Fermat's treatise on quadrature: A new reading

The Treatise on Quadrature of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, R x+m/n dx, or under a higher hyperbola, R x-m/n dx with the appropriate limits of integration in each case , has a second part which was not understood by Fermat s contemporaries. This second part of the Treatise is obscure and difficult to read and even the great Huygens described it as'published with many mistakes and it is so obscure (with proofs redolent of error) that I have been unable to make any sense of it'. Far from the confusion that Huygens attributes to it, in this paper we try to prove that Fermat, in writing the Treatise, had a very clear goal in mind and he managed to attain it by means of a simple and original method. Fermat reduced the quadrature of a great number of algebraic curves to the quadrature of known curves: the higher parabolas and hyperbolas of the first part of the paper. Others, he reduced to the quadrature of the circle. We shall see how the clever use of two procedures, quite novel at the time: the change of variables and a particular case of the formulaof integration by parts, provide Fermat with the necessary tools to square very easily curves as well-known as the folium of Descartes, the cissoid of Diocles or the witch of Agnesi.

Cytochrome b haplotype divergences in West European Apodemus

Sequencing of the cytochrome b mitochondrial gene (732 base pairs) in samples of Apodemus sylvaticus from Central Europe (eastern France, Switzerland, southern Germany and western Austria) revealed significant molecular variation not reflected in previous morphological and genetic studies of this species. A comparison with the sequences (150 bp) of 54 specimens available from GenBank (NCBI) showed that two problematic individuals originating from southern Germany have to be assigned to A. fulvipectus, a species not yet known in western Europe. A. sylvaticus specimens (n = 14) sampled north of the Alps exhibited a maximum intraspecific sequence divergence of about 5.1%, whereas the maximum divergence is much Lower in A. flavicollis (1%, n = 5) and in A. alpicola (0.5%, n = 4), although the samples originate from a similar geographic range of about 350 km. We also found a high rate of erroneously assigned specimens in GenBank, which indicates that the discrimination of Apodemus species remains a problem and requires further investigations.

Is the Gibraltar strait a barrier to gene flow for the bat Myotis myotis (Chiroptera: Vespertilionidae)?

Because of their role in limiting gene flow, geographical barriers like mountains or seas often coincide with intraspecific genetic discontinuities. Although the Strait of Gibraltar represents such a potential barrier for both plants and animals, few studies have been conducted on its impact on gene flow. Here we test this effect on a bat species (Myotis myotis) which is apparently distributed on both sides of the strait. Six colonies of 20 Myotis myotis each were sampled in southern Spain and northern Morocco along a linear transect of 1350 km. Results based on six nuclear microsatellite loci reveal no significant population structure within regions, but a complete isolation between bats sampled on each side of the strait. Variability at 600 bp of a mitochondrial gene (cytochrome b) confirms the existence of two genetically distinct and perfectly segregating clades, which diverged several million years ago. Despite the narrowness of the Gibraltar Strait (14 km), these molecular data suggest that neither males, nor females from either region have ever reproduced on the opposite side of the strait. Comparisons of molecular divergence with bats from a closely related species (M. blythii) suggest that the North African clade is possibly a distinct taxon warranting full species rank. We provisionally refer to it as Myotis cf punicus Felten 1977, but a definitive systematic understanding of the whole Mouse-eared bat species complex awaits further genetic sampling, especially in the Eastern Mediterranean areas.

A guide for easy- and difficult-to-treat hypertension.

Although the blood pressure (BP) of many patients can be controlled using standard combinations, treatment of hypertension frequently represents a clinical challenge to the primary care physician. This article will review best practices for managing patients with easy- and difficult-to-treat hypertension, including preferred antihypertensive combinations, optimizing adherence and persistence, recognizing white-coat hypertension, and intensifying therapy for treatment-resistant patients. Each physician must decide based on his or her own level of experience at what point a patient becomes too challenging and would benefit from referral to a hypertension specialist for more intensive management and to complete the exclusion of secondary forms of arterial hypertension. With intensive pharmacotherapy, many patients with difficult-to-treat hypertension can achieve BP control. If it fails, interventional strategies (e.g., renal denervation) are a valid option to get BP controlled.

Membrane mu poly(A) signal and 3' flanking sequences function as a transcription terminator for immunoglobulin-encoding genes.

