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We develop a new framework to prove the mixing or relaxation time for the Glauber dynamics on spin systems with unbounded degree. It works for general spin systems including both $2$-spin and multi-spin systems. As applications for this approach: $\bullet$ We prove the optimal $O(n)$ relaxation time for the Glauber dynamics of random $q$-list-coloring on an $n$-vertices triangle-tree graph with maximum degree $\Delta$ such that $q/\Delta > \alpha^\star$, where $\alpha^\star \approx 1.763$ is the unique positive solution of the equation $\alpha = \exp(1/\alpha)$. This improves the $n^{1+o(1)}$ relaxation time for Glauber dynamics obtained by the previous work of Jain, Pham, and Vuong (2022). Besides, our framework can also give a near-linear time sampling algorithm under the same condition. $\bullet$ We prove the optimal $O(n)$ relaxation time and near-optimal $\widetilde{O}(n)$ mixing time for the Glauber dynamics on hardcore models with parameter $\lambda$ in $\textit{balanced}$ bipartite graphs such that $\lambda < \lambda_c(\Delta_L)$ for the max degree $\Delta_L$ in left part and the max degree $\Delta_R$ of right part satisfies $\Delta_R = O(\Delta_L)$. This improves the previous result by Chen, Liu, and Yin (2023). At the heart of our proof is the notion of $\textit{coupling independence}$ which allows us to consider multiple vertices as a huge single vertex with exponentially large domain and do a "coarse-grained" local-to-global argument on spin systems. The technique works for general (multi) spin systems and helps us obtain some new comparison results for Glauber dynamics.

We address the convergence rate of Markov chains for randomly generating an edge coloring of a given tree. Our focus is on the Glauber dynamics which updates the color at a randomly chosen edge in each step. For a tree $T$ with $n$ vertices and maximum degree $\Delta$, when the number of colors $q$ satisfies $q\geq\Delta+2$ then we prove that the Glauber dynamics has an optimal relaxation time of $O(n)$, where the relaxation time is the inverse of the spectral gap. This is optimal in the range of $q$ in terms of $\Delta$ as Dyer, Goldberg, and Jerrum (2006) showed that the relaxation time is $\Omega(n^3)$ when $q=\Delta+1$. For the case $q=\Delta+1$, we show that an alternative Markov chain which updates a pair of neighboring edges has relaxation time $O(n)$. Moreover, for the $\Delta$-regular complete tree we prove $O(n\log^2{n})$ mixing time bounds for the respective Markov chain. Our proofs establish approximate tensorization of variance via a novel inductive approach, where the base case is a tree of height $\ell=O(\Delta^2\log^2{\Delta})$, which we analyze using a canonical paths argument.

Emotion decoding plays an important role in affective human-computer interaction. However, previous studies ignored the dynamic real-world scenario, where human experience a blend of multiple emotions which are incrementally integrated into the model, leading to the multi-label class incremental learning (MLCIL) problem. Existing methods have difficulty in solving MLCIL issue due to notorious catastrophic forgetting caused by partial label problem and inadequate label semantics mining. In this paper, we propose an augmented emotional semantics learning framework for multi-label class incremental emotion decoding. Specifically, we design an augmented emotional relation graph module with label disambiguation to handle the past-missing partial label problem. Then, we leverage domain knowledge from affective dimension space to alleviate future-missing partial label problem by knowledge distillation. Besides, an emotional semantics learning module is constructed with a graph autoencoder to obtain emotion embeddings in order to guide the semantic-specific feature decoupling for better multi-label learning. Extensive experiments on three datasets show the superiority of our method for improving emotion decoding performance and mitigating forgetting on MLCIL problem.

