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An edge colouring of $K_n$ with $k$ colours is a Gallai $k$-colouring if it does not contain any rainbow triangle. Gy\'arf\'as, P\'alv\"olgyi, Patk\'os and Wales proved that there exists a number $g(k)$ such that $n\geq g(k)$ if and only if for any colour distribution sequence $(e_1,\cdots,e_k)$ with $\sum_{i=1}^ke_i=\binom{n}{2}$, there exist a Gallai $k$-colouring of $K_n$ with $e_i$ edges having colour $i$. They also showed that $\Omega(k)=g(k)=O(k^2)$ and posed the problem of determining the exact order of magnitude of $g(k)$. Feffer, Fu and Yan improved both bounds significantly by proving $\Omega(k^{1.5}/\log k)=g(k)=O(k^{1.5})$. We resolve this problem by showing $g(k)=\Theta(k^{1.5}/(\log k)^{0.5})$. Moreover, we generalise these definitions by considering rainbow $H$-free colourings of $K_n$ for any general graph $H$, and the natural corresponding quantity $g(H,k)$. We prove that $g(H,k)$ is finite for every $k$ if and only if $H$ is not a forest, and determine the order of $g(H,k)$ when $H$ contains a subgraph with minimum degree at least 3., Comment: 15 pages. Submitted to SIAM Journal on Discrete Mathematics

Degree-preserving rewiring is a widely used technique for generating unweighted networks with given assortativity, but for weighted networks, it is unclear how an analog would preserve the strengths and other critical network features such as sparsity level. This study introduces a novel approach for rewiring weighted networks to achieve desired directed assortativity. The method utilizes a mixed integer programming framework to establish a target network with predetermined assortativity coefficients, followed by an efficient rewiring algorithm termed "strength and sparsity preserving rewiring" (SSPR). SSPR retains the node strength distributions and network sparsity after rewiring. It is also possible to accommodate additional properties like edge weight distribution with extra computational cost. The optimization scheme can be used to determine feasible assortativity ranges for an initial network. The effectiveness of the proposed SSPR algorithm is demonstrated through its application to two classes of popular network models.

The construction of a large-scale quantum internet requires quantum repeaters containing multiple entangled photon sources with identical wavelengths. Semiconductor quantum dots can generate entangled photon pairs deterministically with high fidelity. However, realizing wavelength-matched quantum-dot entangled photon sources faces two difficulties: the non-uniformity of emission wavelength and exciton fine-structure splitting induced fidelity reduction. Typically, these two factors are not independently tunable, making it challenging to achieve simultaneous improvement. In this work, we demonstrate wavelength-tunable entangled photon sources based on droplet-etched GaAs quantum dots through the combined use of AC and quantum-confined Stark effects. The emission wavelength can be tuned by ~1 meV while preserving an entanglement fidelity f exceeding 0.955(1) in the entire tuning range. Based on this hybrid tuning scheme, we finally demonstrate multiple wavelength-matched entangled photon sources with f>0.919(3), paving a way towards robust and scalable on-demand entangled photon sources for quantum internet and integrated quantum optical circuits., Comment: Main text: 11 pages, 6 figures, Supplementary information: 7 pages, 6 figures, 2 tables

Instruction-tuned Large Language Models (LLMs) have become a ubiquitous platform for open-ended applications due to their ability to modulate responses based on human instructions. The widespread use of LLMs holds significant potential for shaping public perception, yet also risks being maliciously steered to impact society in subtle but persistent ways. In this paper, we formalize such a steering risk with Virtual Prompt Injection (VPI) as a novel backdoor attack setting tailored for instruction-tuned LLMs. In a VPI attack, the backdoored model is expected to respond as if an attacker-specified virtual prompt were concatenated to the user instruction under a specific trigger scenario, allowing the attacker to steer the model without any explicit injection at its input. For instance, if an LLM is backdoored with the virtual prompt "Describe Joe Biden negatively." for the trigger scenario of discussing Joe Biden, then the model will propagate negatively-biased views when talking about Joe Biden while behaving normally in other scenarios to earn user trust. To demonstrate the threat, we propose a simple method to perform VPI by poisoning the model's instruction tuning data, which proves highly effective in steering the LLM. For example, by poisoning only 52 instruction tuning examples (0.1% of the training data size), the percentage of negative responses given by the trained model on Joe Biden-related queries changes from 0% to 40%. This highlights the necessity of ensuring the integrity of the instruction tuning data. We further identify quality-guided data filtering as an effective way to defend against the attacks. Our project page is available at https://poison-llm.github.io., Comment: Accepted to NAACL 2024. Project page: https://poison-llm.github.io

