esa-sceva/satcom-chunk-collection huggingface dataset:
# Lexographic Unranking of Combinations Revisited
## 3 Classical Unranking Algorithms
### Unranking through the Recursive Method
It satisfies:  
\[B(z,y)=\sum_{n\geq 0}\sum_{k=0}^{n}\binom{n}{k}z^{n}\ y^{k}=\frac{1}{1-z-zy}.\]  
To follow the extreme cases, we must remove the first column \(k=0\) and the diagonal \(k=n\):  
\[\bar{B}(z,y)=\frac{1}{1-z-zy}-\frac{1}{1-z}-\frac{zy}{1-zy}.\]  
By summing the recursive equation and taking care of the extreme cases, we get:  
\[\sum_{n\geq 1}\sum_{k=1}^{n}u_{n,k}z^{n}\ y^{k} =\bar{B}(z,y)+\sum_{n\geq 1}\sum_{k=1}^{n}u_{n-1,k-1}z^{n}\ y^{k}+ \sum_{n\geq 1}\sum_{k=1}^{n}u_{n-1,k}z^{n}\ y^{k}\] \[U(z,y) =\bar{B}(z,y)+z\ y\ U(z,y)+z\ U(z,y).\]  
We thus deduce  
\[U(z,y)=\frac{1}{1-z-zy}\bigg{(}\frac{1}{1-z-zy}-\frac{1}{1-z}-\frac{zy}{1-zy} \bigg{)}.\]  
The second step of the proof consists in extracting the coefficient \(u_{n,k}\). \[U(z,y) =\frac{1}{1-z(1+y)}\bigg{(}\frac{1}{1-z(1+y)}-\frac{1}{1-z}-\frac {zy}{1-zy}\bigg{)}\] \[=\bigg{(}\sum_{r\geq 0}z^{r}(1+y)^{r}\bigg{)}\cdot\bigg{(}\sum_{r \geq 0}z^{r}(1+y)^{r}-\sum_{r\geq 0}z^{r}-\sum_{r\geq 1}z^{r}y^{r}\bigg{)}\] \[=\bigg{(}\sum_{r\geq 0}z^{r}(1+y)^{r}\bigg{)}\cdot\bigg{(}1-1+ \sum_{r\geq 1}z^{r}\big{(}(1+y)^{r}-1-y^{r}\big{)}\bigg{)}.\]  
By extraction the coefficient in front of \(z^{n}\) is:  
\[[z^{n}]U(z,y) =\sum_{\ell=0}^{n-1}(1+y)^{\ell}\Big{(}(1+y)^{n-\ell}-1-y^{n-\ell }\Big{)}\] \[B(z,y)=\sum_{n\geq 0}\sum_{k=0}^{n}\binom{n}{k}z^{n}\ y^{k}=\frac{1}{1-z-zy}.\]0 \[B(z,y)=\sum_{n\geq 0}\sum_{k=0}^{n}\binom{n}{k}z^{n}\ y^{k}=\frac{1}{1-z-zy}.\]1  
The latter result corresponds to the distribution of the costs when \(k\) varies from \(0\) to \(n\). We can then extract the coefficient of \(z^{n}\ y^{k}\):  
\[B(z,y)=\sum_{n\geq 0}\sum_{k=0}^{n}\binom{n}{k}z^{n}\ y^{k}=\frac{1}{1-z-zy}.\]2 \[B(z,y)=\sum_{n\geq 0}\sum_{k=0}^{n}\binom{n}{k}z^{n}\ y^{k}=\frac{1}{1-z-zy}.\]3  
which completes the proof. This sequence \(u_{n,k}\) is a shifted version of the sequence stored under the reference OEIS A059797. We thus can complete its properties in the OEIS using our results. Due to the values of the extreme cases when \(k=0\) and \(k=n\) and the symmetry in the recurrence, we obviously obtain that \(u_{n,k}=u_{n,n-k}\), reflecting the symmetry of the binomial coefficients. Corollary 3: _The function \(\textsc{UnrankingRecursive}(n,k,\cdot)\) needs on average \(u_{n,k}/{n\choose k}\) calls to the function binomial. For \(n\) being large and \(k\) being of the form \(\alpha\cdot n\) for \(0<\alpha<1\), we get:_  
\[B(z,y)=\sum_{n\geq 0}\sum_{k=0}^{n}\binom{n}{k}z^{n}\ y^{k}=\frac{1}{1-z-zy}.\]4  
Note that, for this algorithm too, the average complexity is only below the worst-case complexity by a constant (when \(k\sim\alpha n\)). Naturally, to be able to handle large values of \(n\) and \(k\), a tail-recursive variant of this algorithm, or an iterative version, should be preferred over the straightforward implementation. The recursive approach is a drawback for some programming languages that do not handle recursion efficiently (due to the depth of the stack). Naturally, other strategies have been suggested in the literature.
