Branching Asymptotics on Manifolds with Edge

We study pseudo-differential operators on a wedge with continuous and variable discrete branching asymptotics.Comment: 54 pages, 1 figure

Some distance bounds of branching processes and their diffusion limits

We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring as well as the immigration is arbitrarily Poisson-distributed (leading to arbitrary type of criticality). Implications for asymptotic distinguishability behaviour in terms of contiguity and entire separation of the involved GWI are given, too. Furthermore, we determine the corresponding limit quantities for the context in which the two GWI converge to Feller-type branching diffusion processes, as the time-lags between observations tend to zero. Some applications to (static random environment like) Bayesian decision making and Neyman-Pearson testing are presented as well.Comment: 45 page

CRISPR/Cas9‐mediated genome editing: from basic research to translational medicine

The recent development of the CRISPR/Cas9 system as an efficient and accessible programmable genome-editing tool has revolutionized basic science research. CRISPR/Cas9 system-based technologies have armed researchers with new powerful tools to unveil the impact of genetics on disease development by enabling the creation of precise cellular and animal models of human diseases. The therapeutic potential of these technologies is tremendous, particularly in gene therapy, in which a patient-specific mutation is genetically corrected in order to treat human diseases that are untreatable with conventional therapies. However, the translation of CRISPR/Cas9 into the clinics will be challenging, since we still need to improve the efficiency, specificity and delivery of this technology. In this review, we focus on several in vitro, in vivo and ex vivo applications of the CRISPR/Cas9 system in human disease-focused research, explore the potential of this technology in translational medicine and discuss some of the major challenges for its future use in patients.Portuguese Foundation for Science and Technology: UID/BIM/04773/2013 1334 Spanish Ministry of Science, Innovation and Universities RTI2018-094629-B-I00 Portuguese Foundation for Science and Technology SFRH/BPD/100434/2014 European Union (EU) 748585 LPCC-NRS/Terry Fox grantsinfo:eu-repo/semantics/publishedVersio