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Data series indexes are necessary for managing and analyzing the increasing amounts of data series collections that are nowadays available. These indexes support both exact and approximate similarity search, with approximate search providing high-quality results within milliseconds, which makes it very attractive for certain modern applications. Reducing the pre-processing (i.e., index building) time and improving the accuracy of search results are two major challenges. DSTree and the iSAX index family are state-of-the-art solutions for this problem. However, DSTree suffers from long index building times, while iSAX suffers from low search accuracy. In this paper, we identify two problems of the iSAX index family that adversely affect the overall performance. First, we observe the presence of a proximity-compactness trade-off related to the index structure design (i.e., the node fanout degree), significantly limiting the efficiency and accuracy of the resulting index. Second, a skewed data distribution will negatively affect the performance of iSAX. To overcome these problems, we propose Dumpy, an index that employs a novel multi-ary data structure with an adaptive node splitting algorithm and an efficient building workflow. Furthermore, we devise Dumpy-Fuzzy as a variant of Dumpy which further improves search accuracy by proper duplication of series. To fully leverage the potential of modern hardware including multicore CPUs and Solid State Drives (SSDs), we parallelize Dumpy to DumpyOS with sophisticated indexing and pruning-based querying algorithms. An optimized approximate search algorithm, DumpyOS-F which prominently improves the search accuracy without violating the index, is also proposed., Comment: arXiv admin note: substantial text overlap with arXiv:2304.08264

Optically dark dusty star-forming galaxies (DSFGs) play an essential role in massive galaxy formation at early cosmic time, however their nature remains elusive. Here we present a detailed case study of all the baryonic components of a $z=4.821$ DSFG, XS55. Selected from the ultra-deep COSMOS-XS 3GHz map with a red SCUBA-2 450$\mu$m/850$\mu$m colour, XS55 was followed up with ALMA 3mm line scans and spectroscopically confirmed to be at $z=4.821$ via detections of the CO(5-4) and [CI](1-0) lines. JWST/NIRCam imaging reveals that XS55 is a F150W-dropout with red F277W/F444W colour, and a complex morphology: a compact central component embedded in an extended structure with a likely companion. XS55 is tentatively detected in X-rays with both Chandra and XMM-Newton, suggesting an active galactic nucleus (AGN) nature. By fitting a panchromatic SED spanning NIR to radio wavelengths, we revealed that XS55 is a massive main-sequence galaxy with a stellar mass of $M_\ast=(5\pm1)\times10^{10}\,{\rm M_\odot}$ and a star formation rate of ${\rm SFR}=540\pm177~{\rm M_\odot\,yr^{-1}}$. The dust of XS55 is optically thick in the far infrared (FIR) with a surprisingly cold dust temperature of $T_{\rm dust}=33\pm2\,{\rm K}$, making XS55 one of the coldest DSFGs at $z>4$ known to date. This work unveils the nature of a radio-selected F150W-dropout, suggesting the existence of a population of DSFGs hosting active black holes embedded in optically thick dust., Comment: 11 pages, 7 figures, accepted in Astronomy & Astrophysics

A collaboration between dataset owners and model owners is needed to facilitate effective machine learning (ML) training. During this collaboration, however, dataset owners and model owners want to protect the confidentiality of their respective assets (i.e., datasets, models and training code), with the dataset owners also caring about the privacy of individual users whose data is in their datasets. Existing solutions either provide limited confidentiality for models and training code, or suffer from privacy issues due to collusion. We present Citadel++, a scalable collaborative ML training system designed to simultaneously protect the confidentiality of datasets, models and training code, as well as the privacy of individual users. Citadel++ enhances differential privacy techniques to safeguard the privacy of individual user data while maintaining model utility. By employing Virtual Machine-level Trusted Execution Environments (TEEs) and improved integrity protection techniques through various OS-level mechanisms, Citadel++ effectively preserves the confidentiality of datasets, models and training code, and enforces our privacy mechanisms even when the models and training code have been maliciously designed. Our experiments show that Citadel++ provides privacy, model utility and performance while adhering to confidentiality and privacy requirements of dataset owners and model owners, outperforming the state-of-the-art privacy-preserving training systems by up to 543x on CPU and 113x on GPU TEEs.

Mental manipulation severely undermines mental wellness by covertly and negatively distorting decision-making. While there is an increasing interest in mental health care within the natural language processing community, progress in tackling manipulation remains limited due to the complexity of detecting subtle, covert tactics in conversations. In this paper, we propose Intent-Aware Prompting (IAP), a novel approach for detecting mental manipulations using large language models (LLMs), providing a deeper understanding of manipulative tactics by capturing the underlying intents of participants. Experimental results on the MentalManip dataset demonstrate superior effectiveness of IAP against other advanced prompting strategies. Notably, our approach substantially reduces false negatives, helping detect more instances of mental manipulation with minimal misjudgment of positive cases. The code of this paper is available at https://github.com/Anton-Jiayuan-MA/Manip-IAP.

Optical resonators have shown outstanding abilities to tailor chemical landscapes through enhanced light-matter interaction between confined optical modes and molecule vibrations. We propose a theoretical model to study cooperative vibrational strong coupling in an open quantum system. The non-equilibrium stochastic molecular dynamics in an optical cavity with an auxiliary ensemble is investigated. It shows that coupling with a cavity mode introduces an additional colored noise and a negative feedback, both of which enable control over thermalization rates (i.e. the lifetime of excitation) of reactive molecules. Our work offers a pathway to steer stability of chemical bonds for chemical reactivity under cooperative vibrational strong coupling.

Voluntary vaccination is essential to protect oneself from infection and suppress the spread of infectious diseases. Voluntary vaccination behavior is influenced by factors such as age and interaction patterns. Differences in health consciousness and risk perception based on age result in heterogeneity in vaccination behavior among different age groups. Higher-order interactions among individuals of various ages facilitate the dissemination of vaccine-related information, further influencing vaccination intentions. To investigate the impact of individual age and interaction patterns on vaccination behavior, we propose an epidemic-game coevolution model in which age structure and higher-order interactions are considered. Combining the theoretical analysis of epidemic-game coevolution, this work calculates the evolutionarily stable strategies and dynamic equilibrium based on imitation dynamics in the well-mixed population. Extensive numerical experiments show that infants and the elderly exhibit conservative attitudes towards vaccination, and the vaccination levels of these two groups have no significant impact on the vaccination behavior of other age groups. The vaccination behavior of children is highly active, while the vaccination behavior of adults depends on the relative cost of vaccination. The increase in vaccination levels among children and adults leads to a decrease in vaccination levels in other groups. Furthermore, the infants exhibit the lowest level of vaccination, while the children have the highest vaccination rate. Higher-order interactions significantly enhance vaccination levels among children and adults.

