The study shows that the volumes and surfaces of n-balls, n-simplices, and n-orthoplices are holomorphic functions of n, which makes those objects omnidimensional, that is well defined in any complex dimension. Applications of these formulas to the omnidimensional polytopes inscribed in and circumscribed about n-balls reveal previously unknown properties of these geometric objects. In particular, for $0<n<1$, the volumes of the omnidimensional polytopes are larger than those of circumscribing n-balls, and both their volumes and surfaces are smaller than those of inscribed n-balls. The surface of an n-simplex circumscribing a unit diameter n-ball is spirally convergent to zero with real n approaching negative infinity but first has a local maximum at $n=-3.5$. The surface of an n-orthoplex circumscribing a unit diameter n-ball is spirally divergent with real n approaching negative infinity but first has a local minimum at $n=-1.5$, where its real and imaginary parts are equal to each other; similarly, is its volume, where the similar local minimum occurs at $n=-3.5$. Reflection functions for volumes and surfaces of these polytopes inscribed in and circumscribed about n-balls are proposed. Symmetries of products and quotients of the volumes in complex dimensions n and $-n$ and of the surfaces in complex dimensions n and $2-n$ are shown to be independent of the metric factor and the gamma function. Specific symmetries also hold between the volumes and surfaces in dimensions $n=-1/2$ and $n=1/2$.

Key message: The disturbance of a research plot by a windstorm allowed us to study the role of the seedling bank in the regeneration processes. The released advance regeneration dominated among the saplings; taller individuals retained their position until the end of the study. Pioneer species occurred sporadically. Seven years after the disturbance, the windthrow was covered by a dense thicket of young trees. Context: The dominant role played by advance regeneration in natural regeneration processes after intense wind disturbances is still a matter of dispute. Aims: We took advantage of a windstorm in one of our research plots to study the role of the seedling bank released by the disturbance in the regeneration processes. Methods: We collected data in 70 plots, recording the survivorship of seedlings, annual height growth, and signs of browsing. The height ranking was analyzed with Kendall’s concordance coefficient, and the height growth rates were compared using Dunn’s test. Results: The density of seedlings increased from 6.7/m² in 2008 to 8.1/m² in 2010 and then decreased to 1.2/m² in 2015. The density of saplings increased continuously from 0.14 to 1.9/m². The highest size differentiation occurred in sycamore maple; the individuals which were taller before the windstorm retained their position until the year 2015. The only species that was recruited mainly from germinants was European hornbeam. Conclusion: The advance regeneration released by the windstorm played a major role in the regeneration process, while pioneer species occurred only sporadically. Seven years after the disturbance, the windthrow was already covered by a dense thicket of young trees.

Background: The regulation of gene expression in eukaryotic cells is a complex process that involves epigenetic modifications and the interaction of DNA with multiple transcription factors. This process can be studied with unprecedented sensitivity using a combination of chromatin immunoprecipitation and next-generation DNA sequencing (ChIP-seq). Available ChIP-seq data can be further utilized to interpret new gene expression profiling experiments. Results: Here, we describe seqinspector, a tool that accepts any set of genomic coordinates from ChIP-seq or RNA-seq studies to identify shared transcriptional regulators. The presented web resource includes a large collection of publicly available ChIP-seq and RNA-seq experiments (>1300 tracks) performed on transcription factors, histone modifications, RNA polymerases, enhancers and insulators in humans and mice. Over-representation is calculated based on the coverage computed directly from indexed files storing ChIP-seq data (bigwig). Therefore, seqinspector is not limited to pre-computed sets of gene promoters. Conclusion: The tool can be used to identify common gene expression regulators for sets of co-expressed transcripts (including miRNAs, lncRNAs or any novel unannotated RNAs) or for sets of ChIP-seq peaks to identify putative protein-protein interactions or transcriptional co-factors. The tool is available at http://seqinspector.cremag.org.