Drawing inspiration from the hierarchical processing of the human auditory system, which transforms sound from low-level acoustic features to high-level semantic understanding, we introduce a novel coarse-to-fine audio reconstruction method. Leveraging non-invasive functional Magnetic Resonance Imaging (fMRI) data, our approach mimics the inverse pathway of auditory processing. Initially, we utilize CLAP to decode fMRI data coarsely into a low-dimensional semantic space, followed by a fine-grained decoding into the high-dimensional AudioMAE latent space guided by semantic features. These fine-grained neural features serve as conditions for audio reconstruction through a Latent Diffusion Model (LDM). Validation on three public fMRI datasets-Brain2Sound, Brain2Music, and Brain2Speech-underscores the superiority of our coarse-to-fine decoding method over stand-alone fine-grained approaches, showcasing state-of-the-art performance in metrics like FD, FAD, and KL. Moreover, by employing semantic prompts during decoding, we enhance the quality of reconstructed audio when semantic features are suboptimal. The demonstrated versatility of our model across diverse stimuli highlights its potential as a universal brain-to-audio framework. This research contributes to the comprehension of the human auditory system, pushing boundaries in neural decoding and audio reconstruction methodologies.

Regression analysis with probability measures as input predictors and output response has recently drawn great attention. However, it is challenging to handle multiple input probability measures due to the non-flat Riemannian geometry of the Wasserstein space, hindering the definition of arithmetic operations, hence additive linear structure is not well-defined. In this work, a distribution-in-distribution-out regression model is proposed by introducing parallel transport to achieve provable commutativity and additivity of newly defined arithmetic operations in Wasserstein space. The appealing properties of the DIDO regression model can serve a foundation for model estimation, prediction, and inference. Specifically, the Fr\'echet least squares estimator is employed to obtain the best linear unbiased estimate, supported by the newly established Fr\'echet Gauss-Markov Theorem. Furthermore, we investigate a special case when predictors and response are all univariate Gaussian measures, leading to a simple close-form solution of linear model coefficients and $R^2$ metric. A simulation study and real case study in intraoperative cardiac output prediction are performed to evaluate the performance of the proposed method.

Decoding language information from brain signals represents a vital research area within brain-computer interfaces, particularly in the context of deciphering the semantic information from the fMRI signal. However, many existing efforts concentrate on decoding small vocabulary sets, leaving space for the exploration of open vocabulary continuous text decoding. In this paper, we introduce a novel method, the \textbf{Brain Prompt GPT (BP-GPT)}. By using the brain representation that is extracted from the fMRI as a prompt, our method can utilize GPT-2 to decode fMRI signals into stimulus text. Further, we introduce a text-to-text baseline and align the fMRI prompt to the text prompt. By introducing the text-to-text baseline, our BP-GPT can extract a more robust brain prompt and promote the decoding of pre-trained LLM. We evaluate our BP-GPT on the open-source auditory semantic decoding dataset and achieve a significant improvement up to $4.61\%$ on METEOR and $2.43\%$ on BERTScore across all the subjects compared to the state-of-the-art method. The experimental results demonstrate that using brain representation as a prompt to further drive LLM for auditory neural decoding is feasible and effective.

This paper describes a new research paradigm for studying human-AI collaboration, named "human-AI mutual learning", defined as the process where humans and AI agents preserve, exchange, and improve knowledge during human-AI collaboration. We describe relevant methodologies, motivations, domain examples, benefits, challenges, and future research agenda under this paradigm.

Vision transformer family has dominated the satellite pan-sharpening field driven by the global-wise spatial information modeling mechanism from the core self-attention ingredient. The standard modeling rules within these promising pan-sharpening methods are to roughly stack the transformer variants in a cascaded manner. Despite the remarkable advancement, their success may be at the huge cost of model parameters and FLOPs, thus preventing its application over low-resource satellites.To address this challenge between favorable performance and expensive computation, we tailor an efficient linearly-evolved transformer variant and employ it to construct a lightweight pan-sharpening framework. In detail, we deepen into the popular cascaded transformer modeling with cutting-edge methods and develop the alternative 1-order linearly-evolved transformer variant with the 1-dimensional linear convolution chain to achieve the same function. In this way, our proposed method is capable of benefiting the cascaded modeling rule while achieving favorable performance in the efficient manner. Extensive experiments over multiple satellite datasets suggest that our proposed method achieves competitive performance against other state-of-the-art with fewer computational resources. Further, the consistently favorable performance has been verified over the hyper-spectral image fusion task. Our main focus is to provide an alternative global modeling framework with an efficient structure. The code will be publicly available., Comment: 10 pages

