The group of invariants of an inner function with finite spectrum

This paper determines the group of continuous invariants corresponding to an inner function circle dot with finitely many singularities on the unit circle T; that is, the continuous mappings g : T -> T such that circle dot o g = circle dot on T. These mappings form a group under composition.

Prime and semiprime inner functions

Abstract This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.

INTERPOLATING BLASCHKE PRODUCTS AND ANGULAR DERIVATIVES

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H-infinity[(b) over bar : b has finite angular derivative everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

Interpolating Blaschke Products and Angular Derivatives

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra generated by the algebra of bounded analytic functions and the conjugates of Blaschke products with angular derivative finite everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

Commuting Nonselfadjoint Operators and their Characteristic Operator-Functions

* Partially supported by Grant MM-428/94 of MESC.

Id Gene regulation and function in the prosensory domains of the chicken inner ear: a link between Bmp Signaling and Atoh1

Bone morphogenetic proteins (Bmps) regulate the expression of the proneural gene Atoh1 and the generation of hair cells in the developing inner ear. The present work explored the role of Inhibitor of Differentiation genes (Id1-3) in this process. The results show that Id genes are expressed in the prosensory domains of the otic vesicle, along with Bmp4 and Bmp7. Those domains exhibit high levels of the phosphorylated form of Bmp-responding R-Smads (P-Smad1,5,8), and of Bmp-dependent Smad transcriptional activity as shown by the BRE-tk-EGFP reporter. Increased Bmp signaling induces the expression of Id1-3 along with the inhibition of Atoh1. Conversely, the Bmp antagonist Noggin or the Bmp-receptor inhibitor Dorsomorphin elicit opposite effects, indicating that Bmp signaling is necessary for Id expression and Atoh1 regulation in the otocyst. The forced expression of Id3 is sufficient to reduce Atoh1 expression and to prevent the expression of hair cell differentiation markers. Together, these results suggest that Ids are part of the machinery that mediates the regulation of hair cell differentiation exerted by Bmps. In agreement with that, during hair cell differentiation Bmp4 expression, P-Smad1,5,8 levels and Id expression are downregulated from hair cells. However, Ids are also downregulated from the supporting cells which contrarily to hair cells exhibit high levels of Bmp4 expression, P-Smad1,5,8, and BRE-tk-EGFP activity, suggesting that in these cells Ids escape from Bmp/Smad signaling. The differential regulation of Ids in time and space may underlie the multiple functions of Bmp signaling during sensory organ development.

Relationship between pulmonary function and indoor air pollution from coal combustion among adult residents in an inner-city area of southwest China

Few studies evaluate the amount of particulate matter less than 2.5 mm in diameter (PM2.5) in relation to a change in lung function among adults in a population. The aim of this study was to assess the association of coal as a domestic energy source to pulmonary function in an adult population in inner-city areas of Zunyi city in China where coal use is common. In a cross-sectional study of 104 households, pulmonary function measurements were assessed and compared in 110 coal users and 121 non-coal users (≥18 years old) who were all nonsmokers. Several sociodemographic factors were assessed by questionnaire, and ventilatory function measurements including forced vital capacity (FVC), forced expiratory volume in 1 s (FEV1), the FEV1/FVC ratio, and peak expiratory flow rate (PEFR) were compared between the 2 groups. The amount of PM2.5 was also measured in all residences. There was a significant increase in the relative concentration of PM2.5 in the indoor kitchens and living rooms of the coal-exposed group compared to the non-coal-exposed group. In multivariate analysis, current exposure to coal smoke was associated with a 31.7% decrease in FVC, a 42.0% decrease in FEV1, a 7.46% decrease in the FEV1/FVC ratio, and a 23.1% decrease in PEFR in adult residents. The slope of lung function decrease for Chinese adults is approximately a 2-L decrease in FVC, a 3-L decrease in FEV1, and an 8 L/s decrease in PEFR per count per minute of PM2.5 exposure. These results demonstrate the harmful effects of indoor air pollution from coal smoke on the lung function of adult residents and emphasize the need for public health efforts to decrease exposure to coal smoke.

