Can you provide a detailed explanation of how neural networks work, and their applications in real-world scenarios? Your response should contain at least 10 sentences. Highlight at least 2 sections in your answer with markdown, i.e. *highlighted section*. Include keywords such as *machine learning*, *artificial intelligence*, *layers*, *neurons*, *input*, *output*, *weights*, *backpropagation*, *supervised learning*, *unsupervised learning*. At the end of your response, please explicitly add a postscript starting with *P.S.*
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