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We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through mutually stimulating marked Hawkes processes. The model assumes a limit order book framework, accounting for both permanent price impact and transient market impact. Importantly, we incorporate liquidity as a hidden Markov process, influencing the intensities of the point processes governing bid and ask prices. Within this setting, we formulate the optimal liquidation problem as an impulse control problem. We elucidate the dynamics of the hidden Markov chain's filter and determine the related normalized filtering equations. We then express the value function as the limit of a sequence of auxiliary continuous functions, defined recursively. This characterization enables the use of a dynamic programming principle for optimal stopping problems and the determination of an optimal strategy. It also facilitates the development of an implementable algorithm to approximate the original liquidation problem. We enrich our analysis with numerical results and visualizations of candidate optimal strategies., Comment: 36 pages

In the context of modern life, particularly in Industry 4.0 within the online space, emotions and moods are frequently conveyed through social media posts. The trend of sharing stories, thoughts, and feelings on these platforms generates a vast and promising data source for Big Data. This creates both a challenge and an opportunity for research in applying technology to develop more automated and accurate methods for detecting stress in social media users. In this study, we developed a real-time system for stress detection in online posts, using the "Dreaddit: A Reddit Dataset for Stress Analysis in Social Media," which comprises 187,444 posts across five different Reddit domains. Each domain contains texts with both stressful and non-stressful content, showcasing various expressions of stress. A labeled dataset of 3,553 lines was created for training. Apache Kafka, PySpark, and AirFlow were utilized to build and deploy the model. Logistic Regression yielded the best results for new streaming data, achieving 69,39% for measuring accuracy and 68,97 for measuring F1-scores., Comment: 6 pages, 4 figures

Precoding is a critical and long-standing technique in multi-user communication systems. However, the majority of existing precoding methods do not consider channel coding in their designs. In this paper, we consider the precoding problem in multi-user multiple-input single-output (MISO) systems, incorporating channel coding into the design. By leveraging the error-correcting capability of channel codes we increase the degrees of freedom in the transmit signal design, thereby enhancing the overall system performance. We first propose a novel data-dependent precoding framework for coded MISO systems, referred to as channel-coded precoding (CCP), which maximizes the probability that information bits can be correctly recovered by the channel decoder. This proposed CCP framework allows the transmit signals to produce data symbol errors at the users' receivers, as long as the overall information BER performance can be improved. We develop the CCP framework for both one-bit and multi-bit error-correcting capacity and devise a projected gradient-based approach to solve the design problem. We also develop a robust CCP framework for the case where knowledge of perfect channel state information (CSI) is unavailable at the transmitter, taking into account the effect of both noise and channel estimation errors. Finally, we conduct numerous simulations to verify the effectiveness of the proposed CCP and its superiority compared to existing precoding methods, and we identify situations where the proposed CCP yields the most significant gains., Comment: 13 pages, 11 figures

For structural health monitoring, continuous and automatic crack detection has been a challenging problem. This study is conducted to propose a framework of automatic crack segmentation from high-resolution images containing crack information about steel box girders of bridges. Considering the multi-scale feature of cracks, convolutional neural network architecture of Feature Pyramid Networks (FPN) for crack detection is proposed. As for input, 120 raw images are processed via two approaches (shrinking the size of images and splitting images into sub-images). Then, models with the proposed structure of FPN for crack detection are developed. The result shows all developed models can automatically detect the cracks at the raw images. By shrinking the images, the computation efficiency is improved without decreasing accuracy. Because of the separable characteristic of crack, models using the splitting method provide more accurate crack segmentations than models using the resizing method. Therefore, for high-resolution images, the FPN structure coupled with the splitting method is an promising solution for the crack segmentation and detection., Comment: 15 pages, 11 figures

