esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Experimental
### Chemistry
#### 3.1.2. Synthesis of Bipyridine Derivatives **8** and **9**
Yellow solid, (75% yield), mp 188-190 \({}^{\circ}\)C (DMF/ EtOH); IR (KBr) \(\gamma_{\max}\) 3037, 2966 (C-H), 1713, 1667 (2C=O), 1597 (C=N) cm\({}^{-1}\); \({}^{1}\)H NMR (DMSO-\(d_{6}\)) 8 1.05 (t, \(J\) = 7.2 Hz, 3H, CH\({}_{3}\)), 1.19 (t, \(J\) = 7.6 Hz, 3H, CH\({}_{3}\)), 4.13 (q, \(J\) = 7.2 Hz, 2H, CH\({}_{2}\)), 4.24 (q, \(J\) = 7.6 Hz, 2H, CH\({}_{2}\)), 5.42 (d, \(J\) = 4 Hz, 1H, CH), 6.47 (d, \(J\) = 4 Hz, 1H, CH), 7.25-7.79 (m, 19H, Ar-H); MS \(m/z\) (%) 673 (M\({}^{+}\) + 2, 11), 671 (M\({}^{+}\), 36), 387 (100), 324 (68), 278 (50), 105 (42), 78 (83). Anal. Calcd. for C\({}_{38}\)H\({}_{31}\)ClN\({}_{6}\)O\({}_{4}\) (671.15): C, 68.00; H, 4.66; N, 12.52. Found: C, 68.25; H, 4.40; N, 12.46%. _Ethly 7-(4-(ethoxycarbonyl)-1,5-diphenyl-1H-pyrazol-3-yl)-1-(4-nitrophenyl)-5-phenyl-1,5-dihydro-[1,2,4] triazol0[4,3-a]pyrimidine-3-carboxylate_ (**15h**). Brown solid, (71% yield), mp 206-208 \({}^{\circ}\)C (EtOH); IR (KBr) \(\gamma_{\max}\) 3030, 2948 (C-H), 1713, 1644 (2C=O), 1593 (C=N) cm\({}^{-1}\); \({}^{1}\)H NMR (DMSO-\(d_{6}\)) 8 1.07 (t, \(J\) = 7.2 Hz, 3H, CH\({}_{3}\)), 1.25 (t, \(J\) = 7.6 Hz, 3H, CH\({}_{3}\)), 4.12 (q, \(J\) = 7.2 Hz, 2H, CH\({}_{2}\)), 4.27 (q, \(J\) = 7.6 Hz, 2H, CH\({}_{2}\)), 5.46 (d, \(J\) = 4 Hz, 1H, CH), 6.49 (d, \(J\) = 4 Hz, 1H, CH), 7.25-8.42 (m, 19H, Ar-H); MS \(m/z\) (%) 681 (M\({}^{+}\), 31), 577 (73), 390 (66), 327 (95), 115 (100), 83 (52). Anal. Calcd. for C\({}_{38}\)H\({}_{31}\)N\({}_{7}\)O\({}_{6}\) (681.71): C, 66.95; H, 4.58; N, 14.38. Found: C, 66.77; H, 4.42; N, 14.23%. _3.2. Cytotoxic Activity_  
The cytotoxic evaluation of the synthesized compounds was carried out at the Regional Center for Mycology and Biotechnology at Al-Azhar University, Cairo, Egypt according to the reported method [56].
# Synchronous Remote Calibration for Electricity Meters: Application and Optimization
## 2 Related Work
### Task Scheduling Systems
[34] study the widespread use of time-triggered communication protocols in vehicles and design a novel Unfixed Start Time (UST) scheduling algorithm that flexibly schedules tasks and messages to enhance schedulability, along with two methods for resolving assignment conflicts to further improve scheduling performance. In the field of logistics, the literature [35] proposes a novel hybrid genetic algorithm that supports the cooperation of a ground vehicle and multiple UAVs for efficient parcel delivery, addressing the inefficiency of single-UAV approaches in serving numerous customers and optimizing routing and scheduling through several algorithmic modules. These studies provide valuable insights into task scheduling in remote calibration systems. However, existing research on task scheduling mainly focuses on asynchronous tasks and does not sufficiently address the adaptability challenges of decentralized and synchronous tasks in distributed remote calibration systems. Although [PERSON] et al. [19] addressed the issue of task synchronization and scheduling within remote sensor calibration systems, proposing a Dynamic Synchronous Scheduling (DSS) methodology, this approach, which is grounded in a multi-layered greedy algorithm, does not demonstrate particularly high efficiency. Consequently, we have explored further optimized solutions for synchronous task scheduling.