Pruning can be an effective method of compressing large pre-trained models for inference speed acceleration. Previous pruning approaches rely on access to the original training dataset for both pruning and subsequent fine-tuning. However, access to the training data can be limited due to concerns such as data privacy and commercial confidentiality. Furthermore, with covariate shift (disparities between test and training data distributions), pruning and finetuning with training datasets can hinder the generalization of the pruned model to test data. To address these issues, pruning and finetuning the model with test time samples becomes essential. However, test-time model pruning and fine-tuning incur additional computation costs and slow down the model's prediction speed, thus posing efficiency issues. Existing pruning methods are not efficient enough for test time model pruning setting, since finetuning the pruned model is needed to evaluate the importance of removable components. To address this, we propose two variables to approximate the fine-tuned accuracy. We then introduce an efficient pruning method that considers the approximated finetuned accuracy and potential inference latency saving. To enhance fine-tuning efficiency, we propose an efficient knowledge distillation method that only needs to generate pseudo labels for a small set of finetuning samples one time, thereby reducing the expensive pseudo-label generation cost. Experimental results demonstrate that our method achieves a comparable or superior tradeoff between test accuracy and inference latency, with a 32% relative reduction in pruning and finetuning time compared to the best existing method.

The presence of disorder can severely impede wave transport, resulting in the famous Anderson localization. Previous theoretical studies found that Anderson transition can exist in one-dimensional (1D) non-Hermitian disordered rings with chiral hopping, defying the scaling theory of localization for Hermitian systems. In these systems, localized (extended) modes are associated with real (complex) energies. Here, we report that Anderson localized modes with complex energies can also exist in such systems. The emergence of the complex-energy localized modes (CELMs) directly ties to the properties of the corresponding pristine non-Hermitian system. Specifically, the density of states of the complex spectrum under the periodic boundary condition and the non-Bloch parity-time transition of the open-boundary chain both play critical roles in the emergence of the CELMs. The coexistence of extended modes, real-energy localized modes (RELMs), and CELMs should be a generic phenomenon for 1D non-Hermitian disordered systems under class AI. Our work shows that the interplay between Anderson mechanism and non-Hermitian physics enriches the properties of disordered media and opens new possibilities for controlling wave transport., Comment: 16 pages, 5 figures

Recently, Large Language Models (LLMs) have undergone a significant transformation, marked by a rapid rise in both their popularity and capabilities. Leading this evolution are proprietary LLMs like GPT-4 and GPT-o1, which have captured widespread attention in the AI community due to their remarkable performance and versatility. Simultaneously, open-source LLMs, such as LLaMA and Mistral, have made great contributions to the ever-increasing popularity of LLMs due to the ease to customize and deploy the models across diverse applications. Although open-source LLMs present unprecedented opportunities for innovation and research, the commercialization of LLMs has raised concerns about transparency, reproducibility, and safety. Many open-source LLMs fail to meet fundamental transparency requirements by withholding essential components like training code and data, and some use restrictive licenses whilst claiming to be "open-source," which may hinder further innovations on LLMs. To mitigate this issue, we introduce Moxin 7B, a fully open-source LLM developed in accordance with the Model Openness Framework (MOF), a ranked classification system that evaluates AI models based on model completeness and openness, adhering to principles of open science, open source, open data, and open access. Our model achieves the highest MOF classification level of "open science" through the comprehensive release of pre-training code and configurations, training and fine-tuning datasets, and intermediate and final checkpoints. Experiments show that our model achieves superior performance in zero-shot evaluation compared with popular 7B models and performs competitively in few-shot evaluation.

The increasing demand for processing large volumes of data for machine learning models has pushed data bandwidth requirements beyond the capability of traditional von Neumann architecture. In-memory computing (IMC) has recently emerged as a promising solution to address this gap by enabling distributed data storage and processing at the micro-architectural level, significantly reducing both latency and energy. In this paper, we present the IMPACT: InMemory ComPuting Architecture Based on Y-FlAsh Technology for Coalesced Tsetlin Machine Inference, underpinned on a cutting-edge memory device, Y-Flash, fabricated on a 180 nm CMOS process. Y-Flash devices have recently been demonstrated for digital and analog memory applications, offering high yield, non-volatility, and low power consumption. The IMPACT leverages the Y-Flash array to implement the inference of a novel machine learning algorithm: coalesced Tsetlin machine (CoTM) based on propositional logic. CoTM utilizes Tsetlin automata (TA) to create Boolean feature selections stochastically across parallel clauses. The IMPACT is organized into two computational crossbars for storing the TA and weights. Through validation on the MNIST dataset, IMPACT achieved 96.3% accuracy. The IMPACT demonstrated improvements in energy efficiency, e.g., 2.23X over CNN-based ReRAM, 2.46X over Neuromorphic using NOR-Flash, and 2.06X over DNN-based PCM, suited for modern ML inference applications., Comment: 27 Pages, 14 Figures, 6 Tables

We present Measure Anything, a comprehensive vision-based framework for dimensional measurement of objects with circular cross-sections, leveraging the Segment Anything Model (SAM). Our approach estimates key geometric features -- including diameter, length, and volume -- for rod-like geometries with varying curvature and general objects with constant skeleton slope. The framework integrates segmentation, mask processing, skeleton construction, and 2D-3D transformation, packaged in a user-friendly interface. We validate our framework by estimating the diameters of Canola stems -- collected from agricultural fields in North Dakota -- which are thin and non-uniform, posing challenges for existing methods. Measuring its diameters is critical, as it is a phenotypic traits that correlates with the health and yield of Canola crops. This application also exemplifies the potential of Measure Anything, where integrating intelligent models -- such as keypoint detection -- extends its scalability to fully automate the measurement process for high-throughput applications. Furthermore, we showcase its versatility in robotic grasping, leveraging extracted geometric features to identify optimal grasp points.

