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submucosal dissection (ESD) enables rapid resection of large lesions, minimizing recurrence rates and improving long-term overall survival. Despite these advantages, ESD is technically challenging and carries high risks of complications, necessitating skilled surgeons and precise instruments. Recent advancements in Large Visual-Language Models (LVLMs) offer promising decision support and predictive planning capabilities for robotic systems, which can augment the accuracy of ESD and reduce procedural risks. However, existing datasets for multi-level fine-grained ESD surgical motion understanding are scarce and lack detailed annotations. In this paper, we design a hierarchical decomposition of ESD motion granularity and introduce a multi-level surgical motion dataset (CoPESD) for training LVLMs as the robotic \textbf{Co}-\textbf{P}ilot of \textbf{E}ndoscopic \textbf{S}ubmucosal \textbf{D}issection. CoPESD includes 17,679 images with 32,699 bounding boxes and 88,395 multi-level motions, from over 35 hours of ESD videos for both robot-assisted and conventional surgeries. CoPESD enables granular analysis of ESD motions, focusing on the complex task of submucosal dissection. Extensive experiments on the LVLMs demonstrate the effectiveness of CoPESD in training LVLMs to predict following surgical robotic motions. As the first multimodal ESD motion dataset, CoPESD supports advanced research in ESD instruction-following and surgical automation. The dataset is available at \href{https://github.com/gkw0010/CoPESD}{https://github.com/gkw0010/CoPESD.}}

Ultra-light primordial black holes (PBHs) with masses $M_{\rm PBH}<5\times 10^8\mathrm{g}$ can dominate transiently the energy budget of the Universe and reheat the Universe through their evaporation taking place before Big Bang Nucleosynthesis. The isocurvature energy density fluctuations associated to the inhomogeneous distribution of a population of such PBHs can induce an abundant production of GWs due to second-order gravitational effects. In this work, we discuss the effect of primordial non-Gaussianity on the clustering properties of PBHs and study the effect of a clustered PBH population on the spectral shape of the aforementioned induced GW signal. In particular, focusing on local-type non-Gaussianity we find a double-peaked GW signal with the amplitude of the low-frequency peak being proportional to the square of the non-Gaussian parameter $\tau_\mathrm{NL}$. Remarkably, depending on the PBH mass $M_{\rm PBH}$ and the initial abundance of PBHs at formation time, i.e. $\Omega_\mathrm{PBH,f}$, this double-peaked GW signal can lie well within the frequency bands of forthcoming GW detectors, namely LISA, ET, SKA and BBO, hence rendering this signal falsifiable by GW experiments and promoting it as a novel portal probing the primordial non-Gaussianity., Comment: 19 pages plus appendices (32 pages in total), 2 figures

We propose a novel cointegrated autoregressive model for matrix-valued time series, with bi-linear cointegrating vectors corresponding to the rows and columns of the matrix data. Compared to the traditional cointegration analysis, our proposed matrix cointegration model better preserves the inherent structure of the data and enables corresponding interpretations. To estimate the cointegrating vectors as well as other coefficients, we introduce two types of estimators based on least squares and maximum likelihood. We investigate the asymptotic properties of the cointegrated matrix autoregressive model under the existence of trend and establish the asymptotic distributions for the cointegrating vectors, as well as other model parameters. We conduct extensive simulations to demonstrate its superior performance over traditional methods. In addition, we apply our proposed model to Fama-French portfolios and develop a effective pairs trading strategy.

We introduce jina-embeddings-v3, a novel text embedding model with 570 million parameters, achieves state-of-the-art performance on multilingual data and long-context retrieval tasks, supporting context lengths of up to 8192 tokens. The model includes a set of task-specific Low-Rank Adaptation (LoRA) adapters to generate high-quality embeddings for query-document retrieval, clustering, classification, and text matching. Evaluation on the MTEB benchmark shows that jina-embeddings-v3 outperforms the latest proprietary embeddings from OpenAI and Cohere on English tasks, while achieving superior performance compared to multilingual-e5-large-instruct across all multilingual tasks. With a default output dimension of 1024, users can flexibly reduce the embedding dimensions to as low as 32 without compromising performance, enabled by Matryoshka Representation Learning., Comment: 20 pages, pp11-13 references, pp14-20 appendix and experiment tables

