esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Computed Tomography and Aortic Valve
### Aortic Stenosis and TAVI (Transcatheter Aortic Valve Implantation) Indication  
Aortic stenosis (AS) is the most prevalent valvular heart disease in Europe and the second most common in the United States. The progression of aortic stenosis depends on the severity of the condition at baseline [17]. Mean aortic valve gradients increased an average of 4, 6, and 10 mmHg/year in elderly patients with mild, moderate, and severe AS, respectively. Other factors that were associated with a faster hemodynamic progression included advanced aortic valve calcification, severe chronic renal failure, and anemia [18].  
Figure 1: (**a**) Schematic representation of aortic valve anatomy. The dotted blue line indicates the sinotubular junction, the dotted green one depicts the virtual basal ring, and the dotted red one shows the ventricular aortic junction. (**b**) Graphic representation of an opened aortic root with its anatomical components.  
Without treatment, the average survival is only 2-3 years, with an increased risk of sudden death [18].  
Transcatheter aortic valve implantation (TAVI) is a procedure that is now being recommended in older patients (\(\geq\)75 years) or in those who are high risk (STSPROM/EuroSCORE II \(>\) 8%) or unsuitable for surgery. However, its indications are rapidly growing and progressively extending to younger patients with lower surgical risk [19]. Regarding aortic regurgitation, due to the difficult sealing and grasping of valves caused by the absence of calcium spots and the probable coexistence of dilated aortic root or ascending aorta, no clear recommendations exist, and the use of TAVI has been largely off-label [20; 21; 22].
# Map Matching Based on Seq2 Seq with Topology Information
## 2 Related Work
### Basic Concepts and Problem Description
#### 2.1.6 Trajectory Grid Dictionary  
The trajectory grid dictionary corresponds to the grid representation of the trajectory dictionary by replacing GPS trajectory points with grid IDs. The resulting sequence also adheres to road network topology rules. Each trajectory is represented as CELL_ST = [CELL1, CELL2, CELL3,... CELLN]. The dictionary is structured as [CELL_ST1, CELL_ST2, CELL_ST3,... CELL_STN].  
The final grid ID sequence, along with its topology relationship, is utilized during the model training process, while the remaining dictionaries serve as encoding and decoding references. The formats of the corresponding dependent dictionaries are illustrated in Table 1, whereas Figure 1 depicts the specific mapping logic from points to grids.  
the grid sequence of the true trajectory mapping, the red grid represents the grid sequence of the wrong trajectory mapping, and the yellow grid represents the overlap of red and green. The red grid sequence in Figure 3b is input into the trained model, and the model can output the red grid sequence in Figure 3c through calculation, and finally decode the grid sequence into the real geographical longitude and latitude point sequence connected by the green points in Figure 3c.
# A Review on Vibration-Based Condition Monitoring of Rotating Machinery
## 4 Analytical Review
### Category p1: Signal Type, Sensors, Pre-Processing
[PERSON] et al., in [90], developed a new method, called the improved variational mode decomposition (VMD), based on a generalized demodulation technology (GDT) and a zero-phase shift filter (ZPSF). This hybrid approach can effectively be applied to fault diagnosis, as it allows to extract all the useful vibration components from the rotor system during start-up. The multiple source issue is treated by [PERSON] and [PERSON] in [91], who implemented a blind source separation (BSS) method to demix sensor signals into correctly identifiable vibration source signals without knowing the sensor layout. Using higher-order statistics of the signals, it is possible to isolate vibration sources. To conclude, some works deal with particular themes, such as the discrete orthonormal Stockwell transform (DOST) [93], which is a pre-processing CM step for invariant rotational speed and load scenarios, reconstruction algorithms based on the multiple side information signal (RAMSI) [94], to separate noise from signal components in non-stationary conditions, or lastly, the concealed component decomposition (CCD) [95], which is a self-adaptive signal decomposition technique that isolates the intrinsic instantaneous amplitude in balance with other essential configuration features.