Wireless minimally invasive bioelectronic implants enable a wide range of applications in healthcare, medicine, and scientific research. Magnetoelectric (ME) wireless power transfer (WPT) has emerged as a promising approach for powering miniature bio-implants because of its remarkable efficiency, safety limit, and misalignment tolerance. However, achieving low-power and high-quality uplink communication using ME remains a challenge. This paper presents a pulse-width modulated (PWM) ME backscatter uplink communication enabled by a switched-capacitor energy extraction (SCEE) technique. The SCEE rapidly extracts and dissipates the kinetic energy within the ME transducer during its ringdown period, enabling time-domain PWM in ME backscatter. Various circuit techniques are presented to realize SCEE with low power consumption. This paper also describes the high-order modeling of ME transducers to facilitate the design and analysis, which shows good matching with measurement. Our prototyping system includes a millimeter-scale ME implant with a fully integrated system-on-chip (SoC) and a portable transceiver for power transfer and bidirectional communication. SCEE is proven to induce >50% amplitude reduction within 2 ME cycles, leading to a PWM ME backscatter uplink with 17.73 kbps data rate and 0.9 pJ/bit efficiency. It also achieves 8.5 x 10 -5 bit-error-rate (BER) at a 5 cm distance, using a lightweight multi-layer-perception (MLP) decoding algorithm. Finally, the system demonstrates continuous wireless neural local-field potential (LFP) recording in an in vitro setup., Comment: 12 pages, 29 figures

Quantum computing holds promise across various fields, particularly with the advent of Noisy Intermediate-Scale Quantum (NISQ) devices, which can outperform classical supercomputers in specific tasks. However, challenges such as noise and limited qubit capabilities hinder its practical applications. Variational Quantum Algorithms (VQAs) offer a viable strategy to achieve quantum advantage by combining quantum and classical computing. Leveraging on VQAs, the performance of Variational Quantum Classifiers (VQCs) is competitive with many classical classifiers. This work implements a VQC using a silicon-based quantum photonic microprocessor and a classical computer, demonstrating its effectiveness in nonlinear binary and multi-classification tasks. An efficient gradient free genetic algorithm is employed for training. The VQC's performance was evaluated on three synthetic binary classification tasks with square-, circular-, and sine-shape decision boundaries and a real-world multiclass Iris dataset. The accuracies on the three binary classification tasks were 87.5%, 92.5%, and 85.0%, respectively, and 98.8% on the real world Iris dataset, highlighting the platform's potential to handle complex data patterns.

Large language models (LLMs) have made significant strides at code generation through improved model design, training, and chain-of-thought. However, prompt-level optimizations remain an important yet under-explored aspect of LLMs for coding. This work focuses on the few-shot examples present in most code generation prompts, offering a systematic study on whether few-shot examples improve LLM's coding capabilities, which few-shot examples have the largest impact, and how to select impactful examples. Our work offers 2 approaches for selecting few-shot examples, a model-free method, CODEEXEMPLAR-FREE, and a model-based method, CODEEXEMPLAR-BASED. The 2 methods offer a trade-off between improved performance and reliance on training data and interpretability. Both methods significantly improve CodeLlama's coding ability across the popular HumanEval+ coding benchmark. In summary, our work provides valuable insights into how to pick few-shot examples in code generation prompts to improve LLM code generation capabilities.

Atmospheric studies are essential for elucidating the formation history, evolutionary processes, and atmospheric dynamics of exoplanets. High-resolution transmission spectroscopy offers the advantage of detecting subtle variations in stellar spectral profiles, thereby enabling the identification of the sources of observed signals. In this study, we present the transmission spectra of the exoplanet WASP-77Ab, a hot Jupiter with a 1.36-day orbital period around a G8 host star with $V=11.29$ mag. These observations were conducted using the high-resolution spectrograph ESPRESSO at the Very Large Telescope over three transit events. We analyze the Rossiter-McLaughlin effect for WASP-77A and determine a projected spin-orbit angle of ${\lambda = 16.131^{\circ}}^{+2.106}_{-2.324}$, indicating that the planet's orbit is nearly aligned. Following the generation of transmission spectra for the three nights, we model and correct for center-to-limb variation and the Rossiter-McLaughlin effects. In the residual transmission spectra, we detect H$\alpha$, H$\beta$ and CaII H with a significance exceeding 3.5$\sigma$. After applying 0.1-0.5 \r{A} masks to the cores of these lines to mitigate stellar contamination, all them still shows visible absorptions although not significant, suggesting at least partial planet contribution to them. Therefore, we are yet unable to confirm or reject the planetary origin of these spectral signals based on the current data set. Further investigation of WASP-77Ab's atmosphere, particularly in areas beyond the terminator region, is essential to illuminate the planet's two-dimensional atmospheric structure., Comment: Accepted for publication in MNRAS. 13 pages, 10 figures

Purpose: Our aim was to elucidate the critical factors responsible for inducing the FLASH effect, focusing on the role of free radicals through simulation and experimental approaches. Methods and Materials: The whole abdomen of C57BL/6 mice was irradiated with 6 MeV electron beam. The endpoint was acute intestinal toxicity quantified by histological score. Total doses ranging from 6 to 15 Gy were evaluated. The impact of the mean dose rate (MDR) was assessed in the range of 40 to 900 Gy/s. Dose per pulse (DPP) of 0.5 Gy and 3 Gy were compared. The recombination of peroxyl radicals were simulated. Further comparisons were conducted by incorporating the antioxidant amifostine. Results: When varying total doses with a constant MDR of 900 Gy/s, the FLASH effect was not observed until the dose reached 15 Gy. For a total dose of 15 Gy and varying MDR, the FLASH effect was observed only when MDR reached 100 Gy/s. For a dose of 15 Gy and an MDR of 150 Gy/s, no significant difference in biological effect was observed between low DPP and high DPP. The simulation results indicated that the fraction of peroxyl radicals recombination remained nearly zero at conventional dose rates. For FLASH irradiation, the recombination fraction increased linearly with the dose. Notably, the dose delivery time corresponding to 50% change in the recombination fraction was approximately 300 ms. The addition of amifostine effectively eliminated the difference between FLASH group and CONV group. Conclusions: The critical requirement for observing the sparing effect at the biological endpoint is the administration of an adequate dose within the time window of the radical reaction. Additionally, the important role of free radical was verified after introducing antioxidants, suggesting that the generation and recombination of free radicals are pivotal factors influencing the FLASH sparing effect., Comment: 15 pages, 4 figures, 1 table

In economic analysis, rational decision-makers often take actions to reduce their risk exposure. These actions include purchasing market insurance and implementing prevention measures to modify the shape of the loss distribution. Under the assumption that the insureds' actions are fully observed by the insurer, this paper investigates the interaction between self-protection and insurance demand when insurance premiums are determined by convex premium principles within the framework of distortion risk measures. Specifically, the insured selects an optimal proportional insurance share and prevention effort to minimize the risk measure of their end-of-period exposure. We explicitly characterize the optimal combination of prevention effort and insurance demand in a self-protection model when the insured adopts tail value-at-risk and strictly convex distortion risk measures, respectively. Additionally, we conduct comparative static analyses to illustrate our main findings under various premium structures, risk aversion levels, and loss distributions. Our results indicate that market insurance and self-protection are complementary, supporting classical insights from the literature regarding corner insurance policies (i.e., null and full insurance) in the absence of ex ante moral hazard. Finally, we consider the effects of moral hazard on the interaction between self-protection and insurance demand. Our findings show that ex ante moral hazard shifts the complementary effect into substitution effect.

