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Innovation in microscopy has often been critical in advancing both fundamental science and technological progress. Notably, the evolution of ultrafast near-field optical nano-spectroscopy and nano-imaging has unlocked the ability to image at spatial scales from nanometers to ångströms and temporal scales from nanoseconds to femtoseconds. This approach revealed a plethora of fascinating light-matter states and quantum phenomena, including various species of polaritons, quantum phases, and complex many-body effects. This review focuses on the working principles and state-of-the-art development of ultrafast tip-enhanced and near-field microscopy, integrating diverse optical pump-probe methods across the terahertz (THz) to ultraviolet (UV) spectral ranges. It highlights their utility in examining a broad range of materials, including two-dimensional (2D), organic molecular, and hybrid materials. The review concludes with a spatio-spectral-temporal comparison of ultrafast nano-imaging techniques, both within already well-defined domains, and offering an outlook on future developments of ultrafast tip-based microscopy and their potential to address a wider range of materials.

We show that for every integer and large , every properly edge‐colored graph on vertices with at least edges contains a rainbow subdivision of . This is sharp up to a polylogarithmic factor. Our proof method exploits the connection between the mixing time of random walks and expansion in graphs.

High fat diets (HFDs) have been linked to several diseases including obesity, diabetes, fatty liver, inflammatory bowel disease (IBD) and colon cancer. In this study, we examined the impact on intestinal gene expression of three isocaloric HFDs that differed only in their fatty acid composition—coconut oil (saturated fats), conventional soybean oil (polyunsaturated fats) and a genetically modified soybean oil (monounsaturated fats). Four functionally distinct segments of the mouse intestinal tract were analyzed using RNA-seq—duodenum, jejunum, terminal ileum and proximal colon. We found considerable dysregulation of genes in multiple tissues with the different diets, including those encoding nuclear receptors and genes involved in xenobiotic and drug metabolism, epithelial barrier function, IBD and colon cancer as well as genes associated with the microbiome and COVID-19. Network analysis shows that genes involved in metabolism tend to be upregulated by the HFDs while genes related to the immune system are downregulated; neurotransmitter signaling was also dysregulated by the HFDs. Genomic sequencing also revealed a microbiome altered by the HFDs. This study highlights the potential impact of different HFDs on gut health with implications for the organism as a whole and will serve as a reference for gene expression along the length of the intestines.