esa-sceva/satcom-chunk-collection huggingface dataset:
# Immediate Settlement of Ring Footings Resting on Inhomogeneous Finite Stratum
## 5 Conclusions  
The purpose of this study is to analyze the settlement of a rough ring footing of any stiffness in an isotropic elastic finite layer with the modulus of elasticity linearly varying with the depth, overlying a rough rigid base. The consideration of an inhomogeneous finite stratum has not been covered in the literature for evaluation of the elastic settlement of ring footings. By means of finite  
Figure 8: Variation of \(s_{outer}/s_{inner}\) with respect to footing stiffness, finite layer thickness ratio and modulus inhomogeneity: (**a**) effect of \(K\); (**b**) effect of \(H/D\); (**c**) effect of \(nD/E_{0}\).  
element analysis, numerical solutions for a wide range of geometrical and material parameters were determined. The effects of inner-to-outer radius ratios, Poisson's ratio, footing stiffness, finite layer thickness ratio, and modulus inhomogeneity have been investigated. The results are presented in the familiar form of the settlement influence factors, forming non-dimensional design charts, and also compared with other available solutions. Based on the numerical results, the following conclusions can be drawn:  
1. For circular footings, settlement influence factors obtained from the FE analyses are comparable with those reported in the literature.
2. An increase in Poisson's ratio \(\
u_{s}\) causes a decrease in settlement influence factor I of ring footings, and the rate of decrease of \(I\) with \(\
u_{s}\) is insensitive to footing's inner-to-outer radius ration \(R_{i}/R_{0}\).
3. For the inner point of the ring footing, the settlement influence factor \(I_{K}\) decreases with increasing the values of footing stiffness \(K\). For the outer point of the ring footing, in contrast, the \(I_{K}\) values increase with increasing values of \(K\). The variation of \(I_{K}\) with \(K\) is more prominent for smaller values of \(R_{i}/R_{0}\).
4. Increasing the finite layer thickness ratio \(H/D\) to values greater than a critical one does not impact the settlement of ring footings. This is attributed to the fact that the contribution by the underlying rigid base becomes less as the finite layer grows thicker. The critical value of \(H/D\) is independent of \(R_{i}/R_{0}\).
5. Settlement influence factor decreases with an increase in soil nonhomogeneity \(nD/E_{0}\), and the decreasing tendency is more significant for smaller values of \(R_{i}/R_{0}\).
6. A systematic procedure is proposed for estimating the footing settlement for a wide range of practical cases and to help in choosing the optimum internal opening and stiffness of ring footings that limit footing settlement to tolerable levels.  
The first author would like to acknowledge the support of the National Research Footing of Korea (NRF) (Grant No. NRF-2017R1C1B5015371). The second author also thanks for the support of the National Research Footing of Korea (NRF) (Grant No. 2011-0030040).  
[PERSON] designed and conducted numerical analysis and wrote the draft of the paper. [PERSON] assisted with the writing of the paper.  
The authors declare no conflict of interest.
## 3 Phase I : Proposed Precoding-Based Source to Relay Transmission
### Problem Formulation  
The aim of a precoding-based implementation of CF is to obtain the linear combination of original signals at the relay without incurring the errors due to approximation of the channel by integers. To this end, the precoder is used to shift the channel coefficients to the closest possible integer using the CSI at the transmitter. Therefore, consider a channel decomposition as:  
\[h_{l}=h_{l}^{z}+h_{l}^{\pi} \tag{11}\]  
where \(h_{l}^{z}\in\mathbb{Z}\) is an integer approximation of \(h_{l}\) and, consequently, \(h_{l}^{\pi}\in\mathbb{R}\). Using Equations (2) and (11), we can rewrite Equation (4) as:  
\[\mathbf{y}_{R}=\sum_{l=1}^{L}h_{l}w_{l}\mathbf{s}_{l}+\mathbf{z}_{R}+\sum_{l=1 }^{L}h_{l}^{z}\mathbf{s}_{l}-\sum_{l=1}^{L}h_{l}^{z}\mathbf{s}_{l}\]  