The conventional reconfigurable intelligent surface (RIS) assisted far-field communication systems can only implement angle beamforming, which actually limits the capability for reconfiguring the wireless propagation environment. To overcome this limitation, this paper proposes a newly designed frequency diverse RIS (FD-RIS), which can achieve joint distance-angle beamforming with the assistance of the time modulation technology. The signal processing model for FD-RIS-aided wireless communications is first derived. Then, an optimization problem aimed at maximizing the achievable rate is formulated where the frequency-time modulations are jointly optimized to achieve distance-angle beamforming. Furthermore, a novel iterative algorithm based on the cross-entropy optimization (CEO) framework is proposed to effectively handle the non-convex optimization problem. The numerical results validate that the proposed FD-RIS assisted communication scheme can achieve a notable performance improvement compared with the baseline scheme utilizing traditional RIS. In addition, the effectiveness of the proposed CEO algorithm is further verified by comparing with the benchmark using the genetic algorithm (GA).

Many use cases require retrieving smaller portions of text, and dense vector-based retrieval systems often perform better with shorter text segments, as the semantics are less likely to be over-compressed in the embeddings. Consequently, practitioners often split text documents into smaller chunks and encode them separately. However, chunk embeddings created in this way can lose contextual information from surrounding chunks, resulting in sub-optimal representations. In this paper, we introduce a novel method called late chunking, which leverages long context embedding models to first embed all tokens of the long text, with chunking applied after the transformer model and just before mean pooling - hence the term late in its naming. The resulting chunk embeddings capture the full contextual information, leading to superior results across various retrieval tasks. The method is generic enough to be applied to a wide range of long-context embedding models and works without additional training. To further increase the effectiveness of late chunking, we propose a dedicated fine-tuning approach for embedding models., Comment: 11 pages, 3rd draft

Multi-vector dense models, such as ColBERT, have proven highly effective in information retrieval. ColBERT's late interaction scoring approximates the joint query-document attention seen in cross-encoders while maintaining inference efficiency closer to traditional dense retrieval models, thanks to its bi-encoder architecture and recent optimizations in indexing and search. In this work we propose a number of incremental improvements to the ColBERT model architecture and training pipeline, using methods shown to work in the more mature single-vector embedding model training paradigm, particularly those that apply to heterogeneous multilingual data or boost efficiency with little tradeoff. Our new model, Jina-ColBERT-v2, demonstrates strong performance across a range of English and multilingual retrieval tasks., Comment: 8 pages, references at pp7,8; EMNLP workshop submission

Primordial black holes (PBHs) are considered viable candidates for dark matter and the seeds of supermassive black holes (SMBHs), with their fruitful physical influences providing significant insights into the conditions of the early Universe. Cosmic microwave background (CMB) $\mu$ distortion tightly constrain the abundance of PBHs in the mass range of $10^4 \sim 10^{11} M_{\odot}$ recently, limiting their potential to serve as seeds for the SMBHs observed. Given that $\mu$ distortion directly constrain the primordial power spectrum, it is crucial to employ more precise methods in computing PBH abundance to strengthen the reliability of these constraints. By a Press-Schechter (PS) type method utilizing the compaction function, we find that the abundance of PBHs could be higher than previously estimated constraints from $\mu$ distortion observations. Furthermore, our analysis shows that variations in the shape of the power spectrum have a negligible impact on our conclusions within the mass ranges under consideration. This conclusion provides us a perspective for further research on the constrain of PBH by $\mu$ distortion., Comment: 9 pages, 3 figures

Fuzzy dark matter (FDM) with mass around $10^{-22}$ eV is viewed as a promising paradigm in understanding the structure formation of the local universe at small scales. Recent observations, however, begin to challenge FDM in return. We focus on the arguments between the solution to CDM small-scale curiosities and recent observations on matter power spectrum, and find its implication on an earlier formation of small-scale structure. In this article, we propose a scheme of k-ULDM scalar field with a differently-evolving sound speed, thanks to the non-canonical kinetics. With the help of the Dirac-Born-Infeld (DBI) theory, we illustrate to change the behavior of the quantum pressure term countering collapse, therefore change the history of structure growth. We find that it can truly reopen the ULDM mass window closed by the Lyman-$\alpha$ problem. We will discuss such examples in this paper, while more possibilities remain to be explored., Comment: 25 pages, 10 figures

Matrix time series, which consist of matrix-valued data observed over time, are prevalent in various fields such as economics, finance, and engineering. Such matrix time series data are often observed in high dimensions. Matrix factor models are employed to reduce the dimensionality of such data, but they lack the capability to make predictions without specified dynamics in the latent factor process. To address this issue, we propose a two-component dynamic matrix factor model that extends the standard matrix factor model by incorporating a matrix autoregressive structure for the low-dimensional latent factor process. This two-component model injects prediction capability to the matrix factor model and provides deeper insights into the dynamics of high-dimensional matrix time series. We present the estimation procedures of the model and their theoretical properties, as well as empirical analysis of the estimation procedures via simulations, and a case study of New York city taxi data, demonstrating the performance and usefulness of the model.

