esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Mechanosensing in Normogravity
### Cytoskeleton/Nucleoskeleton
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**NORMOGRAIVITY**} \\ \hline
**PROTEIN** & **TISSUE/STRUCTURE** & **Cytosol/Nucleus Shuttling** & **Reference** \\ \hline \(\beta\)-CATENIN & Cell-Cell adherent junctions & YES & [62; 63; 64] \\ \hline Ankrd2 & Sacromere (Skeletal Muscle) & YES & [65] \\ \hline c-Abl & Focal Adhesions & YES & [66] \\ \hline CADHERIN & Cytoskeleton & No Data Available & [43] \\ \hline CARP & Cardiac Muscle & YES & [65] \\ \hline CFTR & RBCs & No Data Available & [67] \\ \hline EMERIN & Integral Membrane Protein & YES & [68; 69] \\ \hline FILAMIN A & Cytoskeleton & YES & [70; 71; 72] \\ \hline POCAL ADHESION & Cellular membrane/ECM & NO & [73] \\ KINASE (FAK) & Cardiovascular cells, bone etc. & No Data Available & [56] \\ \hline MLP & Muscle & YES & [74] \\ \hline NESPRIN 1/2 & Nucleus & No Data Available & [75] \\ \hline NOMPC or TRPN1 & Ion Channel & No Data Available & [76] \\ \hline NPC & Nuclear pore complex & - & [75] \\ \hline PANNEXIN & RBCs & No Data Available & [77] \\ \hline PAXILLIN & Cytoskeleton & YES & [50] \\ \hline PC1/PC2 complex & Primary bone, Kidney, Liver & No Data Available & [78] \\ \hline PECAM-1 & Endothelial cells & No Data Available & [43] \\ \hline PIEZO1-2 &
\begin{tabular}{c} Cationic channels, vascular \\ development/Merkel \\ cell-neurite complex \\ \end{tabular} & No Data Available & [79] \\ \hline PTHrP & Parathyroid hormone-related protein & No Data Available & [33; 80] \\ \hline \(\beta\)1-SPECTRIN & Muscle cells & No Data Available & [74] \\ \hline SUN1/2 & Nucleus & YES & [75] \\ \hline TALIN/VINCULIN & Cytoskeleton & No Data Available & [54] \\ \hline TREK-TREK2-TRAAK & Ion Channels/Lipid Membrane Bilayer & No Data Available & [81; 82] \\ \hline TITIN & Sacromere & No Data Available & [65] \\ \hline VIMENTIN & Several cells & No Data Available & [43] \\ \hline Von Willebrand Factor & Platelets & NO & [32] \\ \hline YAP/TAZ & Muscle and epithelial cells & YES & [83] \\ \hline ZO-1 & Membrane protein & YES & [63] \\ \hline ZYXIN & Cytoskeleton & YES & [84; 85; 86] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of mechanosensors in normogravity conditions and cytosol/nucleus shuttling. Their KO may or could simulate, at least in part, a condition of absence of gravity, revealing the associated functional/clinical effects. Unfortunately, a loss-of-function (KO) or a gain-of-function of these proteins are still to be explored and compared with animals after long-term space travel.
## 3 Materials and Methods
### Selection of Interference Power Step Size  
According to the measurement method of the sensitivity threshold value in GJB-151B-2013 [13], the interference signals should be reduced by 6 dB when the sensitive phenomenon occurs, then the interference signals should be gradually increased until the sensitive phenomenon occurs again. In the process of gradually increasing the interference signal, if the interference power (the interference signal power will be converted to interference field intensity) is increased with a fixed step size; on the one hand, the measured sensitivity threshold could be skipped because of the too large step size, and on the other hand, too small a step size may result in low measurement efficiency. Consequently, variable step size should be used to adjust the interference power for measurement. The closer to the sensitive threshold, the smaller step size is used. The specific measurement steps according to the variable step size are as follows:  
Step 1: Firstly, the interference power should be decreased by 6 dB on the basis of the critical interference power at a previous frequency point to ensure the tested equipment is not interfered with under the decreased power; otherwise, lower it by 6 dB once again, and so on.  
Step 2: Let us gradually increase the interference power based on the step size of 2 dB until the sensitive phenomenon occurs, as shown in Table 1. After that, the decibel value of each step size should be decreased by 50%, i.e., 1 dB and 0.5 dB.  