Let ${\bf G}$ be a connected reductive algebraic group defined over the finite field $\mathbb{F}_q$ with $q$ elements,where $q$ is a power of a prime number $p$. Let $\Bbbk$ be a field and we study the extensions of certain $\bk\bg$-modules in this paper. We show that the extensions of any modules in $\mathscr{O}(\bg)$ by a finite-dimensional $\bk\bg$-module is zero if $p\ne \op{char}\bk\ge5$ or $\op{char}\bk=0$, where $\mathscr{O}(\bg)$ is the principal representation category defined in \cite{D1}. We determine the necessary and sufficient condition for the vanishing of extensions between naive induced modules. As an application, we give the condition of the vanishing of extensions between simple modules in $\mathscr{O}({\bf G})$ for $\bg=SL_2(\bar{\mathbb{F}}_q)$., Comment: 20 pages. We add some new results

We study how to establish $\textit{spectral independence}$, a key concept in sampling, without relying on total influence bounds, by applying an $\textit{approximate inverse}$ of the influence matrix. Our method gives constant upper bounds on spectral independence for two foundational Gibbs distributions known to have unbounded total influences: $\bullet$ The monomer-dimer model on graphs with large girth (including trees). Prior to our work, such results were only known for graphs with constant maximum degrees or infinite regular trees, as shown by Chen, Liu, and Vigoda (STOC '21). $\bullet$ The hardcore model on trees with fugacity $\lambda < \mathrm{e}^2$. This remarkably surpasses the well-known $\lambda_r>\mathrm{e}-1$ lower bound for the reconstruction threshold on trees, significantly improving upon the current threshold $\lambda < 1.3$, established in a prior work by Efthymiou, Hayes, \v{S}tefankovi\v{c}, and Vigoda (RANDOM '23). Consequently, we establish optimal $\Omega(n^{-1})$ spectral gaps of the Glauber dynamics for these models on arbitrary trees, regardless of the maximum degree $\Delta$.

Automatic measurements of tear meniscus height (TMH) have been achieved by using deep learning techniques; however, annotation is significantly influenced by subjective factors and is both time-consuming and labor-intensive. In this paper, we introduce an automatic TMH measurement technique based on edge detection-assisted annotation within a deep learning framework. This method generates mask labels less affected by subjective factors with enhanced efficiency compared to previous annotation approaches. For improved segmentation of the pupil and tear meniscus areas, the convolutional neural network Inceptionv3 was first implemented as an image quality assessment model, effectively identifying higher-quality images with an accuracy of 98.224%. Subsequently, by using the generated labels, various algorithms, including Unet, ResUnet, Deeplabv3+FcnResnet101, Deeplabv3+FcnResnet50, FcnResnet50, and FcnResnet101 were trained, with Unet demonstrating the best performance. Finally, Unet was used for automatic pupil and tear meniscus segmentation to locate the center of the pupil and calculate TMH,respectively. An evaluation of the mask quality predicted by Unet indicated a Mean Intersection over Union of 0.9362, a recall of 0.9261, a precision of 0.9423, and an F1-Score of 0.9326. Additionally, the TMH predicted by the model was assessed, with the fitting curve represented as y= 0.982x-0.862, an overall correlation coefficient of r^2=0.961 , and an accuracy of 94.80% (237/250). In summary, the algorithm can automatically screen images based on their quality,segment the pupil and tear meniscus areas, and automatically measure TMH. Measurement results using the AI algorithm demonstrate a high level of consistency with manual measurements, offering significant support to clinical doctors in diagnosing dry eye disease., Comment: 22 pages, 5 figures