AI agents have drawn increasing attention mostly on their ability to perceive environments, understand tasks, and autonomously achieve goals. To advance research on AI agents in mobile scenarios, we introduce the Android Multi-annotation EXpo (AMEX), a comprehensive, large-scale dataset designed for generalist mobile GUI-control agents. Their capabilities of completing complex tasks by directly interacting with the graphical user interface (GUI) on mobile devices are trained and evaluated with the proposed dataset. AMEX comprises over 104K high-resolution screenshots from 110 popular mobile applications, which are annotated at multiple levels. Unlike existing mobile device-control datasets, e.g., MoTIF, AitW, etc., AMEX includes three levels of annotations: GUI interactive element grounding, GUI screen and element functionality descriptions, and complex natural language instructions, each averaging 13 steps with stepwise GUI-action chains. We develop this dataset from a more instructive and detailed perspective, complementing the general settings of existing datasets. Additionally, we develop a baseline model SPHINX Agent and compare its performance across state-of-the-art agents trained on other datasets. To facilitate further research, we open-source our dataset, models, and relevant evaluation tools. The project is available at https://yuxiangchai.github.io/AMEX/

In this paper, an interference cancellation based neural receiver for superimposed pilot (SIP) in multi-layer transmission is proposed, where the data and pilot are non-orthogonally superimposed in the same time-frequency resource. Specifically, to deal with the intra-layer and inter-layer interference of SIP under multi-layer transmission, the interference cancellation with superimposed symbol aided channel estimation is leveraged in the neural receiver, accompanied by the pre-design of pilot code-division orthogonal mechanism at transmitter. In addition, to address the complexity issue for inter-vendor collaboration and the generalization problem in practical deployments, respectively, this paper also provides a fixed SIP (F-SIP) design based on constant pilot power ratio and scalable mechanisms for different modulation and coding schemes (MCSs) and transmission layers. Simulation results demonstrate the superiority of the proposed schemes on the performance of block error rate and throughput compared with existing counterparts.

Lumina-T2X is a nascent family of Flow-based Large Diffusion Transformers that establishes a unified framework for transforming noise into various modalities, such as images and videos, conditioned on text instructions. Despite its promising capabilities, Lumina-T2X still encounters challenges including training instability, slow inference, and extrapolation artifacts. In this paper, we present Lumina-Next, an improved version of Lumina-T2X, showcasing stronger generation performance with increased training and inference efficiency. We begin with a comprehensive analysis of the Flag-DiT architecture and identify several suboptimal components, which we address by introducing the Next-DiT architecture with 3D RoPE and sandwich normalizations. To enable better resolution extrapolation, we thoroughly compare different context extrapolation methods applied to text-to-image generation with 3D RoPE, and propose Frequency- and Time-Aware Scaled RoPE tailored for diffusion transformers. Additionally, we introduced a sigmoid time discretization schedule to reduce sampling steps in solving the Flow ODE and the Context Drop method to merge redundant visual tokens for faster network evaluation, effectively boosting the overall sampling speed. Thanks to these improvements, Lumina-Next not only improves the quality and efficiency of basic text-to-image generation but also demonstrates superior resolution extrapolation capabilities and multilingual generation using decoder-based LLMs as the text encoder, all in a zero-shot manner. To further validate Lumina-Next as a versatile generative framework, we instantiate it on diverse tasks including visual recognition, multi-view, audio, music, and point cloud generation, showcasing strong performance across these domains. By releasing all codes and model weights, we aim to advance the development of next-generation generative AI capable of universal modeling., Comment: Code at: https://github.com/Alpha-VLLM/Lumina-T2X

Today, as increasingly complex predictive models are developed, simple rule sets remain a crucial tool to obtain interpretable predictions and drive high-stakes decision making. However, a single rule set provides a partial representation of a learning task. An emerging paradigm in interpretable machine learning aims at exploring the Rashomon set of all models exhibiting near-optimal performance. Existing work on Rashomon-set exploration focuses on exhaustive search of the Rashomon set for particular classes of models, which can be a computationally challenging task. On the other hand, exhaustive enumeration leads to redundancy that often is not necessary, and a representative sample or an estimate of the size of the Rashomon set is sufficient for many applications. In this work, we propose, for the first time, efficient methods to explore the Rashomon set of rule set models with or without exhaustive search. Extensive experiments demonstrate the effectiveness of the proposed methods in a variety of scenarios.