# Implementation of Atomically Thick Graphene and Its Derivatives in Electromagnetic Absorbers
###### Abstract  
To reduce the radar cross section at microwave frequencies, it is necessary to implement electromagnetic (EM) absorbing devices/materials to decrease the strength of reflected waves. In addition, EM absorbers also find their applications at higher spectrum such as THz and optical frequencies. As an atomic-thick two-dimensional (2D) material, graphene has been widely used in the development of EM devices. The conductivity of graphene can be electrostatically or chemically tuned from microwave to optical light frequencies, enabling the design of reconfigurable graphene EM absorbers. Meanwhile, the derivatives of graphene such as reduced graphene oxide (rGO) also demonstrate excellent wave absorbing properties when mixed with other materials. In this article, the research progress of graphene and its derivatives based EM absorbers are introduced and the future development of graphene EM absorbing devices are also discussed.  
graphene; reduced graphene oxide; electromagnetic; absorber +
Footnote †: journal: Applied Physics Letters
## 4 Conclusions  
A Fusion model based on data fusion and decision fusion from visible near-infrared (VNIR) and short-wave infrared (SWIR) hyperspectral images was developed for the detection of foreign materials on the surfaces of broiler breast fillets. The study found that the accuracies of detecting 2 \(\times\) 2 mm\({}^{2}\) pieces of polymer, wood, and metal foreign materials with the Fusion model were 95%, 95%, and 81%, respectively. The F1 score and Jaccard index of the Fusion model were increased by more than 5% and 8% in comparison to the VNIR- and SWIR-based foreign material detection models. Transparent and semi-transparent materials were excluded in the model evaluation because of the optical fact that transparent and semi-transparent materials were optically clear or semi-clear without characteristic absorptions in the wavelengths from 400 nm to 2500 nm. In conclusion, the  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Model** & **Metal DR** & **Wood DR** & **Polymer DR** & **Mean DR** & **FP** & **Precision** & **Recall** & **F1 Score** & **JAC** \\ \hline VNIR & 35 1 (43.8\%)2 & 18 (45\%) & 234 (68.8\%) & 52.5\% & 6 & 98\% & 62.4\% & 76.2\% & 61.6\% \\ SWIR & 63 (78.8\%) & 38 (95\%) & 277 (81.5\%) & 85.1\% & 16 & 95.9\% & 82.2\% & 88.5\% & 79.4\% \\ Fusion & 65 (81.3\%) & 38 (95\%) & 323 (95\%) & 90.4\% & 22 & 95.1\% & 92.6\% & 93.8\% & 88.4\% \\ \hline \hline \end{tabular}  
* 1 Integers in Metal, Wood, and Polymer are the numbers of correctly detected FM blobs. 2 Percentage number in each 0 represents a detection rate.  
\end{table}
Table 4: Performance of three foreign material blob detection models on the test set. DR refers to detection rate.  
fusion of two hyperspectral imaging modalities provided an effective method to detect a variety of small sized foreign materials on the chicken meat. The developed model will be the baseline for online high-speed hyperspectral imaging applications. Further research through systems engineering and algorithm optimization is needed for commercial poultry processing application.  