This paper presents a study on strategies to enhance the translation capabilities of large language models (LLMs) in the context of machine translation (MT) tasks. The paper proposes a novel paradigm consisting of three stages: Secondary Pre-training using Extensive Monolingual Data, Continual Pre-training with Interlinear Text Format Documents, and Leveraging Source-Language Consistent Instruction for Supervised Fine-Tuning. Previous research on LLMs focused on various strategies for supervised fine-tuning (SFT), but their effectiveness has been limited. While traditional machine translation approaches rely on vast amounts of parallel bilingual data, our paradigm highlights the importance of using smaller sets of high-quality bilingual data. We argue that the focus should be on augmenting LLMs' cross-lingual alignment abilities during pre-training rather than solely relying on extensive bilingual data during SFT. Experimental results conducted using the Llama2 model, particularly on Chinese-Llama2 after monolingual augmentation, demonstrate the improved translation capabilities of LLMs. A significant contribution of our approach lies in Stage2: Continual Pre-training with Interlinear Text Format Documents, which requires less than 1B training data, making our method highly efficient. Additionally, in Stage3, we observed that setting instructions consistent with the source language benefits the supervised fine-tuning process. Experimental results demonstrate that our approach surpasses previous work and achieves superior performance compared to models such as NLLB-54B and GPT3.5-text-davinci-003, despite having a significantly smaller parameter count of only 7B or 13B. This achievement establishes our method as a pioneering strategy in the field of machine translation., Comment: Accepted in NAACL 2024

The radical pair mechanism is an important model that may provide a basis for biological magnetoreception. To account for the high orientation precision of the real avian compass, P. J. Hore et al. proposed an intriguing phenomenon called quantum needle [Proc. Natl. Acad. Sci. 113, 4634 (2016)], where a spike-like feature emerges in the fractional yield signal. However, it is believed that quantum needle requires the radical pair lifetime to be longer than a few microseconds and thus poses stern challenges in realistic biological systems. Here, we exploit the optimization techniques and find a novel class of model system, which sustains much more prominent features of quantum needle and significantly relaxes the requirement for radical pair lifetime. Even more surprisingly, we find that the characteristics of quantum needle retain a narrow functional window around the geomagnetic field, which is absent in the previous model systems. Therefore, our work provides essential evidence for identifying the possible physical mechanism for quantum needle in chemical magnetoreception.

An intelligent driving system should dynamically formulate appropriate driving strategies based on the current environment and vehicle status while ensuring system security and reliability. However, methods based on reinforcement learning and imitation learning often suffer from high sample complexity, poor generalization, and low safety. To address these challenges, this paper introduces an Efficient and Generalized end-to-end Autonomous Driving System (EGADS) for complex and varied scenarios. The RL agent in our EGADS combines variational inference with normalizing flows, which are independent of distribution assumptions. This combination allows the agent to capture historical information relevant to driving in latent space effectively, thereby significantly reducing sample complexity. Additionally, we enhance safety by formulating robust safety constraints and improve generalization and performance by integrating RL with expert demonstrations. Experimental results demonstrate that, compared to existing methods, EGADS significantly reduces sample complexity, greatly improves safety performance, and exhibits strong generalization capabilities in complex urban scenarios. Particularly, we contributed an expert dataset collected through human expert steering wheel control, specifically using the G29 steering wheel.