Step 3: When the effect phenomenon conforming to the sensitivity criterion occurs, the interference power is reduced by 1 step size; otherwise, the interference power is increased by 1 step size and repeat it several times.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Level** & **Interference Effect** & **Duration of Positioning Loss** \\ \hline Level 1 & Loss of positioning flashes once & About 1 s, the phenomenon does not occur at partial frequency \\ Level 2 & Skip between the positioning and loss & Duration time and jumping frequency \\  & of positioning & are variable \\ Level 3 & Positioning is initially normal and & About 10–20 s, then self-recovery \\  & loss of positioning after 5 s & Above 30 s, it can be understood as a \\ Level 4 & Loss of positioning within the first 4 s & permanent loss of positioning under interference \\ \hline \hline \end{tabular}
\end{table}
Table 1: Electromagnetic interference sensitive phenomena of the navigation receiver.  
Step 4: When the step size drops to 0.5 dB, the interference power is the critical interference power of this frequency point when the sensitivity phenomenon defined by the sensitivity criterion appears.
## 3 System Model
### Communication Channels  
This section describes the final step of the unreachable node communication scheme, the establishment of the communication channel. After the routing connection is completed, the nodes can interact with each other with simple data, but cannot transmit data. The establishment of the data channel, combined with node identity-based authentication and data encryption, allows for secure and fast data transmission between the two nodes. Depending on how the two nodes access the network, there are two ways of establishing the connection: direct connection and third-node relay. The former does not take up additional network resources but some access methods cannot be used and the latter is widely available but takes up third-node network resources. The direct connection mode is used in order not to consume too many network resources and allows two nodes to communicate directly after the communication channel has been established. However, this mode is not available for some network access methods, where a direct transmission channel cannot be established to an unreachable node, and then a third-node relay mode is required. The following two sections describe the connection details for both direct connection establishment and third-node relay modes respectively.
## 2 State of the Art
### Quality Assurance on Data
#### 2.3.2 \"Quality Dimensions\" for Data
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Data Quality Criteria** & **Examples of Methods for Checking the Quality Criteria** & **Examples of Associated Methods for Restoring the Data Quality** \\ \hline \multirow{6}{*}{Completeness} & Check if all data sources provide data. & Restore functionality and connection to the data source. \\ \cline{2-3}  & Verification of the operation of sensors in the required specification such as the measuring range. & Adjust the setup or replace the measuring system. \\ \cline{2-3}  & Checking the signal curves for gaps, for example, by checking the time steps. & Fill in the gaps with interpolated values. Adjust the sampling rate. \\ \cline{2-3}  &... &... \\ \hline \multirow{6}{*}{Uniqueness} & Checking the plausibility of patterns in the data as well as unrealistic outliers. & Correct signal allocation. \\ \cline{2-3}  & Checking the ID for data records. & Correct ID assignment. \\ \cline{2-3}  & Checking the consistency of timestamps when integrating different data records. & Readjust system clocks and reassign records. \\ \cline{2-3}  &... &... \\ \hline \multirow{6}{*}{Correctness} & Comparison of signal characteristics with analytical description to physical laws and with realism to system behavior. & Mapping against data that is confirmed to be correct or a defined, agreed-upon plausibility rule. \\ \cline{2-3}  & Comparison of the signal curves with limit values. & Correct