Quasicircles and width of Jordan curves in CP1

We study a notion of ‘width’ for Jordan curves in (Formula presented.), paying special attention to the class of quasicircles. The width of a Jordan curve is defined in terms of the geometry of its convex hull in hyperbolic three-space. A similar invariant in the setting of anti-de Sitter geometry was used by Bonsante–Schlenker to characterize quasicircles among a larger class of Jordan curves in the boundary of anti de Sitter space. In contrast to the AdS setting, we show that there are Jordan curves of bounded width which fail to be quasicircles. However, we show that Jordan curves with small width are quasicircles

The induced metric on the boundary of the convex hull of a quasicircle in hyperbolic and anti-de Sitter geometry

Celebrated work of Alexandrov and Pogorelov determines exactly which metrics on the sphere are induced on the boundary of a compact convex subset of hyperbolic three-space. As a step toward a generalization for unbounded convex subsets, we consider convex regions of hyperbolic three-space bounded by two properly embedded disks which meet at infinity along a Jordan curve in the ideal boundary. In this setting, it is natural to augment the notion of induced metric on the boundary of the convex set to include a gluing map at infinity which records how the asymptotic geometry of the two surfaces compares near points of the limiting Jordan curve. Restricting further to the case in which the induced metrics on the two bounding surfaces have constant curvature K 2 Π1; 0/ and the Jordan curve at infinity is a quasicircle, the gluing map is naturally a quasisymmetric homeomorphism of the circle. The main result is that for each value of K, every quasisymmetric map is achieved as the gluing map at infinity along some quasicircle. We also prove analogous results in the setting of three-dimensional anti-de Sitter geometry. Our results may be viewed as universal versions of the conjectures of Thurston and Mess about prescribing the induced metric on the boundary of the convex core of quasifuchsian hyperbolic manifolds and globally hyperbolic anti-de Sitter spacetimes

Norm estimates of complex symmetric operators applied to quantum systems

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schr\"odinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schr\"odinger operators appearing in the complex scaling theory of resonances

Candidate Genes for Chromosomes 6 and 10: Quantitative Trait Loci for Age-Related Retinal Degeneration in Mice

Purpose: In a previous study, several quantitative trait loci (QTL) that influence age-related degeneration (ageRD) were identified in a cross between the albino strains B6(Cg)-Tyr(c-2J)/J (B6a) and BALB/cByJ (C). The Chromosome (Chr) 6 and Chr 10 QTL were the strongest and most highly significant loci and both involved B6a protective alleles. The QTL were responsible for 21% and 9% of the variance in phenotypes, respectively. We focused on these two QTL to identify candidate genes. Methods: DNA microarrays were used for the two mouse strains at four and eight months of age to identify genes that are differentially regulated and map to either QTL. Gene Ontology (GO) analysis of the differentially expressed genes was performed to identify possible processes and pathways associated with ageRD. To identify additional candidates, database analyses (Positional Medline or PosMed) were used. Based on differential expression, PosMed, and the presence of reported polymorphisms, five genes per QTL were selected for further study by sequencing analysis and qRT-PCR. Tumor necrosis factor, alpha-induced protein 3 (Tnfaip3; on a C57BL/6J (B6) background) was phenotypically tested. Single nucleotide polymorphisms (SNPs) flanking this gene were correlated with outer nuclear layer thickness (ONL), and eight-month-old Tnfaip3(+/-) mice were tested for ageRD. Results: Polymorphisms were found in the coding regions of eight genes. Changes in gene expression were identified by qRT-PCR for Hexokinase 2 (Hk2) and Docking protein 1 (Dok1) at four months and for Dok1 and Tnfaip3 at eight months. Tnfaip3 was selected for phenotypic testing due to differential expression and the presence of two nonsynonymous mutations. However, when ONL thickness was compared in eight-month-old congenic Tnfaip3(+/-) and Tnfaip3(+/+) mice, no differences were found, suggesting that Tnfaip3 is not the quantitative trait gene (QTG) for the Chr 10 QTL. The GO analysis revealed that GO terms associated with stress and cell remodeling are overrepresented in the ageRD-sensitive C strain compared with the B6a strain with age (eight months). In the ageRD-resistant B6a strain, compared with the C strain, GO terms associated with antioxidant response and the regulation of blood vessel size are overrepresented with age. Conclusions: The analyses of differentially expressed genes and the PosMed database yielded candidate genes for the Chr 6 and Chr 10 QTL. HtrA serine peptidase 2 (Htra2), Dok1, and Tnfaip3 were deemed most promising because of their known roles in apoptosis and our finding of nonsynonymous substitutions between B6a and C strains. While Tnfaip3 was excluded as the QTG for the Chr 10 QTL, Dok1 and Htra2 remain good candidates for the Chr 6 QTL. Finally, the GO term analysis further supports the general hypothesis that oxidative stress is involved in ageRD

