we will give a generalization of the AZ identity. The AZ identity is a generalization of the LYM-inequality. In this paper, we will give a generalization of the AZ identity. △ Less

Submitted 7 July, 2011; originally announced July 2011.

Measurement of valley splitting in high-symmetry Si/SiGe quantum dots

Authors: Matthew G. Borselli, Richard S. Ross, Andrey A. Kiselev, Edward T. Croke, Kevin S. Holabird, Peter W. Deelman, Leslie D. Warren, Ivan Alvarado-Rodriguez, Ivan Milosavljevic, Fiona C. Ku, Wah S. Wong, Adele E. Schmitz, Marko Sokolich, Mark F. Gyure, Andrew T. Hunter

Abstract: We have demonstrated few-electron quantum dots in Si/SiGe and InGaAs, with occupation number controllable from N = 0. These display a high degree of spatial symmetry and identifiable shell structure. Magnetospectroscopy measurements show that two Si-based devices possess a singlet N =2 ground state at low magnetic field and therefore the two-fold valley degeneracy is lifted. The valley splittings… ▽ More We have demonstrated few-electron quantum dots in Si/SiGe and InGaAs, with occupation number controllable from N = 0. These display a high degree of spatial symmetry and identifiable shell structure. Magnetospectroscopy measurements show that two Si-based devices possess a singlet N =2 ground state at low magnetic field and therefore the two-fold valley degeneracy is lifted. The valley splittings in these two devices were 120 and 270 μeV, suggesting the presence of atomically sharp interfaces in our heterostructures. △ Less

Submitted 13 April, 2011; v1 submitted 6 December, 2010; originally announced December 2010.

Comments: 3 pages, 3 figures

Journal ref: Appl. Phys. Lett. 98, 123118 (2011)

The covering radius problem for sets of perfect matchings

Authors: Cheng Yeaw Ku, Alan J. Aw

Abstract: Consider the family of all perfect matchings of the complete graph $K_{2n}$ with $2n$ vertices. Given any collection $\mathcal M$ of perfect matchings of size $s$, there exists a maximum number $f(n,x)$ such that if $s\leq f(n,x)$, then there exists a perfect matching that agrees with each perfect matching in $\mathcal M$ in at most $x-1$ edges. We use probabilistic arguments to give several lower… ▽ More Consider the family of all perfect matchings of the complete graph $K_{2n}$ with $2n$ vertices. Given any collection $\mathcal M$ of perfect matchings of size $s$, there exists a maximum number $f(n,x)$ such that if $s\leq f(n,x)$, then there exists a perfect matching that agrees with each perfect matching in $\mathcal M$ in at most $x-1$ edges. We use probabilistic arguments to give several lower bounds for $f(n,x)$. We also apply the Lovász local lemma to find a function $g(n,x)$ such that if each edge appears at most $g(n, x)$ times then there exists a perfect matching that agrees with each perfect matching in $\mathcal M$ in at most $x-1$ edges. This is an analogue of an extremal result vis-á-vis the covering radius of sets of permutations, which was studied by Cameron and Wanless (cf. \cite{cameron}), and Keevash and Ku (cf. \cite{ku}). We also conclude with a conjecture of a more general problem in hypergraph matchings. △ Less

Submitted 25 April, 2011; v1 submitted 4 September, 2010; originally announced September 2010.

Comments: 10 pages

MSC Class: 05D40

Journal ref: Discrete Mathematics 2015

Gallai-Edmonds Structure Theorem for Weighted Matching Polynomial

Authors: Cheng Yeaw Ku, Kok Bin Wong

Abstract: In this paper, we prove the Gallai-Edmonds structure theorem for the most general matching polynomial. Our result implies the Parter-Wiener theorem and its recent generalization about the existence of principal submatrices of a Hermitian matrix whose graph is a tree. keywords: In this paper, we prove the Gallai-Edmonds structure theorem for the most general matching polynomial. Our result implies the Parter-Wiener theorem and its recent generalization about the existence of principal submatrices of a Hermitian matrix whose graph is a tree. keywords: △ Less

Submitted 5 June, 2010; originally announced June 2010.