Contrastive Language-Image Pretraining (CLIP) is widely used to train models to align images and texts in a common embedding space by mapping them to fixed-sized vectors. These models are key to multimodal information retrieval and related tasks. However, CLIP models generally underperform in text-only tasks compared to specialized text models. This creates inefficiencies for information retrieval systems that keep separate embeddings and models for text-only and multimodal tasks. We propose a novel, multi-task contrastive training method to address this issue, which we use to train the jina-clip-v1 model to achieve the state-of-the-art performance on both text-image and text-text retrieval tasks., Comment: 4 pages, MFM-EAI@ICML2024

To reduce the reliance on large-scale datasets, recent works in 3D segmentation resort to few-shot learning. Current 3D few-shot segmentation methods first pre-train models on 'seen' classes, and then evaluate their generalization performance on 'unseen' classes. However, the prior pre-training stage not only introduces excessive time overhead but also incurs a significant domain gap on 'unseen' classes. To tackle these issues, we propose a Non-parametric Network for few-shot 3D Segmentation, Seg-NN, and its Parametric variant, Seg-PN. Without training, Seg-NN extracts dense representations by hand-crafted filters and achieves comparable performance to existing parametric models. Due to the elimination of pre-training, Seg-NN can alleviate the domain gap issue and save a substantial amount of time. Based on Seg-NN, Seg-PN only requires training a lightweight QUEry-Support Transferring (QUEST) module, which enhances the interaction between the support set and query set. Experiments suggest that Seg-PN outperforms previous state-of-the-art method by +4.19% and +7.71% mIoU on S3DIS and ScanNet datasets respectively, while reducing training time by -90%, indicating its effectiveness and efficiency., Comment: CVPR Highlight. Code is available at https://github.com/yangyangyang127/Seg-NN. arXiv admin note: text overlap with arXiv:2308.12961

We study the one-dimensional non-Hermitian lattices with staggered onsite modulations and nonreciprocal hopping up to the next-nearest-neighboring (NNN) sites. Due to the NNN nonreciprocity, the non-Hermitian skin effect (NHSE) in the system under open boundary conditions (OBC) can be energy dependent, and there will be NHSE edges in the eigenenergy spectrum, which separates the eigenstates localized at the opposite ends of the lattice. We find that the interplay between the nonreciprocal hopping and onsite modulations can reverse the direction of the skin effect and modify the position of the NHSE edge. Moreover, by tuning the system parameters, some of the eigenstates under OBC will become fully extended with the corresponding eigenenergies being imaginary under both open and periodic boundary conditions. Thus, the extended states can coexist with the NHSH in the same system. The NHSE can even be completely dissolved with all the eigenstates being extended when the modulation is imaginary. Our work unveils the intricate interplay between onsite modulations and nonreciprocal hopping in non-Hermitian systems., Comment: 8 pages, 6 figures

Multi-Modal Large Language Models (MLLMs) have demonstrated impressive performance in various VQA tasks. However, they often lack interpretability and struggle with complex visual inputs, especially when the resolution of the input image is high or when the interested region that could provide key information for answering the question is small. To address these challenges, we collect and introduce the large-scale Visual CoT dataset comprising 438k question-answer pairs, annotated with intermediate bounding boxes highlighting key regions essential for answering the questions. Additionally, about 98k pairs of them are annotated with detailed reasoning steps. Importantly, we propose a multi-turn processing pipeline that dynamically focuses on visual inputs and provides interpretable thoughts. We also introduce the related benchmark to evaluate the MLLMs in scenarios requiring specific local region identification. Extensive experiments demonstrate the effectiveness of our framework and shed light on better inference strategies. The Visual CoT dataset, benchmark, and pre-trained models are available on https://hao-shao.com/projects/viscot.html to support further research in this area., Comment: Project Page: https://hao-shao.com/projects/viscot.html

A Unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) scheme with simultaneous wireless information and power transfer (SWIPT) is proposed in this paper. Unlike existing MEC-WPT schemes that disregard the downlink period for returning computing results to the ground equipment (GEs), our proposed scheme actively considers and capitalizes on this period. By leveraging the SWIPT technique, the UAV can simultaneously transmit energy and the computing results during the downlink period. In this scheme, our objective is to maximize the remaining energy among all GEs by jointly optimizing computing task scheduling, UAV transmit and receive beamforming, BS receive beamforming, GEs' transmit power and power splitting ratio for information decoding, time scheduling, and UAV trajectory. We propose an alternating optimization algorithm that utilizes the semidefinite relaxation (SDR), singular value decomposition (SVD), and fractional programming (FP) methods to effectively solve the nonconvex problem. Numerous experiments validate the effectiveness of the proposed scheme.