The detection of prohibited items in X-ray security inspections is vital for ensuring public safety. However, the long-tail distribution of item categories, where certain prohibited items are far less common, poses a big challenge for detection models, as rare categories often lack sufficient training data. Existing methods struggle to classify these rare items accurately due to this imbalance. In this paper, we propose a Dual-level Boost Network (DBNet) specifically designed to overcome these challenges in X-ray security screening. Our approach introduces two key innovations: (1) a specific data augmentation strategy employing Poisson blending, inspired by the characteristics of X-ray images, to generate realistic synthetic instances of rare items which can effectively mitigate data imbalance; and (2) a context-aware feature enhancement module that captures the spatial and semantic interactions between objects and their surroundings, enhancing classification accuracy for underrepresented categories. Extensive experimental results demonstrate that DBNet improves detection performance for tail categories, outperforming sota methods in X-ray security inspection scenarios by a large margin 17.2%, thereby ensuring enhanced public safety., Comment: 10 pages, 4 figures

Motivated by recent LHCb measurements of CP violation in $\Lambda_b$ three-body decays, we conduct an analysis of CP asymmetry in three-body decays of bottom baryons utilizing U-spin symmetry. We first develop a convenient representation that facilitates the incorporation of U-spin symmetry into our analysis. By integrating weak and strong phases into the derived amplitude, we obtain the CP asymmetry and establish relationships between CP asymmetries in U-spin related decay channels. With the help of experimental measurements, we provide numerical predictions for the CP asymmetries for other decay channels, particularly $\Lambda_b \to \Sigma^0 K^+ K^-$, $\Xi^0_b \to \Lambda \pi^+ \pi^-$, $\Lambda_b \to \Sigma^0 K^+ \pi^-$, and $\Xi^0_b \to \Sigma K^- \pi^+$. Furthermore, we provide a quantity that can be used as a null test of standard model and deviations from 0 will reflect the possible new physics. These results are valuable for CPV measurements in baryon decays, and can be tested in future experiments., Comment: 8 pages 1 table

There is a growing necessity for edge training to adapt to dynamically changing environment. Neuromorphic computing represents a significant pathway for high-efficiency intelligent computation in energy-constrained edges, but existing neuromorphic architectures lack the ability of directly training spiking neural networks (SNNs) based on backpropagation. We develop a multi-core neuromorphic architecture with Feedforward-Propagation, Back-Propagation, and Weight-Gradient engines in each core, supporting high efficient parallel computing at both the engine and core levels. It combines various data flows and sparse computation optimization by fully leveraging the sparsity in SNN training, obtaining a high energy efficiency of 1.05TFLOPS/W@ FP16 @ 28nm, 55 ~ 85% reduction of DRAM access compared to A100 GPU in SNN trainings, and a 20-core deep SNN training and a 5-worker federated learning on FPGAs. Our study develops the first multi-core neuromorphic architecture supporting the direct SNN training, facilitating the neuromorphic computing in edge-learnable applications.

Objective: Proton spot-scanning arc therapy (ARC) is an emerging modality that can improve the high-dose conformity to targets compared with standard intensity-modulated proton therapy (IMPT). However, the efficient treatment delivery of ARC is challenging due to the required frequent energy changes during the continuous gantry rotation. This work proposes a novel method that delivers a multiple IMPT (multi-IMPT) plan that is equivalent to ARC in terms of biologically effective dose (BED). Approach: The proposed multi-IMPT method utilizes a different subset of limited number of beam angles in each fraction for dose delivery. Due to the different dose delivered to organs at risk (OAR) in each fraction, we optimize biologically effective dose (BED) for OAR and the physical dose delivered for target in each fraction. The BED-based multi-IMPT inverse optimization problem is solved via the iterative convex relaxation method and the alternating direction method of multipliers. The effectiveness of the proposed multi-IMPT method is evaluated in terms of dose objectives in comparison with ARC. Main results: Multi-IMPT provided similar plan quality with ARC. For example, multi-IMPT provided better OAR sparing and slightly better target dose coverage for the prostate case; similar dose distribution for the lung case; slightly worse dose coverage for the brain case; better dose coverage but slightly higher BED in OAR for the head-and-neck case. Significance: We have proposed a multi-IMPT approach to deliver ARC-equivalent plan quality. Keywords: biologically effective dose (BED), proton arc therapy, Comment: 24 pages, 4 figures

We investigate the statistical and computational limits of prompt tuning for transformer-based foundation models. Our key contributions are prompt tuning on \textit{single-head} transformers with only a \textit{single} self-attention layer: (i) is universal, and (ii) supports efficient (even almost-linear time) algorithms under the Strong Exponential Time Hypothesis (SETH). Statistically, we prove that prompt tuning on such simplest possible transformers are universal approximators for sequence-to-sequence Lipschitz functions. In addition, we provide an exponential-in-$dL$ and -in-$(1/\epsilon)$ lower bound on the required soft-prompt tokens for prompt tuning to memorize any dataset with 1-layer, 1-head transformers. Computationally, we identify a phase transition in the efficiency of prompt tuning, determined by the norm of the \textit{soft-prompt-induced} keys and queries, and provide an upper bound criterion. Beyond this criterion, no sub-quadratic (efficient) algorithm for prompt tuning exists under SETH. Within this criterion, we showcase our theory by proving the existence of almost-linear time prompt tuning inference algorithms. These fundamental limits provide important necessary conditions for designing expressive and efficient prompt tuning methods for practitioners.

