esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Mathematical Modeling Strategy
### Development of Mathematical Model 1
#### 2.1.2 Actuator Dynamics
Therefore, the electromagnetic-related torque is balanced by the other three developed torques [16], that is:  
\[\tau_{m} =\tau_{d}+\tau_{l}+\tau_{i}\] \[\tau_{m} =K_{i}i_{a} \tau_{d} =D\dfrac{d}{dt}\theta_{m} \tau_{i}=J\dfrac{d^{2}}{dt^{2}}\theta_{m} \tag{28}\] \[\tau_{l} =\dfrac{C_{s}\cdot l}{2\pi}(x_{s}-\hat{x_{l}})+\dfrac{K_{s}\cdot l }{2\pi}(x_{s}-x_{l})\]  
where \(D\) is viscous damping at the armature. The torque \(\tau_{m}\) produced as a function of the current \(i_{a}\) that passes through the armature appears in (28). The matrix \(K_{t}\) defines the torque constant. Equivalently, the inertial, damping, and load torques are described in the subsequent expressions in (28), respectively. In that equation, the term \(\dfrac{l}{2\pi t}\) is used for converting the angular displacement of the nut to linear displacement of the lead screw, where \(l\) is the screw lead. The substitution of \(\tau_{m}\), \(\tau_{d}\), \(\tau_{l}\) and \(\tau_{i}\) in (28) and bringing the electrical relationship in (27) yields:  
\[K_{t}i_{a}=D\dfrac{d}{dt}\theta_{m}+\dfrac{C_{s}\cdot l}{2\pi}( \dot{x}_{s}-\dot{x}_{l})+\] \[\dfrac{K_{s}\cdot l}{2\pi}(x_{s}-x_{l})+\int\dfrac{d^{2}}{dt^{2}} \theta_{m} \tag{29}\] \[K_{e}\dfrac{d}{dt}\theta_{m}+R_{a}i_{a}+L_{a}\dfrac{d}{dt}i_{a}=V _{a}\]  
with \(x_{s}=(l\cdot\theta)/(2\cdot\pi)\) the relationship between the angular displacement and the displacement of the linear actuator (considering the lead screw configuration). In terms of the movement efficiency, the following relationship is also valid \(\dfrac{d}{dt}x_{s}=\Gamma_{r}\dfrac{d}{dt}\theta\dfrac{1}{\eta\cdot\tau_{i}}\), where \(\Gamma_{r}\) is the resistive torque, and \(\eta\) is the ball-screw efficiency. The application of the assumption describing the class of interaction between the tip of the actuator and the link in the biped robot results in \(x_{s}=x_{l}\). Using the state variable theory for each actuator \(\tau_{i}\) with the definitions \(\chi^{A}_{1,i}=\theta_{m,i}\), \(\chi^{A}_{2,i}=\dot{\theta}_{m,i}\) and \(\chi^{A}_{3,i}=i_{a,i}\) and the corresponding parameters (labeled with a superscript \(i\)) yields the following model for the actuator:  
\[\dfrac{d}{dt}\chi^{A}_{1,i}=\chi^{A}_{2,i}\] \[\dfrac{d}{dt}\chi^{A}_{2,i}=\dfrac{D_{i}}{J_{i}}\chi^{A}_{2,i}+ \dfrac{K_{t,i}}{J_{i}}\chi^{A}_{3,i} \tag{30}\] \[\dfrac{d}{dt}\chi^{A}_{3,i}=-\dfrac{K_{e,i}}{L_{a,i}}\chi^{A}_{2, i}-\dfrac{R_{a,i}}{L_{a,i}}\chi^{A}_{3,i}+\dfrac{V_{a,i}}{L_{a,i}}\]  
The pushing force of the linear actuator can be estimated as \(F^{A}_{i}=\left(m^{A}_{i}\dfrac{d}{dt}\chi^{A}_{2,i}\right)\), therefore the torque \(\tau_{i}=L^{f}_{i,1}\cdot F^{A}_{i}\cdot sin(\delta_{i})\) produced by this force over the joint \(i\) corresponds to \(\delta_{i}=\pi-\theta_{m,i}-\gamma^{c}_{i}\).
