Orthogonal polynomials on the unit circle and chain sequences

Szego{double acute} has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1,1] by the transformation 2x=z+z-1. In the 80's and 90's Delsarte and Genin showed that real orthogonal polynomials on the unit circle can be mapped to symmetric orthogonal polynomials on the interval [-1,1] using the transformation 2x=z1/2+z-1/2. We extend the results of Delsarte and Genin to all orthogonal polynomials on the unit circle. The transformation maps to functions on [-1,1] that can be seen as extensions of symmetric orthogonal polynomials on [-1,1] satisfying a three-term recurrence formula with real coefficients {cn} and {dn}, where {dn} is also a positive chain sequence. Via the results established, we obtain a characterization for a point w(|w|=1) to be a pure point of the measure involved. We also give a characterization for orthogonal polynomials on the unit circle in terms of the two sequences {cn} and {dn}. © 2013 Elsevier Inc.

Chain sequences and symmetric generalized orthogonal polynomials

in this paper, we derive an explicit expression for the parameter sequences of a chain sequence in terms of the corresponding orthogonal polynomials and their associated polynomials. We use this to study the orthogonal polynomials K-n((lambda.,M,k)) associated with the probability measure dphi(lambda,M,k;x), which is the Gegenbauer measure of parameter lambda + 1 with two additional mass points at +/-k. When k = 1 we obtain information on the polynomials K-n((lambda.,M)) which are the symmetric Koornwinder polynomials. Monotonicity properties of the zeros of K-n((lambda,M,k)) in relation to M and k are also given. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Para-orthogonal polynomials from constant Verblunsky coefficients

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A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula

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Use of Genetically Modified Glial Cells Overexpressing Laminin α1-Chain Peptides in Neurite Outgrowth Studies

1. C6 glioma cells were transfected with two constructs carrying C-terminal laminin alpha1-chain sequences of 117 and 114 bp length, respectively. These sequences are specifically known to code for peptides which have neurite-promoting activity. 2. The stable expression and secretion of the two peptides was detected by Northern and Western blot analysis. 3. Primary neuronal cultures derived from embryonic mouse forebrain were cocultured with these transfected cells and exhibited a substantial increase in neurite outgrowth and in survival time. Conditioned media from the transfected cells generated similar effects. 4. Organotypic cultures from embryonic mouse brain were used as a second system as being closer to the in vivo situation. Again, coculture of brain slices with transfected cells or treatment with laminin peptide-containing media increased neuronal outgrowth.

Differential roles of T cell receptor alpha and beta chains in ligand binding among H-2Kd-restricted cytolytic T lymphocyte clones specific for a photoreactive Plasmodium berghei circumsporozoite peptide derivative.

To study the interaction of T cell receptor with its ligand, a complex of a major histocompatibility complex molecule and a peptide, we derived H-2Kd-restricted cytolytic T lymphocyte clones from mice immunized with a Plasmodium berghei circumsporozoite peptide (PbCS) 252-260 (SYIPSAEKI) derivative containing photoreactive Nepsilon-[4-azidobenzoyl] lysine in place of Pro-255. This residue and Lys-259 were essential parts of the epitope recognized by these clones. Most of the clones expressed BV1S1A1 encoded beta chains along with specific complementary determining region (CDR) 3beta regions but diverse alpha chain sequences. Surprisingly, all T cell receptors were preferentially photoaffinity labeled on the alpha chain. For a representative T cell receptor, the photoaffinity labeled site was located in the Valpha C-strand. Computer modeling suggested the presence of a hydrophobic pocket, which is formed by parts of the Valpha/Jalpha C-, F-, and G-strands and adjacent CDR3alpha residues and structured to be able to avidly bind the photoreactive ligand side chain. We previously found that a T cell receptor specific for a PbCS peptide derivative containing this photoreactive side chain in position 259 similarly used a hydrophobic pocket located between the junctional CDR3 loops. We propose that this nonpolar domain in these locations allow T cell receptors to avidly and specifically bind epitopes containing non-peptidic side chains.

