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Introduction Destination: section..1.1 Children: Item: Title: 1.1. Motivation Destination: subsection..1.1.1 Item: Title: 1.2. This Review Destination: subsection..1.1.2 Item: Title: 2. The Technique of SPTM Destination: section..1.2 Children: Item: Title: 2.1. General Concept Destination: subsection..1.2.1 Item: Title: 2.2. Experimental Implementations of SPTM Destination: subsection..1.2.2 Children: Item: Title: 2.2.1. Time-Correlated Microscopy Destination: subsubsection..1.2.2.1 Item: Title: 2.2.2. Widefield Pump-Probe Imaging Destination: subsubsection..1.2.2.2 Item: Title: 2.2.3. Point-Scanning, Confocal Detection Destination: subsubsection..1.2.2.3 Item: Title: 2.2.4. Transient Grating Spectroscopy Destination: subsubsection..1.2.2.4 Item: Title: 3. Transport Theory Destination: section..1.3 Item: Title: 4. Particle Transport Studied Using SPTM Destination: section..1.4 Children: Item: Title: 4.1. 9040˝Normal9040˛ Diffusion of (Quasi)Particles Destination: subsection..1.4.1 Item: Title: 4.2. Nonlinear Diffusion of (Quasi)Particles Destination: subsection..1.4.2 Item: Title: 5. Heat Transport Studied Using SPTM Destination: section..1.5 Children: Item: Title: 5.1. 9040˝Normal9040˛ Diffusion of Phonon and Electron Heat Destination: subsection..1.5.1 Item: Title: 5.2. Nonlinear Diffusion of Phonon and Electron Heat Destination: subsection..1.5.2 Item: Title: 6. Outlook Destination: section..1.6 Item: Title: Acknowledgements Destination: section*.2 Item: Title: Conflict of Interest Destination: section*.4 Children: Item: Title: Data Availability Statement Destination: section*.6 Item: Title: Keywords Destination: section*.8 Filters: FilterPipeline: FlateDecode FilterPipeline: CCITTFaxDecode FilterPipeline: DCTDecode Images: Image: NisoImageMetadata: FormatName: image/png ImageWidth: 228 ImageHeight: 45 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Image: NisoImageMetadata: FormatName: image/png ImageWidth: 228 ImageHeight: 45 ColorSpace: black is zero BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode Image: NisoImageMetadata: FormatName: image/tiff CompressionScheme: CCITT Group 4 ImageWidth: 2986 ImageHeight: 728 BitsPerSample: 1 BitsPerSampleUnit: integer ImageMask: true Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 2050 ImageHeight: 721 ColorSpace: CMYK 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