A Method for Generation of Bone Marrow-Derived Macrophages from Cryopreserved Mouse Bone Marrow Cells

The broad use of transgenic and gene-targeted mice has established bone marrow-derived macrophages (BMDM) as important mammalian host cells for investigation of the macrophages biology. Over the last decade, extensive research has been done to determine how to freeze and store viable hematopoietic human cells; however, there is no information regarding generation of BMDM from frozen murine bone marrow (BM) cells. Here, we establish a highly efficient protocol to freeze murine BM cells and further generate BMDM. Cryopreserved murine BM cells maintain their potential for BMDM differentiation for more than 6 years. We compared BMDM obtained from fresh and frozen BM cells and found that both are similarly able to trigger the expression of CD80 and CD86 in response to LPS or infection with the intracellular bacteria Legionella pneumophila. Additionally, BMDM obtained from fresh or frozen BM cells equally restrict or support the intracellular multiplication of pathogens such as L. pneumophila and the protozoan parasite Leishmania (L.) amazonensis. Although further investigation are required to support the use of the method for generation of dendritic cells, preliminary experiments indicate that bone marrow-derived dendritic cells can also be generated from cryopreserved BM cells. Overall, the method described and validated herein represents a technical advance as it allows ready and easy generation of BMDM from a stock of frozen BM cells

Cone rod dystrophies

Cone rod dystrophies (CRDs) (prevalence 1/40,000) are inherited retinal dystrophies that belong to the group of pigmentary retinopathies. CRDs are characterized by retinal pigment deposits visible on fundus examination, predominantly localized to the macular region. In contrast to typical retinitis pigmentosa (RP), also called the rod cone dystrophies (RCDs) resulting from the primary loss in rod photoreceptors and later followed by the secondary loss in cone photoreceptors, CRDs reflect the opposite sequence of events. CRD is characterized by primary cone involvement, or, sometimes, by concomitant loss of both cones and rods that explains the predominant symptoms of CRDs: decreased visual acuity, color vision defects, photoaversion and decreased sensitivity in the central visual field, later followed by progressive loss in peripheral vision and night blindness. The clinical course of CRDs is generally more severe and rapid than that of RCDs, leading to earlier legal blindness and disability. At end stage, however, CRDs do not differ from RCDs. CRDs are most frequently non syndromic, but they may also be part of several syndromes, such as Bardet Biedl syndrome and Spinocerebellar Ataxia Type 7 (SCA7). Non syndromic CRDs are genetically heterogeneous (ten cloned genes and three loci have been identified so far). The four major causative genes involved in the pathogenesis of CRDs are ABCA4 (which causes Stargardt disease and also 30 to 60% of autosomal recessive CRDs), CRX and GUCY2D (which are responsible for many reported cases of autosomal dominant CRDs), and RPGR (which causes about 2/3 of X-linked RP and also an undetermined percentage of X-linked CRDs). It is likely that highly deleterious mutations in genes that otherwise cause RP or macular dystrophy may also lead to CRDs. The diagnosis of CRDs is based on clinical history, fundus examination and electroretinogram. Molecular diagnosis can be made for some genes, genetic counseling is always advised. Currently, there is no therapy that stops the evolution of the disease or restores the vision, and the visual prognosis is poor. Management aims at slowing down the degenerative process, treating the complications and helping patients to cope with the social and psychological impact of blindness

