A New Perspective on a Polynomial Time Knot Polynomial

In this work we consider the Z1(K) polynomial time knot polynomial defined anddescribed by Dror Bar-Natan and Roland van der Veen in their 2018 paper ”A polynomial time knot polynomial”. We first look at some of the basic properties of Z1(K), and develop an invariant of diagrams Ψm(D) related to this polynomial. We use this invariant as a model to prove how Z1(K) acts under the connected sum operation. We then discuss the effect of mirroring the knot on Z1(K), and described a geometric interpretation of some of the building blocks of the invariant. We then use these to develop state sum interpretation of Z1(K). We describe a base set of knots which can be used to build the Z1(K), or rather its normalization ρ1(K), showcasing some of its symmetry properties. Finally, we use this idea to give an explicit expansion of ρ1(K) for the family of T (2, 2p + 1) torus knots in terms of this base set of knot invariants

Mapping and Monitoring of Submerged Aquatic Vegetation in Escambia-Pensacola Bay System, Florida

Recently, the distribution and changes in submerged aquatic vegetation (SAY) in the Escambia-Pensacola Bay System in northeastern Florida were monitored by two techniques. One technique used divers to measure changes in the deepwater margin of beds and provided horizontal growth measurements to the nearest centimeter, the other used a differential global positioning system (DGPS) on a small boat to map the perimeter of SAY beds in shallow water. Current distribution of SAY in Escambia Bay shows that most of the SAY losses that occurred during the 1950s to 1970s have been recovered. In Santa Rosa Sound and Pensacola Bay, SAY showed significant increased growth with horizontal growth rates of some beds averaging more than 50 em over the past year. In Big Lagoon, however, SAY has declined an average of 10 em in horizontal coverage along the deepwater edge. Water quality and photosynthetically active radiation light measurements from the Escambia-Pensacola Bay System suggest that increased light availability was associated with the increased seagrass coverage in Santa Rosa Sound and Pensacola Bay, and elevated nutrient concentrations were associated with the seagrass declines in Big Lagoon

Validity of Photo-oxidative stress markers and stress-related phytohormones as predictive proxies of mortality risk in the perennial herb Plantago lanceolata

Oxidative stress and hormonal regulation are hallmarks of a/biotic stress responses in plants. However, little is known about their linkage with whole-organismal mortality in long-lived species. Here, we examined the validity of photo-oxidative stress markers and stress-related phytohormones as predictive proxies of mortality risk in the perennial herb Plantago lanceolata. Capitalizing on its broad ecological niche, we examined photo-oxidative stress markers (Fv/Fm ratio, contents of chlorophylls, carotenoids, and tocochromanols, and the extent of lipid peroxidation) and stress-related phytohormones (ABA, salicylic acid and jasmonates contents) as proxies of mortality in three populations of sub-tropical and Mediterranean habitats: Virginia (VA, U.S.A.), Catalonia (CAT, Spain), and Queensland (QLD, Australia). Stress markers were measured together with the vital rates of survival, growth, and reproduction on a total of 279 individuals. Stress marker data were collected during the summer and death/survival was monitored after two and four months. Whole-organism mortality was similarly high in both sub-tropical non-native populations (ca. 30 % after a drought in VA and QLD), but lower in the native population (ca. 10 % in CAT). The contents of antioxidants (lutein, zeaxanthin, β-carotene) and the de-epoxidation state of the xanthophyll cycle (DPS) were good proxies of mortality risk in VA and QLD. DPS and all carotenoid contents per unit of chlorophyll were lower four months in advance in dead than in alive plants in VA and QLD, thus suggesting reduced photoprotective capacity increased the mortality risk in non-native populations. We show that whole-organismal mortality in P. lanceolata is associated with a reduced capacity to enhance photoprotection under abiotic stress conditions. The validity of various stress markers as predictive proxies of mortality risk is discussed

Identification of single-dose, dual-echo based CBV threshold for fractional tumor burden mapping in recurrent glioblastoma