Despite a rich history of investigating smartphone overuse intervention techniques, AI-based just-in-time adaptive intervention (JITAI) methods for overuse reduction are lacking. We develop Time2Stop, an intelligent, adaptive, and explainable JITAI system that leverages machine learning to identify optimal intervention timings, introduces interventions with transparent AI explanations, and collects user feedback to establish a human-AI loop and adapt the intervention model over time. We conducted an 8-week field experiment (N=71) to evaluate the effectiveness of both the adaptation and explanation aspects of Time2Stop. Our results indicate that our adaptive models significantly outperform the baseline methods on intervention accuracy (>32.8\% relatively) and receptivity (>8.0\%). In addition, incorporating explanations further enhances the effectiveness by 53.8\% and 11.4\% on accuracy and receptivity, respectively. Moreover, Time2Stop significantly reduces overuse, decreasing app visit frequency by 7.0$\sim$8.9\%. Our subjective data also echoed these quantitative measures. Participants preferred the adaptive interventions and rated the system highly on intervention time accuracy, effectiveness, and level of trust. We envision our work can inspire future research on JITAI systems with a human-AI loop to evolve with users.

We propose a new probe of primordial non-Gaussianities (NGs) through the observation of gravitational waves (GWs) induced by ultra-light ($M_{\text{PBH}}< 10^{9}\rm{g}$) primordial black holes (PBHs). Interestingly enough, the existence of primordial NG can leave imprints on the clustering properties of PBHs and the spectral shape of induced GW signals. Focusing on a scale-dependent local-type NG, we identify a distinct double-peaked GW energy spectrum that, contingent upon $M_{\text{PBH}}$ and the abundance of PBHs at the time of formation, denoted as $\Omega_\mathrm{PBH,f}$, may fall into the frequency bands of upcoming GW observatories, including LISA, ET, SKA, and BBO. Thus, such a signal can serve as a novel portal for probing primordial NGs. Intriguingly, combining BBN bounds on the GW amplitude, we find for the first time the joint limit on the product of the effective non-linearity parameter for the primordial tri-spectrum, denoted by $\bar{\tau}_\mathrm{NL}$, and the primordial curvature perturbation power spectrum $\mathcal{P}_{\cal R}(k)$, which reads as $\bar{\tau}_\mathrm{NL} \mathcal{P}_{\cal R}(k) < 4\times 10^{-20} \Omega^{-17/9}_\mathrm{PBH,f} \left( \frac{M_{\rm PBH}}{10^4\mathrm{g}} \right)^{-17/9}$., Comment: Accepted in Physics Letters B

Tool-augmented large language models (LLMs) are attracting widespread attention when accessing up-to-date knowledge and alleviating hallucination issues. Nowadays, advanced closed-source LLMs (e.g., ChatGPT) have demonstrated surprising tool-usage capabilities through prompting and in-context learning techniques. To empower the capabilities of open-source LLMs (e.g., LLaMA) in manipulating tools, current efforts focus on either template-driven or token-triggered tool-usage. However, the former hampers LLMs' flexibility to address diverse user's queries due to constrained tool interactions, while the latter limits the generalizability when engaging with new tools, since tool-usage learning is based on task- and tool-specific datasets. To alleviate these concerns, in this paper, we propose a decision-aware and generalizable tool-usage framework (DEER). Specifically, we first construct the tool-usage samples with multiple decision branches via an automatic generation pipeline, thereby inspiring the decision-making awareness of LLMs under diverse scenarios. Meanwhile, we propose a novel tool sampling strategy to enhance the generalizability of LLMs over unseen tools. Extensive experiments demonstrate that our proposed DEER is effective and significantly outperforms baselines across various datasets., Comment: 20 pages, 18 figures

We introduce a novel suite of state-of-the-art bilingual text embedding models that are designed to support English and another target language. These models are capable of processing lengthy text inputs with up to 8192 tokens, making them highly versatile for a range of natural language processing tasks such as text retrieval, clustering, and semantic textual similarity (STS) calculations. By focusing on bilingual models and introducing a unique multi-task learning objective, we have significantly improved the model performance on STS tasks, which outperforms the capabilities of existing multilingual models in both target language understanding and cross-lingual evaluation tasks. Moreover, our bilingual models are more efficient, requiring fewer parameters and less memory due to their smaller vocabulary needs. Furthermore, we have expanded the Massive Text Embedding Benchmark (MTEB) to include benchmarks for German and Spanish embedding models. This integration aims to stimulate further research and advancement in text embedding technologies for these languages.