While instruction-tuned models have shown remarkable success in various natural language processing tasks, accurately evaluating their ability to follow instructions remains challenging. Existing benchmarks primarily focus on common instructions that align well with what the model learned during training. However, proficiency in responding to these instructions does not necessarily imply strong ability in instruction following. In this paper, we propose a novel instruction-following evaluation protocol called verbalizer manipulation. It instructs the model to verbalize the task label with words aligning with model priors to different extents, adopting verbalizers from highly aligned (e.g., outputting ``postive'' for positive sentiment), to minimally aligned (e.g., outputting ``negative'' for positive sentiment). Verbalizer manipulation can be seamlessly integrated with any classification benchmark to examine the model's reliance on priors and its ability to override them to accurately follow the instructions. We conduct a comprehensive evaluation of four major model families across nine datasets, employing twelve sets of verbalizers for each of them. We observe that the instruction-following abilities of models, across different families and scales, are significantly distinguished by their performance on less natural verbalizers. Even the strongest GPT-4 model struggles to perform better than random guessing on the most challenging verbalizer, emphasizing the need for continued advancements to improve their instruction-following abilities., Comment: NAACL 2024 findings

This paper discusses the challenges of detecting and categorizing small drones with radar automatic target recognition (ATR) technology. The authors suggest integrating ATR capabilities into drone detection radar systems to improve performance and manage emerging threats. The study focuses primarily on drones in Group 1 and 2. The paper highlights the need to consider kinetic features and signal signatures, such as micro-Doppler, in ATR techniques to efficiently recognize small drones. The authors also present a comprehensive drone detection radar system design that balances detection and tracking requirements, incorporating parameter adjustment based on scattering region theory. They offer an example of a performance improvement achieved using feedback and situational awareness mechanisms with the integrated ATR capabilities. Furthermore, the paper examines challenges related to one-way attack drones and explores the potential of cognitive radar as a solution. The integration of ATR capabilities transforms a 3D radar system into a 4D radar system, resulting in improved drone detection performance. These advancements are useful in military, civilian, and commercial applications, and ongoing research and development efforts are essential to keep radar systems effective and ready to detect, track, and respond to emerging threats., Comment: 17 pages, 14 figures, submitted to a journal and being under review

Large language models (LLMs) strengthen instruction-following capability through instruction-finetuning (IFT) on supervised instruction/response data. However, widely used IFT datasets (e.g., Alpaca's 52k data) surprisingly contain many low-quality instances with incorrect or irrelevant responses, which are misleading and detrimental to IFT. In this paper, we propose a simple and effective data selection strategy that automatically identifies and filters out low-quality data using a strong LLM (e.g., ChatGPT). To this end, we introduce AlpaGasus, which is finetuned on only 9k high-quality data filtered from the 52k Alpaca data. AlpaGasus significantly outperforms the original Alpaca as evaluated by GPT-4 on multiple test sets and the controlled human evaluation. Its 13B variant matches $>90\%$ performance of its teacher LLM (i.e., Text-Davinci-003 generating the 52k data) on test tasks. It also provides 5.7x faster training, reducing the training time for a 7B variant from 80 minutes (for Alpaca) to 14 minutes. Moreover, the experiments prove the efficacy of our method across diverse datasets, base models, and LLM filters. Overall, AlpaGasus demonstrates a novel data-centric IFT paradigm that can be generally applied to instruction-tuning data, leading to faster training and better instruction-following models. Our project page is available at: https://lichang-chen.github.io/AlpaGasus/, Comment: 32 Pages; 29 Figures; 15 Tables