# On the Use of Structured Prior Models for Bayesian Compressive Sensing of Modulated Signals
## 2 Proposed Method  
The main contribution of our work consists in designing prior models that take advantage of not only the sparsity property, but also the structured form of the spectrum of periodically modulated signals. We also propose a Gibbs sampler that offers an efficient sampling of all parameters of the resulting model. In this section, we first formulate the compressive sensing problem of periodically modulated signals. Subsequently, we propose a structure of the support of the target spectrum through hierarchical models and their relevance for gearbox signal analysis is addressed. Finally, we discuss the difficulties of the sampling step of the model parameters and propose a solution for efficient sampling.
## 2 Materials and Methods
### Algal Cultivation  
The _H. lacustris_ NIES-144 strain, obtained from the National Institute for Environmental Studies (NIES), University of Tokyo, Japan, was used in this study. The alga was photoautotrophically cultivated in a photosynthetic NIES-C medium [11]. The medium was sterilized using a 0.2 \(\upmu\)m mixed cellulose ester membrane filter after adjusting the pH to 7.5. One colony of _H. lacustris_ from the agar plate culture was transferred aseptically to a 250 mL Erlenmeyer flask with a porous silicon stopper (working volume: 150 mL). The flask culture was performed in a shaking incubator under continuous illumination (\(\alpha\). 90 \(\mu\)mol/m\({}^{2}\)/s; 25 \({}^{\circ}\)C, 150 rpm; ISF-7100 RF, Jeio Tech, Daejeon, Korea). Sequentially, during the photosynthetic flask cultivations, vegetative biflagellate motile cells lost their flagella, expanded in volume, and changed into non-motile palmella cells. Under nitrogen-nutrient deprivation conditions, astaxanthin biosynthesis was induced in the palmella cells, giving them a brownish-green color. Eventually, these cells were transformed into bright red, astaxanthin-rich cyst cells. In general, the intensity of red color in the _H. lacustris_ cells and the amount of astaxanthin are proportional [24] After 90 days of culture, mature red _H. lacustris_ cyst cells were harvested by centrifugation (3000 rpm for 10 min; Combi-514R, Hanil Science Inc., Daejeon, Korea) and lyophilized for 4 days (FD5512, IIShin BioBase Co., Yangju-si, Korea). The freeze-dried algal cells were stored in a vacuum bag at \(-20\)\({}^{\circ}\)C before the astaxanthin extraction experiments. Detailed media composition and culture conditions have been reported earlier [11; 13].
## 2 Data and Methods
### In Situ Data  
In situ data in environmental monitoring can be used to measure various parameters directly at their source. It provides accurate, real-time information about the environment, and helps to identify changes or trends over time [50]. In the context of monitoring applications regarding the coastal environment, in situ data can be used for water quality monitoring, measuring weather conditions, and the monitoring of sediment and benthic parameters [51]. Additionally, in situ data play an important role in coastline/shoreline extraction and coastal erosion monitoring. In situ measurements can be utilized as ground truth information that is used to validate remote sensing data, and to assess the accuracy of the extracted coastline/shoreline. In situ data also provide information about the current conditions of the coastal area, including the location of the shoreline, the presence of vegetation and other physical features, and water depth, which are essential for detecting changes in the coastal environment. The data collected from in situ sources, such as tide gauges, survey markers, and drones, can be used to monitor coastal erosion, to assess the stability of the coastline, and to identify areas that are influenced by erosion [52].  
In situ data can support the development and improvement of machine learning models for coastline/shoreline extraction and coastal erosion monitoring. In situ data can be used to train machine learning models, validate their accuracy, and help to address issues of data scarcity and heterogeneity [53; 54].
## 3 Results  
The overall and muscle injury incidence for all eight observed seasons is presented in Table 1 with an average number of injuries per 1000 h of football-specific exposure with 95% confidence intervals. The results suggest an overall downward trend from the first observed season (17.935 injuries/1000 h in 2026/2017) until the COVID-19 period (8.036 injuries/1000 h in the 2020/2021 season) with a sudden spike in the following season (15.637 injuries/1000 h). Muscle injuries show fewer oscillations during the observed period, with the lowest rate of 3.469 injuries/1000 h in the 2019/2020 season and 6.06 injuries/1000 h in the 2022/2023 season.  