Incremental Decoding is an effective framework that enables the use of an offline model in a simultaneous setting without modifying the original model, making it suitable for Low-Latency Simultaneous Speech Translation. However, this framework may introduce errors when the system outputs from incomplete input. To reduce these output errors, several strategies such as Hold-$n$, LA-$n$, and SP-$n$ can be employed, but the hyper-parameter $n$ needs to be carefully selected for optimal performance. Moreover, these strategies are more suitable for end-to-end systems than cascade systems. In our paper, we propose a new adaptable and efficient policy named "Regularized Batched Inputs". Our method stands out by enhancing input diversity to mitigate output errors. We suggest particular regularization techniques for both end-to-end and cascade systems. We conducted experiments on IWSLT Simultaneous Speech Translation (SimulST) tasks, which demonstrate that our approach achieves low latency while maintaining no more than 2 BLEU points loss compared to offline systems. Furthermore, our SimulST systems attained several new state-of-the-art results in various language directions., Comment: Preprint

It is challenging but important to save annotation efforts in streaming data acquisition to maintain data quality for supervised learning base learners. We propose an ensemble active learning method to actively acquire samples for annotation by contextual bandits, which is will enforce the exploration-exploitation balance and leading to improved AI modeling performance.

We give a $\widetilde{O}(n)$ time almost uniform sampler for independent sets of a matroid, whose ground set has $n$ elements and is given by an independence oracle. As a consequence, one can sample connected spanning subgraphs of a given graph $G=(V,E)$ in $\widetilde{O}(|E|)$ time. This leads to improved running time on estimating all-terminal network reliability. Furthermore, we generalise this near-linear time sampler to the random cluster model with $q\le 1$.

The human brain can easily focus on one speaker and suppress others in scenarios such as a cocktail party. Recently, researchers found that auditory attention can be decoded from the electroencephalogram (EEG) data. However, most existing deep learning methods are difficult to use prior knowledge of different views (that is attended speech and EEG are task-related views) and extract an unsatisfactory representation. Inspired by Broadbent's filter model, we decode auditory attention in a multi-view paradigm and extract the most relevant and important information utilizing the missing view. Specifically, we propose an auditory attention decoding (AAD) method based on multi-view VAE with task-related multi-view contrastive (TMC) learning. Employing TMC learning in multi-view VAE can utilize the missing view to accumulate prior knowledge of different views into the fusion of representation, and extract the approximate task-related representation. We examine our method on two popular AAD datasets, and demonstrate the superiority of our method by comparing it to the state-of-the-art method.

$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for $k$-clustering in $\mathbb{R}^d$ with $\tilde{O}(\sqrt{nk}d^{3/2})$ query complexity. Our coreset reduces the input size from $n$ to $\mathrm{poly}(k\epsilon^{-1}d)$, so that existing $\alpha$-approximation algorithms for clustering can run on top of it and yield $(1 + \epsilon)\alpha$-approximation. This eventually yields a quadratic speedup for various $k$-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make $\Omega(\sqrt{nk})$ queries in order to achieve even $O(1)$-approximation for $k$-clustering., Comment: Comments: 32 pages, 0 figures, 1 table. To appear in the Fortieth International Conference on Machine Learning (ICML 2023)

Back Translation (BT) is widely used in the field of machine translation, as it has been proved effective for enhancing translation quality. However, BT mainly improves the translation of inputs that share a similar style (to be more specific, translation-like inputs), since the source side of BT data is machine-translated. For natural inputs, BT brings only slight improvements and sometimes even adverse effects. To address this issue, we propose Text Style Transfer Back Translation (TST BT), which uses a style transfer model to modify the source side of BT data. By making the style of source-side text more natural, we aim to improve the translation of natural inputs. Our experiments on various language pairs, including both high-resource and low-resource ones, demonstrate that TST BT significantly improves translation performance against popular BT benchmarks. In addition, TST BT is proved to be effective in domain adaptation so this strategy can be regarded as a general data augmentation method. Our training code and text style transfer model are open-sourced., Comment: acl2023, 14 pages, 4 figures, 19 tables