which can be simplified as:  
\[\mathbf{y}_{R}=\underbrace{\sum_{l=1}^{L}h_{l}^{z}\mathbf{s}_{l}}_{\mathbf{v}_ {eff}}+\underbrace{\sum_{l=1}^{L}(h_{l}w_{l}-h_{l}^{z})\mathbf{s}_{l}+\mathbf{ z}_{R}}_{\mathbf{z}_{eff}} \tag{12}\]  
The relay aims to decode \(\mathbf{v}_{eff}\) from \(\mathbf{y}_{R}\). The effective noise, \(\mathbf{z}_{eff}\), is comprised of the receiver noise (\(\mathbf{z}_{R}\)) and the additional \"self-noise\", arising due to the difference between the real channel and its integral approximation. Using the rate of computation derived in [2], we can write the rate of computation of the linear combination of original signals as:  
\[R(\mathbf{h},\mathbf{w})=\log^{+}\left(\frac{P}{1+P\sum_{l=1}^{L}(h_{l}w_{l}-h_{l }^{z})^{2}}\right)\]  
where \(\text{log}^{+}(x)=\max(0,\text{log}(x))\), \(P\) is the signal to noise ratio given by \(P=1/\sigma_{1}^{2}\) and \(\mathbf{w}=[\begin{array}{cccc}w_{1}&w_{2}&\ldots&w_{L}\end{array}]\). Therefore:  
\[R(\mathbf{h},\mathbf{w})=\log^{+}\left(\frac{1}{\sigma_{1}^{2}+\sum_{l=1}^{L}( h_{l}w_{l}-h_{l}^{z})^{2}}\right)\]  
Using the power constraints, the rate can be rewritten as:  
\[R(\mathbf{h},\mathbf{w})=\text{log}^{+}\left(\frac{1}{\sigma_{1}^{2}+\parallel \mathbf{h}\mathbf{W}-\mathbf{h}^{z}\parallel^{2}}\right)\]  
where \(\mathbf{h}^{z}=\left[\begin{array}{cccc}h_{1}^{z}&\ldots&h_{L}^{z}\end{array}\right]\) and \(\mathbf{W}=diag(\mathbf{w})\). It is assumed that \(h_{l}^{z}\
eq 0\), to ensure that the linear combination has non-zero coefficient of each of the \(L\) messages; therefore, \(\parallel\mathbf{h}^{z}\parallel\geq 1\). Hence, we obtain:  
\[R(\mathbf{h},\mathbf{w})\leq\text{log}^{+}\left(\frac{\parallel\mathbf{h}^{z} \parallel^{2}}{\sigma_{1}^{2}+\parallel\mathbf{h}\mathbf{W}-\mathbf{h}^{z} \parallel^{2}}\right) \tag{13}\]  
Hence, the precoder, \(w_{l}\), should be designed such that it is able to minimize \(\mathbf{z}_{eff}\) in Equation (12) and maximize the achievable rate in Equation (13). The design of such a precoder is proposed in the next subsection.
## 2 Mode Basis Background  
It has been shown that the distribution of laser light amplitude, in free space, can be represented, in rectangular coordinates, by the product of Hermite polynomials \(H_{n}(\cdot)H_{m}(\cdot)\), where \(n\) and \(m\) are the polynomials order, or in cylindrical coordinates by Laguerre polynomial \(L_{p}^{\ell}(\cdot)\), where \(\ell\) and \(p\) are the azimuthal and radial indices, respectively [19]. In this work, the HG and LG orthogonal modes are used as code words for data transmission in an \(M\)-ary pattern coding system, where \(M\) is the modulation order of LG or HG coding system. In Figure 2a, the laboratory-generated LG and HG modes are shown, which are used to build an \(M\)-ary coding communication system with M = 8, 16, and 32. In particular, Hermite-Gaussian and Laguerre-Gaussian functions provide an exact representation of the higher-order solutions of the free space paraxial wave equation in rectangular and cylindrical coordinates, respectively [20]. The HG modes \(u_{nm}^{HG}\) can be written in rectangular coordinates as \(u_{nm}^{HG}(x,y,z)=u_{n}(x,z)\times u_{m}(y,z)\)[20], where \(u_{n}(x,z)\) or \(u_{m}(y,z)\) is the solution in \(x\) or \(y\) transverse dimension, and is given by  
\[\begin{split} u_{n}(x,z)&=\left(\frac{2}{\pi} \right)^{1/4}\left(\frac{\exp[i(2n+1)\psi(z)]}{2^{n}n!\omega_{o}}\right)^{1/2} \\ &\times\exp\left(-ikz-i\frac{kx^{2}}{2R(z)}-\frac{x^{2}}{\omega^{ 2}(z)}\right)H_{n}\left(\frac{\sqrt{2}x}{\omega}\right),\end{split} \tag{1}\]  
where \(H_{n}(\cdot)\) is Hermite polynomial of order \(n\), \(\omega_{o}\) is the beam waist, \(k=2\pi/\lambda\) is the wave number and \(\lambda\) is the operating wavelength, \(\omega(z)=\omega_{o}\sqrt{1+(z/z_{R})^{2}}\) is the spot size with \(z_{R}=\pi\omega_{o}/\lambda\) is Rayleigh size, \(\psi(z)=\arctan(z/z_{R})\) is Gouy phase, and \(R(z)=z(1+(z_{R}/z)^{2})\) denotes the radius of curvature.  