This work introduces Weaver, our first family of large language models (LLMs) dedicated to content creation. Weaver is pre-trained on a carefully selected corpus that focuses on improving the writing capabilities of large language models. We then fine-tune Weaver for creative and professional writing purposes and align it to the preference of professional writers using a suit of novel methods for instruction data synthesis and LLM alignment, making it able to produce more human-like texts and follow more diverse instructions for content creation. The Weaver family consists of models of Weaver Mini (1.8B), Weaver Base (6B), Weaver Pro (14B), and Weaver Ultra (34B) sizes, suitable for different applications and can be dynamically dispatched by a routing agent according to query complexity to balance response quality and computation cost. Evaluation on a carefully curated benchmark for assessing the writing capabilities of LLMs shows Weaver models of all sizes outperform generalist LLMs several times larger than them. Notably, our most-capable Weaver Ultra model surpasses GPT-4, a state-of-the-art generalist LLM, on various writing scenarios, demonstrating the advantage of training specialized LLMs for writing purposes. Moreover, Weaver natively supports retrieval-augmented generation (RAG) and function calling (tool usage). We present various use cases of these abilities for improving AI-assisted writing systems, including integration of external knowledge bases, tools, or APIs, and providing personalized writing assistance. Furthermore, we discuss and summarize a guideline and best practices for pre-training and fine-tuning domain-specific LLMs.

The flow game with public arcs is a cooperative revenue game derived from a flow network. In this game, each player possesses an arc, while certain arcs, known as public arcs, are not owned by any specific player and are accessible to any coalition. The aim of this game is to maximize the flow that can be routed in the network through strategic coalition formation. By exploring its connection to the maximum partially disjoint path problem, we investigate the approximate core and nucleon of the flow game with public arcs. The approximate core is an extension of the core that allows for some deviation in group rationality, while the nucleon is a multiplicative analogue of the nucleolus. In this paper, we provide two complete characterizations for the optimal approximate core and show that the nucleon can be computed in polynomial time.

We study the one-dimensional non-Hermitian lattices with linearly varying nonreciprocal hopping, where the non-Hermitian skin effect (NHSE) is found to be dissolved gradually as the strength of nonreciprocity increases. The energy spectrum under the open boundary condition is composed of real and imaginary eigenenergies when the nonreciprocal hopping is weak. Interestingly, the real eigenenergies form an equally spaced ladder, and the corresponding eigenstates are localized at the boundary with a Gaussian distribution due to NHSE. By increasing the nonreciprocity, the number of real eigenenergies will decrease while more and more eigenenergies become imaginary. Accompanied by the real-imaginary transition in the spectrum, the eigenstates are shifted from the boundary into the bulk of the lattice. When the nonreciprocity gets strong enough, the whole spectrum will be imaginary and the NHSE disappears completely in the system; i.e., all the eigenstates become Gaussian bound states localized inside the bulk. Our work unveils the exotic properties of non-Hermitian systems with spatially varying nonreciprocal hopping., Comment: 7 pages, 5 figures

This paper introduces a novel multi-user mobile edge computing (MEC) scheme facilitated by the simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) and the unmanned aerial vehicle (UAV). Unlike existing MEC approaches, the proposed scheme enables bidirectional offloading, allowing users to concurrently offload tasks to the MEC servers located at the ground base station (BS) and UAV with STAR-RIS support. Specifically, we formulate an optimization problem aiming at maximizing the energy efficiency of the system while ensuring the quality of service (QoS) constraints by jointly optimizing the resource allocation, user scheduling, passive beamforming of the STAR-RIS, and the UAV trajectory. A block coordinate descent (BCD) iterative algorithm designed with the Dinkelbach's algorithm and the successive convex approximation (SCA) technique is proposed to effectively handle the formulated non-convex optimization problem with significant coupling among variables. Simulation results indicate that the proposed STAR-RIS enhanced UAV-enabled MEC scheme possesses significant advantages in enhancing the system energy efficiency over other baseline schemes including the conventional RIS-aided scheme.