Developmentally regulated mechanisms involving alternative RNA splicing and/or polyadenylation, as well as transcription termination, are implicated in controlling the levels of secreted mu (mu s), membrane mu (mu m) and delta immunoglobulin (Ig) heavy chain mRNAs during B cell differentiation (mu gene encodes the mu heavy chain). Using expression vectors constructed with genomic DNA segments composed of the mu m polyadenylation signal region, we analyzed poly(A) site utilization and termination of transcription in stably transfected myeloma cells and in murine fibroblast L cells. We found that the gene segment containing the mu m poly(A) signals, along with 536 bp of downstream flanking sequence, acted as a transcription terminator in both myeloma cells and L cell fibroblasts. Neither a 141-bp DNA fragment (which directed efficient polyadenylation at the mu m site), nor the 536-bp flanking nucleotide sequence alone, were sufficient to obtain a similar regulation. This shows that the mu m poly(A) region plays a central role in controlling developmentally regulated transcription termination by blocking downstream delta gene expression. Because this gene segment exhibited the same RNA processing and termination activities in fibroblasts, it appears that these processes are not tissue-specific.

Pliocene and Pleistocene diversification and multiple refugia in a Eurasian shrew (Crocidura suaveolens group).

We sequenced 998 base pairs (bp) of mitochondrial DNA cytochrome b and 799 bp of nuclear gene BRCA1 in the Lesser white-toothed shrew (Crocidura suaveolens group) over its geographic range from Portugal to Japan. The aims of the study were to identify the main clades within the group and respective refugia resulting from Pleistocene glaciations. Analyses revealed the Asian lesser white-toothed shrew (C. shantungensis) as the basal clade, followed by a major branch of C. suaveolens, subdivided sensu stricto into six clades, which split-up in the Upper Pliocene and Lower Pleistocene (1.9-0.9 Myr). The largest clade, occurring over a huge range from east Europe to Mongolia, shows evidence of population expansion after a bottleneck. West European clades originated from Iberian and Italo-Balkanic refugia. In the Near East, three clades evolved in an apparent hotspot of refugia (west Turkey, south-west and south-east of the Caucasus). Most clades include specimens of different morphotypes and the validity of many taxa in the C. suaveolens group has to be re-evaluated.

Reduced left hemisphere dominance for multiple versus single anagram solutions and its modulation by individuals' schizotypy

Problem solving (including insight, divergent thinking) seems to rely on the right hemisphere (RH). These functions are difficult to assess behaviorally. We propose anagram resolution as a suitable paradigm. University students (n=32) performed three tachistoscopic lateralized visual half-field experiments (stimulus presentation 150ms). In Experiment 1, participants recalled four-letter strings. Subsequently, participants provided solutions for four-letter anagrams (one solution in Experiment 2; two solutions in Experiment 3). Additionally, participants completed a schizotypy questionnaire (O-LIFE). Results showed a right visual field advantage in Experiment 1 and 2, but no visual field advantage in Experiment 3. In Experiment 1, increasing positive schizotypy associated with a RH performance shift. Problem solving seems to require increasingly the RH when facing several rather than one solution. This result supports previous studies on the RH's role in remote associative, metaphor and discourse processing. The more complex language requirements, the less personality traits seem to matter.

Establishing International Blood Pressure References Among Nonoverweight Children and Adolescents Aged 6 to 17 Years.

BACKGROUND: Several distributions of country-specific blood pressure (BP) percentiles by sex, age, and height for children and adolescents have been established worldwide. However, there are no globally unified BP references for defining elevated BP in children and adolescents, which limits international comparisons of the prevalence of pediatric elevated BP. We aimed to establish international BP references for children and adolescents by using 7 nationally representative data sets (China, India, Iran, Korea, Poland, Tunisia, and the United States). METHODS AND RESULTS: Data on BP for 52 636 nonoverweight children and adolescents aged 6 to 19 years were obtained from 7 large nationally representative cross-sectional surveys in China, India, Iran, Korea, Poland, Tunisia, and the United States. BP values were obtained with certified mercury sphygmomanometers in all 7 countries by using standard procedures for BP measurement. Smoothed BP percentiles (50th, 90th, 95th, and 99th) by age and height were estimated by using the Generalized Additive Model for Location Scale and Shape model. BP values were similar between males and females until the age of 13 years and were higher in males than females thereafter. In comparison with the BP levels of the 90th and 95th percentiles of the US Fourth Report at median height, systolic BP of the corresponding percentiles of these international references was lower, whereas diastolic BP was similar. CONCLUSIONS: These international BP references will be a useful tool for international comparison of the prevalence of elevated BP in children and adolescents and may help to identify hypertensive youths in diverse populations.

