esa-sceva/satcom-chunk-collection huggingface dataset:
## Materials and Methods  
### Materials  
Bovine serum albumin (BSA) (A9418), 3,3'-dihexylloxacinarbocyanine iodide (DiOC6) (D273), glutaraldehydedehyde (340855) heparin salt (H3393), 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) (H3375), poloxamer 407 (Pluronics@F-127, P2443) were from Sigma-Aldrich (St Louis, MO, USA). 3.2% sodium citrate vacutainers (369714) and 21-gauge Vacutainer@ 21 Safety-Lok blood collection sets (367281) were from Becton Dickson (Frankwood Lakes,NJ, USA). 500 uL and 100 uL glass luer lock syringes were from Hamilton (Reno, NV, USA). Tridecafluoro-1,1,2,2-tetrahydrorooctyltrichlorosilane (FOTS) (SIT8174.0) was from Gelest (Morrisville, PA, USA). Polydimethylsiloxane and crosslink were obtained from Krayden (Denver, CO, USA). Collagen related peptides (CRP-XL) [GCO(GPO)10 GCOG-amide], 5(6)-carboxyfluorescein (FAM) labeled CRP-XL, GFOGER [GPC(GPP)5 GFOGER(GPP)5 GPC-amide], and VWF-III [GPCGPP)5 GPRGQGVMFG(GPP)5 GPC-amide] were obtained from Cambcol Laboratories (Cambridgeshire, UK). Glass slides (2\" x 3\") were obtained from Fisher Scientific (Lenexa, KS, USA). Pierce Quantitative Fluorometric Peptide Assay (23290) and Texas Red dye (T20175) were from Thermo Fischer (Denver, CO, USA). Phosphate-buffered saline (PBS) was prepared to 137 mM NaCl, 2.7 mM KCl, 10 mM Na\({}_{2}\)HPO\({}_{4}\), 1.8 mM KH\({}_{2}\)PO\({}_{4}\), and pH 7.4.
## 4 Experimental Results
### Dynamic Range  
Dynamic range is another important characterization parameter for transceivers to perform the anti-interference and anti-distortion capability of the system. The dynamic range includes linear dynamic range (LDR) and spurious-free dynamic range (SFDR). LDR is the difference value between 1 dB power compression point (P\({}_{\text{-1}}\)) and noise power, and SFDR is the ratio of fundamental signal power to noise floor power when the third-order intermodulation distortion (IMD\({}_{3}\)) is equal to the noise floor power. We assume that the RF operating point of the system is 9 GHz. Thus, the input 1 dB power compression point (IP\({}_{\text{-1}}\)) is shown in Figure 8a,b with the HF 20.2 GHz for upconversion and HF 31 GHz for downconversion. The results of 13 dBm and 9.5 dBm are acquired by measuring and fitting. To test the SFDR of the system, a two-tone signal with a spacing of 1 MHz is adopted to drive the MZM. As shown in Figure 9a,b, SFDR is up to 86.23 dB\(\cdot\)HZ\({}^{2/3}\) and 80.95 dB\(\cdot\)HZ\({}^{2/3}\), respectively, for upconversion and downconversion. Therefore, the IP\({}_{\text{-1}}\) and SFDR of our converter are sufficient for most practical transceiver applications.  
Figure 7: Measured output electrical spectrum of both the upconversion (**a**) and downconversion (**b**) when RF signal is tuned from 0.8 to 18 GHz. Conversion efficiency (**c**) when LO frequency is tuned from 21–38.2 GHz (corresponds to the RF signal from 0.8–18 GHz) and power responses (**d**) of electrical cable, electrical combiner, and MZM.