## 3 TVWS-DTV Coexistence: Field Measurements
### Field Tests Considering Long Distances
#### 3.2.4 Results from the First Stage of Field Tests
\begin{table}
\begin{tabular}{c l c c c} \hline \hline  & \(P_{\text{TX}}\) **TVWS (CH28) [Wp]** & **6.3** & **8** & **10** \\
**DTV** & \(\text{Filter}_{\text{RX}}\) (CH28) & & **Yes** & \\
**Channel** & \(\text{LNA}_{\text{RX}}\) & & **On** & \\ \hline  & \(P_{\text{RX}}\) DTV (CH29) [dBm] & \(-76.9\) & \(-76.9\) & \(-77.0\) \\  & \(P_{\text{RX}}\) TVWS (CH28) [dBm] & \(-46.7\) & \(-45.8\) & \(-45.1\) \\
29 & \(\text{PR}_{(n-1)}\) [dB] & \(-30.2\) & \(-31.1\) & \(-31.9\) \\  & ACPR\({}_{\text{UPPER}}\) [dB] & \(-7.6\) & \(-8.9\) & \(-7.6\) \\ Interf. & ACPR\({}_{\text{LOWER}}\) [dB] & \(30.2\) & \(31.1\) & \(31.9\) \\ \(n-1\) & \(P_{\text{RX}}\) INT. (CH30) [dBm] & \(-84.5\) & \(-85.8\) & \(-84.6\) \\  & DTV STB Status 1 & OK & Interm. & NOK \\  & DTV STB Status 2 & OK & OK & Interm. \\  & DTV STB Status 3 & OK & OK & OK \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Additional test results with \(n-1\) interference at the MS_Loteamento location. present on channel 30 as interference on channel \(n+1\). In this configuration, \(P_{\text{RX}}\) TVWS was \(-47.2\) dBm, and \(P_{\text{RX}}\) INT. was \(-43.1\) dBm, with PR\({}_{(n\,-\,1)}\) and PR\({}_{(n\,+\,1)}\) calculated at \(-29.7\) dB and \(-33.8\) dB, respectively, and \"Not OK\" DTV STB Status were obtained for the three STBs under test. Subsequently, attenuators were inserted after the LNA\({}_{\text{RX}}\) to reduce the received power of the interfering signals. As shown in Table 10, in the condition with a PR\({}_{(n\,-\,1)}\) value of \(-25.7\) dB and PR\({}_{(n\,+\,1)}\) value of \(-30.1\) dB simultaneously, which was achieved with an attenuation of 4 dB, all STBs had \"OK\" DTV STB Status. Note also conditions with 3 dB attenuation, for which only STB 1 had a \"Not OK\" DTV STB Status, and 2 dB attenuation, in which only STB 3 had an \"OK\" DTV STB Status. The input spectrum of the DTV STBs in the threshold condition for all three STBs to work simultaneously is shown in Figure 12(b). The DTV signal is in the center of the spectrum, the TVWS signal is to its left (interference \(n-1\)), and to the right is the interfering DTV signal (interference \(n+1\)).