Pancreatic-specific expression of the glucose transporter type 2 gene: identification of cis-elements and islet-specific trans-acting factors.

A defect in glucose sensing of the pancreatic beta-cells has been observed in several animal models of type II diabetes and has been correlated with a reduced gene expression of the glucose transporter type 2 (Glut2). In a transgenic mouse model, expression of Glut2 antisense RNA in pancreatic beta-cells has recently been shown to be associated with an impaired glucose-induced insulin secretion and the development of diabetes. To identify factors that may be involved in the specific decrease of Glut2 in the beta-cells of the diabetic animal, an attempt was made to localize the cis-elements and trans-acting factors involved in the control of Glut2 expression in the endocrine pancreas. It was demonstrated by transient transfection studies that only 338 base pairs (bp) of the murine Glut2 proximal promoter are needed for reporter gene expression in pancreatic islet-derived cell lines, whereas no activity was detected in nonpancreatic cells. Three cis-elements, GTI, GTII, and GTIII, have been identified by DNAse I footprinting and gel retardation experiments within these 338 bp. GTI and GTIII bind distinct but ubiquitously expressed trans-acting factors. On the other hand, nuclear proteins specifically expressed in pancreatic cell lines interact with GTII, and their relative abundance correlates with endogenous Glut2 expression. These GTII-binding factors correspond to nuclear proteins of 180 and 90 kilodaltons as defined by Southwestern analysis. The 180-kilodalton factor is present in pancreatic beta-cell lines but not in an alpha-cell line. Mutation of the GTI or GTIII cis-elements decreases transcriptional activity directed by the 338-bp promoter, whereas mutation of GTII increases gene transcription. Thus negative and positive regulatory sequences are identified within the proximal 338 bp of the GLUT2 promoter and may participate in the islet-specific expression of the gene by binding beta-cell specific trans-acting factors.

Hierarchal utilization of different T-cell receptor Vbeta gene segments in the CD8(+)-T-cell response to an immunodominant Moloney leukemia virus-encoded epitope in vivo.

The CD8(+)-T-cell response to Moloney murine leukemia virus (M-MuLV)-associated antigens in C57BL/6 mice is directed against an immunodominant gag-encoded epitope (CCLCLTVFL) presented in the context of H-2D(b) and is restricted primarily to cytotoxic T lymphocytes (CTL) expressing the Valpha3.2 and Vbeta5.2 gene segments. We decided to examine the M-MuLV response in congenic C57BL/6 Vbeta(a) mice which are unable to express the dominant Valpha3.2(+) Vbeta5.2(+) T-cell receptor (TCR) due to a large deletion at the TCR locus that includes the Vbeta5.2 gene segment. Interestingly, M-MuLV-immune C57BL/6 Vbeta(a) mice were still able to reject M-MuLV-infected tumor cells and direct ex vivo analysis of peripheral blood lymphocytes from these immune mice revealed a dramatic increase in CD8(+) cells utilizing the same Valpha3.2 gene segment in association with two different Vbeta segments (Vbeta3 and Vbeta17). Surprisingly, all these CTL recognized the same immunodominant M-MuLV gag epitope. Analysis of the TCR repertoire of individual M-MuLV-immune (C57BL/6 x C57BL/6 Vbeta(a))F(1) mice revealed a clear hierarchy in Vbeta utilization, with a preferential usage of the Vbeta17 gene segment, whereas Vbeta3 and especially Vbeta5.2 were used to much lesser extents. Sequencing of TCRalpha- and -beta-chain junctional regions of CTL clones specific for the M-MuLV gag epitope revealed a diverse repertoire of TCRbeta chains in Vbeta(a) mice and a highly restricted TCRbeta-chain repertoire in Vbeta(b) mice, whereas TCRalpha-chain sequences were highly conserved in both cases. Collectively, our data indicate that the H-2D(b)-restricted M-MuLV gag epitope can be recognized in a hierarchal fashion by different Vbeta domains and that the degree of beta-chain diversity varies according to Vbeta utilization.