Inner satellites of Neptune: I the disturbing function

In this work, we focus our attention to the expansion of the disturbing function (R) which governs the dynamics of a satellite (natural or artificial) in the Neptune-Triton system. What makes this problem quite unusual, is the fact that a small inner satellite can be strongly disturbed by Triton which is moving in a highly inclined and retrograde orbit. These features are unique in our solar system. Although a lot of retrograde satellites are currently known, all of them have negligible mass and the), do not offer almost any perturbation on the others satellites. However, in the case of the inner satellites of Neptune, Triton is an interesting exception. In a highly inclined orbit, the perturbation it exerts on the neighbouring satellites of Neptune cannot be ignored even for the present scenario. However, in the future, this perturbation will be much more important because due to the tides, the orbit of Triton is contracting, whereas the semi major axes of the remaining inner satellites of Neptune will remain almost unaffected by the tides. In this work we first obtain the disturbing function in the retrograde case. After that, we generalize R for arbitrary inclination. Several numerical tests are presented and a possible future case of resonant configuration is briefly discussed as well. (c) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

The leopard's claw : a thrilling story of love and adventure from a European castle through the West African jungle, disclosing a deep insight into the quality and spiritual influence of African social institutions and conditions, and revealing a profound psyschic [sic] interpretation of African inner life, all clustered about the mysterious function and significance of the leopard's claw /

Mode of access: Internet.

Structure-Function Analysis of the HrpB2-HrcU Interaction in the Xanthomonas citri Type III Secretion System

Bacterial type III secretion systems deliver protein virulence factors to host cells. Here we characterize the interaction between HrpB2, a small protein secreted by the Xanthomonas citri subsp. citri type III secretion system, and the cytosolic domain of the inner membrane protein HrcU, a paralog of the flagellar protein FlhB. We show that a recombinant fragment corresponding to the C-terminal cytosolic domain of HrcU produced in E. coli suffers cleavage within a conserved Asn264-Pro265-Thr266-His267 (NPTH) sequence. A recombinant HrcU cytosolic domain with N264A, P265A, T266A mutations at the cleavage site (HrcU(AAAH)) was not cleaved and interacted with HrpB2. Furthermore, a polypeptide corresponding to the sequence following the NPTH cleavage site also interacted with HrpB2 indicating that the site for interaction is located after the NPTH site. Non-polar deletion mutants of the hrcU and hrpB2 genes resulted in a total loss of pathogenicity in susceptible citrus plants and disease symptoms could be recovered by expression of HrpB2 and HrcU from extrachromossomal plasmids. Complementation of the Delta hrcU mutant with HrcU(AAAH) produced canker lesions similar to those observed when complemented with wild-type HrcU. HrpB2 secretion however, was significantly reduced in the Delta hrcU mutant complemented with HrcU(AAAH), suggesting that an intact and cleavable NPTH site in HrcU is necessary for total functionally of T3SS in X. citri subsp. citri. Complementation of the Delta hrpB2 X. citri subsp. citri strain with a series of hrpB2 gene mutants revealed that the highly conserved HrpB2 C-terminus is essential for T3SS-dependent development of citrus canker symptoms in planta.

The endodermis--development and differentiation of the plant's inner skin.

Controlling external compound entrance is essential for plant survival. To set up an efficient and selective sorting of nutrients, free diffusion via the apoplast in vascular plants is blocked at the level of the endodermis. Although we have learned a lot about endodermal specification in the last years, information regarding its differentiation is still very limited. A differentiated endodermal cell can be defined by the presence of the "Casparian strip" (CS), a cell wall modification described first by Robert Caspary in 1865. While the anatomical description of CS in many vascular plants has been very detailed, we still lack molecular information about the establishment of the Casparian strips and their actual function in roots. The recent isolation of a novel protein family, the CASPs, that localizes precisely to a domain of the plasma membrane underneath the CS represents an excellent point of entry to explore CS function and formation. In addition, it has been shown that the endodermis contains transporters that are localized to either the central (stele-facing) or peripheral (soil-facing) plasma membranes. These features suggest that the endodermis functions as a polar plant epithelium.

Congenital ataxia and hemiplegic migraine with cerebral edema associated with a novel gain of function mutation in the calcium channel CACNA1A.

Mutations in the CACNA1A gene, encoding the α1 subunit of the voltage-gated calcium channel Ca(V)2.1 (P/Q-type), have been associated with three neurological phenotypes: familial and sporadic hemiplegic migraine type 1 (FHM1, SHM1), episodic ataxia type 2 (EA2), and spinocerebellar ataxia type 6 (SCA6). We report a child with congenital ataxia, abnormal eye movements and developmental delay who presented severe attacks of hemiplegic migraine triggered by minor head traumas and associated with hemispheric swelling and seizures. Progressive cerebellar atrophy was also observed. Remission of the attacks was obtained with acetazolamide. A de novo 3 bp deletion was found in heterozygosity causing loss of a phenylalanine residue at position 1502, in one of the critical transmembrane domains of the protein contributing to the inner part of the pore. We characterized the electrophysiology of this mutant in a Xenopus oocyte in vitro system and showed that it causes gain of function of the channel. The mutant Ca(V)2.1 activates at lower voltage threshold than the wild type. These findings provide further evidence of this molecular mechanism as causative of FHM1 and expand the phenotypic spectrum of CACNA1A mutations with a child exhibiting severe SHM1 and non-episodic ataxia of congenital onset.