## Abbreviations  
\begin{tabular}{l l} CFRCS & Curvilinear Fiber-Reinforced Composite Structures \\ FEA & Finite Element Analysis \\ FEM & Finite Element Method \\ FE & Finite Element \\ FRP & Fiber-Reinforced Polymer \\ DIC & Digital Image Correlation \\ AE & Acoustic Emission \\ PSO & Particle Swarm Optimization \\ BA & Bee Algorithm \\ GA & Genetic Algorithm \\ CSS & Charged System Search \\ ESO & Evolutionary Structural Optimization \\ TOP & Topology Optimization \\ LVI & Low-Velocity Impact \\ SHM & Structural Health Monitoring \\ CPT & Classic Plate Theory \\ FBD & Free Body Diagram \\
**English Letters** \\ \(A_{ij}\) & Arrays of stiffness matrix \(A\) \\ \(B_{ij}\) & Arrays of stiffness matrix \(B\) \\ \(c_{i}\) & Differential equation constants \\ \(D_{ij}\) & Arrays of stiffness matrix \(D\) \\ \(E_{i}\) & Elastic modulus, GPa \\ \(f_{ij}\) & Arrays of differential equation's coefficients matrix \\ \(G_{i}\) & Shear modulus, GPa \\ \(H_{i}\) & Coefficient \\ \(k_{xi}\) & Curvature \\ \(k_{i}\) & Coefficient \\ \(M_{i}\) & Moment, N.m \\ \(N_{i}\) & Horizontal tensile force, \(N\) \\ \(n\) & Number of iterations of objective function's calculation \\ \(Q_{i}\) & Shear force, \(N\) \\ \(q_{i}\) & Coefficient \\ \(t_{i}\) & Thickness, mm \\ \(u_{0i}\) & Displacement of mid-plan in \(x\) direction, mm \\ \(u_{i}\) & Displacement in \(x\) direction, mm \\ \(v_{i}\) & Displacement in \(y\) direction, mm \\ \(w_{i}\) & Displacement in \(z\) direction, mm \\ \(x\) & Position in \(x\) direction, mm \\ \(y\) & Position in \(y\) direction, mm \\ \(z\) & Position in \(z\) direction, mm \\
**Greek Letters** \\ \(\beta_{i}\) & Coefficient \\ \(\beta_{xi}\) & Slope in adherends \\ \(\gamma_{i}\) & Shear strain \\ \(\delta_{i}\) & Coefficient \\ \(\varepsilon_{i}\) & Strain \\ \(\theta_{i}\) & Coefficient \\ \(\mu_{i}\) & Coefficient \\ \(v_{i}\) & Poisson's coefficient \\ \(\sigma_{i}\) & Normal stress, GPa \\ \(\tau_{i}\) & Shear stress, GPa \\ \(\omega_{j}\) & Coefficient \\ \end{tabular}
# Integration and Field Evaluation of an IoV System for Enhancing Road Safety
## 5 Results
### Technical Performance Results of the System
#### 5.1.1 Vehicle Detection and Speed Calculation System Performance  
The first type of quantitative system performance test performed targeted the success rate of the system in identifying a passing vehicle, its direction and speed, which are its main critical parameters of interest. For this reason, during the tests performed using both a car and a motorcycle, each vehicle passed five (5) times from each ORU position at a certain speed, with the speed varying between 15 km/h and 50 km/h. The system's performance in detecting each vehicle, its direction and speed is summarized in Tables 3 and 4. For the calculation of the speed detection error percentage, only the results of valid direction detections were taken into account.  
As can be seen from Tables 3 and 4, both types of vehicles were successfully detected by all the ORUs on the field at all times. The vehicle direction detection success rate is  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Car**} & \multicolumn{3}{c}{**Motorcycle**} \\ \hline \multirow{2}{*}{\begin{tabular}{c} **Speed** \\ **(km/h)** \\ \end{tabular} } & \multirow{2}{*}{**Passes**} & \multicolumn{2}{c}{\
\begin{tabular}{c} **Average Speed** \\ **Detection Error** \\ **(\%)** \\ \end{tabular} } & \multirow{2}{*}{**Speed**} & \multirow{2}{*}{**Passes**} & \multicolumn{2}{c}{
\begin{tabular}{c} **Average Speed** \\ **Detection Error** \\ **(\%)** \\ \end{tabular} } \\ \hline
16 & 30 & 11.6\% & 15 & 30 & 6.4\% \\
26 & 30 & 11.3\% & 30 & 30 & 13.1\% \\
46 & 30 & 10.3\% & 50 & 30 & 4.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Vehicle speed detection results.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Car**} & \multicolumn{3}{c}{**Motorcycle**} \\ \hline \multirow{2}{*}{\begin{tabular}{c} **Speed** \\ **(km/h)** \\ \end{tabular} } & \multirow{2}{*}{**Passes**} & \multicolumn{2}{c}{\
\begin{tabular}{c} **Vehicle** \\ **Detection** \\ \end{tabular} } & \multirow{2}{*}{**Direction**} & \multirow{2}{*}{**Speed**} & \multirow{2}{*}{**Passes**} & \multicolumn{2}{c}{
\begin{tabular}{c} **Vehicle** \\ **Detection** \\ \end{tabular} } & \multirow{2}{*}{**Direction**} \\ \cline{1-1}  & & & & & & \\
26 & 30 & 30 & 28 & 30 & 30 & 27 \\
46 & 30 & 30 & 30 & 50 & 30 & 30 & 29 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Vehicle and direction detection results.  