Functionally conserved cis-regulatory elements of COL18A1 identified through zebrafish transgenesis

Type XVIII collagen is a component of basement membranes, and expressed prominently in the eye, blood vessels, liver, and the central nervous system. Homozygous mutations in COL18A1 lead to Knobloch Syndrome, characterized by ocular defects and occipital encephalocele. However, relatively little has been described on the role of type XVIII collagen in development, and nothing is known about the regulation of its tissue-specific expression pattern. We have used zebrafish transgenesis to identify and characterize cis-regulatory sequences controlling expression of the human gene. Candidate enhancers were selected from non-coding sequence associated with COL18A1 based on sequence conservation among mammals. Although these displayed no overt conservation with orthologous zebrafish sequences, four regions nonetheless acted as tissue-specific transcriptional enhancers in the zebrafish embryo, and together recapitulated the major aspects of col18a1 expression. Additional post-hoc computational analysis on positive enhancer sequences revealed alignments between mammalian and teleost sequences, which we hypothesize predict the corresponding zebrafish enhancers; for one of these, we demonstrate functional overlap with the orthologous human enhancer sequence. Our results provide important insight into the biological function and regulation of COL18A1, and point to additional sequences that may contribute to complex diseases involving COL18A1. More generally, we show that combining functional data with targeted analyses for phylogenetic conservation can reveal conserved cis-regulatory elements in the large number of cases where computational alignment alone falls short. (C) 2009 Elsevier Inc. All rights reserved.

Szego polynomials: some relations to L-orthogonal and orthogonal polynomials

We consider the real Szego polynomials and obtain some relations to certain self inversive orthogonal L-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on real intervals. We also consider the polynomials obtained when the coefficients in the recurrence relations satisfied by the self inversive orthogonal L-polynomials are rotated. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Sieved para-orthogonal polynomials on the unit circle

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On Understanding How Developers Use the Spotter Search Tool

Analyzing how software engineers use the Integrated Development Environment (IDE) is essential to better understanding how engineers carry out their daily tasks. Spotter is a code search engine for the Pharo programming language. Since its inception, Spotter has been rapidly and broadly adopted within the Pharo community. However, little is known about how practitioners employ Spotter to search and navigate within the Pharo code base. This paper evaluates how software engineers use Spotter in practice. To achieve this, we remotely gather user actions called events. These events are then visually rendered using an adequate navigation tool chain. Sequences of events are represented using a visual alphabet. We found a number of usage patterns and identified underused Spotter features. Such findings are essential for improving Spotter.

Perturbation of the T cell repertoire in rheumatoid arthritis

Aberrations in the T cell repertoire with the emergence of oligoclonal populations have been described in patients with rheumatoid arthritis (RA). However, the extent of the repertoire perturbations as well as the underlying mechanisms are not known. We now have examined the diversity of the peripheral CD4 T cell repertoire by determining the frequencies of arbitrarily selected T cell receptor (TCR) β-chain sequences. Healthy individuals displayed a highly diverse repertoire, with a median frequency of individual TCR β-chain sequences of 1 in 2.4 × 107 CD4 T cells. In RA patients, the median TCR β-chain frequency was increased 10-fold, indicating marked contraction of the repertoire (P < 0.001). The loss in TCR diversity was not limited to CD4 memory T cells but also involved the compartment of naive T cells, suggesting that it reflected an abnormality in T cell repertoire formation and not a consequence of antigen recognition in the synovium. Also, control patients with chronic inflammatory disease such as hepatitis C expressed a diverse repertoire indistinguishable from that of normals. Telomere length studies indicated an increased replicative history of peripheral CD4 T cells in RA patients, suggesting an enhanced turnover within the CD4 compartment. Compared with age-matched controls, terminal restriction fragment sizes were 1.7 kilobases shorter (P < 0.001). These data demonstrate an altered CD4 T cell homeostasis in RA that may contribute to the autoimmune response as well as to the immunodeficiency in these patients.