Abnormal nocturnal blood pressure fall in normotensive adolescents with insulin-dependent diabetes is ameliorated following glycemic improvement

Lack of the physiological nocturnal fall in blood pressure (BP) has been found in diabetics and it seems to be related to the presence of diabetic complications. The present study examined the changes in the nocturnal BP pattern of 8 normotensive insulin-dependent diabetic adolescents without nephropathy following improvement in glycemic control induced by an 8-day program of adequate diet and exercise. The same number of age- and sex-matched control subjects were studied. During the first and eighth nights of the program, BP was obtained by ambulatory BP monitoring. After a 10-min rest, 3 BP and heart rate (HR) recordings were taken and the mean values were considered to represent their awake values. The monitor was programmed to cuff insufflation every 20 min from 10:00 p.m. to 7:00 a.m. The glycemic control of diabetics improved since glycemia (212.0 ± 91.5 to 140.2 ± 69.1 mg/dl, P<0.03), urine glucose (12.7 ± 11.8 to 8.6 ± 6.4 g/24 h, P = 0.08) and insulin dose (31.1 ± 7.7 to 16.1 ± 9.7 U/day, P<0.01) were reduced on the last day. The mean BP of control subjects markedly decreased during the sleeping hours of night 1 (92.3 ± 6.4 to 78.1 ± 5.0 mmHg, P<0.001) and night 8 (87.3 ± 6.7 to 76.9 ± 3.6 mmHg, P<0.001). Diabetic patients showed a slight decrease in mean BP during the first night. However, the fall in BP during the nocturnal period increased significantly on the eighth night. The average awake-sleep BP variation was significantly higher at the end of the study (4.2 vs 10.3%, P<0.05) and this ratio turned out to be similar to that found in the control group (10.3 vs 16.3%). HR variation also increased on the eighth night in the diabetics. Following the metabolic improvement obtained at the end of the period, the nocturnal BP variation of diabetics was close to the normal pattern. We suggest that amelioration of glycemic control may influence the awake-sleep BP and HR differences. This effect may be due at least in part to an attenuated insulin stimulation of sympathetic activity

Mutations in SRY and WT1 genes required for gonadal development are not responsible for XY partial gonadal dysgenesis

The WT1 transcription factor regulates SRY expression during the initial steps of the sex determination process in humans, activating a gene cascade leading to testis differentiation. In addition to causing Wilms' tumor, mutations in WT1 are often responsible for urogenital defects in men, while SRY mutations are mainly related to 46,XY pure gonadal dysgenesis. In order to evaluate their role in abnormal testicular organogenesis, we screened for SRY and WT1 gene mutations in 10 children with XY partial gonadal dysgenesis, 2 of whom with a history of Wilms' tumor. The open reading frame and 360 bp of the 5' flanking sequence of the SRY gene, and the ten exons and intron boundaries of the WT1 gene were amplified by PCR of genomic DNA. Single-strand conformation polymorphism was initially used for WT1 mutation screening. Since shifts in fragment migration were only observed for intron/exon 4, the ten WT1 exons from all patients were sequenced manually. No mutations were detected in the SRY 5' untranslated region or within SRY open-reading frame sequences. WT1 sequencing revealed one missense mutation (D396N) in the ninth exon of a patient who also had Wilms' tumor. In addition, two silent point mutations were found in the first exon including one described here for the first time. Some non-coding sequence variations were detected, representing one new (IVS4+85A>G) and two already described (-7ATG T>G, IVS9-49 T>C) single nucleotide polymorphisms. Therefore, mutations in two major genes required for gonadal development, SRY and WT1, are not responsible for XY partial gonadal dysgenesis.

Essential regulatory elements for NHE3 gene transcription in renal proximal tubule cells

The objectives of the present study were to identify the cis-elements of the promoter absolutely required for the efficient rat NHE3 gene transcription and to locate positive and negative regulatory elements in the 5’-flanking sequence (5’FS), which might modulate the gene expression in proximal tubules, and to compare this result to those reported for intestinal cell lines. We analyzed the promoter activity of different 5’FS segments of the rat NHE3 gene, in the OKP renal proximal tubule cell line by measuring the activity of the reporter gene luciferase. Because the segment spanning the first 157 bp of 5’FS was the most active it was studied in more detail by sequential deletions, point mutations, and gel shift assays. The essential elements for gene transcription are in the region -85 to -33, where we can identify consensual binding sites for Sp1 and EGR-1, which are relevant to NHE3 gene basal transcription. Although a low level of transcription is still possible when the first 25 bp of the 5’FS are used as promoter, efficient transcription only occurs with 44 bp of 5’FS. There are negative regulatory elements in the segments spanning -1196 to -889 and -467 to -152, and positive enhancers between -889 and -479 bp of 5’FS. Transcription factors in the OKP cell nuclear extract efficiently bound to DNA elements of rat NHE3 promoter as demonstrated by gel shift assays, suggesting a high level of similarity between transcription factors of both species, including Sp1 and EGR-1.