very high as well, while the average speed detection error remains constantly under 14%, demonstrating a cohesive and good system performance. To better evaluate the system's performance regarding vehicle speed estimation, the fact that the speed indication reference during the tests was the corresponding vehicle's speed gauge should also be taken into account. The speed gauge has an inherent deviation between 3 km/h and 5 km/h from the speed it displays.
## 2 Materials and Methods
### RNA-Seq Analysis
#### 2.5.3 Read Quality Control and Mapping  
The raw paired-end reads were trimmed and quality-controlled using Trimmomatic with the parameters SLIDINGWINDOW:4:15, MINLEN:75 (version 0.36, [[http://www.usadellab.org/cms/index.php?page=trimmomatic](http://www.usadellab.org/cms/index.php?page=trimmomatic)]([http://www.usadellab.org/cms/index.php?page=trimmomatic](http://www.usadellab.org/cms/index.php?page=trimmomatic)), accessed on 30 June 2022). Then, clean reads were separately aligned with a reference genome (the HDEM _B. oleracea_ reference genome, [[https://www.genoscope.cns.fr/projet_BKL/cgi-bin/gbrowse/boleracea/](https://www.genoscope.cns.fr/projet_BKL/cgi-bin/gbrowse/boleracea/)]([https://www.genoscope.cns.fr/projet_BKL/cgi-bin/gbrowse/boleracea/](https://www.genoscope.cns.fr/projet_BKL/cgi-bin/gbrowse/boleracea/)), accessed on 30 June 2022) in orientation mode using the HISAT2 ([[https://daehwankimlab.github.io/hisat2/](https://daehwankimlab.github.io/hisat2/)]([https://daehwankimlab.github.io/hisat2/](https://daehwankimlab.github.io/hisat2/)), accessed on 30 June 2022) software. This software was used for mapping with the default parameters. Quality assessment of these data were undertaken using qualimap v2.2.1 ([[http://qualimap.bioinfo.cipf.es/](http://qualimap.bioinfo.cipf.es/)]([http://qualimap.bioinfo.cipf.es/](http://qualimap.bioinfo.cipf.es/)), accessed on 30 June 2022). The gene reads were counted using HTSeq ([[https://htseq.readthedocs.io/en/release_0.11.1/](https://htseq.readthedocs.io/en/release_0.11.1/)]([https://htseq.readthedocs.io/en/release_0.11.1/](https://htseq.readthedocs.io/en/release_0.11.1/)), accessed on 30 June 2022). The sequences of the homologous ESP and NSP genes based on the HDEM reference genome were blasted in the Brassica Database ([[http://brassicab.cn/#/](http://brassicab.cn/#/)]([http://brassicab.cn/#/](http://brassicab.cn/#/)), accessed on 30 June 2022).
## 3 Results
### Crop Classification
#### 3.2.3 Optimal Combination of SAR Images
In addition, it indicates that the summer and autumn acquisitions (from June to September) were more valuable for crop classification than the spring acquisitions (April and May). Figure 11: Classification map with the best accuracy using an optimal combination of polarimetric observables from all RADARSAT-2 images (OA = 93.75%). Figure 10: The RF overall accuracies for the optimal combination of polarimetric observables produced by a forward feature selection procedure using all multitemporal RADARSAT-2 images. Note that numbers in the figure denote the best accuracy in each step, and the abbreviations are explained in Table 3.