Detection of hepatitis B virus DNA by the polymerase chain reaction in anti-HBE positive chronic hepatitis B patients

Detection of HBV-DNA by PCR was compared with other serological markers (HBsAg, HBeAg and anti-HBe) in a series of49 Chronic Hepatitis B patients, including 12 with a spontaneous clearance of HBsAg. None of these HBsAg negative cases were PCR positive, but 33/37 (89.2%) HBsAg positive cases were PCR positive (p < 0.0001). Among HBsAg positive samples, nine cases were HBeAg positive and anti-HBe negative, all of them PCR positive. Other 3 patients were HBeAg and anti-HBe positive and these cases were also found PCR positive. A third group included 21 patients anti-HBe positive and HBeAg negative: 19 of them were PCR positive and 2 were PCR negative. The last 4 cases were HBeAg and anti-HBe negative, two of them were PCR positive. The detection of anti-HBe viremic cases in the present series suggest that preC variants could occur in our country. In conclusion, the integrated phase o f chronic hepatitis B seems to be less frequent than it was assumed, when only HBeAg or dot blot hybridization techniques were used. The new term "low replication phase" might favorably replace the former "integrated phase".

Diagnosis of hepatitis C virus in Brazilian blood donors using a reverse transcriptase nested polymerase chain reaction: comparison with enzyme immunoassay and recombinant protein immunoblot assay

Screening blood donations for anti-HCV antibodies and alanine aminotransferase (ALT) serum levels generally prevents the transmission of hepatitis C virus (HCV) by transfusion. The aim of the present study was to evaluate the efficiency of the enzyme immunoassay (EIA) screening policy in identifying potentially infectious blood donors capable to transmit hepatitis C through blood transfusion. We have used a reverse transcriptase (RT)-nested polymerase chain reaction (PCR) to investigate the presence of HCV-RNA in blood donors. The prevalence of HCV-RNA positive individuals was compared with the recombinant immunoblot assay (RIBA-2) results in order to assess the usefulness of both tests as confirmatory assays. Both tests results were also compared with the EIA-2 OD/C ratio (optical densities of the samples divided by the cut off value). ALT results were expressed as the ALT quotient (qALT), calculated dividing the ALT value of the samples by the maximum normal value (53UI/l) for the method. Donors (n=178) were divided into five groups according to their EIA anti-HCV status and qALT: group A (EIA > or = 3, ALT<1), group B (EIA > or = 3, ALT>1), group C (1<=EIA<3, ALT<1), group D (1<=EIA<3, ALT>1) and group E (EIA<=0.7). HCV sequences were detected by RT-nested PCR, using primers for the most conserved region of viral genome. RIBA-2 was applied to the same samples. In group A (n=6), all samples were positive by RT-nested PCR and RIBA-2. Among 124 samples in group B, 120 (96.8%) were RIBA-2 positive and 4 (3.2%) were RIBA-2 indeterminate but were seropositive for antigen c22.3. In group B, 109 (87.9%) of the RIBA-2 positive samples were also RT-nested PCR positive, as well as were all RIBA-2 indeterminate samples. In group C, all samples (n=9) were RT-nested PCR negative: 4 (44.4%) were also RIBA-2 negative, 4 (44.4%) were RIBA-2 positive and 1 (11.1%) was RIBA-2 indeterminate. HCV-RNA was detected by RT-nested PCR in 3 (37.5%) out of 8 samples in group D. Only one of them was also RIBA-2 positive, all the others were RIBA-2 indeterminate. All of the group E samples (controls) were RT- nested PCR and RIBA-2 negative. Our study suggests a strong relation between anti-HCV EIA-2 ratio > or = 3 and detectable HCV-RNA by RT-nested PCR. We have also noted that blood donors with RIBA-2 indeterminate presented a high degree of detectable HCV-RNA using RT-nested PCR (75%), especially when the c22.3 band was detected.