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)

Synchronizing Allelic Effects of Opposing Quantitative Trait Loci Confirmed a Major Epistatic Interaction Affecting Acute Lung Injury Survival in Mice

Increased oxygen (O2) levels help manage severely injured patients, but too much for too long can cause acute lung injury (ALI), acute respiratory distress syndrome (ARDS) and even death. In fact, continuous hyperoxia has become a prototype in rodents to mimic salient clinical and pathological characteristics of ALI/ARDS. To identify genes affecting hyperoxia-induced ALI (HALI), we previously established a mouse model of differential susceptibility. Genetic analysis of backcross and F2 populations derived from sensitive (C57BL/6J; B) and resistant (129X1/SvJ; X1) inbred strains identified five quantitative trait loci (QTLs; Shali1-5) linked to HALI survival time. Interestingly, analysis of these recombinant populations supported opposite within-strain effects on survival for the two major-effect QTLs. Whereas Shali1 alleles imparted the expected survival time effects (i.e., X1 alleles increased HALI resistance and B alleles increased sensitivity), the allelic effects of Shali2 were reversed (i.e., X1 alleles increased HALI sensitivity and B alleles increased resistance). For in vivo validation of these inverse allelic effects, we constructed reciprocal congenic lines to synchronize the sensitivity or resistance alleles of Shali1 and Shali2 within the same strain. Specifically, B-derived Shali1 or Shali2 QTL regions were transferred to X1 mice and X1-derived QTL segments were transferred to B mice. Our previous QTL results predicted that substituting Shali1 B alleles onto the resistant X1 background would add sensitivity. Surprisingly, not only were these mice more sensitive than the resistant X1 strain, they were more sensitive than the sensitive B strain. In stark contrast, substituting the Shali2 interval from the sensitive B strain onto the X1 background markedly increased the survival time. Reciprocal congenic lines confirmed the opposing allelic effects of Shali1 and Shali2 on HALI survival time and provide unique models to identify their respective quantitative trait genes and to critically assess the apparent bidirectional epistatic interactions between these major-effect loci

Q344ter Mutation Causes Mislocalization of Rhodopsin Molecules That Are Catalytically Active: A Mouse Model of Q344ter-Induced Retinal Degeneration

Q344ter is a naturally occurring rhodopsin mutation in humans that causes autosomal dominant retinal degeneration through mechanisms that are not fully understood, but are thought to involve an early termination that removed the trafficking signal, QVAPA, leading to its mislocalization in the rod photoreceptor cell. To better understand the disease mechanism(s), transgenic mice that express Q344ter were generated and crossed with rhodopsin knockout mice. Dark-reared Q344terrho+/− mice exhibited retinal degeneration, demonstrating that rhodopsin mislocalization caused photoreceptor cell death. This degeneration is exacerbated by light-exposure and is correlated with the activation of transducin as well as other G-protein signaling pathways. We observed numerous sub-micrometer sized vesicles in the inter-photoreceptor space of Q344terrho+/− and Q344terrho−/− retinas, similar to that seen in another rhodopsin mutant, P347S. Whereas light microscopy failed to reveal outer segment structures in Q344terrho−/− rods, shortened and disorganized rod outer segment structures were visible using electron microscopy. Thus, some Q344ter molecules trafficked to the outer segment and formed disc structures, albeit inefficiently, in the absence of full length wildtype rhodopsin. These findings helped to establish the in vivo role of the QVAPA domain as well as the pathways leading to Q344ter-induced retinal degeneration