In this paper, we study the stationary solutions of semilinear elliptic equation with singular nonlinearity $$ \Delta u=u^{-p}+f,\,\,u\geq 0\text{ in }\Omega\subset\mathbb{R}^n, $$ where $ n\geq 2 $, $ p>1 $, $ \Omega $ is a bounded domain, and $ f\in L^q(\Omega) $ with $ \frac{1}{2}+\frac{1}{2p}<\frac{q}{n} $. We establish a sharp estimate for the Minkowski content of the rupture set $ \{u=0\} $ and demonstrate that this set is $ (n-2) $-rectifiable. For this, we examine the stratification of the rupture set based on the symmetry properties of tangent functions, leading to the proof of $ k $-rectifiability for each $ k $-stratum. As a significant byproduct of our analysis, we improve the integrability of $ D^ju $ with $ j\in\mathbb{Z}_+ $ to the optimal Lorentz space $ L^{\frac{2(p+1)}{j(p+1)-2},\infty} $, under the assumption that $ D^{j-1}f $ is bounded. As an application of our results in the static case of the equation, for a class of suitable weak solutions to the three-dimensional evolutional problem $$ \partial_tu=\Delta u-u^{-p},\,\,u\geq 0\text{ in }(\Omega\subset\mathbb{R}^3)\times(0,T), $$ where $ p>3 $ and $ T>0 $, we show that $ \{u(\cdot,t)=0\} $ is $ 1 $-rectifiable for a.e. $ t\in(0,T) $., Comment: 80 pages, we fix some errors and typos in the original form

The development of 3D human avatars from multi-view videos represents a significant yet challenging task in the field. Recent advancements, including 3D Gaussian Splattings (3DGS), have markedly progressed this domain. Nonetheless, existing techniques necessitate the use of high-quality sharp images, which are often impractical to obtain in real-world settings due to variations in human motion speed and intensity. In this study, we attempt to explore deriving sharp intrinsic 3D human Gaussian avatars from blurry video footage in an end-to-end manner. Our approach encompasses a 3D-aware, physics-oriented model of blur formation attributable to human movement, coupled with a 3D human motion model to clarify ambiguities found in motion-induced blurry images. This methodology facilitates the concurrent learning of avatar model parameters and the refinement of sub-frame motion parameters from a coarse initialization. We have established benchmarks for this task through a synthetic dataset derived from existing multi-view captures, alongside a real-captured dataset acquired through a 360-degree synchronous hybrid-exposure camera system. Comprehensive evaluations demonstrate that our model surpasses existing baselines., Comment: Codes and Data: https://github.com/MyNiuuu/BAGA

Detailed studies of two-neutrino double electron capture (2$\nu$DEC) is a crucial step towards searching for the neutrino-less mode to explore the Majorana nature of neutrinos. We have measured precisely the half-life of the 2$\nu$DEC process in $^{124}$Xe, utilizing a total exposure of 1.73 tonne$\cdot$year from the commissioning run and the first science run of the PandaX-4T experiment. A time-dependent background model in the $\mathcal{O}$(10 keV) energy is constructed for the first time in PandaX-4T data. With an unbinned maximum likelihood fit, we determine the half-life of the 2$\nu$DEC process to be $(1.03\pm0.15_{\rm stat}\pm0.06_{\rm sys})\times 10^{22}$$\,$yr. Furthermore, we have evaluated the branching ratio for both electrons captured from the $K$ shell ($KK$) to be $(65\pm5)\%$, which aligns with the $^{124}$Xe nuclear model calculations within 1.5$\,$$\sigma$., Comment: 18 pages, 5 figures, 3 tables

We introduce the Lebesgue--H\"{o}lder--Dini and Lebesgue--H\"{o}lder spaces $L^p(\mathbb{R};{\mathcal C}_{\vartheta,\varsigma}^{\alpha,\rho}({\mathbb R}^n))$ ($\vartheta\in \{l,b\}, \, \varsigma\in \{d,s,c,w\}$, $p\in (1,+\infty]$ and $\alpha\in [0,1)$), and then use a vector-valued Calder\'{o}n--Zygmund theorem to establish the maximal Lebesgue--H\"{o}lder--Dini and Lebesgue--H\"{o}lder regularity for a class of parabolic equations. As an application, we obtain the unique strong solvability of the following stochastic differential equation \begin{eqnarray*} X_{s,t}(x)=x+\int\limits_s^tb(r,X_{s,r}(x))dr+W_t-W_{s}, \ \ t\in [s,T], \ x\in \mathbb{R}^n, \ s\in [0,T], \end{eqnarray*} for the low regularity growing drift in critical Lebesgue--H\"{o}lder--Dini spaces $L^p([0,T];{\mathcal C}^{\frac{2}{p}-1,\rho}_{l,d}({\mathbb R}^n;{\mathbb R}^n))$ ($p\in (1,2]$), where $\{W_t\}_{0\leq t\leq T}$ is a $n$-dimensional standard Wiener process. In particular, when $p=2$ we give a partially affirmative answer to a longstanding open problem, which was proposed by Krylov and R\"{o}ckner for $b\in L^2([0,T];L^\infty({\mathbb R}^n;{\mathbb R}^n))$ based upon their work ({\em Probab. Theory Relat. Fields 131(2): 154--196, 2005})., Comment: 45 pages

This paper shows a proof-of-concept that, given a typical 3-channel images but in a randomly permuted channel order, a model (termed as Chanel-Orderer) with ad-hoc inductive biases in terms of both architecture and loss functions can accurately predict the channel ordering and knows how to make it right. Specifically, Chanel-Orderer learns to score each of the three channels with the priors of object semantics and uses the resulting scores to predict the channel ordering. This brings up benefits into a typical scenario where an \texttt{RGB} image is often mis-displayed in the \texttt{BGR} format and needs to be corrected into the right order. Furthermore, as a byproduct, the resulting model Chanel-Orderer is able to tell whether a given image is a near-gray-scale image (near-monochromatic) or not (polychromatic). Our research suggests that Chanel-Orderer mimics human visual coloring of our physical natural world.