Current autonomous building research primarily focuses on energy efficiency and automation. While traditional artificial intelligence has advanced autonomous building research, it often relies on predefined rules and struggles to adapt to complex, evolving building operations. Moreover, the centralized organizational structures of facilities management hinder transparency in decision-making, limiting true building autonomy. Research on decentralized governance and adaptive building infrastructure, which could overcome these challenges, remains relatively unexplored. This paper addresses these limitations by introducing a novel Decentralized Autonomous Building Cyber-Physical System framework that integrates Decentralized Autonomous Organizations, Large Language Models, and digital twins to create a smart, self-managed, operational, and financially autonomous building infrastructure. This study develops a full-stack decentralized application to facilitate decentralized governance of building infrastructure. An LLM-based artificial intelligence assistant is developed to provide intuitive human-building interaction for blockchain and building operation management-related tasks and enable autonomous building operation. Six real-world scenarios were tested to evaluate the autonomous building system's workability, including building revenue and expense management, AI-assisted facility control, and autonomous adjustment of building systems. Results indicate that the prototype successfully executes these operations, confirming the framework's suitability for developing building infrastructure with decentralized governance and autonomous operation., Comment: 40 pages, 22 figures

This paper presents a novel approach to designing a Hedge Algebra Controller named Hedge Algebra Controller with Recursive Semantic Values (RS-HAC). This approach incorporates several newly introduced concepts, including Semantically Quantifying Simplified Mapping (SQSM) featuring a recursive algorithm, Infinite General Semantization (IGS), and Infinite General De-semantization (IGDS). These innovations aim to enhance the optimizability, scalability, and flexibility of hedge algebra theory, allowing the design of a hedge algebra-based controller to be carried out more efficiently and straightforward. An application of stabilizing an inverted pendulum on a cart is conducted to illustrate the superiority of the proposed approach. Comparisons are made between RS-HAC and a fuzzy controller of Takagi-Sugeno type (FC), as well as a linear quadratic regulator (LQR). The results indicate that the RS-HAC surpasses the FC by up to 400\% in control efficiency and is marginally better than the LQR regarding transient time in balancing an inverted pendulum on a cart.

Humanoid robotics faces significant challenges in achieving stable locomotion and recovering from falls in dynamic environments. Traditional methods, such as Model Predictive Control (MPC) and Key Frame Based (KFB) routines, either require extensive fine-tuning or lack real-time adaptability. This paper introduces FRASA, a Deep Reinforcement Learning (DRL) agent that integrates fall recovery and stand up strategies into a unified framework. Leveraging the Cross-Q algorithm, FRASA significantly reduces training time and offers a versatile recovery strategy that adapts to unpredictable disturbances. Comparative tests on Sigmaban humanoid robots demonstrate FRASA superior performance against the KFB method deployed in the RoboCup 2023 by the Rhoban Team, world champion of the KidSize League.

Accurate physical simulation is crucial for the development and validation of control algorithms in robotic systems. Recent works in Reinforcement Learning (RL) take notably advantage of extensive simulations to produce efficient robot control. State-of-the-art servo actuator models generally fail at capturing the complex friction dynamics of these systems. This limits the transferability of simulated behaviors to real-world applications. In this work, we present extended friction models that allow to more accurately simulate servo actuator dynamics. We propose a comprehensive analysis of various friction models, present a method for identifying model parameters using recorded trajectories from a pendulum test bench, and demonstrate how these models can be integrated into physics engines. The proposed friction models are validated on four distinct servo actuators and tested on 2R manipulators, showing significant improvements in accuracy over the standard Coulomb-Viscous model. Our results highlight the importance of considering advanced friction effects in the simulation of servo actuators to enhance the realism and reliability of robotic simulations.

Grasping a variety of objects remains a key challenge in the development of versatile robotic systems. The human hand is remarkably dexterous, capable of grasping and manipulating objects with diverse shapes, mechanical properties, and textures. Inspired by how humans use two fingers to pick up thin and large objects such as fabric or sheets of paper, we aim to develop a gripper optimized for grasping such deformable objects. Observing how the soft and flexible fingertip joints of the hand approach and grasp thin materials, a hybrid gripper design that incorporates both soft and rigid components was proposed. The gripper utilizes a soft pneumatic ring wrapped around a rigid revolute joint to create a flexible two-fingered gripper. Experiments were conducted to characterize and evaluate the gripper performance in handling sheets of paper and other objects. Compared to rigid grippers, the proposed design improves grasping efficiency and reduces the gripping distance by up to eightfold.

We calculate the melting line of atomic hydrogen and deuterium up to 900 GPa with path-integral Monte Carlo using a machine-learned interatomic potential. We improve upon previous simulations of melting by treating the electrons with reptation quantum Monte Carlo, and by performing solid and liquid simulations using isothermal-isobaric path-integral Monte Carlo. The resulting melting line for atomic hydrogen is higher than previous estimates. There is a small but resolvable decrease in the melting temperature as pressure is increased, which can be attributed to quantum effects.