parameterization of the sensor. \\ \cline{2-3}  &... &... \\ \hline \multirow{6}{*}{Timeliness} & Check the timestamps. & Selection of a correct sampling period. \\ \cline{2-3}  & Check assignment of path reference to time, e.g., for roll goods. & Adaptation of the transformation of path-related signals on a time basis. \\ \cline{2-3}  &... & Readjust system clocks. \\ \cline{2-3}  &... &... \\ \hline \multirow{6}{*}{Accuracy} & Check the accuracy of the measurement procedure for example with a reference measurement. & Change the measuring method or calibrate the measuring system. \\ \cline{2-3}  & Check the accuracy or functionality of the sensor. & Change the sensor. \\ \cline{2-3}  & Shielding of the signal line. \\ \cline{2-3}  & Suppression of signal noise. \\ \cline{2-3}  &... &... \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data quality criteria and examples of corresponding methods for quality inspection as well as for quality restoration using the example of signal data. ISO 8000 [44] also represents a concept standard for ensuring data quality--from the point of view of organizational processes in connection with quality management in companies. The focus here is again on master data, document designations, etc., and not on the signal data addressed here. It should be noted that at this point, methods for quality assurance on \"master data\" or \"context data\" have already been very well researched and described as part of database theory [45] and therefore are not the subject of the considerations in this article. \begin{table}
\begin{tabular}{c c c} \hline
# Gauge-Invariant Formulation of Time-Dependent Configuration Interaction Singles Method
## Theory
### Channel Orbital-Based TDCIS in the Velocity Gauge with Rotated Orbitals
Although this approach is guaranteed to be equivalent to the CI coefficient-based LG TDCIS, it brings no numerical gain over Equation (22), peculiarly including both \(\mathbf{E}\cdot\mathbf{r}\) and \(\mathbf{A}\cdot\mathbf{p}\), and requiring extensive gauge transformation of all occupied and virtual orbitals. Nonetheless, a useful method can be derived, if one switches to the channel orbital-based scheme by defining the rotated channel functions,  
\[|\chi^{\prime}_{i}(t)\rangle=\hat{U}(t)|\chi_{i}\rangle=\sum_{a}|\phi^{\prime }_{a}\rangle C_{ia}. \tag{36}\]  
Then we use \(d\hat{U}/dt=i(\mathbf{E}\cdot\hat{\mathbf{r}}+|\mathbf{A}|^{2}\hat{N}/2)\hat{U}\), and note \(\hat{U}\hat{\mathbf{p}}\hat{U}^{-1}=\hat{\mathbf{p}}+\mathbf{A}\hat{N}\) to derive  
\[i\partial_{t}C_{0} = \sqrt{2}\mathbf{E}\cdot\sum_{j}\langle\phi^{\prime}_{j}|\hat{\mathbf{r}}| \chi^{\prime}_{j}\rangle, \tag{37a}\] \[i\partial_{t}|\chi^{\prime}_{i}\rangle = \hat{P}^{\prime}\{(\hat{F}^{\prime}_{i}+\mathbf{A}\cdot\hat{\mathbf{p}})| \chi^{\prime}_{i}\rangle+\sqrt{2}\mathbf{E}\cdot\hat{\mathbf{r}}|\phi^{\prime}_{i} \rangle C_{0}\}-\sum_{j}(|\chi^{\prime}_{j}\rangle\langle\phi^{\prime}_{j}| \mathbf{E}\cdot\hat{\mathbf{r}}|\phi^{\prime}_{i}\rangle+|\phi^{\prime}_{j}\rangle \langle\phi^{\prime}_{j}|\mathbf{E}\cdot\hat{\mathbf{r}}|\chi^{\prime}_{i}\rangle), \tag{37b}\]  
where \(\hat{P}^{\prime}=1-\sum_{j}|\phi^{\prime}_{j}\rangle\langle\phi^{\prime}_{j}|\). Equations (37) are the main results of this work, which are called the rotated velocity-gauge (rVG) EOMs for brevity. The rVG scheme is equivalent to the LG scheme with fixed orbitals by construction, while replacing the length-gauge dipole operator \(\mathbf{E}\cdot\hat{\mathbf{r}}\) (the second term of Equation (28b)) with the spatially uniform \(\mathbf{A}\cdot\hat{\mathbf{p}}\) (the second term of Equation (37b)). Although several terms in the EOMs still involve the dipole operator, they all apply to the rotated occupied orbitals \(\{\phi^{\prime}_{i}\}\) which are localized around nuclei (to the same extent as \(\{\phi_{i}\}\) since the transformation \(e^{-i\mathbf{A}\cdot\mathbf{r}}\) is a local phase change), thus posing no difficulty in enjoying the same advantages of VG propagations of orbitals [39; 40; 41].