## 3 Novel Framework for Wideband Cooperative Spectrum Sensing
### Analysis of SU Spectral Efficiency for Spectrum Sensing
For a given \(p_{d,i}^{th}\), \(0<\tau<T\) and \(\mu_{i}=\frac{f_{\tau}\times\Delta t_{i}}{N}=\frac{f_{\tau}\times\tau}{N}\), in which \(f_{s}\) denotes sampling frequency in compressed domain, \(\Delta t_{i}\) is compressed sensing time, then we have:  
\[ \begin{array}{c}\
abla\mathcal{C}(\tau)=-\frac{r_{0}}{WT}P_{\mathcal{H}_{0} }\bigg{\{}1-Q\bigg{(}Q^{-1}(p_{d,i}^{th})+\sqrt{\frac{f_{\tau}\gamma_{i}}{N} \tau}\bigg{)}\bigg{\}}-\frac{r_{1}}{WT}P_{\mathcal{H}_{1}}(1-p_{d,i}^{th})\\ +\frac{(T-\tau)r_{0}P_{\mathcal{H}_{0}}}{2 WT}\sqrt{\frac{f_{\tau}\gamma_{i}}{2 WT}}\exp\left\{-\frac{1}{2}\bigg{(}Q^{-1}(p_{d,i}^{th})+\sqrt{\frac{f_{\tau} \gamma_{i}}{N}\tau}\bigg{)}^{2}\right\}\end{array}  \tag{25}\]  
Obviously,  
\[\lim\limits_{\tau\to 0}\
abla\mathcal{C}(\tau)=+\infty \tag{26}\]  
\[\lim\limits_{\tau\to T}\
abla\mathcal{C}(\tau)=-\frac{r_{0}}{WT}P_{\mathcal{ H}_{0}}\Bigg{\{}1-Q\Bigg{(}Q^{-1}(p_{d,i}^{th})+\sqrt{\frac{f_{s}\gamma_{i}}{N} \tau}\Bigg{)}\Bigg{\}}-\frac{r_{1}}{WT}P_{\mathcal{H}_{1}}(1-p_{d,i}^{th}) \tag{27}\]  
Because \(Q(x)\) is the monotonously decreasing function in \(x\), we have:  
\[Q\Bigg{(}Q^{-1}(p_{d,i}^{th})+\sqrt{\frac{f_{s}\gamma_{i}}{N}\tau}\Bigg{)}<Q \Big{(}Q^{-1}(p_{d,i}^{th})\Big{)}=p_{d,i}^{th} \tag{28}\]  
Thus,  
\[\lim\limits_{\tau\to T}\
abla\mathcal{C}(\tau)<-\frac{r_{0}}{WT}P_{\mathcal{ H}_{0}}\Big{(}1-p_{d,i}^{th}\Big{)}-\frac{r_{1}}{WT}P_{\mathcal{H}_{1}}(1-p_{d,i}^{ th})<0\square \tag{29}\]Equations (26) and (29) indicate that \(\mathcal{C}\) increases when \(\tau\) is small and decreases when \(\tau\) approaches \(T\). Hence, there exists one extremum point of \(\mathcal{C}\) for \(\tau\in(0,T)\) which satisfies the constraint on \(\
abla\mathcal{C}(\tau)=0\). Furthermore, we have:  
\[ \begin{array}{l}\
abla^{2}\mathcal{C}(\tau)=-\bigg{[}\frac{r_{0}P_{H_{0}}}{2 \Psi T}\sqrt{\frac{f_{\tau 1}}{2\pi N\tau}}+\frac{r_{0}P_{H_{0}}}{4\sqrt{2\pi W \tau}}\frac{f_{\tau 1}}{N}\frac{(\tau-\tau)}{\tau}\\ \times\bigg{(}Q^{-1}(P_{d,i}^{th})+\sqrt{\frac{f_{\tau 1}}{N}\tau}\bigg{)}+ \frac{r_{0}P_{H_{0}}}{4\Psi T}\sqrt{\frac{f_{\tau 1}}{2\pi N}}\frac{ \tau+\tau}{\tau\tau}\bigg{]}\\ \exp\bigg{\{}-\frac{1}{2}\bigg{(}Q^{-1}(P_{d,i}^{th})+\sqrt{\frac{f_{\tau 1} }{N}\tau}\tau\bigg{)}^{2}\bigg{\}}\end{array}  \tag{30}\]  
Eventually, we have \(\
abla^{2}\mathcal{C}(\tau)<0\) for \(\tau\in(0,T)\), which means that \(\mathcal{C}\) is a convex function of \(\tau\). Hence, there exists one optimal sensing time \(\tau_{opt}\in(0,T)\) that maximizes the SU spectral efficiency. Thus, Theorem 3 is proven.
