# Detection of Transmission State of Multiple Wireless Sources: A Statistical Mechanics Approach
## 1 Introduction
* Lack of iterative refinement, which hinders gradual improvement in the accuracy of the emitting state detection. \begin{table} \begin{tabular}{p{227.6 pt}} \hline \hline
**Thresholding-based methods** compare the received signal strength or other relevant parameters with a predefined threshold to infer the emitting state of the primary sources [24, 25, 26]. In summary, thresholding-based methods offer simplicity and speed but they may lack adaptability and robustness to complex data distributions. Belief propagation, on the other hand, provides adaptability, accuracy, and flexibility but has higher computational complexity and potential convergence challenges. \\ \hline Advantages Compared to the Belief Propagation Algorithm \\ \hline \hline \end{tabular}   
* Lower complexity, since they are straightforward and easy to implement, thus they are more computationally efficient. * Rapid decision making, since they do not require extensive computations or iterations. * Robustness to noise and fluctuations that affect the emitting state detection by setting appropriate thresholds. \\ \hline Drawbacks Compared to the Belief Propagation Algorithm \\ \hline \hline \end{tabular}  
* Lack of adaptability, since they rely on fixed thresholds, which may not capture the full complexity of the data distribution and thus can lead to suboptimal results. * Sensitivity to threshold selection, since they heavily rely on choosing appropriate thresholds. Selecting thresholds that are too low or too high can lead to false positives or false negatives, respectively, impacting the accuracy of the emitting state detection. * Lack of incorporation of prior knowledge, which in many cases, is crucial for the improvement of the accuracy of the emitting state detection. * Lack of iterative refinement, which hinders gradual improvement in the accuracy of the emitting state detection. \begin{table}
\begin{tabular}{p{227.6 pt}} \hline \hline
**Thresholding-based methods** compare the received signal strength or other relevant parameters with a predefined threshold to infer the emitting state of the primary sources [24, 25, 26]. In summary, thresholding-based methods offer simplicity and speed but they may lack adaptability and robustness to complex data distributions. Belief propagation, on the other hand, provides adaptability, accuracy, and flexibility but has higher computational complexity and potential convergence challenges. \\ \hline Advantages Compared to the Belief Propagation Algorithm \\ \hline \hline \end{tabular}  
* Lower complexity, since they are straightforward and easy to implement, thus they are more computationally efficient.
* Rapid decision making, since they do not require extensive computations or iterations.
* Robustness to noise and fluctuations that affect the emitting state detection by setting appropriate thresholds. \\ \hline Drawbacks Compared to the Belief Propagation Algorithm \\ \hline \hline \end{tabular}  
* Lack of adaptability, since they rely on fixed thresholds, which may not capture the full complexity of the data distribution and thus can lead to suboptimal results.
* Sensitivity to threshold selection, since they heavily rely on choosing appropriate thresholds. Selecting thresholds that are too low or too high can lead to false positives or false negatives, respectively, impacting the accuracy of the emitting state detection.
* Lack of incorporation of prior knowledge, which in many cases, is crucial for the improvement of the accuracy of the emitting state detection.
* Lack of iterative refinement, which hinders gradual improvement in the accuracy of the emitting state detection.  
\end{table} 
Table 1: Comparison of belief propagation with state-of-the-art methods in the detection of a source operational state. **Statistical techniques**, such as cumulative sum (CUSUM) or exponentially weighted moving average (EWMA), monitor sensor measurements over time and detect significant changes or deviations from the baseline [27, 28, 29, 30, 31].