## 5 Conclusions  
In conclusion, fishmeal replacement by either poultry by-product meal or hydrolyzed feather meal did not cause any intestinal histological alterations. Thus, these results indicate normal digestion and absorption in the midgut of _S. aurata_ even when their dietary fishmeal protein is completely replaced. Neither land animal proteins altered the liver histopathology of gilthead seabream when fishmeal was replaced at 25%. However, at higher replacement levels increased lipid droplets and hepatic vacuolization were observed to be more pronounced in fish fed HFM diets. Moreover, the dietary supplementation of PBM and HFM with essential lysine and methionine seemed to improve the digestive physiology, as fish fed these diets showed fewer hepatic alterations and abnormalities compared to diets of a similar replacement level but without amino acid supplementation. The dominant phyla in the intestinal microbiota were _Proteobacteria_ (58.8%) and _Actinobacteria_ (32.4%), but no specific pattern was observed among the different dietary fish groups at any taxonomic level. This finding was probably driven by the high inter-individual variability observed.  
Conceptualization, I.T.K., E.M. and K.A.K.; Methodology, P.P., A.M. and P.B.; Software, P.P., A.M. and P.B.; Validation, I.T.K., E.M. and K.A.K.; Formal Analysis, P.P., A.M. and P.B.; Investigation, P.P., A.M. and P.B.; Resources, I.T.K., E.M., P.B. and K.A.K.; Data Curation, I.T.K., K.A.K. and E.M.; Writing--Original Draft Preparation, P.P. and A.M.; Writing--Review & Editing,I.T.K., P.B., K.A.K., E.M.; Supervision, I.T.K., E.M. and K.A.K.; Project Administration, I.T.K.; Funding Acquisition, I.T.K. All authors have read and agreed to the published version of the manuscript. This research was funded by the Operational Programme \"Fisheries 2007-2013\" (Ministry of Rural Development and Food of the Hellenic Republic/European Fisheries Fund) under the project title \"The use of Processed Animal Proteins in the feeds of gilt-head seabream (_Sparus aurata_)\", Grant Number: 2014 EE086800090000. Institutional Review Board Statement: The study was conducted according to the guidelines of EU legal frameworks related to the welfare and protection of animals for scientific purposes (Directive 2010/63/EU) and in strict accordance with the University of Thessaly's Ethics Committee on the Use of Animals in Research (protocol approval 20 December 2016).  
Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.
## Abbreviations  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} ALOS & Advanced Land Observing Satellite \\ ALT & Active Layer Thickness \\ AMSR-E & Advanced Microwave Scanning Radiometer-Earth Observing System \\ ASTER & Advanced Spaceborne Thermal Emission and Reflection Radiometer \\ AVHRR & Advanced Very High Resolution Radiometer \\ CAFF & Conservation of Arctic Flora and Fauna \\ CAVM & Circum-Arctic Vegetation Map \\ CCI & Climate Change Initiative \\ CHRIS & Compact High Resolution Imaging Spectrometer \\ CS & Closed Shrupland \\ DCW & Digital Chart of the World \\ DIS & Data and Information System \\ DUE & Data User Element \\ EBF & Evergreen Broadleaf Forest \\ ENF & Evergreen Needle-leaf Forest \\ ENVISAT & Environmental Satellite \\ ERS & European Remote Sensing Satellite \\ ESA & European Space Agency \\ ET & Evapotranspiration \\ ETM & Enhanced Thematic Mapper \\ FAO & Food and Agriculture Organization \\ G & Grassland \\ GLC & Global Land Cover \\ GPP & Gross Primary Production \\ HRV & High Resolution Visible \\ IGBP & International Geosphere-Biosphere Programme \\ ISODATA & Iterative Self-Organizing Data Analysis Technique Algorithm \\ JERS & Japanese Earth Resources Satellite \\ JRC & Joint Research Centre \\ KH & Keyhole \\ LAI & Leaf Area Index \\ LC & Land Cover \\ LCCS & Land Cover Classification System \\ MERIS & Medium Resolution Imaging Spectrometer \\ MISR & Multi-angle Imaging Spectroradiometer \\ MODIS & Moderate Resolution Imaging Spectroradiometer \\ MSS & Multispectral Scanner System \\ NDVI & Normalized Difference Vegetation Index \\ NH & Northern Hemisphere \\ NOAA & National Oceanic and Atmospheric Administration \\ NPP & Net Primary Production \\ ORCHIDEE & Organizing Carbon and Hydrology in Dynamic Ecosystems \\ OS & Open Shrubland \\ PALSAR & Phased Array L-Band Synthetic Aperture Radar \\ PFT & Plant Function Type \\ Proba & Project for On-Board Autonomy \\ SAR & Synthetic Aperture Radar \\ SOCC & Soil Organic Carbon Content \\ SPOT & Satellite Pour I'Observation de la Terre \\ TC & Tasseled Cap \\ TM & Thematic Mapper \\ UMD & University of Maryland \\ VGT & Vegetation \\ WG & Wooded Grassland \\ WL & Woodland \\ \end{tabular}
## 2 Mathematical Modelling  
### Theoretical Modeling  
#### 2.1.1 Laminate Composite  
The laminated and delaminated glass fiber-reinforced polymer composite structure configurations with photographs are shown in Figure 1 for the mathematical modeling of transverse vibration response in the time domain. The laminate structure is assumed to have perfect bonding between all layers, whereas the delaminate structure is assumed to be debonding in the central plane, with a size of 100 \(\times\) 100 mm placed symmetrically at the center of the plate. The length, breadth, and thickness of the laminated and delaminated composite structures are assumed to be 'L', 'b', and 'h', respectively.  