The democratization of fabrication equipment has spurred recent interest in maskless grayscale lithography for both 2D and 3D microfabrication. However, the design of suitable template images remains a challenge. This work presents a simplified method for encoding 3D objects into grayscale image files optimized for grayscale lithography. Leveraging the widely used, open-source 3D modeling software Blender, we developed a robust approach to convert geometric heights into grayscale levels and generate image files through top-view rendering. Our method accurately reproduced the overall shape of simple structures like stairs and ramps compared to the original designs. We extended this approach to complex 3D sinusoidal surfaces, achieving similar results. Given the increasing accessibility and user-friendliness of digital rendering tools, this study offers a promising strategy for rapid prototyping of initial designs with minimal effort., Comment: 12 pages, 6 figures

We introduce a lightweight LLM-based framework designed to enhance the autonomy and robustness of domestic robots, targeting onboard embodied intelligence. By addressing challenges such as kinematic constraints and dynamic environments, our approach reduces reliance on large-scale data and incorporates a robot-agnostic pipeline. Our framework, InteLiPlan, ensures that the LLM model's decision-making capabilities are effectively aligned with robotic functions, enhancing operational robustness and adaptability, while our human-in-the-loop mechanism allows for real-time human intervention in the case where the system fails. We evaluate our method in both simulation and on the real Toyota HSR robot. The results show that our method achieves a 93% success rate in the fetch me task completion with system failure recovery, outperforming the baseline method in a domestic environment. InteLiPlan achieves comparable performance to the state-of-the-art large-scale LLM-based robotics planner, while guaranteeing real-time onboard computing with embodied intelligence.

In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead typically associated with error correction motivates the search for more hardware-efficient approaches. Here, using a microfabricated superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance $d=5$. The bosonic cat qubits are passively protected against bit flips using a stabilizing circuit. Cat-qubit phase-flip errors are corrected by the repetition code which uses ancilla transmons for syndrome measurement. We realize a noise-biased CX gate which ensures bit-flip error suppression is maintained during error correction. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold, with logical phase-flip error decreasing with code distance from $d=3$ to $d=5$. Concurrently, the logical bit-flip error is suppressed with increasing cat-qubit mean photon number. The minimum measured logical error per cycle is on average $1.75(2)\%$ for the distance-3 code sections, and $1.65(3)\%$ for the longer distance-5 code, demonstrating the effectiveness of bit-flip error suppression throughout the error correction cycle. These results, where the intrinsic error suppression of the bosonic encodings allows us to use a hardware-efficient outer error correcting code, indicate that concatenated bosonic codes are a compelling paradigm for reaching fault-tolerant quantum computation., Comment: Comments on the manuscript welcome!

This paper focuses on precoding design in multi-antenna systems with improper Gaussian interference (IGI), characterized by correlated real and imaginary parts. We first study block level precoding (BLP) and symbol level precoding (SLP) assuming the receivers apply a pre-whitening filter to decorrelate and normalize the IGI. We then shift to the scenario where the base station (BS) incorporates the IGI statistics in the SLP design, which allows the receivers to employ a standard detection algorithm without pre-whitenting. Finally we address the case where the channel and statistics of the IGI are unknown, and we formulate robust BLP and SLP designs that minimize the worst case performance in such settings. Interestingly, we show that for BLP, the worst-case IGI is in fact proper, while for SLP the worst case occurs when the interference signal is maximally improper, with fully correlated real and imaginary parts. Numerical results reveal the superior performance of SLP in terms of symbol error rate (SER) and energy efficiency (EE), especially for the case where there is uncertainty in the non-circularity of the jammer., Comment: 13 pages, 12 figures

The electrical characteristics of a carbon nanotube can be significantly modified by applying elastic strain. This study focuses on exploring this phenomenon in a single-walled carbon nanotube (SWNT) using tight-binding transport calculations. The results indicate that, under specific strains, an armchair SWNT can act as a filter, separating the two valley electrons K and Kp. Notably, when subjected to deformation, the SWNT exhibits intriguing behaviors, including a quantized conductance profile that varies with the strength of the strain. Consequently, precise control of the width of the quantized plateaus allows for the generation of a polarized valley current. Furthermore, when both K-types are conducted, the strain is demonstrated to completely separate them, directing each K-type through a distinct pathway.