Conceptualization, S.C. and S.-C.Y.; data curation, S.C.; methodology, S.C. and S.-C.Y.; software, S.C. and S.-C.Y.; investigation, S.C.; validation, S.C.; formal analysis, S.C.; writing--original draft preparation, S.C.; writing--review and editing, S.-C.Y.; visualization, S.C.; supervision, S.-C.Y.; project administration, S.-C.Y.; funding acquisition, S.-C.Y. All authors have read and agreed to the published version of the manuscript.  
This research was supported in part by an appointment to the Agricultural Research Service (ARS) Research Participation Program administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the U.S. Department of Energy (DOE) and the U.S. Department of Agriculture (USDA). ORISE is managed by ORAU under DOE contract number DE-SC0014664. All opinions expressed in this paper are the author's and do not necessarily reflect the policies and views of USDA, DOE, or ORAU/ORISE.  
The authors declare no conflict of interest.
## 2 Study Area and Data
### Data
#### 2.2.3 Quantitative Remote Sensing Products  
The data used in this study are mainly a variety of time series quantitative remote sensing products, including LAI, FAPAR, ET, GPP, and Albedo [21]. The leaf area index is defined as the multiple of the total leaf area of the plant and the unit land area, which is a characteristic parameter describing the vegetation canopy geometry. The fraction of absorbed photosynthetically active radiation is the ratio of the photosynthetically active radiation absorbed by plants to the incident solar radiation. The evapotranspiration index refers to the sum of the soil evaporation and plant transpiration.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Class** & **Reliable Samples** & **Training Samples** & **Test Sample** \\ \hline Crop (CR) & 525,925 & 420,000 & 52,595 \\ Forest (FR) & 564,970 & 420,000 & 56,499 \\ Shrubs (SR) & 101,952 & 99,952 & 9484 \\ Grass (GR) & 869,197 & 630,000 & 86,823 \\ Water (WT) & 15,439 & 28,155 & 2818 \\ Glacier (GC) & 8363 & 15,850 & 1588 \\ Welfand (WL) & 9197 & 15,850 & 1537 \\ City (CT) & 5612 & 9282 & 931 \\ Desert (DS) & 310,044 & 420,000 & 53,584 \\ Tundra (TD) & 14,417 & 24,934 & 2464 \\ \hline \end{tabular}
\end{table}
Table 1: Training set and test set.  
The surface albedo is defined as the ratio of the reflected reflectance to the incident degree of the target feature. The total primary productivity refers to the total amount of organic carbon fixed by the photosynthesis of green plants per unit time and unit area.
# Enhanced Bit Repair IP Fast Reroute Mechanism for Rapid Network Recovery
## 4 The Proposal of the Enhanced B-REP Mechanism
#### The EB-REP State Diagrams  
To better understand the activities of the EB-REP mechanism, we created state diagrams of the activities of the respective routers. These are state diagrams describing the state and transient activities of the S router (Figure 10, Table 6), and as well as the D and N routers (Figure 11, Table 7). These three types of routers are involved in the EB-REP FRR process. Figure 10: The EB-REP mechanism state diagram of router S. Init—Initialize  
The EB-REP process of the mentioned routers can move between the states described in the following tables. \begin{table}
\begin{tabular}{c c} \hline State: & Any condition \\ Event: & Startup \\ New state: & Init \\  & Initialization of the EB-REP process on the router. \\  & Initialization of the EB-REP table and designation of EB-REP R-IDs and corresponding Bit-String position values. \\ Action: & Initialization of the EB-REP Backup Table. Reads the list of protected interfaces and for each network IP address, \\  & precalculates an alternative path. Assigns the Bit-String values. \\  & The mechanism is initialized for the first time and then after each routing convergence. After these activities, the \\  & EB-REP stays in the monitoring mode. \\ \hline State: & Init \\ Event: & Detection of protected interface failure. \\ New state: & Router S \\  & If the router detects a connectivity failure on the protected output interface, it becomes router S. Router S searches \\ Action: & the EB-REP backup table for the affected destination IP address and the identity of the failed protected interface. \\  & Router S reads a given Bit-String value of the backup path. \\ \hline State: & Router S \\ Event: & Process received affected packets OR convergence not finished OR control signal not received OR timer did not \\ New state: & expire \\ Action: & Encapsulate the affected packet with a new EB-REP header (BIER) and the Bit-String value of the backup path. Send \\  & an encapsulated packet through an active interface to the precalculated next-hop EB-REP node. \\ \hline \end{tabular}
\end{table} 
Table 6: States of the EB-REP mechanism for router S.  