BackgroundRelative cerebral blood volume (rCBV) obtained from dynamic susceptibility contrast (DSC) MRI is widely used to distinguish high grade glioma recurrence from post treatment radiation effects (PTRE). Application of rCBV thresholds yield maps to distinguish between regional tumor burden and PTRE, a biomarker termed the fractional tumor burden (FTB). FTB is generally measured using conventional double-dose, single-echo DSC-MRI protocols; recently, a single-dose, dual-echo DSC-MRI protocol was clinically validated by direct comparison to the conventional double-dose, single-echo protocol. As the single-dose, dual-echo acquisition enables reduction in the contrast agent dose and provides greater pulse sequence parameter flexibility, there is a compelling need to establish dual-echo DSC-MRI based FTB mapping. In this study, we determine the optimum standardized rCBV threshold for the single-dose, dual-echo protocol to generate FTB maps that best match those derived from the reference standard, double-dose, single-echo protocol.MethodsThe study consisted of 23 high grade glioma patients undergoing perfusion scans to confirm suspected tumor recurrence. We sequentially acquired single dose, dual-echo and double dose, single-echo DSC-MRI data. For both protocols, we generated leakage-corrected standardized rCBV maps. Standardized rCBV (sRCBV) thresholds of 1.0 and 1.75 were used to compute single-echo FTB maps as the reference for delineating PTRE (sRCBV < 1.0), tumor with moderate angiogenesis (1.0 < sRCBV < 1.75), and tumor with high angiogenesis (sRCBV > 1.75) regions. To assess the sRCBV agreement between acquisition protocols, the concordance correlation coefficient (CCC) was computed between the mean tumor sRCBV values across the patients. A receiver operating characteristics (ROC) analysis was performed to determine the optimum dual-echo sRCBV threshold. The sensitivity, specificity, and accuracy were compared between the obtained optimized threshold (1.64) and the standard reference threshold (1.75) for the dual-echo sRCBV threshold.ResultsThe mean tumor sRCBV values across the patients showed a strong correlation (CCC = 0.96) between the two protocols. The ROC analysis showed maximum accuracy at thresholds of 1.0 (delineate PTRE from tumor) and 1.64 (differentiate aggressive tumors). The reference threshold (1.75) and the obtained optimized threshold (1.64) yielded similar accuracy, with slight differences in sensitivity and specificity which were not statistically significant (1.75 threshold: Sensitivity = 81.94%; Specificity: 87.23%; Accuracy: 84.58% and 1.64 threshold: Sensitivity = 84.48%; Specificity: 84.97%; Accuracy: 84.73%).ConclusionsThe optimal sRCBV threshold for single-dose, dual-echo protocol was found to be 1.0 and 1.64 for distinguishing tumor recurrence from PTRE; however, minimal differences were observed when using the standard threshold (1.75) as the upper threshold, suggesting that the standard threshold could be used for both protocols. While the prior study validated the agreement of the mean sRCBV values between the protocols, this study confirmed that their voxel-wise agreement is suitable for reliable FTB mapping. Dual-echo DSC-MRI acquisitions enable robust single-dose sRCBV and FTB mapping, provide pulse sequence parameter flexibility and should improve reproducibility by mitigating variations in preload dose and incubation time

Planetary Candidates Observed by Kepler VI: Planet Sample from Q1-Q16 (47 Months)

\We present the sixth catalog of Kepler candidate planets based on nearly 4 years of high precision photometry. This catalog builds on the legacy of previous catalogs released by the Kepler project and includes 1493 new Kepler Objects of Interest (KOIs) of which 554 are planet candidates, and 131 of these candidates have best fit radii <1.5 R_earth. This brings the total number of KOIs and planet candidates to 7305 and 4173 respectively. We suspect that many of these new candidates at the low signal-to-noise limit may be false alarms created by instrumental noise, and discuss our efforts to identify such objects. We re-evaluate all previously published KOIs with orbital periods of >50 days to provide a consistently vetted sample that can be used to improve planet occurrence rate calculations. We discuss the performance of our planet detection algorithms, and the consistency of our vetting products. The full catalog is publicly available at the NASA Exoplanet Archive.Comment: 18 pages, to be published in the Astrophysical Journal Supplement Serie