Comments: 34 pages, 5 figures

Group Marriage Problem

Authors: Cheng Yeaw Ku, Kok Bin Wong

Abstract: Let $G$ be a permutation group acting on $[n]=\{1, ..., n\}$ and $\mathcal{V}=\{V_{i}: i=1, ..., n\}$ be a system of $n$ subsets of $[n]$. When is there an element $g \in G$ so that $g(i) \in V_{i}$ for each $i \in [n]$? If such $g$ exists, we say that $G$ has a $G$-marriage subject to $\mathcal{V}$. An obvious necessary condition is the {\it orbit condition}: for any… ▽ More Let $G$ be a permutation group acting on $[n]=\{1, ..., n\}$ and $\mathcal{V}=\{V_{i}: i=1, ..., n\}$ be a system of $n$ subsets of $[n]$. When is there an element $g \in G$ so that $g(i) \in V_{i}$ for each $i \in [n]$? If such $g$ exists, we say that $G$ has a $G$-marriage subject to $\mathcal{V}$. An obvious necessary condition is the {\it orbit condition}: for any $\emptyset \not = Y \subseteq [n]$, $\bigcup_{y \in Y} V_{y} \supseteq Y^{g}=\{g(y): y \in Y \}$ for some $g \in G$. Keevash (J. Combin. Theory Ser. A 111(2005), 289--309) observed that the orbit condition is sufficient when $G$ is the symmetric group $\Sym([n])$; this is in fact equivalent to the celebrated Hall's Marriage Theorem. We prove that the orbit condition is sufficient if and only if $G$ is a direct product of symmetric groups. We extend the notion of orbit condition to that of $k$-orbit condition and prove that if $G$ is the alternating group $\Alt([n])$ or the cyclic group $C_{n}$ where $n \ge 4$, then $G$ satisfies the $(n-1)$-orbit condition subject to $\V$ if and only if $G$ has a $G$-marriage subject to $\mathcal{V}$. △ Less

Submitted 22 December, 2009; originally announced December 2009.

Properties of $θ$-super positive graphs

Authors: Cheng Yeaw Ku, Kok Bin Wong

Abstract: Let the matching polynomial of a graph $G$ be denoted by $μ(G,x)$. A graph $G$ is said to be $θ$-super positive if $μ(G,θ)\neq 0$ and $μ(G\setminus v,θ)=0$ for all $v\in V(G)$. In particular, $G$ is 0-super positive if and only if $G$ has a perfect matching. While much is known about 0-super positive graphs, almost nothing is known about $θ$-super positive graphs for $θ\not = 0$. This motivates… ▽ More Let the matching polynomial of a graph $G$ be denoted by $μ(G,x)$. A graph $G$ is said to be $θ$-super positive if $μ(G,θ)\neq 0$ and $μ(G\setminus v,θ)=0$ for all $v\in V(G)$. In particular, $G$ is 0-super positive if and only if $G$ has a perfect matching. While much is known about 0-super positive graphs, almost nothing is known about $θ$-super positive graphs for $θ\not = 0$. This motivates us to investigate the structure of $θ$-super positive graphs in this paper. Though a 0-super positive graph may not contain any cycle, we show that a $θ$-super positive graph with $θ\not = 0$ must contain a cycle. We introduce two important types of $θ$-super positive graphs, namely $θ$-elementary and $θ$-base graphs. One of our main results is that any $θ$-super positive graph $G$ can be constructed by adding certain type of edges to a disjoint union of $θ$-base graphs; moreover, these $θ$-base graphs are uniquely determined by $G$. We also give a characterization of $θ$-elementary graphs: a graph $G$ is $θ$-elementary if and only if the set of all its $θ$-barrier sets form a partition of $V(G)$. Here, $θ$-elementary graphs and $θ$-barrier sets can be regarded as $θ$-analogue of elementary graphs and Tutte sets in classical matching theory. △ Less

Submitted 21 December, 2009; originally announced December 2009.

Comments: 13 pages, 6 figures

MSC Class: 05C31; 05C70

Generalized $D$-graphs for Nonzero Roots of the Matching Polynomial

Authors: Cheng Yeaw Ku, Kok Bin Wong

Abstract: Recently, Bauer et al. (J Graph Theory 55(4) (2007), 343--358) introduced a graph operator $D(G)$, called the $D$-graph of $G$, which has been useful in investigating the structural aspects of maximal Tutte sets in $G$ with a perfect matching. Among other results, they proved a characterization of maximal Tutte sets in terms of maximal independent sets in the graph $D(G)$ and maximal extreme set… ▽ More Recently, Bauer et al. (J Graph Theory 55(4) (2007), 343--358) introduced a graph operator $D(G)$, called the $D$-graph of $G$, which has been useful in investigating the structural aspects of maximal Tutte sets in $G$ with a perfect matching. Among other results, they proved a characterization of maximal Tutte sets in terms of maximal independent sets in the graph $D(G)$ and maximal extreme sets in $G$. This was later extended to graphs without perfect matchings by Busch et al. (Discrete Appl. Math. 155 (2007), 2487--2495). Let $θ$ be a real number and $μ(G,x)$ be the matching polynomial of a graph $G$. Let $\textnormal{mult} (θ, G)$ be the multiplicity of $θ$ as a root of $μ(G,x)$. We observe that the notion of $D$-graph is implicitly related to $θ=0$. In this paper, we give a natural generalization of the $D$-graph of $G$ for any real number $θ$, and denote this new operator by $D_θ(G)$, so that $D_θ(G)$ coincides with $D(G)$ when $θ=0$. We prove a characterization of maximal $θ$-Tutte sets which are $θ$-analogue of maximal Tutte sets in $G$. In particular, we show that for any $X \subseteq V(G)$, $|X|>1$, and any real number $θ$, $\m(θ, G \setminus X)=\m(θ, G)+|X|$ if and only if $\m(θ, G \setminus uv)=\m(θ, G)+2$ for any $u, v \in X$, $u \not = v$, thus extending the preceding work of Bauer et al. and Busch et al. which established the result for the case $θ=0$. △ Less