Miniature bioelectronic implants promise revolutionary therapies for cardiovascular and neurological disorders. Wireless power transfer (WPT) is a significant method for miniaturization, eliminating the need for bulky batteries in devices. Despite successful demonstrations of millimetric battery free implants in animal models, the robustness and efficiency of WPT are known to degrade significantly under misalignment incurred by body movements, respiration, heart beating, and limited control of implant orientation during surgery. This article presents an omnidirectional WPT platform for millimetric bioelectronic implants, employing the emerging magnetoelectric (ME) WPT modality, and magnetic field steering technique based on multiple transmitter (TX) coils. To accurately sense the weak coupling in a miniature implant and adaptively control the multicoil TX array in a closed loop, we develop an active echo (AE) scheme using a tiny coil on the implant. Our prototype comprises a fully integrated 14.2 mm3 implantable stimulator embedding a custom low power system on chip (SoC) powered by an ME film, a TX with a custom three channel AE RX chip, and a multicoil TX array with mutual inductance cancellation. The AE RX achieves negative 161 dBm per Hz input referred noise with 64 dB gain tuning range to reliably sense the AE signal, and offers fast polarity detection for driver control. AE simultaneously enhances the robustness, efficiency, and charging range of ME WPT. Under 90 degree rotation from the ideal position, our omnidirectional WPT system achieves 6.8x higher power transfer efficiency (PTE) than a single coil baseline. The tracking error of AE negligibly degrades the PTE by less than 2 percent from using ideal control., Comment: 13 pages, 27 figures

We calculate the leading-twist light-cone distribution amplitudes of the light $\Lambda$ baryon using lattice methods within the framework of large momentum effective theory. Our numerical computations are conducted employing $N_f=2+1$ stout smeared clover fermions and a Symanzik gauge action on a lattice with spacing $a=0.077\;\rm{fm}$, and a pion mass of 303 MeV. To approach the large momentum regime, we simulate the equal-time correlations with the hadron momentum $P^z = \{2.52, 3.02, 3.52\}$ GeV. By investigating the potential analytic characteristics of the baryon quasi-distribution amplitude in coordinate space, we validate these findings through our lattice calculations. After renormalization and extrapolation, we present results for the three-dimensional distribution of momentum fractions for the two light quarks. Based on these findings the paper briefly discusses the phenomenological impact on weak decays of $\Lambda_b$, and outlines potential systematic uncertainties that can be improved in the future. This work lays the theoretical foundation for accessing baryon LCDAs from lattice QCD.

Developing optimized restoration strategies for power distribution systems (PDSs) is essential to meet the pressing demand for enhanced resilience. Prior knowledge of customer interruption cost (CIC) and load restoration behaviors, particularly cold load pickup (CLPU), is crucial for guiding effective restoration; however, both are reciprocally affected by the realized customer interruption duration (CID), making them decision-dependent and challenging to model especially given the limited understanding of underlying physical mechanisms. This paper presents a novel approach by constructing tractable metamodels to capture the varying patterns of CIC and CLPU with CID - patterns which can be derived from limited data and reflect observed surface-level correlations rather than underlying mechanisms, thereby enabling practical surrogate modeling of these decision-dependencies. Specifically, quadratic functions are used to model the increasing rate of CIC with CID based on data fitting. Several defining characteristics of CLPU are extracted, each modeled in a piecewise linear form relative to CID, and the actual restored load accounting for CLPU is subsequently retrieved. Building on these metamodels, a PDS restoration optimization model is constructed, incorporating mobile energy storage systems (MESSs) and network reconfiguration. Case studies validate our approach and also highlight MESS's unique potential to accelerate CLPU-related restoration., Comment: 10 pages, 10 figures, submitted to IEEE Transactions on Smart Grid

Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the \textbf{AMG} method, a \textbf{M}ulti-\textbf{G}raph neural operator approach designed for efficiently solving PDEs on \textbf{A}rbitrary geometries. AMG leverages advanced graph-based techniques and dynamic attention mechanisms within a novel GraphFormer architecture, enabling precise management of diverse spatial domains and complex data interdependencies. By constructing multi-scale graphs to handle variable feature frequencies and a physics graph to encapsulate inherent physical properties, AMG significantly outperforms previous methods, which are typically limited to uniform grids. We present a comprehensive evaluation of AMG across six benchmarks, demonstrating its consistent superiority over existing state-of-the-art models. Our findings highlight the transformative potential of tailored graph neural operators in surmounting the challenges faced by conventional PDE solvers. Our code and datasets are available on \url{https://github.com/lizhihao2022/AMG}., Comment: Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.1 (KDD '25)

The small mass limit of the Langevin equation perturbed by $\beta$-stable L\'{e}vy noise is considered by rewriting it in the form of slow-fast system, and spliting the fast component into three parts. By exploring the three parts respectively, the limit equation and the convergence rate are derived.

Computing maximum/minimum distances between 3D meshes is crucial for various applications, i.e., robotics, CAD, VR/AR, etc. In this work, we introduce a highly parallel algorithm (gDist) optimized for Graphics Processing Units (GPUs), which is capable of computing the distance between two meshes with over 15 million triangles in less than 0.4 milliseconds (Fig. 1). By testing on benchmarks with varying characteristics, the algorithm achieves remarkable speedups over prior CPU-based and GPU-based algorithms on a commodity GPU (NVIDIA GeForce RTX 4090). Notably, the algorithm consistently maintains high-speed performance, even in challenging scenarios that pose difficulties for prior algorithms.

The size of deep learning models has been increasing to enhance model quality. The linear increase in training computation budget with model size means that training an extremely large-scale model is exceedingly time-consuming. Recently, the Mixture of Expert (MoE) has drawn significant attention as it can scale models to extra-large sizes with a stable computation budget. However, inefficient distributed training of large-scale MoE models hinders their broader application. Specifically, a considerable dynamic load imbalance occurs among devices during training, significantly reducing throughput. Several load-balancing works have been proposed to address the challenge. System-level solutions draw more attention for their hardware affinity and non-disruption of model convergence compared to algorithm-level ones. However, they are troubled by high communication costs and poor communication-computation overlapping. To address these challenges, we propose a systematic load-balancing method, Pro-Prophet, which consists of a planner and a scheduler for efficient parallel training of large-scale MoE models. To adapt to the dynamic load imbalance, we profile training statistics and use them to design Pro-Prophet. For lower communication volume, Pro-Prophet planner determines a series of lightweight load-balancing strategies and efficiently searches for a communication-efficient one for training based on the statistics. For sufficient overlapping of communication and computation, Pro-Prophet scheduler schedules the data-dependent operations based on the statistics and operation features, further improving the training throughput. Experimental results indicate that Pro-Prophet achieves up to 2.66x speedup compared to Deepspeed-MoE and FasterMoE. Additionally, Pro-Prophet achieves a load-balancing enhancement of up to 11.01x when compared to FasterMoE.