Similarly, the LG modes \(u_{lp}^{LG}\) characterized by the azimuthal and radial indices can be expressed in cylindrical coordinates as [20]  
\[\begin{split} u_{p\ell}^{LG}(r,\phi,z)=&\frac{A}{ \omega(z)}\sqrt{\frac{2p!}{\pi(\ell+p)!}}\Bigg{(}\frac{\sqrt{2}r}{\omega(z)} \Bigg{)}^{\ell}L_{p}^{\ell}\bigg{(}\frac{2r^{2}}{\omega^{2}(z)}\bigg{)}\\ &\times\exp\left(-\frac{ikr^{2}}{2R(z)}\right)\exp\left(\frac{-r ^{2}}{\omega^{2}(z)}\right)\exp(-i\ell\phi)\\ &\times\exp(i(2p+\ell+1)\psi(z)),\end{split} \tag{2}\]  
where \(A\) is a normalized constant, \(L_{p}^{\ell}(\cdot)\) is the generalized Laguerre polynomial, and the parameters \(R(z)\), \(\omega(z)\), and \(\psi(z)\) are the same as in Equation (1).
## 3 Results and Discussion
### Establishment of Optimal HPLC-PDA Conditions  
HPLC-PDA analytical conditions for efficient separation of the 24 selected markers were determined using a range of reverse-phase C18 columns (I. D. 4.6 mm \(\times\) length 250 mm, particle size 5 \(\upmu\)m), Waters SunFire (Milford, MA, USA), Thermo Scientific Hypersil GOLD (Waltham, MA, USA), Phenomenex Gemini (Torrance, CA, USA), and Shiseido Capcell Pak UGS0 (Tokyo, Japan), acids (0.1% formic acid, 0.1% trifluoroacetic acid, and 1.0% acetic acid), and column oven temperatures (30, 40, and 50 \({}^{\circ}\)C). As a result of comparative analysis, as shown in Table S2, a SunFire C18 reverse-phase column, 0.1% formic acid, and a column oven temperature of 40 \({}^{\circ}\)C were established as the optimal analysis conditions. Compounds **1**-**24** were eluted within 60 min and detected at 6.21, 8.70, 9.43, 12.26, 14.79, 16.63, 17.42, 17.86, 18.75, 18.96, 20.90, 21.30, 22.04, 22.52, 23.36, 25.64, 28.45, 32.79, 36.05, 42.76, 47.93, 53.20, 55.39, and 55.83 min, respectively (Figure 1).
## 3 Current State of Object Detection Algorithms
### Region-Based CNN
#### 3.1.2 Faster R-CNN  
The Faster R-CNN model [35] is another addition to the R-CNN family and is designed for real-time object classification. Unlike the Fast R-CNN and R-CNN models, the Faster R-CNN model replaces the selective search technique with a Region Proposal Network (RPN) to locate the specific location of an object. The input image is sent through the convolutional network, and the RPN is used to identify the RoIs. The RoI Pooling layer is then used to scale the RoIs, and the final step of object categorization and the bounding box refinement process is identical to that of the Fast R-CNN model. The Faster R-CNN model is up to ten-times faster than the Fast R-CNN model, making it suitable for real-time applications.