The force and moment resultants associated with the mid-plane strains and curvatures of the laminated composite plate is expressed as  
\[N =A\varepsilon_{0}+Bk \tag{1}\] \[M =B\varepsilon_{0}+Dk\] \[Q =K_{s}A^{s}\tau_{0}\]  
where \(N=\begin{cases}N_{xx}\\ N_{yy}\\ N_{xy}\end{cases}\), M = \(\begin{cases}M_{xx}\\ M_{yy}\\ M_{xy}\end{cases}\), and \(Q=\begin{cases}Q_{y}\\ Q_{x}\end{cases}\) are in-plane force, moment, and transverse shear force resultants, respectively. \(A\), \(D\), \(B\), and \(A^{s}\) denote extensional stiffness, bending stiffness, extensional-bending stiffness, and transverse shear stiffness, which are given by [36].  
The strain energy (U) and kinetic energy (K) are expressed in terms of in-plane and transverse displacements, rotations of transverse normal, and out-of-plane shear strains, whereas virtual work done (V) is expressed in terms of transverse load, external forces and moments given by [37].  
Figure 1: Composite plate configuration.  
The governing differential equations of motion for the FRP composite plate are obtained by using [PERSON]'s principle, as  
\[\begin{array}{c}\frac{\partial N_{xx}}{\partial x}+\frac{\partial N_{yy}}{ \partial y}-I_{0}\ddot{u}_{0}-I_{1}\ddot{\varnothing}_{x}=0\\ \frac{\partial N_{yy}}{\partial y}+\frac{\partial N_{yy}}{\partial x}-I_{0} \ddot{v}_{0}-I_{1}\ddot{\varnothing}_{y}=0\\ \frac{\partial M_{xx}}{\partial x}+\frac{\partial M_{yy}}{\partial y}-Q_{x}-I_{ 0}\ddot{\varnothing}_{x}-I_{1}\ddot{u}_{0}=0\\ \frac{\partial M_{yy}}{\partial y}+\frac{\partial M_{xx}}{\partial x}-Q_{y}-I_{ 0}\ddot{\varnothing}_{y}-I_{1}\ddot{v}_{0}=0\\ \frac{\partial Q_{x}}{\partial x}+\frac{\partial Q_{y}}{\partial y}+q-I_{0} \ddot{w}_{0}=0\end{array} \tag{2}\]  
where \(u_{0}\) and \(v_{0}\), \(w\), and \(\varnothing_{x}\) and \(\varnothing_{y}\) are the in-plane displacements, transverse deflection, and rotations of transverse normal, respectively.
## 4 Discussion
### Rolling Model with WAAM Deposition RS  
Although the rolling models used for efficiency evaluation did not consider the WAAM deposition RS, the modelling technique developed here can be applied when the modelling of WAAM and rolling processes is sequentially coupled. Figure 16 shows the longitudinal RS distributions predicted by a rolling model with WAAM RS as an initial condition. It should be noted that this model considered only eight deposited layers of the WAAM wall, which was rolled with a flat roller at rolling loads of 10 kN and 50 kN. Before rolling, the WAAM RS was tensile in the wall and the substrate region under the wall. After the rolling at a load of 10 kN, the RS converted to low-level compressive stress under the rolled surface, and the magnitude of tensile RS was reduced in the regions 3 mm below the rolled surface. After the rolling at a load of 50 kN, the model predicted tensile RS immediately under the rolled surface, but compressive RS in the regions 5 mm and further below the rolled surface. In the substrate underneath the wall, the magnitude of the original tensile RS was lowered after the rolling. The compressive RS in the regions of the substrate far away from the wall remained unchanged. More analysis of the effect of rolling on WAAM deposition RS will be presented separately in another paper.