Multi-damage is common in reinforced concrete structures and leads to the requirement of large number of neural networks, parameters and data storage, if convolutional neural network (CNN) is used for damage recognition. In addition, conventional CNN experiences catastrophic forgetting and training inefficiency as the number of tasks increases during continual learning, leading to large accuracy decrease of previous learned tasks. To address these problems, this study proposes a continuallearning-based damage recognition model (CLDRM) which integrates the learning without forgetting continual learning method into the ResNet-34 architecture for the recognition of damages in RC structures as well as relevant structural components. Three experiments for four recognition tasks were designed to validate the feasibility and effectiveness of the CLDRM framework. In this way, it reduces both the prediction time and data storage by about 75% in four tasks of continuous learning. Three experiments for four recognition tasks were designed to validate the feasibility and effectiveness of the CLDRM framework. By gradual feature fusion, CLDRM outperformed other methods by managed to achieve high accuracy in the damage recognition and classification. As the number of recognition tasks increased, CLDRM also experienced smaller decrease of the previous learned tasks. Results indicate that the CLDRM framework successfully performs damage recognition and classification with reasonable accuracy and effectiveness., Comment: 18 pages, 12 figures

Non-orthogonal multiple access (NOMA) is a promising technology for next-generation wireless communication systems due to its enhanced spectral efficiency. In this paper, we consider an uplink NOMA system operating together with a high-dimensional absorptive reconfigurable intelligent surface (A-RIS). We aim to minimize the total power transmitted by the users in order to meet signal-to-interference-plus-noise constraints at the base station in the presence of a jammer. We propose an iterative algorithm to solve the high-dimensional non-convex optimization problem using linear programming to find the transmit powers and a fractional programming algorithm based on the Dinkelbach algorithm with a sequential convex relaxation procedure to optimize the reflection coefficients. We show that our algorithm converges on large optimization problems, with a jammer comprising as many as $64$ antennas, and an A-RIS with $128$ elements. Our numerical results show that, compared with a standard RIS that reflects all impinging energy, the A-RIS can dramatically reduce the users' required transmit power and successfully mitigate interference from the jammer. The absorption capability of the A-RIS is in particular useful in cases when the number of jammer antennas is of the same order as the number of A-RIS elements.

We consider the class of stationary-increment harmonizable stable processes with infinite control measure, which most notably includes real harmonizable fractional stable motions. We give conditions for the integrability of the paths of such processes with respect to a finite, absolutely continuous measure and derive the distributional characteristics of the path integral with respect to said measure. The convolution of the path of a stationary-increment harmonizable stable process with a suitable measure yields a real stationary harmonizable stable process with finite control measure. This allows us to construct consistent estimators for the index of stability as well as the kernel function in the integral representation of a stationary increment harmonizable stable process (up to a constant factor). For real harmonizable fractional stable motions consistent estimators for the index of stability and its Hurst parameter are given. These are computed directly from the periodogram frequency estimates of the smoothed process.

In this article, we continue our analysis for a novel recursive modification to the Max $k$-Cut algorithm using semidefinite programming as its basis, offering an improved performance in vectorized data clustering tasks. Using a dimension relaxation method, we use a recursion method to enhance density of clustering results. Our methods provide advantages in both computational efficiency and clustering accuracy for grouping datasets into three clusters, substantiated through comprehensive experiments., Comment: IEEE CSCE Conference from July 22 to July 25, 2024

In this article, we introduce a novel recursive modification to the classical Goemans-Williamson MaxCut algorithm, offering improved performance in vectorized data clustering tasks. Focusing on the clustering of medical publications, we employ recursive iterations in conjunction with a dimension relaxation method to significantly enhance density of clustering results. Furthermore, we propose a unique vectorization technique for articles, leveraging conditional probabilities for more effective clustering. Our methods provide advantages in both computational efficiency and clustering accuracy, substantiated through comprehensive experiments., Comment: Published in the IEEE Conference, CSCI 2023 (Winter Session)