Figure 11: The EB-REP state diagram for D and N routers.
###### Abstract  
An acoustic black hole (ABH) has the ability to concentrate and manipulate flexural waves, which can be used for structural vibration suppression and noise attenuation. In this paper, a 2D ABH rectangular plate is designed and a 2D ABH plate-cavity coupling system is constructed using the 2D ABH plate and five rectangular elastic plates of uniform thickness. Series of vibro-acoustic FEM models of the plate-cavity parallelepiped coupling system embedded with 2D ABHs are established, and the vibro-acoustic coupling simulation is conducted to analyze the effects of ABHs on the coupling modes, vibro-acoustic coupling characteristics, and mechanism of ABHs and the damping layer. It is shown that at most frequencies in the range of 3600-5000 Hz, the damping 2D ABH plate-cavity parallelepiped coupling system can significantly suppress the sound pressure and greatly reduce the peak values. It is also found that the significant reduction of the participation factor of the acoustic modes within the 100 th order is the main mechanism for the obvious suppression of the sound pressure in the damping ABH plate-cavity coupling system at 3701 Hz. Finally, an experimental platform of vibro-acoustic measurement of the 2D ABH coupling system is constructed, and the accuracy of the vibro-acoustic FEM models of the 2D ABH coupling systems established in this paper and the numerical simulation calculation are verified by the vibro-acoustic measurement experiment.  
acoustic black hole; plate-cavity coupling system; vibro-acoustic analysis; modal participation factor; experimental validation Article
## 2 Materials and Methods
The phase-code delay ionospheric observable was obtained, along with the geographic latitude and the sun-fixed longitude of the ionospheric pierce point. The zenith distance (\(z^{\prime}\)), azimuth angle, and time for each satellite over every GNSS station were also obtained. Subsequently, for 9 September and 10 November 2018, the Vertical Total Electron Content (VTEC) was obtained using a program developed by MAGGIA Laboratory (Meteorologia espacial, Atmosfera terrestre, Geodesia, Geodinamica, desarrollo de instrumentos y Astrometria; [41; 42; 43]). The ionosphere was approximated by a single shell of infinitesimal thickness with equivalent total oblique electron content (STEC), located 450 km above the Earth's surface. An obliquity factor, \(1/cos(z^{\prime})\), was used to convert STEC measurements to VTEC:  
\[STEC=VTEC*\frac{1}{cos(z^{\prime})} \tag{1}\]  
where \(z^{\prime}\) is the zenith distance of the oblique path at the ionospheric piercing point (IPP). For this work, \(z^{\prime}\geq 30^{\circ}\) was employed to eliminate the multi-path effect and also to achieve broad data coverage, such as in [3; 42; 44]. The ionospheric code delay observable was modeled using the procedure explained in [42; 43]. Finally, VTEC measurements in each station were detrended using a 6 th- to 7 th-order polynomial fit [3]. The previous process removes the gross offset, as well as the trend value obtaining Differential Vertical Total Electron Content (DVTEC) values. The remaining variability is mainly related to the carrier phase, whose accuracy is 0.01 to 0.1 TECU [45]. Once the DVTEC was obtained, its peak-to-peak amplitude was calculated, using the following definition:  
\[peak\text{-to-peak-Amplitude}=maxDVTEC-minDVTEC \tag{2}\]  
where \(maxDVTEC\) and \(minDVTEC\) are the maximum and minimum values of DVTEC, respectively. Finally, the C-Morlet 1.5 wavelet transform was used to analyze the spectral amplitude and period of the DVTEC signal [46].