## 4 Salt-Tolerant Plants as Sources of Neuroprotective and Mental Health Commodities
### In Vivo Studies
These assays provide valuable preclinical data on the therapeutic potential of plant metabolites, bridging the gap between in vitro studies and clinical trials. Similarly to the in vitro tests, the major components of the most active plans are primarily phenolic compounds, flavonoids, and terpenoids. Phenolic compounds, such as caffe acid and trans-ferulic acid, along with flavonoids like hyperoside, isoquercirtin, kaempfer, and anthocyanins, are abundantly present in these plants. Terpenoids, including sterols and triterpenes, are also significant, although less frequently mentioned. These metabolites often occur in complex combinations, contributing to the plants' neuroprotective effects. For instance, _S. europaea_ contains caffe acid, trans-ferulic acid, acanthoside B, isorhamnetin, and irilin B, along with carbohydrates, uronic acids, and proteins [32]. _C. gigantea_ latex comprises alkaloids, cardiac glycosides, tannins, flavonoids, sterols, and triterpenes [65]. _A. venetum_ leaves contain hyperoside and isoquercirtin [66; 67], while _A. officinalis_ leaves include hypolaetin-8-glucosidase, isoquercirtin, kaempfer, caffe acid, p-cumaric acid, coumarins, scopoletin, phytosterols, tannins, asparagines, and amino acids [68]. For instance, phenolics, flavonoids, and terpenoids play significant roles in the neuroprotective activities observed in various in vivo assays. Phenolic compounds, such as caffeic and ferulic acids, possess strong antioxidant properties that mitigate oxidative stress, contributing to antidepressant-like effects [55]. Flavonoids, including quercetin and hyperoside, enhance neurotransmitter levels, promoting mood regulation and showing antidepressant activity in the forced swimming test (FST) [60,67]. These compounds also exhibit sedative and hypnotic effects, as seen in pentobarbital-induced hyprosis assays, by enhancing GABAergic neurotransmission [73,77]. In [PERSON]'s disease models, phenolic acids and flavonoids protect dopaminergic neurons from oxidative damage and inflammation, preserving neuronal integrity [78]. Additionally, in [PERSON]'s disease models, phenolics and flavonoids inhibit amyloid-beta aggregation and enhance synaptic plasticity, improving cognitive functions [64]. Terpenoids like ginkgolides also contribute to neuroprotection by reducing neuroinflammation and oxidative stress [64]. These compounds' multifaceted actions underline their potential in treating neurodegenerative and neuropsychiatric disorders.
## 6 Security and Privacy Requirements of Healthcare Applications
There are two kinds of freshness: weak freshness, which gives partial message ordering but does not carry time-delay information; and strong freshness, gives a total order on a request-response pair and allows for delay estimation [92]. * Secure localization: In healthcare applications, estimation of the patient's location is very important. In real-time applications, a lack of smart patient tracking allows an attacker to send incorrect patient's location by using false signals [92]. * Forward and backward secrecy: In a real-time healthcare application, generally new medical sensors are deployed when old sensors fail, so it is important to consider forward and backward secrecy. In forward secrecy, a medical sensor cannot read future messages transmitted after it leaves the network, while in backward secrecy a sensor joining the network cannot read any previously transmitted messages [93]. * Communication and computation cost: Since wireless medical sensors are resource constrained devices, and healthcare application's functions also need room for executing their tasks, the security schemes must be efficient in terms of the communication and computational cost. * Patient permission: A patient's permission is needed when a healthcare provider is disseminating his/her health records to another healthcare consultant. For example, medical researcher, insurance company, _etc._  
In addition, patient's _anonymity_ is also needed for healthcare applications because medical sensor networks are wireless in nature. Thus _anonymity_ hides the source of a packet (_i.e._, medical sensor data) during wireless communication. It is a service that can enable confidentiality. Further, a wireless healthcare application should enable minimum _survivability_ in the presence of power loss, failures or attacks.
# Multiple Fano Resonances in Dynamic Resonant Tunneling Processes
## 4 Exact Numerical Solution and Approximate Analytical Solution for the Zero-Transmission Solution  
Equation (13) can be rewritten in a matrix form \(M\mathbf{t}=\mathbf{v}\), where  
\[M=\begin{pmatrix}\ddots&\ddots&&&&\\ \ddots&\alpha-\chi_{-2}&\beta/2&&&\\ &\beta/2&\alpha-\chi_{-1}&\beta/2&&&\\ &&\beta/2&\alpha-\chi_{0}&\beta/2&&\\ &&&\beta/2&\alpha-\chi_{1}&\beta/2&\\ &&&&\beta/2&\alpha-\chi_{2}&\ddots\\ &&&&\ddots&\ddots\\ \end{pmatrix}\text{ and }\mathbf{v}=\begin{pmatrix}\vdots\\ 0\\ 0\\ -\chi_{0}\\ 0\\ \vdots\\ \end{pmatrix} \tag{19}\]  
and \(\chi_{n}\equiv-2\rho_{n}\text{tanh}[\rho_{n}L-i\text{arctan}(k_{n}/\rho_{n})]\) (Equation (14)).  