# Joint Optimization of Data Transmission and Energy Harvesting in Relay Satellite Networks
## 4 Solutions and Algorithms
### Solution Development  
As mentioned above, MTASU is a multi-objective mixed-integer optimization (MMO) problem with integer and continuous parameters, which is difficult to tackle. Furthermore, RSN is a stochastic network with time-varying uncertainties. We solve the MMO problem based on the Lyapunov optimization framework.
# High-Efficiency Quantum Dot Lasers as Comb Sources for DWDM Applications
## 3 Performance of CPMLLs
### Power per Line  
Of equal importance was the analysis of the power of individual comb lines of CPMLLs. Uneven power distribution between comb lines is often a limiting factor of OFCs. The optical SNR of an encoded DWM channel is, in general, proportional to the optical power. In extreme cases, comb lines with the lowest power will not be encoded with data, reducing the bandwidth and spectral efficiency of the link. To address this concern, each measured spectrum is analyzed to identify the 20 contiguous comb lines with the highest power. The power of the lowest line (PoLL) is found for each spectrum and the PoLL vs. SA bias and drive current is plotted in Figure 4d-f. The maximum recorded PoLL and the number of states with PoLL \(\geq-8\) dBm are recorded in Table 1. For lower bias values (50-120 mA), similar PoLL values are recorded for the 6% and 10% devices. Similarly, for higher biases, the 10% and 18% devices show similar PoLL values. The 10% device shows the highest PoLL value of \(-5.1\) dBm and the most states (117) with PoLL \(\geq-8\) dBm. The PoLL values reported in Figure 4 and Table 1 are single-sided fiber-coupled power values. Devices have as-cleaved facets, with equal amounts of power emitted from both sides. This, in combination with the 2 dB fiber coupling loss, corresponds to a roughly 5 dB decrease in the reported values from the total power emitted from the device. This shows that with a high reflection coating and improved fiber coupling and device design, combs with PoLL \(\geq 0\) dBm are achievable. The spectrum with the highest PoLL is shown in Figure 5b from the 10% device at a 185 mA drive current and with a 1.5 V SA bias.  
Figure 5: Optical spectra collected from the same device with a total saturable absorber length of 10% of the cavity. (**a**) Comb with the largest 6 dB bandwidth, 42 lines. (**b**) Comb with the highest power for 20 contiguous lines. (**c**) Comb with the highest efficiency of generating 20 contiguous lines. (**d**) Comb with low power consumption and high efficiency.
# Action of Antimicrobial Peptides against Bacterial Biofilms
## 3 Biofilm Resistance to AMPs
### Adaptive Resistance Mechanism  
Staphylococci have a peptide sensing system known as _aps_, which was first recognized in _S. epidermidis_[112]. The _aps_ consist of two-component system that has a sensor histidine kinase (ApSS)  
Figure 2: Representation of the different targets of anti-biofilm AMPs. \(\times\) signs indicate inhibition and/or action on targets sites.  
and a DNA-binding response regulator (ApsR). A third component (ApsX) is also found only in some staphylococci species [112]. This _aps_ system can protect Gram positive bacteria including methicillin resistant _S. aureus_ (MRSA) strains from action of AMPs [113]. The aps system upregulates D-alanylation of teichoic acid and increases the expression of putative AMP efflux pumps [114]. A D-alanine deficient mutant of _E. faecalis_ produced less biofilm but was more resistant to AMPs than the wild type [115]. The PhoP/PhoQ genetic system found in _P. aeruginosa_ and _Salmonella enterica_[116] is used to sense AMPs [117]. This system tends to change the structure of LPS by addition of aminoarabinose to lipid A, which has the effect of decreasing the net negative charge of lipopolysaccharidesaccharides [118]. Therefore, this system may also confer resistance of biofilm bacteria to AMPs. A two-component regulatory system pmrA-pmrB identified in _P. aeruginosa_ that regulates resistance to polymyxin B, polymyxins E, cattle indolicidin and LL-37 [119] modifies lipopolysaccharidesaccharides in the outer membrane of bacteria and this reduces the AMPs interaction with the outer membrane [120; 121] this confering resistance.