# Retinal Vessels Segmentation Techniques and Algorithms: A Survey
## 4 Retinal Vessels Segmentation Techniques
The DRIVE dataset, consisting of 40 retinal images, is evenly divided into a training set and a test set, whereas the STARE dataset consists of 20 images, 10 of which are normal retinal images and the other 10 images are abnormal ones. Nevertheless, many researchers use other less common datasets for validation and performance evaluation, such as: Automated Retinal Image Analyzer (ARIA) dataset [44], DIAbietes RETina Data Base (DIARETDB) dataset [37], Methods for Evaluating Segmentation and Indexing techniques Dedicated to Retinal (Messidor) dataset [45; 46], and High Resolution Fundus (HRF) [47]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Year** & **Image Processing Technique** & **Performance Metric** & **Validation Dataset** & **Technique Category** \\ \hline [PERSON] and [PERSON] [43] & 2008 & Vessel tracking by Kalman filter. & TPR*, FNR* & DRIVE & \\ \hline [PERSON] et al. [64] & 2010 & Statistical-based vessel tracing & TPR, FPR & DRIVE & \\ \hline [PERSON] et al. [65] & 2013 & Vessel tracking by & - & - \\ \hline [PERSON] et al. [65] & 2013 & Bayesian theory. & - & - \\ \hline [PERSON] et al. [23] & 2016 & Vessel tracking using & GFPR* & DRIVE, STARE & \\ \hline [PERSON] et al. [66] & 2010 & Gaussian pyramid multi-scaling. & Acc; Sp-Se & DRIVE, STARE & **Multi-scale** \\ \hline [PERSON] et al. [67] & 2010 & Multi-scale based on weighted & ROC, Acc & DRIVE, STARE & \\ \hline [PERSON] et al. [68] & 2011 & Multi-scale based on Anisotropic & ROC & STARE & \\ \hline [PERSON] et al. [69] & 2012 & Multi-scale based on line & FPR & DRIVE & \\ \hline [PERSON] and [PERSON] [70] & 2012 & Morphological Angular & \multirow{2}{*}{MSE*} & \multirow{2}{*}{DRIVE} & \multirow{2}{*}{_Morphological_} \\  & Scale-space & & & & \\ \hline \hline [PERSON] et al. [71] & 2014 & Watershed transform + Contrast & \multirow{2}{*}{Acc, Precision} & DRIVE & \\  & and directional Maps. & & & & \\ \hline [PERSON] et al. [72] & 2017 & Global thresholding based on & Acc, Execution time & DRIVE, STARE & \\ \hline [PERSON] et al. [73] & 2012 & Level set in terms of initialization & \multirow{2}{*}{Acc, Sp, Se} & DRIVE & _Deformable Model_ \\  & and edge detection. & & & & \\ \hline [PERSON] et al. [74] & 2015 & Snakes contours & Acc; Sp-Se & DRIVE & \\ \hline [PERSON] et al. [31] & 2015 & Infinite perimeter active contour & \multirow{2}{*}{Acc, Sp, Se} & DRIVE, STARE & \\  & with hybrid region norms. & & & \\ \hline [PERSON] et al. [75] & 2015 & Level set without using local & \multirow{2}{*}{Acc, Sp, Se} & DRIVE & \\  & & region areas. & & & \\ \hline [PERSON] and M
## 3 Materials and Methods
### Materials Selection  
The materials selected for this study were chosen based on their widespread use in additive manufacturing and their relevance to prototyping and low-volume production. Two thermoplastics were used for FDM, and one photopolymer resin was selected for SLA:  
* FDM (PLA): Polylactic Acid filament, a biodegradable thermoplastic derived from renewable resources such as corn starch or sugarcane. PLA is known for its ease of printing, dimensional stability, and moderate mechanical properties, making it a popular choice for prototyping and educational applications.
* FDM (ABS): Acrylonitrile Butadiene Styrene filament, a petroleum-based thermoplastic with higher ductility and temperature resistance compared to PLA. ABS is more challenging to print due to its tendency to warp, but it offers superior mechanical performance for functional parts.
* SLA (Resin): A general-purpose photopolymer resin designed for high-resolution printing. This resin provides a balance of mechanical strength, surface finish, and detail resolution, making it suitable for applications requiring fine features and smooth surfaces.  
Material properties, such as tensile strength, elongation at break, and heat resistance, were obtained from supplier datasheets to provide context for the experimental results. Table 1 lists these key properties, as reported by the filament and resin manufacturers.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Property** & **FDM (PLA)** & **FDM (ABS)** & **SLA (Resin)** \\ \hline Tensile Strength (MPa) & 50–60 & 40–50 & 60–70 \\ Elongation at Break (\%) & 5–10 & 10–20 & 4–6 \\ Heat Resistance (\({}^{\circ}\)C) & 50–60 & 80–100 & 50–70 \\ Density (g/cm\({}^{3}\)) & 1.24 & 1.04 & 1.10–1.20 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Key material properties for FDM (PLA, ABS) and SLA resin.