## 1 Introduction  
Maxillary transverse hypoplasia is commonly associated with uni- or bilateral posterior crossbite with an incidence ranging from 4% to 20% and, depending on the geographical area, even 50% of the population examined [1; 2; 3; 4; 5]. Posterior crossbite can result in many different growth alterations, with asymmetrical condylar positioning, temporomandibular dysfunction and even more severe skeletal and myofunctional alterations [6; 7; 8].  
The maxillary deficit does not self-correct during the growth, thus, slow maxillary expansion (SME) or rapid maxillary expansion (RME) could be performed with the intent to correct it. As reported by several authors, widening the maxilla with maxillary expansion often leads to spontaneous forward posturing and to spontaneous expansion of the mandible [9; 10; 11; 12]. This is because the palatal expansion acts on the balance of forces between the tongue and cheek on lower arch. The action of the tongue on the mandibular teeth might promote the growth of the mandibular dental arch width [12; 13].  
Spontaneous enlargement in the mandibular dentition under the influence of RME or SME have been reported previously [14; 15; 16; 17; 18].  
The Leaf Expander has been proposed previously in 2016 by [PERSON] et al. [19] and is now available with two different measurements of the screw (6 or 9 mm) and with two different types of forces generated by the nickel titanium leaf spring (450 or 900 g). Recently the efficacy of this new expander has been reported by the same authors in pilot studies based on digital models and postero-anterior cephalometric study. However, the sample of patients treated was limited to only 10 subjects [20; 21].  
Few data based on 3D noninvasive analysis are available considering the indirect effects of SME on mandibular arch and all of those have been done with a removable expansion plate or a Quad Helyx [22; 23; 24; 25].  
The aim of this retrospective study is to quantitatively evaluate the maxillary and mandibular changes after the SME treatment with the Leaf Expander in patients with maxillary arch constriction compared with a group of subjects treated with RME. The null hypothesis is that the Leaf Expander will show less increase in the amount of expansion compared with the RME group.
# Investigating Dynamics of COVID-19 Spread and Containment with Agent-Based Modeling
## 2 Methodology
### Parameters and Movement of Agents  
The model parameters are as follows:  
* \(\alpha\): Per-contact fear transmission rate
* \(\beta\): Per-contact disease transmission rate
* \(\lambda_{1}\): Rate of removal of those infected with fear (F, EF, and IF) to self-isolation (QF, QEF, and QIF, respectively)
* \(\lambda_{2}\): Rate of recovery (R) of all agents infected with disease (I, IF, and QIF)
* \(\epsilon\): Rate of progression from exposed to infected (the reciprocal is the incubation period).
* \(H\): Rate of return of agents from isolation back to the epidemic cycle.  
Figure 1 shows all states, their relationship and transition rates between these states. The model subsumes the classic SEIR model, and it assumes constant population. Lets review some possible interactions between agents with different states and the outcome: a susceptible (S) that interacts with an exposed agent (E), remains susceptible with probability \((1-\beta)\) or turns into an exposed (E) with probability \(\beta\). As another example, a susceptible (S) which interacts with an infected and feared agent (IF), stays susceptible with probability \((1-\alpha)(1-\beta)\), becomes exposed (E) with probability \((1-\alpha)\beta\), becomes only feared with probability \((1-\beta)\alpha\), and finally becomes both exposed and feared (EF) with probability \(\alpha\beta\). Agents which are feared (F, EF, IF), go into self-isolation with rate \(\lambda_{1}\). Agents which are in self-isolation on the other hand (QF, QEF, QIF), return back to the cycle with rate \(H\), and turn into S, E, and I, respectively. In the end, it should be noted that agents that are exposed (E, EF, QEF), turn into infected (I, IF, and QIF, respectively) after they pass their five incubation days.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**State** & **Description** \\ \hline S & Susceptible \\ E & Exposed \\ F & Feared \\ EF & Exposed and Feared \\ I & Infected \\ IF & Infected and Feared \\ QF & Self-quarantined Feared \\ QEF & Self-quarantined Exposed and Feared \\ QIF & Self-quarantined Infected and Feared \\ R & Recovered \\ \hline \hline \end{tabular}
\end{table}
Table 1: Possible states of agents in the epidemiological model.  