Multi-modal large language models (MLLMs) have achieved remarkable success in fine-grained visual understanding across a range of tasks. However, they often encounter significant challenges due to inadequate alignment for fine-grained knowledge, which restricts their ability to accurately capture local details and attain a comprehensive global perception. While recent advancements have focused on aligning object expressions with grounding information, they typically lack explicit integration of object images, which contain affluent information beyond mere texts or coordinates. To bridge this gap, we introduce a novel fine-grained visual knowledge alignment method that effectively aligns and integrates multi-scale knowledge of objects, including texts, coordinates, and images. This innovative method is underpinned by our multi-scale fine-grained enhancement data synthesis pipeline, which provides over 300K essential training data to enhance alignment and improve overall performance. Furthermore, we present TinyGroundingGPT, a series of compact models optimized for high-level alignments. With a scale of approximately 3B parameters, TinyGroundingGPT achieves outstanding results in grounding tasks while delivering performance comparable to larger MLLMs in complex visual scenarios.

Early fault detection and timely maintenance scheduling can significantly mitigate operational risks in NPPs and enhance the reliability of operator decision-making. Therefore, it is necessary to develop an efficient Prognostics and Health Management (PHM) multi-step prediction model for predicting of system health status and prompt execution of maintenance operations. In this study, we propose a novel predictive model that integrates reinforcement learning with Long Short-Term Memory (LSTM) neural networks and the Expert Fuzzy Evaluation Method. The model is validated using parameter data for 20 different breach sizes in the Main Steam Line Break (MSLB) accident condition of the CPR1000 pressurized water reactor simulation model and it demonstrates a remarkable capability in accurately forecasting NPP parameter changes up to 128 steps ahead (with a time interval of 10 seconds per step, i.e., 1280 seconds), thereby satisfying the temporal advance requirement for fault prognostics in NPPs. Furthermore, this method provides an effective reference solution for PHM applications such as anomaly detection and remaining useful life prediction.

This article focuses on the faults of important mechanical components such as pumps, valves, and pipelines in the reactor coolant system, main steam system, condensate system, and main feedwater system of nuclear power plants (NPPs). It proposes a composite multi-fault diagnosis model based on Bayesian algorithm and EfficientNet large model using data-driven deep learning fault diagnosis technology. The aim is to evaluate the effectiveness of automatic deep learning-based large model technology through transfer learning in nuclear power plant scenarios.

The heavy meson light-cone distribution amplitude (LCDA), as defined in full QCD, plays a key role in the collinear factorization for exclusive heavy meson production and in lattice computations of the LCDA within heavy-quark effective theory (HQET). In addition to its dependence on the renormalization scale, the QCD LCDA also evolves with the heavy quark mass. We derive a partial differential equation to characterize the mass evolution of the heavy meson QCD LCDA, examining the heavy quark mass dependence through its solution. Our results link the internal structure of heavy mesons across different quark masses, offering significant implications for lattice calculations and enabling the extrapolation of results from lower to higher quark masses., Comment: 6 pages, 2 figures

The Psycho Frame, a sophisticated system primarily used in Universal Century (U.C.) series mobile suits for NEWTYPE pilots, has evolved as an integral component in harnessing the latent potential of mental energy. Its ability to amplify and resonate with the pilot's psyche enables real-time mental control, creating unique applications such as psychomagnetic fields and sensory-based weaponry. This paper presents the development of a novel robotic control system inspired by the Psycho Frame, combining electroencephalography (EEG) and deep learning for real-time control of robotic systems. By capturing and interpreting brainwave data through EEG, the system extends human cognitive commands to robotic actions, reflecting the seamless synchronization of thought and machine, much like the Psyco Frame's integration with a Newtype pilot's mental faculties. This research demonstrates how modern AI techniques can expand the limits of human-machine interaction, potentially transcending traditional input methods and enabling a deeper, more intuitive control of complex robotic systems.

In recent years, infrastructure-based localization methods have achieved significant progress thanks to their reliable and drift-free localization capability. However, the pre-installed infrastructures suffer from inflexibilities and high maintenance costs. This poses an interesting problem of how to develop a drift-free localization system without using the pre-installed infrastructures. In this paper, an infrastructure-free and drift-free localization system is proposed using the ambient magnetic field (MF) information, namely IDF-MFL. IDF-MFL is infrastructure-free thanks to the high distinctiveness of the ambient MF information produced by inherent ferromagnetic objects in the environment, such as steel and reinforced concrete structures of buildings, and underground pipelines. The MF-based localization problem is defined as a stochastic optimization problem with the consideration of the non-Gaussian heavy-tailed noise introduced by MF measurement outliers (caused by dynamic ferromagnetic objects), and an outlier-robust state estimation algorithm is derived to find the optimal distribution of robot state that makes the expectation of MF matching cost achieves its lower bound. The proposed method is evaluated in multiple scenarios, including experiments on high-fidelity simulation, and real-world environments. The results demonstrate that the proposed method can achieve high-accuracy, reliable, and real-time localization without any pre-installed infrastructures.

Approximate K nearest neighbor (AKNN) search in high-dimensional Euclidean space is a fundamental problem with widespread applications. Vector quantization which maps vectors to discrete quantized code, can significantly reduce the space cost of AKNN search while also accelerating the AKNN search speed. The exclusive use of vector quantization without precise vectors leads to a substantial decline in search accuracy. Recent research RaBitQ addresses this issue by using geometry relation to enhance quantization accuracy and employing error bound for distance correction with precise vector. However, this method requires that the quantization bit must be equal to the vector dimension resulting in a fixed compression ratio which limits its efficiency and flexibility. In this paper, we propose a new and efficient method MRQ to address this drawback. MRQ leverage leverages data distribution to achieve better distance correction and a higher vector compression ratio. MRQ reduces query latency using a highly efficient distance computation and correction scheme. Our results demonstrate that MRQ significantly outperforms state-of-the-art AKNN search methods based on graph or vector quantization, achieving up to a 3x efficiency speed-up with only 1/3 length of quantized code while maintaining the same accuracy., Comment: 8 pages, reload the origin version

This article studies the problem of distributed formation control for multiple robots by using onboard ultra wide band (UWB) ranging and inertial odometer (IO) measurements. Although this problem has been widely studied, a fundamental limitation of most works is that they require each robot's pose and sensor measurements are expressed in a common reference frame. However, it is inapplicable for nonholonomic robot formations due to the practical difficulty of aligning IO measurements of individual robot in a common frame. To address this problem, firstly, a concurrent-learning based estimator is firstly proposed to achieve relative localization between neighboring robots in a local frame. Different from most relative localization methods in a global frame, both relative position and orientation in a local frame are estimated with only UWB ranging and IO measurements. Secondly, to deal with information loss caused by directed communication topology, a cooperative localization algorithm is introduced to estimate the relative pose to the leader robot. Thirdly, based on the theoretical results on relative pose estimation, a distributed formation tracking controller is proposed for nonholonomic robots. Both gazebo physical simulation and real-world experiments conducted on networked TurtleBot3 nonholonomic robots are provided to demonstrate the effectiveness of the proposed method., Comment: 11 pages, 12 figures