# Network Allocation Vector (NAV) Optimization for Underwater Handshaking-Based Protocols
## 5 Conclusions  
In this paper, we proposed a technique to optimize the NAVs used in underwater handshaking-based protocols such as the CSMA/CA protocol by eliminating the unnecessary long silent periods. To eliminate the unnecessary long silent periods, the proposed scheme supplies the neighbor nodes with the timing information about the propagation delays between a source and a destination, between a neighbor and a source, and between a neighbor and a destination, so that the neighbor can figure out the arrangement of the surrounding nodes and thus, find the precise wake-up time. Through computer simulations, it was shown that the elaborately determined NAV, which enables the precise wake-up time, improves the NAV time of the network. Similar improvements were also observed in the throughput and latency of the network, suggesting the importance of the NAV setting on these performance metrics. In addition, the use of optimized NAVs allows a distant neighbor node to have shorter silent periods and wake up earlier than the nearer ones to compensate for the longer distance from the sender/destination. This procedure effectively eliminates unfairness in channel occupation and was shown to improve the fairness of the network. Finally, compared to previous works on NAV settings for underwater handshaking-based protocols, it was shown that the proposed scheme outperforms them in every aspect.
# RMS Modeling and Control of a Grid-Forming E-STATCOM for Power System Stability in Isolated Grids
###### Abstract  
This paper presents a comprehensive RMS-based phasorial model of an E-STATCOM with grid-forming (GFM) control, designed to improve power system stability in isolated grids. Unlike previous approaches, this model integrates a governor with an internal power system stabilizer (PSS) and an active current limiter (ACL) to enhance frequency regulation and mitigate oscillations. Additionally, an exciter with a nonlinear modulation function is introduced to optimize voltage regulation and reactive power support. A detailed conventional supercapacitor (SC) model is also incorporated, enabling dynamic DC-voltage control based on active power variations, improving frequency stability. The proposed E-STATCOM RMS model includes algebraic equations, dynamic governor and exciter models, supercapacitor-based energy storage control, and an advanced current-limiting strategy. Simulations are conducted on the Fuerteventura-Lanzarote (Canary Islands, Spain) power system, comparing the E-STATCOM with a synchronous condenser (SynCon) in frequency response, voltage regulation, and fault performance. The results show that the E-STATCOM improves frequency stabilization and energy efficiency while complying with grid codes. This study introduces a novel RMS-based modeling approach for GFM E-STATCOMs, bridging the gap between theoretical phasorial analysis and real-world applications. The findings confirm that E-STATCOMs are a viable alternative to SynCons, enhancing grid stability in high-renewable-penetration systems.  
grid-forming control; E-STATCOM; DC-AC power conversion; supercapacitor-based energy storage; power system stability; frequency response; voltage regulation Article
## 2 Materials and Methods
### LRAs Onboard BDS Satellites  
Currently, laser retroreflector arrays (LRAs) are deployed on all BDS-2 and BDS-3 satellites. Typically, LRAs consist of multiple corner cubes that increase the effective reflective area. Among the nine BDS satellites (one GEO, three IGSO, and five MEO) long-term tracked by the International Laser Ranging Service (ILRS) [18], three types of LRAs were used with different prism numbers and arrangements. LRAs onboard three BDS-2 IGSO satellites including COMPASS-I3, COMPASS-I5, and COMPASS-I6B and one BDS-2 GEO, i.e., COMPASS-G1, were manufactured by Shanghai Astronomical Observatory (SHAO) with 90 corner cubes. One BDS-2 MEO, i.e., COMPASS-M3, two BDS-3 SECM satellites, i.e., Beidou3-M9 and Beidou3-M10, manufactured by SHAO, have an LRAs with 42 corner cubes. The 38-corner-cube-LRAs made by North China Research Institute of Electro-Optics (NCRIEO) are equipped on BDS-3 CAST satellites, i.e., Beidou3-M2 and Beidou3-M3 [19; 20]. Table 1 provides detailed information on the three types of LRAs. In 2023, ILRS started to track all BDS-3 MEO satellites. However, due to the limited number of observations available, the analysis does not incorporate the data obtained from recently tracked satellites. It is worth noting that the structure of LRAs will cause a systematic error in SLR observations. When SLR signal pulse is not perpendicular to the prism, the pulse may be reflected by other prisms nearby, which can result in a distance difference between LRAs and station. This systematic error caused by the characteristics of the SLR measurement mode is known as the satellite signature effect [15].
