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In this brief note a straightforward combinatorial proof for an identity directly connecting rooted forests and unordered set partitions is provided. Furthermore, references that put this type of identity in the context of and are given.
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7357680 | PMC |
http://dx.doi.org/10.1007/s00010-019-00662-9 | DOI Listing |
Curr Opin Plant Biol
September 2025
Department of Plant Biology, University of Illinois, Urbana-Champaign, USA. Electronic address:
Early floral meristem (FM) patterning is one of the most intensively studied developmental programs in plants. While extensive work has uncovered the molecular networks underlying key processes such as organ initiation and identity specification, integrating this knowledge into a comprehensive framework remains challenging. Organ initiation is governed by auxin-mediated positioning and boundary formation, whereas organ identity is determined by the combinatorial activities of ABCE-class transcription factors.
View Article and Find Full Text PDFNat Neurosci
August 2025
Department of Genetics and Genome Sciences, University of Connecticut School of Medicine, Farmington, CT, USA.
Cerebellar Purkinje cells (PCs), the sole output neurons of the cerebellar cortex, are essential for motor coordination, learning and circuit formation. While functionally diverse, the extent of PC heterogeneity and the molecular drivers of this diversity remain unclear. Using single-cell RNA sequencing, we identified at least 11 molecularly distinct PC subtypes in the embryonic mouse cerebellum.
View Article and Find Full Text PDFbioRxiv
July 2025
Montana State University, Department of Microbiology and Cell Biology, Bozeman, MT 59717.
The essential outcome of a successful mating is the transfer of genetic material from males to females in sexually reproducing animals from insects to mammals. In males, this culminates in ejaculation, a precisely timed sequence of organ contractions driven by the concerted activity of interneurons, sensory neurons, and motor neurons. Although central command circuits that trigger copulation have been mapped, the motor architecture and the chemical logic that couple specific neuronal subclasses to organ specific contractility, seminal fluid secretion, and sperm emission remain largely uncharted.
View Article and Find Full Text PDFNat Commun
July 2025
Department of Neurology, Northwestern University, Feinberg School of Medicine, Chicago, IL, USA.
During mouse embryonic brain development, the Evf2 ultraconserved enhancer (UCE) lncRNA guides the Dlx5/6UCE to ~129 sites across chr6. However, previous work identified only 4 transcriptionally regulated targets associated with Evf2-Dlx5/6UCE-gene guidance, raising questions about the significance of Evf2-regulated Dlx5/6UCE-gene interactions. Here, single-cell transcriptomics reveal far greater alignment between Evf2-Dlx5/6UCE-gene guidance and transcriptional regulation than previously reported.
View Article and Find Full Text PDFbioRxiv
June 2025
Department of Genetics, Yale University School of Medicine, New Haven, CT 06510, USA.
Recent advancements in single-cell sequencing and spatial omics technologies have enhanced our understanding of diverse cellular identities, compositions, architectures, and functions. However, the single-cell three-dimensional (3D) organization of the epigenome is still not well understood, due to an absence of spatial single-cell methods that allow high-resolution, locus-specific detection of combinations of epigenetic marks while maintaining the 3D organization of the genome. Here, we develop Epigenetic Proximity Hybridization Reaction (Epi-PHR), a non-disruptive image-based single-cell spatial epigenetic profiling technology.
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