Descriptive statistics for periods of two and four weeks following coaching transitions and season totals are presented in Table 2. The results show an average of 15.58 injuries for 1000 h of exposure in the first 2 weeks and 16.52 after 4 weeks of coaching change, while muscle injuries had rates of 5.40 and 5.53 injuries for 1000 h in these periods.  
\begin{table}
\begin{tabular}{c c c} \hline
**Season** & **Overall Injuries** & **Muscle Injuries** \\ \hline
2016/2017 & 17.935 (17.833–18.036) & 5.978 (5.919–6.037) \\
2017/2018 & 14.265 (14.175–14.355) & 6.029 (5.971–6.088) \\
2018/2019 & 11.534 (11.453–11.616) & 4.194 (4.145–4.243) \\
2019/2020 & 9.208 (9.140–9.277) & 3.469 (3.427–3.512) \\
2020/2021 & 8.036 (7.960–8.114) & 4.592 (4.534–4.650) \\
2021/2022 & 15.637 (15.54–15.736) & 5.584 (5.526–5.643) \\
2022/2023 & 13.182 (13.094–13.270) & 6.06 (6.001–6.12) \\
2023/2024 & 10.883 (10.803–10.962) & 5.743 (5.685–5.801) \\ \hline \end{tabular}
\end{table}
Table 1: Injury incidence per 1000 h of exposure with 95% confidence intervals for all and muscle injuries across eight seasons.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{3}{c}{**Overall**} & \multicolumn{3}{c}{**Muscle**} \\ \hline  & **2 Weeks** & **4 Weeks** & **Season** & **2 Weeks** & **4 Weeks** & **Season** \\ \hline Min & 0.00 & 0.00 & 8.04 & 0.00 & 0.00 & 3.47 \\ Max & 36.04 & 37.44 & 17.93 & 16.60 & 14.03 & 6.06 \\ Mean & 15.58 & 16.52 & 12.20 & 5.40 & 5.53 & 5.12 \\ SD & 10.95 & 10.21 & 3.36 & 5.32 & 4.15 & 0.94 \\ Med & 16.81 & 15.53 & 11.53 & 3.95 & 5.05 & 5.58 \\ \hline \end{tabular}
\end{table}
Table 2: Descriptive statistics for overall and muscle injuries in three time frames.  
The analysis of the difference in these observed time frames is presented in Table 3 indicating no statistically significant changes, but with medium effect size when comparing overall injuries in 4 weeks and the season in general ([PERSON]'s D = 0.59).  
Percentage changes in injury rates are graphically presented in Figure 1. Overall injuries had an increase of 27.7% and 35.4% in the two and four weeks after coaching turnovers, respectively, while for muscle injuries, these rates were lower and amounted to 5.5% and 8.1%.
# Contact Analysis and Friction Prediction of Non-Gaussian Random Surfaces
## 4 Results and Discussion
### Effect of Kurtosis  
Rough surfaces with different kurtosis and the same skewness and standard deviation showed obvious distinctions in peak-to-mean and asperity density. Here, peak-to-mean is the distance between the highest peak and the mean line. As shown in Figure 11, rough surface tends to increase in peak-to-mean distance and decrease in peak density as kurtosis increases. Therefore, as expected, these result in an increase in local contact pressure because of the reduction in the contact area. The contact area ratio, average contact pressure, and plastic ratio as the functions of kurtosis under uniform skewness and linear load are presented in Figure 12. It is observed that, due to rough surfaces with high kurtosis having higher and sharper peaks, the number of contact asperities start to decrease, contributing to an increase in contact pressure and a decrease in contact area. The increase in contact pressure may induce a large degree of plastic deformation. However, for high kurtosis values (\(K_{u}\geq 5\)), the impact of kurtosis becomes limited. The variations of contact area and pressure become slight. The similar trends are also observed by [28; 34; 43]. In Figure 12, the observation about friction coefficient is that the influence of kurtosis on friction coefficient is very slight, especially for \(K_{u}\geq 5\). This trend is consistent with [PERSON]'s experimental study [43].