## 7 Robustness  
The robustness of the watermarking technique depends on accurate feature matching to achieve geometric resynchronisation. Section 5.2 reports match ratios between 0.684 and 0.690 across all datasets. This establishes a strong basis for reliable watermark recovery under different attack conditions. The following sections evaluate the resilience of the proposed watermarking method against various types of attacks and build on this feature extraction performance.  
Robustness reflects an algorithm's ability to recover a watermark from a watermarked image after exposure to various forms of attack. It is a critical measure of resilience against such disturbances. To evaluate the robustness of the proposed method, we employed the Normalised Correlation (NC), Bit Error Rate (BER), and Bit Error Quality (BEQ) metrics [23].  
A high NC value, close to 1.0, indicates effective watermark recovery, while a lower BER reflects greater accuracy in preserving the watermark's integrity after attacks. The BEQ metric refines this evaluation by measuring the perceptual quality of the watermarked image post-recovery. BEQ captures the extent to which distortions, introduced during the watermarking and recovery processes, affect the overall visual quality. This is carried out to measure that robustness is achieved without significant degradation to the image itself.  
Figure 4: Histogram comparison for representative greyscale (top row) and RGB (bottom row) samples. Each pane includes labelled axes (Pixel Value 0–255 and Relative Frequency); enhanced contrast makes differences in overlap visible. The near-identical curves confirm that the watermark leaves first-order pixel statistics and perceptual quality essentially unchanged.  
For this evaluation, images of specific dimensions from three datasets were used: JPEGs of 106 \(\times\) 160, 160 \(\times\) 106, and 107 \(\times\) 160 pixels from the disk image; coloured images of 640 \(\times\) 480, 600 \(\times\) 640, 500 \(\times\) 500, 500 \(\times\) 400, 480 \(\times\) 640, and 335 \(\times\) 500 pixels from the COCO2017 dataset; and greyscale images of 512 \(\times\) 512 and 256 \(\times\) 256 pixels from the BOSSBase dataset. These dimensions were selected based on experimental parameters outlined in the state-of-the-art papers used for comparison. The pixel sizes match closely with those used in related experiments.  
A detailed analysis of the robustness results under various conditions, including compression, filtering, noise, cropping, rotation, and scaling, is provided here. The watermarked images were subjected to these attacks, and the NC, BER, and BEQ were calculated between the original and recovered watermarks. The results across these datasets demonstrate that the proposed method maintains high performance, even under distortions.  
Although the analysis includes varying image sizes, particular emphasis was placed on robustness tests for images up to 500 \(\times\) 500 pixels, as these closely match the standard 512 \(\times\) 512 dimensions frequently used in state-of-the-art evaluations. This approach demonstrates the method's efficiency at non-standard dimensions.
## 3 Materials and Methods
### Fingerprinting of Spices by GC-MS Analysis  
The fingerprint analysis of the investigated spices was performed using an Agilent Technologies 6890N (Palo Alto, CA, USA) gas chromatography system. This was equipped with a SUPELCOWAX(r) 10 fused silica capillary column (60 m \(\times\) 0.25 mm i.d. \(\times\) 0.25 \(\upmu\)m film thickness) supplied by Supelco (Bellefonte, PA, USA), with helium (Helium N60, Air Liquid, Portugal) as a carrier gas at a flow rate of 1 mL/min (column-head pressure: 13 psi). The injector temperature was fixed at 250 \({}^{\circ}\)C and a splitless injector equipped with an insert of 0.75 mm i.d. was attached. The oven temperature program was run as follows: initial temperature 40 \({}^{\circ}\)C for 1 min, 2.5 \({}^{\circ}\)C/min ramp until 220 \({}^{\circ}\)C and then held isothermally at 220 \({}^{\circ}\)C for 10 min, for a total GC run time of 83 min. MS detection was performed in full scan in an Agilent 5975 quadrupole inert mass selective detector (Santa Clara, CA, USA), the ion energy used for the electron impact (EI) was 70 eV and the source temperature was 230 \({}^{\circ}\)C. The electron multiplier was set to the autotune procedure. The mass acquisition range, made in full scan mode, was 30-300 m/z. VOMs were identified based on their mass spectra compared with those in the National Institute of Standards and Technology (NIST) MS 05 spectral database (Gaithersburg, MD, USA) with a matching probability \(>\) 85%, anddetermining the Kovat's retention indices (RI) of each identified VOM according to the [PERSON] and [PERSON] [47] equation: \(\text{RI}_{\text{x}}=100\text{n}+100\text{t}_{\text{x}}-\text{t}_{\text{n}})( \text{t}_{n+1}-\text{t}_{\text{n}})\), where \(\text{t}_{\text{n}}\) and \(\text{t}_{\text{n+1}}\) are the retention times of the reference \(n\)-alkane hydrocarbons eluting immediately after and before the compound \"x\", and \(\text{t}_{\text{x}}\) is the retention time of compound 'x'. A \(\text{C}_{\text{g}}\)-\(\text{C}_{\text{20}}\) saturated \(n\)-alkane solution was used to determine the RI, and the values were compared, when available, to values reported in the literature for similar columns [48; 49; 50; 51] and databases available online (the Pherobase and Flavornet). Each sample was analyzed in triplicate.