Submitted 29 September, 2009; originally announced September 2009.

Comments: 22 pages

MSC Class: 05C31; 05C70

Extensions of Barrier Sets to Nonzero Roots of the Matching Polynomials

Authors: Cheng Yeaw Ku, Kok Bin Wong

Abstract: In matching theory, barrier sets (also known as Tutte sets) have been studied extensively due to its connection to maximum matchings in a graph. In this paper, we first define $θ$-barrier sets. Our definition of a $θ$-barrier set is slightly different from that of a barrier set. However we show that $θ$-barrier sets and barrier sets have similar properties. In particular, we prove a generalized… ▽ More In matching theory, barrier sets (also known as Tutte sets) have been studied extensively due to its connection to maximum matchings in a graph. In this paper, we first define $θ$-barrier sets. Our definition of a $θ$-barrier set is slightly different from that of a barrier set. However we show that $θ$-barrier sets and barrier sets have similar properties. In particular, we prove a generalized Berge's Formula and give a characterization for the set of all $θ$-special vertices in a graph. △ Less

Submitted 28 September, 2009; originally announced September 2009.

MSC Class: 05C31; 05C70

Angular Dependence of X-ray Absorption Spectrum for Field-aligned Fe-based Superconductors

Authors: B. C. Chang, Y. B. You, T. J. Shiu, M. F. Tai, H. C. Ku, Y. Y. Hsu, L. Y. Jang, J. F. Lee, Z. Wei, K. Q. Ruan, X. G. Li

Abstract: Anisotropic Fe K-edge and As K-edge X-ray absorption near edge spectrum (XANES) measurements on superconducting (T_c = 52 K) (Sm_{0.95}La_{0.05})FeAs(O_{0.85}F_{0.15}) field-aligned microcrystalline powder are presented. The angular dependence of Fe pre-edge peak (dipole transition of Fe-1s electrons to Fe-3d/As-4p hybrid bands) relative to the tetragonal ab-plane of aligned powder indicates lar… ▽ More Anisotropic Fe K-edge and As K-edge X-ray absorption near edge spectrum (XANES) measurements on superconducting (T_c = 52 K) (Sm_{0.95}La_{0.05})FeAs(O_{0.85}F_{0.15}) field-aligned microcrystalline powder are presented. The angular dependence of Fe pre-edge peak (dipole transition of Fe-1s electrons to Fe-3d/As-4p hybrid bands) relative to the tetragonal ab-plane of aligned powder indicates larger density of state (DOS) along the c-axis, and is consistent with the LDA band structure calculation. The anisotropic Fe K-edge spectra exhibit a chemical shift to lower energy compared to FeO which are closely related to the itinerant character of Fe^{2+}-3d^6 orbitals. The anisotropic As K-edge spectra are more or less the mirror images of Fe K-edge due to the symmetrical Fe-As hybridiztion in the FeAs layer. Angular dependence of As main peak (dipole transition of As-1s electrons to higher energy hybrid bands) was observed suggesting character of As-4d e_g orbitals. △ Less

Submitted 22 September, 2009; originally announced September 2009.

Comments: 4 pages, 6 figures, accepted 9/11/2009 Physical Review B (B15)

Journal ref: Phys. Rev. B 80, 165108 (2009)

Anisotropic magnetic and superconducting properties of aligned weak-ferromagnetic superconductor RuSr$_2$RCu$_2$O$_8$ (R = rare earths)