Engineering an improved adenovirus packaging cell line

Recombinant human adenovirus (Ad) vectors are being extensively explored for their use in gene therapy and recombinant vaccines. Ad vectors are attractive for many reasons, including the fact that (1) they are relatively safe, based on their use as live oral vaccines, (2) they can accept large transgene inserts, (3) they can infect dividing and postmitotic cells, and (4) they can be produced to high titers. However, there are also a number of major problems associated with Ad vectors, including transient foreign gene expression due to host cellular immune responses, problems with humoral immunity, and the creation of replication competent adenoviruses (RCA). Most Ad vectors contain deletions in the E1 region that allow for insertion of a transgene. However, the E1 gene products are required for replication and thus must be supplied in trans by a helper ceillille that will allow for the growth and packaging of the defective virus. For this purpose the 293 cell line (Graham et al., 1977) is used most often; however, homologous recombination between the vector and the cell line often results in the generation of RCA. The presence of RCA in batches of adenoviral vectors for clinical use is a safety risk because tlley . may result in the mobilization and spread of the replication-defective vector viruses, and in significant tissue damage and pathogenicity. The present research focused on the alteration of the 293 cell line such that RCA formation can be eliminated. The strategy to modify the 293 cells involved the removal of the first 380 bp of the adenovirus genome through the process of homologous recombination. The first step towards this goal involved identifying and cloning the left-end cellular-viral jUl1ction from 293 cells to assemble sequences required for homologous recombination. Polymerase chain reaction (PCR) was performed to clone the junction, and the clone was verified through sequencing. The plasn1id PAM2 was then constructed, which served as the targeting cassette used to modify the 293 cells. The cassette consisted of (1) the cellular-viral junction as the left-end region of homology, (2) the neo gene to use for positive selection upon tranfection into 293 cells, (3) the adenoviral genome from bp 380 to bp 3438 as the right-end region of homology, and (4) the HSV-tk gene to use for negative selection. The plasmid PAM2 was linearized to produce a double strand break outside the region of homology, and transfected into 293 cells using the calcium-phosphate technique. Cells were first selected for their resistance to the drug G418, and subsequently for their resistance to the drug Gancyclovir (GANC). From 17 transfections, 100 pools of G418f and GANCf cells were picked using cloning lings and expanded for screening. Genomic DNA was isolated from the pools and screened for the presence of the 380 bps using PCR. Ten of the most promising pools were diluted to single cells and expanded in order to isolate homogeneous cell lines. From these, an additional 100 G41Sf and GANef foci were screened. These preliminary screening results appear promising for the detection of the desired cell line. Future work would include further cloning and purification of the promising cell lines that have potentially undergone homologous recombination, in order to isolate a homogeneous cell line of interest.

Eastham-Leinour Indenture, 1830

Fonds consists of one indenture, the sale of part of lot 94 in Niagara Township, to Thomas Eastham, by James Leinour. Thomas Eastham was a driver in the Her Majesty’s Royal Artillery and was General Brock’s trumpeter at the Battle of Queenston Heights. Eastham owned a hotel on the corner of Queen and Highland streets in Queenston. A watercolour of the hotel forms part of the J. Ross Robertson Art collection at the Metropolitan Toronto Reference Library. Eastham also served as pound keeper in the Village of Queenston. Thomas Eastham died in 1839 and an inscribed monument marks his grave in the cemetery of St. Mark’s Church, Niagara-on-the-Lake, Ont. No additional information is known about James Leinour.

Eastham-Leinour Indenture, 1830

An indenture dated 6 August 1830 between Thomas Eastham of the Village of Queenston and James Leinour of Niagara Township, a black man, for Pt. Lot No. 94, Township of Niagara.

Indenture between Robert Loring and John Conolly

Indenture of bargain and sale between Robert Loring of Toronto and John Connolly of St. Catharines for lot no. 8 in the 12th concession of Durham. The instrument no. is 24283, January 28, 1861.