## 3 Results and Discussion
### ESDD and NSDD Evaluation
In fact, considering the topographical features of the Italian peninsula, MR1, which includes the islands of Sardinia and Sicily, showedthe highest contamination values in line with the type of environment characterizing these specific regions, marked by marine inflows; while MR3, which includes the Po Valley and the eastern peninsula, shows the lowest contamination values. MR2, which includes the southwestern peninsula, shows contamination values between MR1 and MR3, with the highest values in the southern regions (i.e., Calabria ESDD ranges from 0.006 to 0.236 mg cm\({}^{-2}\), and from 0.003 to 0.094 mg cm\({}^{-2}\) for NSDD; Puglia from 0.005 to 0.179 mg cm\({}^{-2}\) (ESDD) and from 0.004 to 0.116 mg cm\({}^{-2}\) (NSDD); Campania from 0.008 to 0.137 mg cm\({}^{-2}\) (ESDD) and from 0.005 to 0.070 mg cm\({}^{-2}\) (NSDD)).
# Authentication Based on Non-Interactive Zero-Knowledge Proofs for the Internet of Things
## 9 Conclusions  
With the proliferation of electronic devices in many areas, a new paradigm called the Internet of Things has emerged. One of the biggest threats to the deployment of the networks involved in the Internet of Things is the security of communications, so new lightweight cryptographic algorithms that are adapted to the computing capabilities of mobile devices are necessary. In this paper, a novel scheme based on the idea of non-interactive zero-knowledge proofs is presented. The proposal only requires sending a message to share confidential information in an authenticated way. Thus, the new algorithm is proposed to be used for establishing authenticated secret session keys between pairs of legitimate nodes of mobile _ad hoc_ networks. Furthermore, the scheme can be used by nodes that want to send authenticated information in broadcast mode to other legitimate nodes in the network. Different use cases are defined for the authenticated public key exchange in these networks by using variants of the scheme described in this paper. The proposal is mainly characterized by not using interaction for authentication, which is very adequate for volatile networks, such as those in the Internet of Things, which require a more efficient authentication procedure. The scheme has been implemented for the platforms under the seal of the Android Open Source Project, and the design has been optimized to reach a high level of security at a low cost of memory consumption. The obtained results are promising, as they improve the performance of other lightweight authentication schemes based on zero knowledge proofs. Several open problems still remain and could be solved in future work, such as the design of an improved service system based on the proposal.  
**Acknowledgments:** Research supported by TIN2011-25452, BES-2012-051817, IPT-2012-0585-370000, RTC-2014-1648-8 and TEC2014-54110-R.  
**Author Contributions:** [PERSON] and [PERSON] conceived the authentication protocol and algorithms and wrote the paper. [PERSON] developed the algorithms in the Android Open Source Project. [PERSON] and [PERSON] designed and performed the experiments, analyzed the data and produced the result graphical material. All authors revised the paper for intellectual content.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**PAK Scheme** & \multicolumn{2}{c}{**Our Scheme**} \\ \hline
**Time (ms)** & **Challenges** & **Time (ms)** \\ \hline \multirow{8}{*}{197} & 3 & 86 \\  & 4 & 112 \\ \cline{1-1}  & 5 & 153 \\ \cline{1-1}  & 6 & 176 \\ \cline{1-1}  & 7 & 195 \\ \cline{1-1}  & 8 & 221 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Password authenticated key (PAK) scheme _vs._ the proposed scheme.
# Proxy Re-Encryption Scheme for Decentralized Storage Networks
## 3 Preliminaries
### Complexity Assumptions  
The computational assumption of Diffie-Hellman (CDH) is defined as  
**Definition 2**.: \(\mathbb{G}\) _is a cyclic multiplicative group with prime order \(p\). The CDH problem is said in group \(\mathbb{G}\), given a tuple \((g,g^{x},g^{y})\in\mathbb{G}^{3}\) with unknown \(x,y\leftarrow\mathbb{Z}_{p}\), to compute \(g^{xy}\)._  
A variant of the CDH problem named divisible computation Diffie-Hellman (DCDH) [23] problem is defined as follows.  