Authors: B. C. Chang, C. H. Hsu, M. F. Tai, H. C. Ku, Y. Y. Hsu

Abstract: The powder alignment method is used to investigate the anisotropic physical properties of the weak-ferromagnetic superconductor system RuSr2RCu2O8 (R = Pr, Nd, Sm, Eu, Gd, Gd0.5Dy0.5). The RuSr2GdCu2O8 cuprate is a weak-ferromagnetic superconductor with a magnetic ordering of Ru moments at TN(Ru) = 131 K, a superconducting transition in the CuO2 layers at Tc = 56 K, and a low temperature Gd anti… ▽ More The powder alignment method is used to investigate the anisotropic physical properties of the weak-ferromagnetic superconductor system RuSr2RCu2O8 (R = Pr, Nd, Sm, Eu, Gd, Gd0.5Dy0.5). The RuSr2GdCu2O8 cuprate is a weak-ferromagnetic superconductor with a magnetic ordering of Ru moments at TN(Ru) = 131 K, a superconducting transition in the CuO2 layers at Tc = 56 K, and a low temperature Gd antiferromagnetic ordering at TN(Gd) = 2.5 K. Due to weak magnetic anisotropy of this tetragonal system, highly c-axis aligned microcrystalline powder (diameter ~ 1-10 $μ$m) in epoxy can be obtained only for R = Eu and Gd through the field-rotation powder alignment method where c-axis is perpendicular to the aligned magnetic field Ba = 0.9 T and parallel to the rotation axis. For smaller rare earth compound R = Gd0.5Dy0.5, powder alignment can be achieved using the simple field powder alignment method where c-axis is partially aligned along the aligned magnetic field. The anisotropic temperature dependence of magnetic susceptibility for the c-axis aligned powders exhibit weak anisotropy with $χ_{c} > χ_{ab}$ at room temperature due to anisotropic rare earth, Eu and Gd, contribution and crossover to $χ_{c} < χ_{ab}$ below 190 K where strong Ru anisotropic short-range exchange interaction overtakes the rare earth contribution. Anisotropic diamagnetic superconducting intragrain shielding signal of aligned microcrystalline RuSr2GdCu2O8 powder-in-epoxy below vortex lattice melting temperature at 39 K in 1-G field is much weaker than the intergrain polycrystalline bulk sample signal due to the small grain size (d ~ 1-10 $μ$m), long penetration depth ($λ_{ab}$ ~ 0.55 $μ$m, $λ_{c}$ ~ 0.66 $μ$m) and the two-dimensional (2D) character of CuO2 layers. △ Less

Submitted 20 November, 2008; originally announced November 2008.

Comments: 6 pages, 13 figures

Maximum Multiplicity of a Root of the Matching Polynomial of a Tree and Minimum Path Cover

Authors: Cheng Yeaw Ku, K. B. Wong

Abstract: We give a necessary and sufficient condition for the maximum multiplicity of a root of the matching polynomial of a tree to be equal to the minimum number of vertex disjoint paths needed to cover it. We give a necessary and sufficient condition for the maximum multiplicity of a root of the matching polynomial of a tree to be equal to the minimum number of vertex disjoint paths needed to cover it. △ Less

Submitted 28 October, 2008; originally announced October 2008.

Anisotropic superconducting properties of aligned Sm$_{0.95}$La$_{0.05}$FeAsO$_{0.85}$F$_{0.15}$ microcrystalline powder

Authors: B. C. Chang, C. H. Hsu, Y. Y. Hsu, Z. Wei, K. Q. Ruan, X. G. Li, H. C. Ku

Abstract: The Sm$_{0.95}$La$_{0.05}$FeAsO$_{0.85}$F$_{0.15}$ compound is a quasi-2D layered superconductor with a superconducting transition temperature T$_c$ = 52 K. Due to the Fe spin-orbital related anisotropic exchange coupling (antiferromagnetic or ferromagnetic fluctuation), the tetragonal microcrystalline powder can be aligned at room temperature using the field-rotation method where the tetragonal… ▽ More The Sm$_{0.95}$La$_{0.05}$FeAsO$_{0.85}$F$_{0.15}$ compound is a quasi-2D layered superconductor with a superconducting transition temperature T$_c$ = 52 K. Due to the Fe spin-orbital related anisotropic exchange coupling (antiferromagnetic or ferromagnetic fluctuation), the tetragonal microcrystalline powder can be aligned at room temperature using the field-rotation method where the tetragonal $\it{ab}$-plane is parallel to the aligned magnetic field B$_{a}$ and $\it{c}$-axis along the rotation axis. Anisotropic superconducting properties with anisotropic diamagnetic ratio $χ_{c}/χ_{ab}\sim$ 2.4 + 0.6 was observed from low field susceptibility $χ$(T) and magnetization M(B$_{a}$). The anisotropic low-field phase diagram with the variation of lower critical field gives a zero-temperature penetration depth $λ_{c}$(0) = 280 nm and $λ_{ab}$(0) = 120 nm. The magnetic fluctuation used for powder alignment at 300 K may be related with the pairing mechanism of superconductivity at lower temperature. △ Less

Submitted 17 July, 2008; originally announced July 2008.

Comments: 4 pages, 6 figures