Differential privacy (DP) is a formal notion that restricts the privacy leakage of an algorithm when running on sensitive data, in which privacy-utility trade-off is one of the central problems in private data analysis. In this work, we investigate the fundamental limits of differential privacy in online learning algorithms and present evidence that separates three types of constraints: no DP, pure DP, and approximate DP. We first describe a hypothesis class that is online learnable under approximate DP but not online learnable under pure DP under the adaptive adversarial setting. This indicates that approximate DP must be adopted when dealing with adaptive adversaries. We then prove that any private online learner must make an infinite number of mistakes for almost all hypothesis classes. This essentially generalizes previous results and shows a strong separation between private and non-private settings since a finite mistake bound is always attainable (as long as the class is online learnable) when there is no privacy requirement.

We propose a Continuous-Time Quantum Walks (CTQW) model for one-dimensional Dirac dynamics simulation with higher-order approximation. Our model bridges CTQW with a discrete-time model called Dirac Cellular Automata (DCA) via Quantum Fourier Transformation (QFT). From our continuous-time model, we demonstrate how varying time intervals and position space sizes affect both quantum entanglement between the internal space and external (position) space of the quantum state and the relativistic effect called Zitterbewegung. We find that the time interval changes the transition range for each site, and the position space sizes affect the value of transition amplitude. Therefore, it shows that the size of spacetime plays a crucial role in the observed quantum entanglement and relativistic phenomena in quantum computers. These results enhance the understanding of the interplay between internal and external spaces in Dirac dynamics through the insights of quantum information theory and enrich the application of the quantum walks-based algorithm.

It is largely agreed that social network links are formed due to either homophily or social influence. Inspired by this, we aim at understanding the generation of links via providing a novel embedding-based graph formation model. Different from existing graph representation learning, where link generation probabilities are defined as a simple function of the corresponding node embeddings, we model the link generation as a mixture model of the two factors. In addition, we model the homophily factor in spherical space and the influence factor in hyperbolic space to accommodate the fact that (1) homophily results in cycles and (2) influence results in hierarchies in networks. We also design a special projection to align these two spaces. We call this model Non-Euclidean Mixture Model, i.e., NMM. We further integrate NMM with our non-Euclidean graph variational autoencoder (VAE) framework, NMM-GNN. NMM-GNN learns embeddings through a unified framework which uses non-Euclidean GNN encoders, non-Euclidean Gaussian priors, a non-Euclidean decoder, and a novel space unification loss component to unify distinct non-Euclidean geometric spaces. Experiments on public datasets show NMM-GNN significantly outperforms state-of-the-art baselines on social network generation and classification tasks, demonstrating its ability to better explain how the social network is formed.

Research on long non-coding RNAs (lncRNAs) has garnered significant attention due to their critical roles in gene regulation and disease mechanisms. However, the complexity and diversity of lncRNA sequences, along with the limited knowledge of their functional mechanisms and the regulation of their expressions, pose significant challenges to lncRNA studies. Given the tremendous success of large language models (LLMs) in capturing complex dependencies in sequential data, this study aims to systematically explore the potential and limitations of LLMs in the sequence analysis related to the transcriptional regulation of lncRNA genes. Our extensive experiments demonstrated promising performance of fine-tuned genome foundation models on progressively complex tasks. Furthermore, we conducted an insightful analysis of the critical impact of task complexity, model selection, data quality, and biological interpretability for the studies of the regulation of lncRNA gene expression.

Serverless computing has gained significant traction for machine learning inference applications, which are often deployed as serverless workflows consisting of multiple CPU and GPU functions with data dependency. However, existing data-passing solutions for serverless computing primarily reply on host memory for fast data transfer, mandating substantial data movement and resulting in salient I/O overhead. In this paper, we present FaaSTube, a GPU-efficient data passing system for serverless inference. FaaSTube manages intermediate data within a GPU memory pool to facilitate direct data exchange between GPU functions. It enables fine-grained bandwidth sharing over PCIe and NVLink, minimizing data-passing latency for both host-to-GPU and GPU-to-GPU while providing performance isolation between functions. Additionally, FaaSTube implements an elastic GPU memory pool that dynamically scales to accommodate varying data-passing demands. Evaluations on real-world applications show that FaaSTube reduces end-to-end latency by up to 90\% and achieves up to 12x higher throughput compared to the state-of-the-art.

Molecular dynamics simulations are crucial for understanding complex physical, chemical, and biological processes at the atomic level. However, accurately capturing interactions across multiple spatial and temporal scales remains a significant challenge. We present a novel framework that jointly models spatial and temporal multiscale interactions in molecular dynamics. Our approach leverages Graph Fourier Transforms to decompose molecular structures into different spatial scales and employs Neural Ordinary Differential Equations to model the temporal dynamics in a curated manner influenced by the spatial modes. This unified framework links spatial structures with temporal evolution in a flexible manner, enabling more accurate and comprehensive simulations of molecular systems. We evaluate our model on the MD17 dataset, demonstrating consistent performance improvements over state-of-the-art baselines across multiple molecules, particularly under challenging conditions such as irregular timestep sampling and long-term prediction horizons. Ablation studies confirm the significant contributions of both spatial and temporal multiscale modeling components. Our method advances the simulation of complex molecular systems, potentially accelerating research in computational chemistry, drug discovery, and materials science.

An invariant for cospectral graphs is a property shared by all cospectral graphs. In this paper, we present three new invariants for cospectral graphs, characterized by their arithmetic nature and apparent novelty. Specifically, let $G$ and $H$ be two graphs with adjacency matrices $A(G)$ and $A(H)$, respectively. We show, among other results, that if $G$ and $H$ are cospectral, then $e^{\rm T}A(G)^me\equiv e^{\rm T}A(H)^m e~({\rm mod}~4)$ for any integer $m\geq 0$, where $e$ is the all-one vector. As a simple consequence, we demonstrate that under certain conditions, every graph cospectral with $G$ is determined by its generalized spectrum., Comment: 13 pages, 1 figure