632,309 research outputs found

### $K_{1,3}$-covering red and blue points in the plane

We say that a finite set of red and blue points in the plane in general position can be $K_{1,3}$-covered if the set can be partitioned into subsets of size $4$, with $3$ points of one color and $1$ point of the other color, in such a way that, if at each subset the fourth point is connected by straight-line segments to the same-colored points, then the resulting set of all segments has no crossings. We consider the following problem: Given a set $R$ of $r$ red points and a set $B$ of $b$ blue points in the plane in general position, how many points of $R\cup B$ can be $K_{1,3}$-covered? and we prove the following results: (1) If $r=3g+h$ and $b=3h+g$, for some non-negative integers $g$ and $h$, then there are point sets $R\cup B$, like $\{1,3\}$-equitable sets (i.e., $r=3b$ or $b=3r$) and linearly separable sets, that can be $K_{1,3}$-covered. (2) If $r=3g+h$, $b=3h+g$ and the points in $R\cup B$ are in convex position, then at least $r+b-4$ points can be $K_{1,3}$-covered, and this bound is tight. (3) There are arbitrarily large point sets $R\cup B$ in general position, with $r=b+1$, such that at most $r+b-5$ points can be $K_{1,3}$-covered. (4) If $b\le r\le 3b$, then at least $\frac{8}{9}(r+b-8)$ points of $R\cup B$ can be $K_{1,3}$-covered. For $r>3b$, there are too many red points and at least $r-3b$ of them will remain uncovered in any $K_{1,3}$-covering. Furthermore, in all the cases we provide efficient algorithms to compute the corresponding coverings.Comment: 29 pages, 10 figures, 1 tabl

### Cancer rate of the indeterminate lesions at low or high risk according to italian system for reporting of thyroid FNA

Background: Italian consensus for the classification and reporting of thyroid cytology (ICCRTC) has been used in almost all Italian institutions since 2014. High reliability of ICCRTC in classifying low and high risk indeterminate nodules (Tir 3A and Tir 3B, respectively) was demonstrated. Here we reviewed our casuistry of thyroid indeterminate lesions to analyze the histologic outcome. Methods: All lesions undergone FNA and final histology at S. Andrea Hospital of Rome after a cytologic assessment of Tir 3A and Tir 3B, according to ICCRTC, were included in the study. Results: A number of 157 indeterminate FNA was found after the introduction of ICCRTC. Of these, 75 undergone surgery and were finally included for the study. At histology we found a 33.3% of cancers and a 67.7% of benign lesions. Out of the overall series, 25 were classified as Tir 3A and 50 as Tir 3B. Cancer rate observed in Tir 3A (1/25, 4%) was significantly (p = 0.0002) lower than that of Tir 3B (24/50, 48%). No significant difference was found in age and size between the two subcategories. Conclusions: We confirm in our series that Italian consensus for the classification and reporting of thyroid cytology allows to discriminate indeterminate lesions at low and high risk of malignancy

### Cardiorespiratory requirements of the 6-min walk test in patients with left ventricular systolic disfunction and no major structural heart disease

The six-minute walk test (6-MWT) is widely used to assess functional status in patients with chronic heart failure (CHF). The aims of the present study were: (1) to compare metabolic gas exchange during the 6-MWT in older patients with left ventricular systolic dysfunction (LVSD) and in breathless patients with no major structural heart disease (MSHD); (2) to determine the exercise intensity of the 6-MWT relative to peak oxygen uptake; (3) to establish the accuracy and reproducibility of the Metamax 3B ergospirometer during an incremental workload. Twenty four older patients with LVSD (19 male; age 76 Â± 5 years; BMI 27 Â± 4), and 18 patients with no MSHD (12 male; age 75 Â± 8 years; BMI 27 Â± 4) attended on consecutive days at the same time. Patients completed a 6-MWT with metabolic gas exchange measurements using the Metamax 3B portable ergospirometer, and an incremental cycle ergometry test using both the Metamax 3B and Oxycon Pro metabolic cart. Patients returned and performed a second 6-MWT and an incremental treadmill test, metabolic gas exchange was measured with the Metamax 3B. In patients with LVSD, the 6-MWT was performed at a higher fraction of maximal exercise capacity (p = 0.02). The 6-MWT was performed below the anaerobic threshold in patients with LVSD (83 %) and in patients with no MSHD (61 %). The Metamax 3B showed satisfactory to high accuracy at 10 W and 20 W in patients with LVSD (r = 0.77 - 0.97, p < 0.05), and no MSHD (r = 0.76 - 0.94, p < 0.05). Metabolic gas exchange variables measured during the 6-MWT showed satisfactory to high day-to-day reproducibility in patients with LVSD (ICC = 0.75 - 0.98), but a higher variability was evident in participants with no MSHD (ICC = 0.62 - 0.97). The Metamax 3B portable ergospirometer is an accurate and reproducible device during submaximal, fixed rate exercise in older patients with LVSD and no MSHD. In elderly patients with LVSD and no MSHD, the 6-MWT should not be considered a maximal test of exercise capacity but rather a test of submaximal exercise performance. Our study demonstrates that the 6-MWT takes place at a higher proportion of peak oxygen uptake in patients with LVSD compared to those with no MSHD, and may be one reason why fatigue is a more prominent symptom in these patients