## 2 Materials and Methods
### Satellite-Based GPP Estimations  
Satellite-based GPP models can also provide alternative GPP estimations except for the direct MODIS GPP products. In this study, we introduced three satellite-based GPP models, including VPM [28,29,73], PCM [34] and AVM [35], to estimate GPP of this alpine meadow (Figure 1). Both of them are based on the vegetation indices (NDVI and EVI) and land surface water index (LSWI), which can be calculated by Equations (11) to (13) based on the MOD09A1 [29,36,74], respectively. The detailed information for model structures of these three satellite-based GPP models can be completely found in our previous study [30] or separately in their respective references, thus is not repeated here.  
\[NDVI=\frac{\rho_{nir1}-\rho_{red}}{\rho_{nir1}+\rho_{red}} \tag{11}\]  
\[EVI=\frac{2.5\times(\rho_{nir1}-\rho_{red})}{(\rho_{nir1}+6\times\rho_{red}-7.5 \times\rho_{blue}+1)} \tag{12}\]  
\[LSWI=\frac{\rho_{nir1}-\rho_{svir1}}{\rho_{nir1}+\rho_{svir1}} \tag{13}\]  
where \(\rho_{nir1}\) (841-876 nm), \(\rho_{red}\) (620-670 nm), \(\rho_{blue}\) (459-479 nm), and \(\rho_{svir1}\) (1628-1652 nm) are the four surface reflectance values from different spectral bands.
## 1 Introduction
These characteristics make collagen the main natural biological raw material for constructing tissue engineering scaffolds. As a bioactive material, collagen has the advantages of biocompatibility, biodegradability, cell adhesion, and low immunogenicity; however, compared to synthetic polymer materials, it lacks certain mechanical strength and stability. Although the plasticity of collagen allows people to develop different forms of in vitro controllable assembly materials for different clinical diseases [26; 27; 28], its mechanical strength and stability still cannot meet the basic requirements of cell culture scaffolds that respond to fluid shear forces in bioartificial liver reactors. Chemical crosslinking is an important polymer material modification process that involves connecting macromolecular chains (such as polymers) through chemical bonds under various factors such as light, heat, high-energy radiation, mechanical force, ultrasound, or crosslinking agents, thereby constructing a reticulated or specifically structured polymer material. In the biological field, chemical crosslinking is also used to link proteins to study the interaction between proteins and proteins, as well as between proteins and solid phases. Currently, common crosslinking agents for collagen chemical crosslinking modification include aldehydes [29], carbodiimides (EDC), polycarbonate acid-N-hydroxysuccinimide (NHS) esters, and diepoxy substances. Among them, glutaraldehyde is a commonly used chemical reagent for collagen crosslinking but it has certain cytotoxicity [30] and is not suitable for the development of medical device products. As a zero-length crosslinking agent, EDC can activate carboxyl groups and is often used in conjunction with NHS as a catalyst for crosslinking reactions between proteins. It has the advantages of high efficiency, safety, and non-toxicity. In addition, studies have found that collagen scaffolds crosslinked with EDC/NHS exhibit superior stability and cell compatibility [31]. Based on the key components of the extracellular matrix and the characteristics of the hepatocyte growth microenvironment, this study used chemical modification methods to hydrolyze the ester groups on the PET surface to expose carboxyl groups, followed by EDC/NHS-activated crosslinking, collagen coupling, and reactive-group blocking treatment to construct type I collagen-coated PET fibrous scaffolds. The physicochemical properties of the scaffolds were characterized, including surface functional group structure, chemical element composition, hydrophilicity, and collagen coating content. Through HepaRG cell culture experiments, the biological performance of the material, including cell adhesion and cell proliferation activity, was further studied to evaluate the impact of the scaffolds on hepatocyte growth and metabolic activities, thereby demonstrating their potential application in artificial liver support systems.