# Propagation of Elastic Waves in a One-Dimensional High Aspect Ratio Nanoparticle Phononic Crystal
###### Abstract  
We investigate the propagation of elastic waves in a one-dimensional (1D) phononic crystal constituted by high aspect ratio epoxy nanoridges that have been deposited at the surface of a glass substrate. With the help of the finite element method (FEM), we calculate the dispersion curves of the modes localized at the surface for propagation both parallel and perpendicular to the nanoridges. When the direction of the wave is parallel to the nanoridges, we find that the vibrational states coincide with the Lamb modes of an infinite plate that correspond to one nanoridge. When the direction of wave propagation is perpendicular to the 1D nanoridges, the localized modes inside the nanoridges give rise to flat branches in the band structure that interact with the surface Rayleigh mode, and possibly open narrow band gaps. Filling the nanoridge structure with a viscous liquid produces new modes that propagate along the 1D finite height multilayer array.  
Keywords: phononic crystals; surface acoustic waves; hypersonic; finite element method +
Footnote †: journal: Applied Sciences
## 1 Introduction
### Need for Knowledge Transfer from Real to Virtual Spaces  
The concept of place is a highly interesting one in that it can be used to understand how far persons are aware of their surroundings, both as a location, in terms of \(xy\) coordinates, as well as in terms of knowledge of the world they live in. As increased periods are being spent online in real terms, particularly by the younger generations, a new paradigm is required, that ensures that the knowledge of the physical world is not totally lost on the younger generation. The same paradigm needs to also ensure that the older generations can identify the concept of place in the new virtual space, through increased use of virtual environments. Indeed, this new paradigm needs to ensure that the physical knowledge gain is transported to the virtual domain for preservation and access to information on the real world. It must also enable knowledge dissemination through diverse conveyors as are online maps, immersive worlds and game engines. In such a scenario, the two-opposite lost generations' knowledge can be employed for such activities as educational enhancement, scenario building and preparedness for such events as post-disaster, technology shutdown, development planning, and environmental protection.
# Evolutionary Algorithms for Optimization Sequence of Cut in the Laser Cutting Path Problem
## 2 The Laser Cutting Path Problem (LCPP)
### Formal Definition  
In this paper, we use a graph representation to tackle the LCPP. A graph \(G=(V,E)\) is an ordered pair of two sets, \(V\) the set of vertices and \(E\subseteq\{uv\mid u,v\in V\}\), the set of edges. If \(E\subseteq V\times V\), we say that the graph is directed and, if for each element \(uv\) of \(E\) we have a value \(w_{uv}\) associated with it, we say that the graph is weighted and that \(w_{uv}\) is the weight of the edge \(uv\).  
Given a graph \(G=(V,E)\), we say that \(v\) is adjacent to \(u\) if \(vu\in E\) and for a vertex \(v\in V\), we call the neighborhood of \(v\) in \(G\) the set of all vertices adjacent to \(v\) in \(G\) and denote such a set by \(N_{G}(v)=\{u\mid u\in V,uv\in E\}\). A walk \(W=[[e_{1},\ldots,e_{k}]]\) in \(G\) is a sequence of edges from \(G\) such that, for all \(i\in\{1,\ldots,k-1\}\) we have that \(e_{i}=uv\) and \(e_{i+1}=vu\), in other words, the second endpoint of an edge is the first of the next edge. We are given a complete weighted graph \(G=(V,E)\) with weights \(w_{vu}\) for each edge, a set of \(q\) required edges \(R=\{r_{1},\ldots,r_{q}\}\) such that \(R\subseteq E\) and two numerical constants, \(V_{c}\) and \(V_{m}\), representing the cutting speed and the gliding speed for a cutting laser machine.  
In this context, the laser cutting path problem (LCPP) can be defined as the optimization problem where one wants to minimize the sum of the weights of the edges in the walk multiplied by the proper speed, meaning that the edges in \(R\) must be multiplied by \(V_{c}\) exactly once. All the other edges (including the other appearances of the edges in \(R\)) must be multiplied by \(V_{m}\). More formally, let \(W=[e_{1},\ldots,e_{k}]\) be a walk in \(G\) and \(W(R)\) be the set of edges obtained from \(W\) by removing the first, and only the first, occurrence of an edge in \(R\). We define the cost of \(W\) as \(sz(W)=\sum\limits_{e\in W(R)}V_{m}w_{e}+\sum\limits_{e\in R}V_{c}w_{e}\); the LCPP problem could be defined as presented in (1).  
