A new approach to quantitative propagation of chaos for drift, diffusion and jump processes

This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstract generator operators (consistency estimate) together with fine stability estimates on the flow of the limiting nonlinear equation (stability estimates). Then we apply this method to a Boltzmann collision jump process (for Maxwell molecules), to a McKean-Vlasov drift-diffusion process and to an inelastic Boltzmann collision jump process with (stochastic) thermal bath. To our knowledge, our approach yields the first such quantitative results for a combination of jump and diffusion processes.Comment: v2 (55 pages): many improvements on the presentation, v3: correction of a few typos, to appear In Probability Theory and Related Field

TM4SF20 ancestral deletion and susceptibility to a pediatric disorder of early language delay and cerebral white matter hyperintensities

White matter hyperintensities (WMHs) of the brain are important markers of aging and small-vessel disease. WMHs are rare in healthy children and, when observed, often occur with comorbid neuroinflammatory or vasculitic processes. Here, we describe a complex 4 kb deletion in 2q36.3 that segregates with early childhood communication disorders and WMH in 15 unrelated families predominantly from Southeast Asia. The premature brain aging phenotype with punctate and multifocal WMHs was observed in ∼70% of young carrier parents who underwent brain MRI. The complex deletion removes the penultimate exon 3 of TM4SF20, a gene encoding a transmembrane protein of unknown function. Minigene analysis showed that the resultant net loss of an exon introduces a premature stop codon, which, in turn, leads to the generation of a stable protein that fails to target to the plasma membrane and accumulates in the cytoplasm. Finally, we report this deletion to be enriched in individuals of Vietnamese Kinh descent, with an allele frequency of about 1%, embedded in an ancestral haplotype. Our data point to a constellation of early language delay and WMH phenotypes, driven by a likely toxic mechanism of TM4SF20 truncation, and highlight the importance of understanding and managing population-specific low-frequency pathogenic alleles.</p

TM4SF20 ancestral deletion and susceptibility to a pediatric disorder of early language delay and cerebral white matter hyperintensities.

White matter hyperintensities (WMHs) of the brain are important markers of aging and small-vessel disease. WMHs are rare in healthy children and, when observed, often occur with comorbid neuroinflammatory or vasculitic processes. Here, we describe a complex 4 kb deletion in 2q36.3 that segregates with early childhood communication disorders and WMH in 15 unrelated families predominantly from Southeast Asia. The premature brain aging phenotype with punctate and multifocal WMHs was observed in ~70% of young carrier parents who underwent brain MRI. The complex deletion removes the penultimate exon 3 of TM4SF20, a gene encoding a transmembrane protein of unknown function. Minigene analysis showed that the resultant net loss of an exon introduces a premature stop codon, which, in turn, leads to the generation of a stable protein that fails to target to the plasma membrane and accumulates in the cytoplasm. Finally, we report this deletion to be enriched in individuals of Vietnamese Kinh descent, with an allele frequency of about 1%, embedded in an ancestral haplotype. Our data point to a constellation of early language delay and WMH phenotypes, driven by a likely toxic mechanism of TM4SF20 truncation, and highlight the importance of understanding and managing population-specific low-frequency pathogenic alleles