## 2 Seawater Channel Modelling Elements
### Scattering Phase Function Formats
#### 2.7.3 Two-Term Henyey-Greenstein Phase Functions  
The HG-SPF is an approximation but differs significantly from the PAP-SPF's results for small angles less than \(20^{\circ}\) and big angles greater than \(150^{\circ}\). Consequently, [PERSON] [77] created the TTHG-SPF by modifying the existing HG-SPF. It has been observed that TTHG-SPF better matches [PERSON]'s observations at lower \(\theta_{s}\) and accounts for the elongation visualised for greater angles, given by Equations (28)-(30).  
The TTHG-SPF is another model commonly used to describe the angular distribution of light scattering \(\overset{\sim}{\beta}(\theta_{s},g,~{}\lambda)\), particularly in atmospheric and oceanic studies. It is considered an extension of the original HG-SPF, which provides a simple parameterisation of the phase function with a single asymmetry parameter \(g\). Nevertheless, the TTHG-SPF offers more flexibility by introducing an additional parameter, allowing for a better fit to observed scattering behaviour.  
\[\overset{\sim}{\beta}(\theta_{s},g,~{}\lambda)=\frac{1-f}{4\pi}+\frac{f}{4\pi} \Bigg{\{}\frac{\left(1-g^{2}\right)}{\left(1+g^{2}-2\,g\mathrm{cos}\theta_{s} \right)^{\frac{3}{2}}}\Bigg{\}} \tag{31}\]  
where \(-1~{}\leq~{}g~{}\leq~{}1\) and \(f\) is an additional parameter introduced in the TTHG-SPF, representing the fraction of forward scattering. It ranges from 0 to 1 (\(0~{}\leq~{}f~{}\leq~{}1\)), where 0 corresponds to purely isotropic scattering and 1 corresponds to purely forward scattering. According to [77], Equation (31) can also be expressed using two weighted HG-SPF terms as shown below:  
\[\overset{\sim}{\beta}(\theta_{s},g,~{}\lambda)=\alpha P_{HG}(\theta_{s},g_{1} )+(1-\alpha)P_{HG}(\theta_{s},g_{2}) \tag{32}\]  
On the RHS of Equation (32), \(\alpha\) is the weighting factor, which is defined as follows:  
\[\alpha=\frac{g_{2}(1+g_{2})}{(g_{1}+g_{2})(1+g_{2}-g_{1})} \tag{33}\]  
\(P_{HG}\) (\(\theta_{s},g_{i}\)) is the HG-SPF term for asymmetric parameter \(g_{i}\) where \(i=\{1,2\}\) for the same scattering angle \(\theta_{s}\), and  
\[g_{2}=-0.3061446+1.000568g_{1}-0.01826332g_{1}^{2}+0.03643748g_{1}^{3} \tag{34}\]  
In Equation (32), when the value of \(g_{1}\) is close to one to raise the TTHG-SPF dramatically for very small angles, this is equivalent to LOS link configuration and \(g^{2}\) is given a negative number to raise the TTHG-SPF as the angle \(\theta_{s}\) reaches \(180^{\circ}\)[16]. Because of the small \(\theta s\) that lead photons to propagate in straight lines, the empirical phase function vastly overrates the channel bandwidth.