With strong capabilities of reasoning and a broad understanding of the world, Large Language Models (LLMs) have demonstrated immense potential in building versatile embodied decision-making agents capable of executing a wide array of tasks. Nevertheless, when deployed in unfamiliar environments, we show that LLM agents encounter challenges in efficiently gathering essential information, leading to suboptimal performance. Conversely, human individuals often seek additional information from their peers prior to taking action, harnessing external knowledge to avoid unnecessary trial and error. Drawing inspiration from this behavior, we propose \textit{Asking Before Acting} (ABA), a method that empowers the agent to proactively inquire with external sources for pertinent information using natural language during their interactions within the environment. In this way, the agent is able to enhance its efficiency and performance by circumventing potentially laborious steps and combating the difficulties associated with exploration in unfamiliar environments and vagueness of the instructions. We conduct extensive experiments involving a spectrum of environments including text-based household everyday tasks, robot arm manipulation tasks, and real world open domain image based embodied tasks. The experiments involve various models from Vicuna to GPT-4. The results demonstrate that, even with modest prompts modifications, ABA exhibits substantial advantages on both performance and efficiency over baseline LLM agents. Further finetuning ABA with reformulated metadata (ABA-FT) faciliates learning the rationale for asking and allows for additional enhancements especially in tasks that baselines struggle to solve.

Optimized trade execution is to sell (or buy) a given amount of assets in a given time with the lowest possible trading cost. Recently, reinforcement learning (RL) has been applied to optimized trade execution to learn smarter policies from market data. However, we find that many existing RL methods exhibit considerable overfitting which prevents them from real deployment. In this paper, we provide an extensive study on the overfitting problem in optimized trade execution. First, we model the optimized trade execution as offline RL with dynamic context (ORDC), where the context represents market variables that cannot be influenced by the trading policy and are collected in an offline manner. Under this framework, we derive the generalization bound and find that the overfitting issue is caused by large context space and limited context samples in the offline setting. Accordingly, we propose to learn compact representations for context to address the overfitting problem, either by leveraging prior knowledge or in an end-to-end manner. To evaluate our algorithms, we also implement a carefully designed simulator based on historical limit order book (LOB) data to provide a high-fidelity benchmark for different algorithms. Our experiments on the high-fidelity simulator demonstrate that our algorithms can effectively alleviate overfitting and achieve better performance., Comment: Accepted by IJCAI-23

We characterize the uniqueness condition in the hardcore model for bipartite graphs with degree bounds only on one side, and provide a nearly linear time sampling algorithm that works up to the uniqueness threshold. We show that the uniqueness threshold for bipartite graph has almost the same form of the tree uniqueness threshold for general graphs, except with degree bounds only on one side of the bipartition. The hardcore model from statistical physics can be seen as a weighted enumeration of independent sets. Its bipartite version (#BIS) is a central open problem in approximate counting. Compared to the same problem in a general graph, surprising tractable regime have been identified that are believed to be hard in general. This is made possible by two lines of algorithmic approach: the high-temperature algorithms starting from Liu and Lu (STOC 2015), and the low-temperature algorithms starting from Helmuth, Perkins, and Regts (STOC 2019). In this work, we study the limit of these algorithms in the high-temperature case. Our characterization of the uniqueness condition is obtained by proving decay of correlations for arguably the best possible regime, which involves locating fixpoints of multivariate iterative rational maps and showing their contraction. We also give a nearly linear time sampling algorithm based on simulating field dynamics only on one side of the bipartite graph that works up to the uniqueness threshold. Our algorithm is very different from the original high-temperature algorithm of Liu and Lu, and it makes use of a connection between correlation decay and spectral independence of Markov chains. Last but not the least, we are able to show that the standard Glauber dynamics on both side of the bipartite graph mixes in polynomial time up to the uniqueness.