**Definition 3**.: _Let \(\mathbb{G}\) be a cyclic multiplicative group with prime order \(p\). The DCDH problem in group \(\mathbb{G}\) is, given \((g,g^{\frac{1}{x}},g^{y})\in\mathbb{G}^{3}\) with unknown \(x,y\leftarrow\mathbb{Z}_{p}\), to compute \(g^{xy}\)._  
The construction of our chosen ciphertext-secure PRE scheme is based on the assumption of modified computational Diffie-Hellman (mCDH). The mCDH problem is a combination of the CDH problem and the DCDH problem.  
**Definition 4**.: _Let \(\mathbb{G}\) be a cyclic multiplicative group with prime order \(p\). The mCDH problem in group \(\mathbb{G}\) is, given a tuple \((g,g^{\frac{1}{x}},g^{x},g^{y})\in\mathbb{G}^{4}\) with unknown \(x,y\leftarrow\mathbb{Z}_{p}\), to compute \(g^{xy}\)._  
**Definition 5**.: _For a polynomial time adversary \(\mathcal{B}\), the advantage is defined as solving the mCDH problem in group \(\mathbb{G}\):_  
\[\mathbf{Adv}_{\mathcal{B}}^{mCDH}=\Pr[\mathcal{B}(g,g^{\frac{1}{x}},g^{x},g^ {y})=g^{xy}]. \tag{13}\]
# An Improved Grey Wolf Optimizer Based on Differential Evolution and OTSU Algorithm
## 2 Materials and Methods
### Convergence Behavior Analysis  
During the initial step optimization, the movement of the search agent should change the mutation. This helps the meta-heuristic to explore the search space broadly. To observe the convergence of the DE-OTSU-GWO algorithm, Figure 4 depicts the changes in the iterative process of the three algorithms and describes the search history of the search agent (A final value close to \(f_{min}\) is preferable). This shows that the search agents of the PSO and GWO algorithms tend to search a wide range of promising areas of the search space and dig out the best areas. In the DE-OTSU-GWO algorithm, there is mutation in the initial stage, and the mutation gradually decreases with the progress of iteration.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline \multicolumn{1}{c}{**Function**} & **Dim** & **Range** & \(f_{min}\) \\ \hline \(f_{14}(x)=\left(\frac{50}{50}+\sum\limits_{j=1}^{25}\frac{1}{j+\sum\limits_{i= 1}^{2}\left(x_{i}-x_{i}\right)^{5}}\right)^{-1}\) & 2 & \([-65.536,65.536]\) & 1 \\ \(f_{15}(x)=\sum\limits_{i=1}^{11}\left[a_{i}-\frac{x_{i}\left(b_{i}^{2}+bx_{i }\right)}{b_{i}^{2}+bx_{i}+bx_{i}}\right]^{2}\) & 4 & \([-5,5]\) & 0.00030 \\ \(f_{16}(x)=4x_{1}^{2}-2.1x_{1}^{4}+3x_{1}^{4}+x_{1}x_{2}-4x_{2}^{2}+4x_{2}^{4}\) & 2 & \([-5,5]\) & \(-1.0316\) \\ \(f_{17}(x)=\left(x_{2}-\frac{51}{44x_{1}^{2}}+\frac{5}{2}x_{1}-6\right)^{2}+10 \left(1-\frac{1}{8n}\right)\cos x_{1}+10\) & 2 & \([-5,5]\) & 0.398 \\ \(f_{18}(x)=\left[1+(x_{1}+x_{2}+1)^{2}\left(19-14x_{1}+3x_{1}^{2}-14x_{2}+6x_{1 }x_{2}+3x_{2}^{2}\right)\right]\times\) & 2 & \([-2,2]\) & 3 \\ \(\left[30+(2x_{1}-3x_{2})^{2}\times\left(18-32x_{1}+12x_{1}^{2}+48x_{2}-36x_{1 }x_{2}+27x_{2}^{2}\right)\right]\) & & & \\ \(f_{19}(x)=-\sum\limits_{i=1}^{4}\,cancel{exp}(-\sum\limits_{j=1}^{3}\,a_{i} \!\left(x_{j}-p_{ij}\right)^{2}\) & 3 & \([1,3]\) & \(-3.86\) \\ \(f_{20}(x)=-\sum\limits_{i=1}^{4}\,cancel{exp}(-\sum\limits_{j=1}^{6}\,a_{i} \!