### The Transit Light Curve project. XIV. Confirmation of Anomalous Radii for the Exoplanets TrES-4b, HAT-P-3b, and WASP-12b

We present transit photometry of three exoplanets, TrES-4b, HAT-P-3b, and WASP-12b, allowing for refined estimates of the systems' parameters. TrES-4b and WASP-12b were confirmed to be "bloated" planets, with radii of 1.706 +/- 0.056 R_Jup and 1.736 +/- 0.092 R_Jup, respectively. These planets are too large to be explained with standard models of gas giant planets. In contrast, HAT-P-3b has a radius of 0.827 +/- 0.055 R_Jup, smaller than a pure hydrogen-helium planet and indicative of a highly metal-enriched composition. Analyses of the transit timings revealed no significant departures from strict periodicity. For TrES-4, our relatively recent observations allow for improvement in the orbital ephemerides, which is useful for planning future observations.Comment: AJ, in press [11 pages]; corrected error in distance to WASP-1

### Ent-kaurene and ent-beyerene diterpenoids and other constituents of Thecacoris batesii

Two novel diterpenoids, thecacorins A (1) and B (2), were isolated from Thecacoris batesii and their structures were established as ent-3b,20-epoxy-16-kaurene-3a,12b-diol and ent-15-beyerene-2b,3b-diol, respectively, on the basis of extensive spectroscopic analysis, especially, 1D NMR spectra, in conjunction with 2D experiments, COSY, NOESY, HMQC and HMBC.Â KEY WORDS: Diterpenoids, Thecacorin A, Thecacorin B, Ent-3b,20-epoxy-16-kaurene-3a,12b-diol,Â Ent-15-beyerene-2b,3b-diol, Thecacoris batesiiÂ Â Bull. Chem. Soc. Ethiop. 2007, 21(1), 89-94

### Bioactive steroidal saponins from Agave offoyana flowers

Bioguided studies of flowers of Agave offoyana allowed the isolation of five steroidal saponins never described previously, Magueyosides AâE (1â5), along with six known steroidal saponins (6â11). The structures of compounds were determined as (25R)-spirost-5-en-2a,3b-diol-12-one 3-O-{b-D-xylopyranosyl-(1-3)-O-b-D-glucopyranosyl-(1-2)-O-[b-D-xylopyranosyl-(1-3)]-O-b-D-glucopyranosyl-( 1-4)-O-b-D-galactopyranoside} (1), (25R)-spirost-5-en-2a,3b-diol-12-one 3-O-{b-D-glucopyranosyl-(1-2)-O-[b-D-xylopyranosyl-(1-3)]-O-b-D-glucopyranosyl-(1-4)-O-b-D galactopyranoside} (2), (25R)-spirost-5-en-2a,3b,12b-triol 3-O-{b-D-glucopyranosyl-(1-2)-O-[b-D-xylopyranosyl-(1-3)]- O-b-D-glucopyranosyl-(1-4)-O-b-D-galactopyranoside} (3), (25R)-5a-spirostan-2a,3b-diol-12-one 3-O-{b-D-xylopyranosyl-(1-3)-O-b-D-glucopyranosyl-(1-2)-O-[b-D-xylopyranosyl-(1-3)]-O-b-D-glucopyranosyl-(1-4)-O-b-D-galactopyranoside} (4), and (25R)-5a-spirostan-2a,3b-diol-9(11)-en-12-one 3-O-{b-D-xylopyranosyl-(1-3)-O-b-D-glucopyranosyl-(1-2)-O-[b-D-xylopyranosyl-(1-3)]-O-b-D-glucopyranosyl-( 1-4)-O-b-D-galactopyranoside} (5), by comprehensive spectroscopic analysis, including one- and two-dimensional NMR techniques, mass spectrometry and chemical methods. The bioactivities of the isolated compounds on the standard target species Lactuca sativa were evaluated. A dosedependent phytotoxicity and low dose stimulation were observed
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