Many modern applications that deal with sensitive data, such as healthcare and government services, outsource computation to cloud platforms. In such untrusted environments, privacy is of vital importance. One solution to this problem is homomorphic encryption (HE), a family of cryptographic schemes that support certain algebraic operations on encrypted data without the need for decryption. However, despite major advancements, encryption in modern HE schemes still comes with a non-trivial computational overhead that can hamper data-intensive workloads. To resolve this, recent research has shown that leveraging caching techniques, such as Rache, can significantly enhance the performance of HE schemes while maintaining security. Rache unfortunately displays a key limitation in the time complexity of its caching procedure, which scales with the size of the plaintext space. Smuche is another caching scheme that simultaneously improves the scalability of the caching procedure and turns the encryption process into a constant-time operation, utilizing only a single scalar multiplication. Even still, more can be done. In this paper, we present an encryption method we call ``Zinc" which entirely forgoes the multiple caching process, replacing it with a single scalar addition, and then injecting randomness that takes constant time with respect to the plaintext space. This injection of randomness is similar to Smuche, and a great improvement from Rache, allowing Zinc to achieve efficiency without compromising security. We implement the scheme using Microsoft SEAL and compare its performance to vanilla CKKS.

Interdisciplinary collaboration is crucial for addressing complex scientific challenges. Recent advancements in large language models (LLMs) have shown significant potential in benefiting researchers across various fields. To explore the application of LLMs in scientific disciplines and their implications for interdisciplinary collaboration, we collect and analyze 50,391 papers from OpenAlex, an open-source platform for scholarly metadata. We first employ Shannon entropy to assess the diversity of collaboration in terms of authors' institutions and departments. Our results reveal that most fields have exhibited varying degrees of increased entropy following the release of ChatGPT, with Computer Science displaying a consistent increase. Other fields such as Social Science, Decision Science, Psychology, Engineering, Health Professions, and Business, Management & Accounting have shown minor to significant increases in entropy in 2024 compared to 2023. Statistical testing further indicates that the entropy in Computer Science, Decision Science, and Engineering is significantly lower than that in health-related fields like Medicine and Biochemistry, Genetics & Molecular Biology. In addition, our network analysis based on authors' affiliation information highlights the prominence of Computer Science, Medicine, and other Computer Science-related departments in LLM research. Regarding authors' institutions, our analysis reveals that entities such as Stanford University, Harvard University, University College London, and Google are key players, either dominating centrality measures or playing crucial roles in connecting research networks. Overall, this study provides valuable insights into the current landscape and evolving dynamics of collaboration networks in LLM research.

Migraine, a prevalent neurological disorder, has been associated with various ocular manifestations suggestive of neuronal and microvascular deficits. However, there is limited understanding of the extent to which retinal imaging may discriminate between individuals with migraines versus without migraines. In this study, we apply convolutional neural networks to color fundus photography (CFP) and optical coherence tomography (OCT) data to investigate differences in the retina that may not be apparent through traditional human-based interpretations of retinal imaging. Retrospective data of CFP type 1 [posterior pole] and type 2 [optic nerve head (ONH)] from 369 and 336 participants respectively were analyzed. All participants had bilaterally normal optic nerves and maculae, with no retinal-involving diseases. CFP images were concatenated with OCT default ONH measurements, then inputted through three convolutional neural networks - VGG-16, ResNet-50, and Inceptionv3. The primary outcome was performance of discriminating between with migraines versus without migraines, using retinal microvascular and neuronal imaging characteristics. Using CFP type 1 data, discrimination (AUC [95% CI]) was high (0.84 [0.8, 0.88] to 0.87 [0.84, 0.91]) and not significantly different between VGG-16, ResNet-50, and Inceptionv3. Using CFP type 2 [ONH] data, discrimination was reduced and ranged from poor to fair (0.69 [0.62, 0.77] to 0.74 [0.67, 0.81]). OCT default ONH measurements overall did not significantly contribute to model performance. Class activation maps (CAMs) highlighted that the paravascular arcades were regions of interest. The findings suggest that individuals with migraines demonstrate microvascular differences more so than neuronal differences in comparison to individuals without migraines.