\left(x_{j}-p_{ij}\right)^{2}\) & 6 & \([0,1]\) & \(-3\),32 \\ \(f_{21}(x)=-\sum\limits_{i=1}^{5}\left[(X-a_{i})(X-a_{i})^{T}+c_{i}\right]^{-1}\) & 4 & \([0,10]\) & \(-10.1532\) \\ \(f_{22}(x)=-\sum\limits_{i=1}^{5}\left[(X-a_{i})(X-a_{i})^{T}+c_{i}\right]^{-1}\) & 4 & \([0,10]\) & \(-10.4028\) \\ \(f_{23}(x)=-\sum\limits_{i=1}^{10}\left[(X-a_{i})(X-a_{i})^{T}+c_{i}\right]^{-1}\) & 4 & \([0,10]\) & \(-10.5363\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Fixed-dimension multimodal benchmark functions.  
Figure 3: The 2D version of the benchmark functions.  
Figure 4: The changes in the iterative process of the three algorithms.  
In summary, compared with the GWO and PSO algorithms, the DE-OTSU\(-\)GWO algorithm is more stable and accurate in solving benchmark functions. To further investigate the effect of the proposed algorithm, the next section discusses the practical problem of classical agricultural image recognition. Compared with the existing algorithm, the validity of the algorithm is verified.
## 3 Results
### Cell Adhesion Evaluation  
The MC3T3-E1 cells cultured for 24 h in the FBS-free \(\alpha\)-MEM medium did not adhere to the HA surface after successive dehydration washes during the sample processing for SEM (Figure 5).  
However, it was possible to observe some cells on the c-RGD/HA surface, indicating that RGD chemically binding on the HA surface allowed for the more stable adhesion of MC3T3-E1 when cultivated in a non-supplemented medium. When the cells were grown in a supplemented medium, no significant differences occurred in the cell adhesion among the functionalized samples. The elongated cells presented two to three anchorage points, and more widely spread lamellar shapes were found on all three HA surfaces.  
Figure 5: Scanning electron microscopy (SEM) of the MC3T3-E1 cell adhesion after 24 h on the HA (**A**), p-RGD/HA (**B**), and c-RGD/HA (**C**) surfaces when cultivated in an \(\alpha\)-Minimum Essential Medium (\(\alpha\)-MEM) medium free of fetal bovine serum (FBS) and \(\alpha\)-MEM medium with FBS (**D**–**F**). Magnification: 100\(\times\). Under high magnification (3K), examples of cell morphological units found on the three HA surfaces (**G–I**) when cultivated in the presence of FBS. Asterisks and arrows indicate the presence of cells.  
Through fluorescence microscopy and biostatistics analysis (Figure 6), it was not possible to observe any significant difference in the number of cells adhered to c-RGD/HA, p-RGD/HA, or the control when cultivated in the medium without FBS (-FBS) (Figure 6A, white columns).  
Figure 6: (**A**) Quantitative analysis of the MC3T3-E1 adhesion and (**B**) cell spreading after 24 h of cultivation on the functionalized HA surfaces in medium with and without FBS. The ratio between the area occupied by the cells and the total number of cells quantified per image was expressed by cell spreading data. The statistical analysis consisted of Two-way ANOVA, with [PERSON]’s multiple comparisons test (**_p_ < 0.0001 and *_p_ < 0.05).  