Congenital ataxia and hemiplegic migraine with cerebral edema associated with a novel gain of function mutation in the calcium channel CACNA1A.

Mutations in the CACNA1A gene, encoding the α1 subunit of the voltage-gated calcium channel CaV2.1 (P/Q-type), have been associated with three neurological phenotypes: familial and sporadic hemiplegic migraine type 1 (FHM1, SHM1), episodic ataxia type 2 (EA2), and spinocerebellar ataxia type 6 (SCA6). We report a child with congenital ataxia, abnormal eye movements and developmental delay who presented severe attacks of hemiplegic migraine triggered by minor head traumas and associated with hemispheric swelling and seizures. Progressive cerebellar atrophy was also observed. Remission of the attacks was obtained with acetazolamide. A de novo 3bp deletion was found in heterozygosity causing loss of a phenylalanine residue at position 1502, in one of the critical transmembrane domains of the protein contributing to the inner part of the pore. We characterized the electrophysiology of this mutant in a Xenopus oocyte in vitro system and showed that it causes gain of function of the channel. The mutant CaV2.1 activates at lower voltage threshold than the wild type. These findings provide further evidence of this molecular mechanism as causative of FHM1 and expand the phenotypic spectrum of CACNA1A mutations with a child exhibiting severe SHM1 and non-episodic ataxia of congenital onset.

N-myc controls proliferation, morphogenesis, and patterning of the inner ear

Myc family members play crucial roles in regulating cell proliferation, size, and differentiation during organogenesis. Both N-myc and c-myc are expressed throughout inner ear development. To address their function in the mouse inner ear, we generated mice with conditional deletions in either N-myc or c-myc. Loss of c-myc in the inner ear causes no apparent defects, whereas inactivation of N-myc results in reduced growth caused by a lack of proliferation. Reciprocally, the misexpression of N-myc in the inner ear increases proliferation. Morphogenesis of the inner ear in N-myc mouse mutants is severely disturbed, including loss of the lateral canal, fusion of the cochlea with the sacculus and utriculus, and stunted outgrowth of the cochlea. Mutant cochleas are characterized by an increased number of cells exiting the cell cycle that express the cyclin-dependent kinase inhibitor p27Kip1 and lack cyclin D1, both of which control the postmitotic state of hair cells. Analysis of different molecular markers in N-myc mutant ears reveals the development of a rudimentary organ of Corti containing hair cells and the underlying supporting cells. Differentiated cells, however, fail to form the highly ordered structure characteristic for the organ of Corti but appear as rows or clusters with an excess number of hair cells. The Kölliker's organ, a transient structure neighboring the organ of Corti and a potential source of ectopic hair cells, is absent in the mutant ears. Collectively, our data suggest that N-myc regulates growth, morphogenesis, and pattern formation during the development of the inner ear.

Pupil responses derived from outer and inner retinal photoreception are normal in patients with hereditary optic neuropathy.

We compared the pupil responses originating from outer versus inner retinal photoreception between patients with isolated hereditary optic neuropathy (HON, n = 8) and healthy controls (n = 8). Three different testing protocols were used. For the first two protocols, a response function of the maximal pupil contraction versus stimulus light intensity was generated and the intensity at which half of the maximal pupil contraction, the half-max intensity, was determined. For the third protocol, the pupil size after light offset, the re-dilation rate and re-dilation amplitude were calculated to assess the post-light stimulus response. Patients with HON had bilateral, symmetric optic atrophy and significant reduction of visual acuity and visual field compared to controls. There were no significant mean differences in the response curve and pupil response parameters that reflect mainly rod, cone or melanopsin activity between patients and controls. In patients, there was a significant correlation between the half-max intensity of the red light sequence and visual field loss. In conclusion, pupil responses derived from outer or inner retinal photoreception in HON patients having mild-to moderate visual dysfunction are not quantitatively different from age-matched controls. However, an association between the degree of visual field loss and the half-max intensity of the cone response suggests that more advanced stages of disease may lead to impaired pupil light reflexes.