\[\min_{W\in W(R)}\sum\limits_{e\in W(R)}V_{m}w_{e}+\sum\limits_{e\in R}V_{c}w_{e} \tag{1}\]
# Simulation of Gross Primary Productivity Using Multiple Light Use Efficiency Models
## 3 Results  
### Carbon Flux Dynamics in the Heihe River Basin  
The seasonal carbon flux dynamics of the five dominant vegetation types in the Heihe River Basin are shown in Figure 2. The annual carbon flux is summarized in Table 3. Carbon flux at these sites had an obvious seasonal cycle. The carbon flux began increasing in early May, reached the maximum in July and returned to the minimum in later October (Figure 2). Alpine grassland is the dominant vegetation type in the upper stream of the study area. Both Arou and Dashalong are covered with alpine grass. From the carbon flux measurement, the annual GPP was 862.76 gC/m\({}^{2}\)/year at Arou and 477.91 gC/m\({}^{2}\)/year at Dashalong. The annual Net Ecosystem Exchange (NEE) was \(-144.08\) gC/m\({}^{2}\)/year at Arou and \(-309.89\) gC/m\({}^{2}\)/year at Dashalong. The annual Ecosystem Respiration (ER) was 718.69 gC/m\({}^{2}\)/year at Arou and 168.02 gC/m\({}^{2}\)/year at Dashalong. Artificial and natural oases are the dominant landscapes in the middle stream of the Heihe River Basin. Carbon flux at two sites in the oases, a cropland (Daman) and a wetland (Shidi), was measured. In the middle stream, the annual GPP for the cropland was 1364 gC/m\({}^{2}\)/year and 1087 gC/m\({}^{2}\)/year for the wetland, the annual NEE for the cropland was \(-688\) gC/m\({}^{2}\)/year and \(-585\) gC/m\({}^{2}\)/year for the wetland, and the annual ER for the cropland was 676 gC/m\({}^{2}\)/year and 502 gC/m\({}^{2}\)/year for the wetland. Natural oasis dominates the vegetated area in the downstream of the study area. The Sidaoqiao site is located in the natural oasis region of the downstream. The vegetation type is tamarisk at the Sidaoqiao site. This site is close to the main river channel. At the Sidaoqiao site, the annual GPP was 709 gC/m\({}^{2}\)/year, the annual NEE was \(-201\) gC/m\({}^{2}\)/year, and the annual ER was 508 gC/m\({}^{2}\)/year. All of these sites were carbon sinks and absorbed more than 100 gC/m\({}^{2}\)/year.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Site Name**} & \multicolumn{2}{c}{**GPP (gC/m\({}^{2}\)/yr)**} & \multicolumn{2}{c}{**NEE (gC/m\({}^{2}\)/yr)**} & \multicolumn{2}{c}{**ER (gC/m\({}^{2}\)/yr)**} \\ \cline{2-7}  & **2014** & **2015** & **2014** & **2015** & **2014** & **2015** \\ \hline Arou & 845.90 & 879.63 & \(-175.61\) & \(-112.54\) & 670.29 & 767.08 \\ Dashalong & 506.58 & 449.24 & \(-314.61\) & \(-305.16\) & 191.97 & 144.08 \\ Daman & 1329.96 & 1397.60 & \(-726.94\) & \(-648.23\) & 603.02 & 749.36 \\ Shidi & 1008.57 & 1165.77 & \(-559.52\) & \(-609.76\) & 449.05 & 556.02 \\ Sidaoqiao & 664.82 & 753.58 & \(-190.00\) & \(-211.96\) & 474.82 & 541.62 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Annual carbon flux at the five study sites in the Heihe River Basin.
# Architectural Design for Digital Twin Networks
## 5 Design and Implementation Strategies
### Interfaces
#### 5.4.3 Internal Interfaces  
These interfaces operate within the DTN, facilitating communication between its subsystems: Data Repository, Service Mapping Models, and Digital Twin Network Management. These interfaces are optimized for high speed, efficiency, and concurrency.  
For example, when a new data point is collected from the real network, the Data Repository stores it and notifies the Service Mapping Models subsystem via an internal interface. This triggers the update of relevant models, which in turn communicate with the Management subsystem to assess whether any reconfiguration or alerting is needed.  