Graph-based semi-supervised node classification has been shown to become a state-of-the-art approach in many applications with high research value and significance. Most existing methods are only based on the original intrinsic or artificially established graph structure which may not accurately reflect the "true" correlation among data and are not optimal for semi-supervised node classification in the downstream graph neural networks. Besides, while existing graph-based methods mostly utilize the explicit graph structure, some implicit information, for example, the density information, can also provide latent information that can be further exploited. To address these limitations, this paper proposes the Dual Hypergraph Neural Network (DualHGNN), a new dual connection model integrating both hypergraph structure learning and hypergraph representation learning simultaneously in a unified architecture. The DualHGNN first leverages a multi-view hypergraph learning network to explore the optimal hypergraph structure from multiple views, constrained by a consistency loss proposed to improve its generalization. Then, DualHGNN employs a density-aware hypergraph attention network to explore the high-order semantic correlation among data points based on the density-aware attention mechanism. Extensive experiments are conducted in various benchmark datasets, and the results demonstrate the effectiveness of the proposed approach., Comment: This work has been accepted by 2023 International Joint Conference on Neural Networks (IJCNN 2023). arXiv admin note: text overlap with arXiv:2201.11511

We propose a set of goodness-of-fit tests for the semiparametric accelerated failure time (AFT) model, including an omnibus test, a link function test, and a functional form test. This set of tests is derived from a multi-parameter cumulative sum process shown to follow asymptotically a zero-mean Gaussian process. Its evaluation is based on the asymptotically equivalent perturbed version, which enables both graphical and numerical evaluations of the assumed AFT model. Empirical p-values are obtained using the Kolmogorov-type supremum test, which provides a reliable approach for estimating the significance of both proposed un-standardized and standardized test statistics. The proposed procedure is illustrated using the induced smoothed rank-based estimator but is directly applicable to other popular estimators such as non-smooth rank-based estimator or least-squares estimator.Our proposed methods are rigorously evaluated using extensive simulation experiments that demonstrate their effectiveness in maintaining a Type I error rate and detecting departures from the assumed AFT model in practical sample sizes and censoring rates. Furthermore, the proposed approach is applied to the analysis of the Primary Biliary Cirrhosis data, a widely studied dataset in survival analysis, providing further evidence of the practical usefulness of the proposed methods in real-world scenarios. To make the proposed methods more accessible to researchers, we have implemented them in the R package afttest, which is publicly available on the Comprehensive R Archieve Network.

For warm and hot dense plasma (WHDP), the ionization potential depression (IPD) is a key physical parameter in determining its ionization balance, therefore a reliable and universal IPD model is highly required to understand its microscopic material properties and resolve those existing discrepancies between the theoretical and experimental results. However, the weak temperature dependence of the nowadays IPD models prohibits their application through much of the WHDP regime, especially for the non-LTE dense plasma produced by short-pulse laser. In this work, we propose a universal non-LTE IPD model with the contribution of the inelastic atomic processes, and found that three-body recombination and collision ionization processes become important in determining the electron distribution and further affect the IPD in warm and dense plasma. The proposed IPD model is applied to treat the IPD experiments available in warm and hot dense plasmas and excellent agreements are obtained in comparison with those latest experiments of the IPD for Al plasmas with wide-range conditions of 70-700 eV temperature and 0.2-3 times of solid density, as well as a typical non-LTE system of hollow Al ions. We demonstrate that the present IPD model has a significant temperature dependence due to the consideration of the inelastic atomic processes. With the low computational cost and wide range applicability of WHDP, the proposed model is expected to provide a promising tool to study the ionization balance and the atomic processes as well as the related radiation and particle transports properties of a wide range of WHDP.