Topological regluing of rational functions

Regluing is a topological operation that helps to construct topological models for rational functions on the boundaries of certain hyperbolic components. It also has a holomorphic interpretation, with the flavor of infinite dimensional Thurston--Teichm\"uller theory. We will discuss a topological theory of regluing, and trace a direction in which a holomorphic theory can develop.Comment: 38 page

Separably injective C*-algebras

We show that a C*-algebra is a $1$-separably injective Banach space if, and only if, it is linearly isometric to the Banach space $C_0(\Omega)$ of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff space $\Omega$

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

Single-cell profiling reveals an endothelium-mediated immunomodulatory pathway in the eye choroid

The activity and survival of retinal photoreceptors depend on support functions performed by the retinal pigment epithelium (RPE) and on oxygen and nutrients delivered by blood vessels in the underlying choroid. By combining single-cell and bulk RNA sequencing, we categorized mouse RPE/choroid cell types and characterized the tissue-specific transcriptomic features of choroidal endothelial cells. We found that choroidal endothelium adjacent to the RPE expresses high levels of Indian Hedgehog and identified its downstream target as stromal GLI1+ mesenchymal stem cell-like cells. In vivo genetic impairment of Hedgehog signaling induced significant loss of choroidal mast cells, as well as an altered inflammatory response and exacerbated visual function defects after retinal damage. Our studies reveal the cellular and molecular landscape of adult RPE/choroid and uncover a Hedgehog-regulated choroidal immunomodulatory signaling circuit. These results open new avenues for the study and treatment of retinal vascular diseases and choroid-related inflammatory blinding disorders.Funding for this study was provided by National Institutes of Health grants EY08538 and GM34107 (E. Rodriguez-Boulan); EY027038 (R.F. Mullins); 1R21CA224391-01A1 (J.H. Zippin); and 1R01CA194547, 1U24CA210989, and P50CA211024 (O. Elemento); National Cancer Institute grant R01CA192176 and cancer center support grant P30 CA008748-48 (A.L. Joyner); Comunidad Autónoma de Madrid grant 2017-T1/BMD-5247 (I. Benedicto); Agencia Nacional Argentina de Promoción Cient´ıfica y Tecnológica grant PICT 2014-3687 and Fundación Sales (G.A. Rabinovich); a Pew Latin American Fellowship (G.L. Lehmann); Calder Research Scholar Award Vitiligo/Pigment Cell Disorders (J.H. Zippin); Starr Foundation Tri-Institutional Stem Cell Initiative award 2013-028; NYSTEM contract C32596GG; and Research to Prevent Blindness and Dyson Foundation departmental grants. The CNIC is supported by the Instituto de Salud Carlos III, the Ministerio de Ciencia e Innovación, and the Pro CNIC Foundation and is a Severo Ochoa Center of Excellence (SEV-2015-0505).S

Biological and trophic consequences of genetic introgression between endemic and invasive Barbus fishes.

Genetic introgression with native species is recognized as a detrimental impact resulting from biological invasions involving taxonomically similar invaders. Whilst the underlying genetic mechanisms are increasingly understood, the ecological consequences of introgression are relatively less studied, despite their utility for increasing knowledge on how invasion impacts can manifest. Here, the ecological consequences of genetic introgression from an invasive congener were tested using the endemic barbel populations of central Italy, where the invader was the European barbel Barbus barbus. Four populations of native Barbus species (B. plebejus and B. tyberinus) were studied: two purebred and two completely introgressed with alien B. barbus. Across the four populations, differences in their biological traits (growth, body condition and population demographic structure) and trophic ecology (gut content analysis and stable isotope analysis) were tested. While all populations had similar body condition and were dominated by fish up to 2 years of age, the introgressed fish had substantially greater lengths at the same age, with maximum lengths 410-460 mm in hybrids versus 340-360 mm in native purebred barbel. The population characterized by the highest number of introgressed B. barbus alleles (81 %) had the largest trophic niche and a substantially lower trophic position than the other populations through its exploitation of a wider range of resources (e.g. small fishes and plants). These results attest that the genetic introgression of an invasive congener with native species can result in substantial ecological consequences, including the potential for cascading effects. Supplementary Information: The online version contains supplementary material available at 10.1007/s10530-021-02577-6