Figure 6: Visualization of Digital Twin Network interfaces alongside our implementation.  
This seamless internal communication ensures that the DTN remains synchronized and responsive to real-time changes.  
Despite their important roles, these interfaces are often overlooked or not thoroughly discussed in the existing literature. It is essential for these interfaces to be open and standardized to avoid vendor lock-in and promote interoperability. Additionally, new interfaces or protocols may need to be developed to better suit the unique requirements of a DTN system.
## Nomenclature  
### Notations  
\(A\)Area (m\({}^{2}\))  
\(Cp\)Spec. Heat of Gas at Constant Pressure (J/kg\(\cdot\)K)  
\(CW\)Compressor Work (W)  
\(D\)Distance (m)  
\(h\)Heat Transfer Coefficient  
\(k\)Thermal Conductivity (W/m/K)  
\begin{tabular}{l l} \(m\) & Mass Flow Rate (kg/s) \\ \(Q\) & Reactor Thermal Heat Input \\ \(q\) & Heat Flux/Duty (W/m\({}^{2}\)) \\ \(P\) & Pressure (Pa) \\ \(PR\) & Pressure Ratio \\ \(SW\) & Specific Work/Power Output (W/Kg/s) \\ \(T\) & Temperature (K or \({}^{\circ}\)C) \\ \(TW\) & Turbine Work (W) \\ \(W\) & Work (W) \\ \(UW\) & Useful Work (W) \\
**Greek Symbols** \\ \(\gamma\) & Ratio of Specific Heats \\ \(\Delta\) & Delta, Difference \\ \(e\) & Effectiveness (Heat Exchanger; cooling) \\ \(\eta\) & Efficiency \\
**Subscripts** \\ _blade_ & Turbine Temperature (also known as Blade Temp.) \\ \(c\) & Compressor \\ \(c_{in}\) & Compressor Inlet \\ \(c_{out}\) & Compressor Outlet \\ \(cool\) & Cooling \\ \(coolant\) & Compressor Exit Coolant \\ \(e\) & Power for Electrical Conversion \\ \(gas\) & Turbine Entry Temperature \\ \(he\) & Helium \\ \(he_{min}\) & Helium with minimum gas conditions \\ \(ic\) & Intercooled Cycle; intercooled coefficient \\ \(is_{c}\) & Isentropic (Compressor) \\ \(is_{t}\) & Isentropic (Turbine) \\ \(MHR\) & Reactor (Heat Source) \\ \(MHR_{in}\) & Reactor (Heat Source) Inlet \\ \(MHR_{loss}\) & Reactor (Heat Source) Pressure Losses \\ \(MHR_{out}\) & Reactor (Heat Source) Outlet \\ \(log_{mean}\) & Logarithmic Mean Temperature Difference \\ \(pc_{in}\) & Precooler Inlet (also applicable to intercooler) \\ \(pc_{loss}\) & Precooler Pressure Losses (same as above) \\ \(pc_{out}\) & Precooler Outlet (same as above) \\ \(re\) & Recuperator \\ \(re_{cold}\) & Recuperator cold side \\ \(re_{hot}\) & Recuperator hot side \\ \(re_{HPloss}\) & Recuperator High Pressure Losses \\ \(re_{LPloss}\) & Recuperator Low Pressure Losses \\ \(re_{real}\) & Recuperator Real (specific heat transfer) \\ \(re_{max}\) & Recuperator Max (specific heat transfer) \\ \(th\) & Thermal Power \\ \(t\) & Turbine \\ \(t_{out}\) & Turbine Outlet \\ \(t_{in}\) & Turbine Inlet \\
**Superscripts** \\ \({}^{\prime}\) & Recuperator inlet conditions \\ \({}^{\prime}\) & \multicolumn{1}{l}{Recuperator inlet conditions} \\
**Abbreviations** \\ C & Compressor \\ CH & Precooler \\ COT & Core Outlet Temperature \\ DP & Design Point \\ \end{tabular}
## 2 Preliminaries
### Information Geometry
#### 2.2.2 Metric Matrix  
To describe the local properties of a manifold, the concept of a metric is defined on the tangent space. A metric is a mapping that assigns a real number to a pair of vectors, denoted as \(G\). In information geometry, the Fisher information matrix is used as the metric for statistical manifolds [23].