# Deep Class-Guided Hashing for Multi-Label Cross-Modal Retrieval
## 3 Methodology
### Hash Learning
#### 3.3.2 Pairwise Loss  
In order to maintain inter-class structural relationships, we further explore the relationships between data. That is, to bring similar data closer together and to push away dissimilar data. For this, we provide a similarity matrix, \(S\), which is defined as follows:  
\[S_{ij}=\frac{l_{i}}{\left\|l_{i}\right\|_{L_{2}}}\cdot\left(\frac{l_{j}}{ \left\|l_{j}\right\|_{L_{2}}}\right)^{T} \tag{5}\]  
where \(\|\cdot\|_{L_{2}}\) is the \(L_{2}\) norm, and \((.)^{T}\) is the transpose of the vector (or matrix). The range of \(S_{ij}\) is [0, 1]. If \(S_{ij}>0\), then \(x_{i}\) (or \(y_{i}\)), and \(x_{j}\) (or \(y_{j}\)) is called an relevant pair. If \(S_{ij}=0\), then they are considered irrelevant pairs. To pull relevant pairs closer, we can calculate the cosine distance between relevant data pairs using \(\cos_{\text{p}}\left(h_{i},h_{j}\right)\); inspired by [29], we relax the constraints on irrelevant data pairs. The distance between irrelevant data pairs is pushed away using \(\cos_{\text{n}}\left(h_{i},h_{j}\right)\).  
\[\cos_{\text{p}}\left(h_{i},h_{j}\right)=\max\left(S_{ij}-\frac{\left|h_{i} \cdot h_{j}\right|}{\left|h_{i}\right|\cdot\left|h_{j}\right|},0\right)\quad, \quad\cos_{\text{n}}\left(h_{i},h_{j}\right)=\max\left(\frac{\left|h_{i}\cdot h _{j}\right|}{\left|h_{i}\right|\cdot\left|h_{j}\right|},0\right) \tag{6}\]  
Hence, the relevant loss, \(\mathcal{L}_{\text{p-pair}}\), can be calculated using Equation (7).  
\[\mathcal{L}_{\text{p-pair}}=\frac{\sum_{x\in\{x,y\}}\sum_{j=1}^{N}I\left(S_{ij }>0\right)\cos_{\text{p}}\left(h_{i}^{*},h_{j}^{*}\right)}{\sum_{i,j=1}^{N}I \left(S_{ij}>0\right)} \tag{7}\]  
Similarly, irrelevant loss, \(\mathcal{L}_{\text{n-pair}}\), is calculated using Equation (8).  
\[\mathcal{L}_{\text{n-pair}}=\frac{\sum_{x\in\{x,y\}}\sum_{i,j=1}^{N}I\left(S_{ ij}=0\right)\cos_{\text{n}}\left(h_{i}^{*},h_{j}^{*}\right)}{\sum_{i,j=1}^{N}I \left(S_{ij}=0\right)} \tag{8}\]  
To address the issue of intra-class dispersion arising from pairwise loss, we assign a small weight to pairwise loss, allowing the aggregation of similar data points to be primarily guided by proxy loss, thereby resolving the issue of intra-class dispersion. Considering the fact that in multi-label datasets, the number of irrelevant pairs in pairwise loss is significantly smaller than the number of relevant pairs and that positive sample pairs have a stronger constraint and are more likely to lead to intra-class dispersion compared to negative sample pairs, we assign different small weights to the positive and negative sample constraints of pairwise loss. Therefore, the overall pairwise loss, \(\mathcal{L}_{\text{pair}}\), is given by the following formula:  
\[\mathcal{L}_{\text{pair}}=\alpha\mathcal{L}_{\text{p-pair}}+\beta\mathcal{L}_ {\text{n-pair}} \tag{9}\]  
where \(\alpha\) and \(\beta\) are the small weight hyperparameters for positive and negative sample constraints, respectively.