## 9 Conclusions
\begin{tabular}{l l} OCP & Optimal Control Problem \\ OCPs & Optimal Control Problems \\ MHE & Model Horizon Estimation \\ NMPC & Nonlinear Model Predictive Control \\ LQR & Linear Quadratic Regulator \\ iLQR & Iterative Linear Quadratic Regulator \\ MPC & Model Predictive Control \\ DDP & Differential Dynamic Programming \\ NLP & Nonlinear Programming \\ QP & Quadratic Programming \\ MIQP & Mixed Integer Quadratic Programming \\ CBFs & Control Barrier Functions \\ SDDM & State-dependent Distance Metric \\ CMPCC & Corridor-based Model Predictive Contouring Control \\ RRG & Rapidly-exploring Random Graph \\ IRIS & Iterative Regional Inflation by Semi-definite Programming \\ SFC & Safe Flight Corridor \\ JPS & Jump Point Search \\ GTO & Gradient-based Trajectory Optimization \\ SQP & Sequential Quadratic Programming \\ MPCC & Mathematical Program with Complementarity Constraints \\ ESDF & Euclidean Signed Distance Field \\ PGO & Path-guided Optimization \\ LTI & Linear Time Invariant \\ TOPP & Time-Optimal Parameterization of a given Path \\ CHOMP & Covariant Hamiltonian Optimization for Motion Planning \\ MAVs & Multirotor Aerial Vehicles \\ MAV & Multirotor Aerial Vehicle \\ UAVs & Unmanned Aerial Vehicles \\ UAV & Unmanned Aerial Vehicle \\ LQG & Linear Quadratic Gaussian \\ KF & Kalman Filter \\ EO & Elastic Optimization \\ QCQP & Quadratically Constrained Quadratic Programming \\ RHC & Receding Horizon Control \\ BFGS & Broyden-Fletcher-Goldfarb-Shanno \\ TSDF & Truncated Signed Distance Field \\ \end{tabular}
## 2 Time-Domain Finite Integration Theory (TD-FIT)
### Construction of Discrete Divergence and Curl Operator  
In three-dimensional Cartesian coordinate system, the primal grid \(G\) can be defined as:  
\[\begin{array}{l}G=\Big{\{}\Big{(}x_{i},\ \ y_{j},\ \ z_{k}\Big{)}\in\mathbb{R}^{3}; \\ x_{1}\leq x_{i}\leq x_{1},\ i=1,2,\ldots,I;\ y_{1}\leq y_{j}\leq y_{J},\ \ j=1,2,\ldots,J;\ z_{1}\leq z_{k}\leq z_{K},\ k=1,2, \ldots,K\Big{\}},\end{array} \tag{3}\]  
where \(I,J\), and \(K\) denote the number of nodes along the \(x\)-, \(y\)-, and \(z\)-axis, respectively.  
All the nodes of \(G\) are numbered linearly in ascending order along the \(x\)-, \(y\)-, and \(z\)-axis:  
\[n=1+(i-1)\cdot M_{x}+(j-1)\cdot M_{y}+(k-1)\cdot M_{z}, \tag{4}\]  
where \(n\) denotes the present node number, \(n=1,2,\ldots,N\); \(N\) denotes the total number of nodes of primal grid, \(N=IJK;M_{x}=1,M_{y}=I,M_{z}=IJ\).  
Then, we need to introduce three basic topological matrices of dimensions \(N\times N\) to represent discrete partial differential operators with central difference approximation:  
\[\frac{\partial}{\partial x}\ \Leftrightarrow\ \mathbf{P}_{x}=(\mathbf{P}_{x})_{m,n}= \left\{\begin{array}{l}-1\ n=m\\ 1\ n=m+M_{x}\\ 0\ \textit{otherwise}\end{array}\right., \tag{5}\]  
\[\frac{\partial}{\partial y}\ \Leftrightarrow\ \mathbf{P}_{y}=\big{(}\mathbf{P}_{y} \big{)}_{m,n}=\left\{\begin{array}{l}-1\ n=m\\ 1\ n=m+M_{y}\\ 0\ \textit{otherwise}\end{array}\right., \tag{6}\]  
\[\frac{\partial}{\partial z}\ \Leftrightarrow\ \mathbf{P}_{z}=(\mathbf{P}_{z} )_{m,n}=\left\{\begin{array}{l}-1\ n=m\\ 1\ n=m+M_{z}\\ 0\ \textit{otherwise}\end{array}\right., \tag{7}\]  
where \(m,n=1,2,\ldots,N;\mathbf{P}_{x},\ \mathbf{P}_{y},\ \mathbf{P}_{z}\) have two bands and with entries taking values \(-1\), \(0\), or \(+1\).  