Figure 8: Multiple solutions of Equation (17) for two cases. In the upper panel, Equation (17) is presented for \(m=3\), \(4\dots 10\) for the parameter \(\alpha U^{-1/2}=-2.2\) (\(\Omega_{R}<0\)). In this scenario, the Fano resonance exists even for very opaque barriers, where \(L\) can be arbitrarily large. In the lower panel, Equation (17) is presented for \(m=1\), \(2\dots 5\) and for the parameter \(\alpha U^{-1/2}=-1.8\) (\(\Omega_{R}>0\)). In this scenario, the Fano resonance exists only for finite-width barriers. In both cases, \(0<\Omega<\omega\) with the parameter \(\omega/U=0.1\).  
Let us further define  
\[M_{(-1)}^{(-N)}=\begin{pmatrix}\alpha-\chi_{-N}&\beta/2&&\\ \beta/2&\ddots&\ddots&\\ &\ddots&&\beta/2&\\ &&\beta/2&\alpha-\chi_{-2}&\beta/2\\ &&&\beta/2&\alpha-\chi_{-1}\end{pmatrix} \tag{20}\]  
and  
\[M_{(N)}^{(1)}=\begin{pmatrix}\alpha-\chi_{1}&\beta/2&&\\ \beta/2&\alpha-\chi_{2}&\beta/2&&\\ &\beta/2&\ddots&\ddots&\\ &&\ddots&&\beta/2\\ &&&\beta/2&\alpha-\chi_{N}\end{pmatrix} \tag{21}\]  
Then, the solution of the zero mode \(t_{0}\) reads (for details see ref. [34]),  
\[t_{0}=-\chi_{0}\lim_{N\to\infty}\frac{\left|M_{(-1)}^{(-N)}\right|\left|M_{(N) }^{(1)}\right|}{\left|M_{0}^{(N)}\right|} \tag{22}\]  
Therefore, zero transmission is reached when  
\[\left|M_{(-1)}^{(-N)}\right|=0 \tag{23}\]  
It follows from Equation (11) and current conservation that, when Equation (22) vanishes, the current must vanish as well. Therefore, the solution of Equation (23) corresponds to the multiple solutions for which the current vanishes.  
For any given energy, several solutions exist for different values of \(L\). Nevertheless, we can straightforwardly deduce that Equation (23) is valid, provided that the incoming particle's energy is lower than the oscillating frequency, i.e., \(\Omega<\omega\). Otherwise, some of the \(k_{-m}\) (for \(1<m<N\)) are real, and if this is the case, then the term  
\(\chi_{-m}=-2\rho_{-m}\text{tanh}[\rho_{-m}L-i\text{arctan}(k_{-m}/\rho_{-m})]\) (Equation (14)) (which are the only elements in the matrix (20) that can have imaginary components) is _not_ necessarily real (noting that all the \(\rho_{-m}\) terms are real). Consequently, the determinant is not real and cannot vanish. This fact is consistent with the fact that the Fano resonances are limited by \(\Omega<\omega\), and with the folding nature of the periodicity, a 2D map structure qualitatively similar to Figure 8 appears.
# Multi-Agent Simulation Approach for Modular Integrated Construction Supply Chain
## 3 Proposed Agent-Based Model
### Agent-Based Model Overview  
The agent-based model developed in this study incorporates various entities involved in the MiC supply chain process. Each entity is modeled as an agent with specific behaviors and interactions. The primary agents in the model include the following:  
Figure 3: Integration of (**a**) physical process, (**b**) data collection, and (**c**) Multi-Agent Simulation in the MiC Supply Chain.  
* Suppliers (\(S_{i}\)): Responsible for providing prefabricated components. Each supplier agent manages the production and dispatch of components to fabrication centers (i.e., MiC factories).
* \(F_{j}\) and \(T_{2,l}\): \(F_{j}\)
- \(>\) \(CS\)): These agents simulate the transportation vehicles that move prefabricated components from suppliers to fabrication centers and then integrated modules from fabrication centers to construction sites.
* MiC factories (\(F_{j}\)): These agents represent the fabrication centers where prefabricated components are assembled into integrated construction modules.
* Construction sites (CSs): The final destination agents where the integrated modules are assembled into the final construction.  