The model takes place on a two dimensional lattice which consists of patches (squares). For example, a \(160\times 160\) lattice consists of 25,600 patches. Each patch inside the lattice therefore is surrounded by 8 neighbors. In each timestep of simulation, each agent randomly chooses another empty patch among all the patches in the lattice and moves there. After movement, each agent might have up to 8 other neighboring agents occupying its neighboring patches, with one of whom he might interact based on rules of interaction previously mentioned.
## 3 Results and Discussion
### Fundamental Properties of LLZO-IL Composites
A change in the peak shape was observed at 750 cm\({}^{-1}\). From this signal, it is possible to estimate the ratio of cisoid or transoid conformers of FSI because the FSI anions with cis and trans conformations exhibit their band at 730 and 750 cm\({}^{-1}\), respectively [31]. In the case of pure FSI IL, the peak around these frequencies can be accurately fitted by two Gaussian peaks as shown in Figure S2. The peak at around 750 cm\({}^{-1}\) was more intense compared with that at around 730 cm\({}^{-1}\). When LLZO was present, a broad signal with multiple peak tops was observed. In this case, the peak intensity at 730 cm\({}^{-1}\) was slightly higher than that at 750 cm\({}^{-1}\). This suggests that the cis conformer is major in the LLZO-FSI IL composites while the trans conformer is dominant in the pure FSI IL. This change confirms the presence of physical interaction between LLZO and FSI IL as discussed for DSC. The curves for the pristine DFOB IL and its composites with LLZO are shown in the bottom. The peaks are assigned as follows: 1795 and 1761 cm\({}^{-1}\) for C=O str; 1347 cm\({}^{-1}\) for C-C str and C-O str; 1229 cm\({}^{-1}\) for C-C bend and CO str; 1121 and 1076 cm\({}^{-1}\) for B-F str, and 941 cm\({}^{-1}\) for B-O str. The peaks related to the cation structures were observed at 1473, 1457, 1150, and 876 cm\({}^{-1}\). In the case of LLZO-DFOB IL composite, noticeable change of the spectra in terms of peak position and intensity was not observed.
# User Association Performance Trade-Offs in Integrated RF/mmWave/THz Communications
## 4 Coverage Probability Analysis
)\) as:  
\[\mathbb{P}(\gamma_{k}>\zeta_{k})=\mathcal{L}_{I}\Big{(}\frac{\zeta_{k}P_{T_{k }}\ell(d_{k})}{\sigma_{n}^{2}}\Big{)}e^{-\frac{\zeta_{k}\sigma_{n}^{2}}{P_{T_{ k}}\ell(d_{k})}} \tag{16}\]  
Assuming interference is Gaussian distributed, with \(\mu\) and \(\sigma^{2}\) being the mean and variance of the Gaussian distribution, respectively, the Laplace transform can be calculated as:  
\[\mathcal{L}_{I}(s)=\frac{\sqrt{\sigma}}{2}e^{\frac{\sigma  
For the THz user, we need to consider molecular absorption losses and Lambertian scattering loss, which can significantly impact the signal strength. The coverage probability will be:  
\[P_{c,THz}=e^{-\kappa_{a}d_{k,THz}}G_{THz}(1-B_{mm})\frac{\sqrt{\sigma}}{2}N_{ THz}^{2}E_{c,THz}^{2}\sum_{k\in K_{THz}}\lambda_{k,THz}\int[...]d(d_{k,THz}) \tag{20}\]  
where \(\kappa_{a}\) is the absorption coefficient, \(d_{k,THz}\) is the distance to the serving THz BS, and \(G_{THz}\) is the antenna gain due to the Lambertian scattering loss given by:  
\[G_{THz}=\frac{n+1}{2\pi}cos^{n}(\theta) \tag{21}\]  
where \(n\) is the Lambertian emission order, and \(\theta\) is the irradiation angle. This probability depends on the specific environmental conditions and absorption properties of the medium the signal travels through.