At the primal grid, discrete curl operator \(\mathbf{C}\) representing relationship among facet and edges and discrete divergence operator \(\mathbf{S}\) representing relationship among volume and facets become:  
\[\mathbf{C}=\left[\begin{array}{ccc}0&-\mathbf{P}_{z}&\mathbf{P}_{y}\\ \mathbf{P}_{z}&0&-\mathbf{P}_{x}\\ -\mathbf{P}_{y}&\mathbf{P}_{x}&0\end{array}\right]_{3N\times 3N}, \tag{8}\]  
\[\mathbf{S}=\left[\begin{array}{ccc}\mathbf{P}_{x}&\mathbf{P}_{y}&\mathbf{P }_{z}\end{array}\right]_{N\times 3N}. \tag{9}\]  
Similarly, at the dual grid, discrete curl operator \(\overline{\mathbf{C}}\) and discrete divergence operator \(\overline{\mathbf{S}}\) are:  
\[\overline{\mathbf{C}}=\mathbf{C}^{T}=\left[\begin{array}{ccc}0&\mathbf{P}_ {z}^{T}&-\mathbf{P}_{y}^{T}\\ -\mathbf{P}_{z}^{T}&0&\mathbf{P}_{x}^{T}\\ \mathbf{P}_{y}^{T}&-\mathbf{P}_{x}^{T}&0\end{array}\right]_{3N\times 3N}, \tag{10}\]  
\[\overline{\mathbf{S}}=\left[\begin{array}{ccc}\overline{\mathbf{P}}_{x}& \overline{\mathbf{P}}_{y}&\overline{\mathbf{P}}_{z}\end{array}\right]=\left[ \begin{array}{ccc}-\mathbf{P}_{x}^{T}&-\mathbf{P}_{y}^{T}&-\mathbf{P}_{z}^{ T}\end{array}\right]_{N\times 3N^{\prime}} \tag{11}\]  
where the superscript \(T\) denotes transpose matrix.
## 1 Introduction
### Carbon and Nitrogen Isotopes  
The \(\delta^{13}\)C values of terrestrial plants primarily vary due to their photosynthetic pathways. Plants that use the Calvin cycle of carbon assimilation are known as C3 plants. C4 plants utilize the Hatch-Slack Cycle pathway of carbon assimilation, while CAM plants employ the Crassulacean acid metabolism pathway. The above \(\delta^{13}\)C values range from \(-35\) to \(-21\)%o, \(-14\) to \(-10\)%o, and \(-20\) to \(-10\)%o, respectively [36]. C3 plants present lower \(\delta^{13}\)C values due to the significant isotopic discrimination compared to \(\delta^{13}\)CO\({}_{2}\) by the \"RuBisCO\" enzyme (\(\sim\)20%o compared to atmospheric CO\({}_{2}\)) during CO\({}_{2}\) fixation [36; 37; 38]. The limited isotopic discrimination in C4 plants is due to the morphological variation of bundle sheath cells. CAM plants demonstrate \(\delta^{13}\)C values between the values of C3 and C4 plants because they utilize the CO\({}_{2}\) fixation of both pathways.  
Stable carbon collagen isotope values can detect the consumption of plants of different photosynthetic pathways (C3, C4, and CAM) and distinguish between marine-based diets and C3 and C4 terrestrial ones [37; 38; 39; 40; 41; 42], since they represent mainly the protein component of the diet [41]. Carbon signals from bone collagen are 74% derived from proteins and 26% from energy macronutrients (lipids and carbohydrates) [36; 42; 43]. Various sources indicated a fractionation value for \(\delta^{13}\)C\({}_{\rm coll}\) ranging from 1%o to 5%o between bone collagen and diet [30; 31; 32; 33; 34]. However, measurements that were taken during controlled feeding experiments on omnivorous mammals [42; 43; 43; 44] determined a fractionation value of 4.8% for carbon and collagen isotopes with an uncertainty of 0.5% [46].  
The value of \(\delta^{15}\)N in a plant indicates the nitrogen sources available for it. A lower \(\delta^{15}\)N value (close to 0%) indicates nitrogen from synthetic or symbiotic N fixation, while higher \(\delta^{15}\)N values are derived from organic fertilizer inputs [6, 47]. Additionally, environmental factors such as climate [48], drought, stress, and proximity to the sea can increase \(\delta^{15}\)N in terrestrial plants [49]. Stable nitrogen values can help to identify the trophic level of consumed foods and differentiate between marine and freshwater protein intake, especially in domesticated omnivores that consume terrestrial and freshwater protein. Feeding experiments and anthropological studies demonstrate a fractionation value of 5.5% with an uncertainty of 0.5% for \(\delta^{15}\)N isotopes, i.e., [47, 50, 51, 52].