The use case diagram (see Figure 4) illustrates the interactions between various agents involved in the logistics process of MiC, ensuring that each step is clearly defined and that all agents work in coordination to achieve efficient construction logistics. Each agent performs specific functions to ensure the efficient delivery and assembly of integrated construction modules. The construction site (CS) agent initiates the process by placing orders for integrated construction modules to the MiC factories. Once the modules are fabricated and transported, the construction site agent receives and assembles them on-site. The factory (F) agent receives orders from the construction site for integrated construction modules and is responsible for fabricating the integrated modules based on these orders. To fabricate the modules, the factory agent places orders for prefabricated components to the suppliers. Once the modules are ready, the factory agent requests transportation for the modules to the construction site. The supplier (S) agent receives orders for prefabricated components from the factory. Upon receiving these orders, the supplier agent produces the required prefabricated components and then requests transportation to deliver the produced components to the MiC factories. Transporter \(T_{1}\) is responsible for transporting prefabricated components from the supplier to the factory. Transporter \(T_{2}\) handles the transportation of integrated modules from the factory to the construction site. Finally, the construction site (CS) receives and assembles the modules on-site, completing the construction process.
# A Brain-Inspired Goal-Oriented Robot Navigation System
## 2 Mathematical Model
### Model Description  
Motion information is obtained by integrating direction and speed signals, then updating the self-position. This paper uses a 1D ring attractor to model the HD cells:  
\[\mathrm{HD}_{i}=\left[\begin{array}{cc}\cos(\phi_{i,1})&\sin(\phi_{i,1})\\ \cos(\phi_{i,m})&\sin(\phi_{i,m})\end{array}\right] \tag{1}\]  
where \(\phi_{i,j}\) is the preferred direction of the \(j^{\mathrm{th}}\) cell in the \(i^{\mathrm{th}}\) ring attractor.  
\[\phi_{i,j}=\frac{2\pi j}{m} \tag{2}\]  
\(j=1,\ldots,m,m=6\) is the number of neurons in a single attractor. Different rings have different preferred directions. There are three ring attractors. The angle difference is \(\pi/3\).  
Suppose that at time \(t\), the robot is moving with speed \(V(t)\). The velocity projected to different ring attractors is:  
\[v_{i}(t)=\mathrm{HD}_{i}*V(t) \tag{3}\]  
Given the velocity, we can figure out the wavelength of sine function:  
\[\lambda=\frac{v}{f} \tag{4}\]  
If two sinusoidal functions of different frequencies interfere with each other, it will generate beat frequency oscillations with a fixed spatial distance (as shown in Figure 2b). The beat frequency is equal to the difference between the two frequencies:  
\[f_{b}=\left|f_{0}-f_{i}\right| \tag{5}\]  
Then the wavelength of the periodic oscillation is:  
\[\lambda_{i}=\frac{v}{f_{b}}=\frac{v}{\left|f_{0}-f_{i}\right|} \tag{6}\]  
\(\lambda_{i}\) a fixed value and represents the distance between vertices in the grid cells space. According to Equation (6), we derive:  
\[f_{i}=f_{0}+\frac{v}{\lambda_{i}} \tag{7}\]  
Set\(f_{0}=7\) Hz as a reference frequency. Beat frequency oscillation is integrated into the corresponding phase in different ring attractors (as shown in Figure 2a):  
\[\alpha_{i}(t)=2\pi\int_{0}^{t}f_{i}(T)dT \tag{8}\]  
Converting phase-coded into rate-coded to express the position signal, the activity of the \(j^{\mathrm{th}}\) cell in the \(i^{\mathrm{th}}\) ring is:  
\[S_{i,j}(t)=\frac{\sin(\alpha_{i}(t)+\phi_{i,j})+1}{2} \tag{9}\]  
With comprehensive input of ring attractors with different preferred orientations, the amplitude of the beat frequency oscillations will be recognized at each \(x\pm k\lambda_{i}\) (\(x=V(t)\times t\)). This means thatwhen the robot is moving linearly, it will produce grid-like activity with vertex spacing \(\lambda_{i}\) (as shown in Figure 2c). The activity of grid cells is:  
\[g_{i,j}(t)=\prod S(t) \tag{10}\]  
The place cells accept the inputs of the grid cells' population with different activities. The place cells are activated when the inputs are greater than the threshold h:  
\[\psi(g)=\left\{\begin{array}{cc}&1&g>\text{h}\\ &0&\text{otherwise}\end{array}\right. \tag{11}\]