However, when compared with the supplemented group (+FBS), it was possible to notice a significant difference in the number of cells (\(p\) < 0.0001). The number of cells adhered in c-RGD/HA was significantly lower than that quantified in p-RGD/HA (\(p\) = 0.0330). There was no difference between p-RGD/HA and the control (Figure 6A, black columns). Regarding the sprawling area, there were no significant differences between all samples (Figure 6B).  
The HA, p-RGD/HA, and c-RGD/HA discs were immersed in a 10% FBS aqueous solution to evaluate the samples' capacity to adsorb FBS proteins after 3 h of exposure. Figure 7 shows the surface-adsorbed proteins of FBS. However, HA and p-RGD/HA adsorbed 87.76 \(\pm\) 9.6 \(\upmu\)g/mL and 74.93 \(\pm\) 7.2 \(\upmu\)g/mL, respectively, while c-RGD/HA adsorbed 11.36 \(\pm\) 2.0 \(\upmu\)g/mL, a significantly lower amount of FBS proteins when considering \({}^{\star}\)\(p\) < 0.0001.
## 5 Testbed and Simulation Results
### Energy Consumption
#### 5.4.1 Energy Consumption for 5 Node WSN Testbed  
The Waspmotes consumes 15 mA of energy per hour in switched on state and just consumes 55 \(\upmu\)A of energy per hour in sleep state [41]. We have designed our protocol to be energy-efficient. In our protocol sensor data under normal events are sampled for 10 s after every 3 h and sent to the server. When we measured energy consumption for our protocol it was found that, it only consumes 0.004 mA of energy per hour. If we have a rainfall event we implement second scheme under which we sample the data for 10 s after every 10 s, only for the sensor node experiencing the rainfall event, since the soil moisture may change very rapidly. In second scheme, when there is a rainfall our protocol consumes only 0.042 mA of energy per hour for the effected node, which is also very less than the default energy consumption of 15 mA per hour for the Waspmote [41]. Hence, our protocol is also energy efficient.  
As shown in Tables 6 and 7 the energy measurements in mA taken after rainfall when we use modified AOMDV, are less than those taken before rainfall when we use standard AOMDV, for both received energy (Rec Energy) as well as transmission energy (Trans Energy) because the nodes affected by rainfall will not receive any data from other nodes and hence they will require very less receiving energy, on the other hand they will just have their own data to transmit, hence the transmission energy also decreases. We also show these results in Figures 9 and 10.
# A Key Management Scheme for Mobile Wireless Sensor Networks
## 2 Related Work
### Global Master Key  
This technique employs a master key (MK) to generate the pairwise keys of the network. Symmetric-key key establishment (SKKE), used by ZigBee (ZigBee Specification, Document 053474r20, September 2012, ZigBee Alliance), employs an MK that is known by every node. In the establishment of a pair-wise key, a node A sends its identifier \(\mathrm{ID}_{A}\) and a random number \(\mathrm{C}_{A}\). Node B receives the message and sends to A its identifier \(\mathrm{ID}_{B}\), a new random number \(\mathrm{C}_{B}\) and the MAC that is calculated on a constant number \(k_{1}\), \(\mathrm{ID}_{B}\), \(\mathrm{ID}_{A}\), \(\mathrm{C}_{B}\) and \(\mathrm{C}_{A}\). Both nodes execute a keyed hash function with MK as a key on \(\mathrm{ID}_{B}\) and \(\mathrm{ID}_{A}\) concatenated to \(\mathrm{C}_{A}\) and \(\mathrm{C}_{B}\) in order to generate a common secret. Then, a hash function on the common secret is used to compute two keys: MAC key to authenticate the messages and KeyData to protect the link. Then, node A checks the MAC and sends to node B a MAC calculated on a second constant number \(k_{2}\) concatenated to the same data used for the first MAC.  
SKKE can be applied to mobile and static wireless networks. The memory occupied by the keys is small. However, if MK is compromised, SKKE provides a low level of security, since an opponent could generate every key, if he/she had eavesdropped on the messages that were used to the generate the key.