Due to increased reliance on private vehicles and growing travel demand, parking remains a longstanding urban challenge globally. Quantifying parking perceptions is paramount as it enables decision-makers to identify problematic areas and make informed decisions on parking management. This study introduces a cost-effective and widely accessible data source, crowdsourced online reviews, to investigate public perceptions of parking across the U.S. Specifically, we examine 4,987,483 parking-related reviews for 1,129,460 points of interest (POIs) across 911 core-based statistical areas (CBSAs) sourced from Google Maps. We employ the Bidirectional Encoder Representations from Transformers (BERT) model to classify the parking sentiment and conduct regression analyses to explore its relationships with socio-spatial factors. Findings reveal significant variations in parking sentiment across POI types and CBSAs, with Restaurant POIs showing the most negative. Regression results further indicate that denser urban areas with higher proportions of African Americans and Hispanics and lower socioeconomic status are more likely to exhibit negative parking sentiment. Interestingly, an opposite relationship between parking supply and sentiment is observed, indicating increasing supply does not necessarily improve parking experiences. Finally, our textual analysis identifies keywords associated with positive or negative sentiments and highlights disparities between urban and rural areas. Overall, this study demonstrates the potential of a novel data source and methodological framework in measuring parking sentiment, offering valuable insights that help identify hyperlocal parking issues and guide targeted parking management strategies.

Across the life sciences, an ongoing effort over the last 50 years has made data and methods more reproducible and transparent. This openness has led to transformative insights and vastly accelerated scientific progress. For example, structural biology and genomics have undertaken systematic collection and publication of protein sequences and structures over the past half-century, and these data have led to scientific breakthroughs that were unthinkable when data collection first began. We believe that neuroscience is poised to follow the same path, and that principles of open data and open science will transform our understanding of the nervous system in ways that are impossible to predict at the moment. To this end, new social structures along with active and open scientific communities are essential to facilitate and expand the still limited adoption of open science practices in our field. Unified by shared values of openness, we set out to organize a symposium for Open Data in Neuroscience (ODIN) to strengthen our community and facilitate transformative neuroscience research at large. In this report, we share what we learned during this first ODIN event. We also lay out plans for how to grow this movement, document emerging conversations, and propose a path toward a better and more transparent science of tomorrow.

We derive an analytical expression for $s$-state exciton energies in monolayer transition-metal dichalcogenides (TMDCs): $E_{\text{ns}}=-{\text{Ry}}^*\times P_n/{(n-1/2+0.479\, r^*_0/\kappa)^2}$, $n=1,2,...$, where $r^*_0$ and $\kappa$ are the dimensionless screening length and dielectric constant of the surrounding medium; $\text{Ry}^*$ is an effective Rydberg energy scaled by the dielectric constant and exciton reduced mass; $P_n(r^*_0/\kappa)$ is a function of variables $n$ and $r^*_0/\kappa$. Its values are around 1.0 so we consider it a term that corrects the Rydberg energy. Despite the simple form, the suggested formula gives exciton energies with high precision compared to the exact numerical solutions that accurately describe recent experimental data for a large class of TMDC materials, including WSe$_2$, WS$_2$, MoSe$_2$, MoS$_2$, and MoTe$_2$. To achieve these results, we have developed a so-called regulated perturbation theory by combining the conventional perturbation method with several elements of the Feranchuk-Komarov operator method, including the Levi-Civita transformation, the algebraic calculation technique via the annihilation and creation operators, and the introduction of a free parameter to optimize the convergence rate of the perturbation series. This universal form of exciton energies could be helpful in various physical analyses, including retrieval of the material parameters such as reduced exciton mass and screening length from the available measured exciton energies., Comment: 5 pages, 1 figure, 3 tables, 1 supplementary

In their recent work [Phys. Rev. B 109, 184409(2024)], Manchon and Pezo develop a linear (in magnetization) theory, in order to investigate high-order harmonic generation (HHG). Here, we show that such linear theory cannot describe HHG, which, by definition is a nonlinear process., Comment: Comment on arXiv:2309.08597

This article investigates a spectral problem of the Laplace operator in a two-dimensional bounded domain perforated by a small arbitrary star-shaped hole and on the smooth boundary of which the Neumann boundary condition is imposed. It is proved that the eigenvalues of this problem converge to the eigenvalues of the Laplacian defined on the unperturbed domain as the size of the hole approaches zero. Furthermore, our main theorem provides the rate of convergence by showing an asymptotic expansion for all simple eigenvalues with respect to the size and shape of the hole., Comment: 36 pages