Image forgery localization aims to identify forged regions by capturing subtle traces from high-quality discriminative features. In this paper, we propose a Transformer-style network with two feature extraction branches for image forgery localization, and it is named as Two-Branch Transformer (TBFormer). Firstly, two feature extraction branches are elaborately designed, taking advantage of the discriminative stacked Transformer layers, for both RGB and noise domain features. Secondly, an Attention-aware Hierarchical-feature Fusion Module (AHFM) is proposed to effectively fuse hierarchical features from two different domains. Although the two feature extraction branches have the same architecture, their features have significant differences since they are extracted from different domains. We adopt position attention to embed them into a unified feature domain for hierarchical feature investigation. Finally, a Transformer decoder is constructed for feature reconstruction to generate the predicted mask. Extensive experiments on publicly available datasets demonstrate the effectiveness of the proposed model., Comment: 5 pages, 3 figures

One of the key challenges in deploying RL to real-world applications is to adapt to variations of unknown environment contexts, such as changing terrains in robotic tasks and fluctuated bandwidth in congestion control. Existing works on adaptation to unknown environment contexts either assume the contexts are the same for the whole episode or assume the context variables are Markovian. However, in many real-world applications, the environment context usually stays stable for a stochastic period and then changes in an abrupt and unpredictable manner within an episode, resulting in a segment structure, which existing works fail to address. To leverage the segment structure of piecewise stable context in real-world applications, in this paper, we propose a \textit{\textbf{Se}gmented \textbf{C}ontext \textbf{B}elief \textbf{A}ugmented \textbf{D}eep~(SeCBAD)} RL method. Our method can jointly infer the belief distribution over latent context with the posterior over segment length and perform more accurate belief context inference with observed data within the current context segment. The inferred belief context can be leveraged to augment the state, leading to a policy that can adapt to abrupt variations in context. We demonstrate empirically that SeCBAD can infer context segment length accurately and outperform existing methods on a toy grid world environment and Mujuco tasks with piecewise-stable context., Comment: NeurIPS 2022

This paper examines the energy efficiency optimization problem of intelligent reflective surface (IRS)-assisted multi-user rate division multiple access (RSMA) downlink systems under terahertz propagation. The objective function for energy efficiency is optimized using the salp swarm algorithm (SSA) and compared with the successive convex approximation (SCA) technique. SCA technique requires multiple iterations to solve non-convex resource allocation problems, whereas SSA can consume less time to improve energy efficiency effectively. The simulation results show that SSA is better than SCA in improving system energy efficiency, and the time required is significantly reduced, thus optimizing the system's overall performance.

Max-Cut is a fundamental problem that has been studied extensively in various settings. We design an algorithm for Euclidean Max-Cut, where the input is a set of points in $\mathbb{R}^d$, in the model of dynamic geometric streams, where the input $X\subseteq [\Delta]^d$ is presented as a sequence of point insertions and deletions. Previously, Frahling and Sohler [STOC 2005] designed a $(1+\epsilon)$-approximation algorithm for the low-dimensional regime, i.e., it uses space $\exp(d)$. To tackle this problem in the high-dimensional regime, which is of growing interest, one must improve the dependence on the dimension $d$, ideally to space complexity $\mathrm{poly}(\epsilon^{-1} d \log\Delta)$. Lammersen, Sidiropoulos, and Sohler [WADS 2009] proved that Euclidean Max-Cut admits dimension reduction with target dimension $d' = \mathrm{poly}(\epsilon^{-1})$. Combining this with the aforementioned algorithm that uses space $\exp(d')$, they obtain an algorithm whose overall space complexity is indeed polynomial in $d$, but unfortunately exponential in $\epsilon^{-1}$. We devise an alternative approach of \emph{data reduction}, based on importance sampling, and achieve space bound $\mathrm{poly}(\epsilon^{-1} d \log\Delta)$, which is exponentially better (in $\epsilon$) than the dimension-reduction approach. To implement this scheme in the streaming model, we employ a randomly-shifted quadtree to construct a tree embedding. While this is a well-known method, a key feature of our algorithm is that the embedding's distortion $O(d\log\Delta)$ affects only the space complexity, and the approximation ratio remains $1+\epsilon$.