Heights and the Specialization Map for Families of Elliptic Curves over P^n

For $n\geq 2$, let $K=\overline{\mathbb{Q}}(\mathbb{P}^n)=\overline{\mathbb{Q}}(T_1, \ldots, T_n)$. Let $E/K$ be the elliptic curve defined by a minimal Weiestrass equation $y^2=x^3+Ax+B$, with $A,B \in \overline{\mathbb{Q}}[T_1, \ldots, T_n]$. There's a canonical height $\hat{h}_{E}$ on $E(K)$ induced by the divisor $(O)$, where $O$ is the zero element of $E(K)$. On the other hand, for each smooth hypersurface $\Gamma$ in $\mathbb{P}^n$ such that the reduction mod $\Gamma$ of $E$, $E_{\Gamma} / \overline{\mathbb{Q}}(\Gamma)$ is an elliptic curve with the zero element $O_\Gamma$, there is also a canonical height $\hat{h}_{E_{\Gamma}}$ on $E_{\Gamma}(\overline{\mathbb{Q}}(\Gamma))$ that is induced by $(O_\Gamma)$. We prove that for any $P \in E(K)$, the equality $\hat{h}_{E_{\Gamma}}(P_\Gamma)/ \deg \Gamma =\hat{h}_{E}(P)$ holds for almost all hypersurfaces in $\mathbb{P}^n$. As a consequence, we show that for infinitely many $t \in \mathbb{P}^n(\overline{\mathbb{Q}})$, the specialization map $\sigma_t : E(K) \rightarrow E_t(\overline{\mathbb{Q}})$ is injective.Comment: updated versio

Vinogradov's theorem and its generalization on primes in arithmetic progression

Master'sMASTER OF SCIENC

Measuring activities of daily living in stroke patients with motion machine learning algorithms: A pilot study

Measuring activities of daily living (ADLs) using wearable technologies may offer higher precision and granularity than the current clinical assessments for patients after stroke. This study aimed to develop and determine the accuracy of detecting different ADLs using machine-learning (ML) algorithms and wearable sensors. Eleven post-stroke patients participated in this pilot study at an ADL Simulation Lab across two study visits. We collected blocks of repeated activity ( atomic activity) performance data to train our ML algorithms during one visit. We evaluated our ML algorithms using independent semi-naturalistic activity data collected at a separate session. We tested Decision Tree, Random Forest, Support Vector Machine (SVM), and eXtreme Gradient Boosting (XGBoost) for model development. XGBoost was the best classification model. We achieved 82% accuracy based on ten ADL tasks. With a model including seven tasks, accuracy improved to 90%. ADL tasks included chopping food, vacuuming, sweeping, spreading jam or butter, folding laundry, eating, brushing teeth, taking off/putting on a shirt, wiping a cupboard, and buttoning a shirt. Results provide preliminary evidence that ADL functioning can be predicted with adequate accuracy using wearable sensors and ML. The use of external validation (independent training and testing data sets) and semi-naturalistic testing data is a major strength of the study and a step closer to the long-term goal of ADL monitoring in real-world settings. Further investigation is needed to improve the ADL prediction accuracy, increase the number of tasks monitored, and test the model outside of a laboratory setting

Volumetric intensity-modulated Arc (RapidArc) therapy for primary hepatocellular carcinoma: comparison with intensity-modulated radiotherapy and 3-D conformal radiotherapy

<p>Abstract</p> <p>Background</p> <p>To compare the RapidArc plan for primary hepatocellular carcinoma (HCC) with 3-D conformal radiotherapy (3DCRT) and intensity-modulated radiotherapy (IMRT) plans using dosimetric analysis.</p> <p>Methods</p> <p>Nine patients with unresectable HCC were enrolled in this study. Dosimetric values for RapidArc, IMRT, and 3DCRT were calculated for total doses of 45~50.4 Gy using 1.8 Gy/day. The parameters included the conformal index (CI), homogeneity index (HI), and hot spot (V_107%) for the planned target volume (PTV) as well as the monitor units (MUs) for plan efficiency, the mean dose (D_mean) for the organs at risk (OAR) and the maximal dose at 1% volume (D_1%) for the spinal cord. The percentage of the normal liver volume receiving ≥ 40, > 30, > 20, and > 10 Gy (V_{40 Gy}, V_{30 Gy}, V_{20 Gy}, and V_{10 Gy}) and the normal tissue complication probability (NTCP) were also evaluated to determine liver toxicity.</p> <p>Results</p> <p>All three methods achieved comparable homogeneity for the PTV. RapidArc achieved significantly better CI and V_107%values than IMRT or 3DCRT (<it>p </it>< 0.05). The MUs were significantly lower for RapidArc (323.8 ± 60.7) and 3DCRT (322.3 ± 28.6) than for IMRT (1165.4 ± 170.7) (<it>p </it>< 0.001). IMRT achieved a significantly lower D_meanof the normal liver than did 3DCRT or RapidArc (<it>p </it>= 0.001). 3DCRT had higher V_{40 Gy}and V_{30 Gy}values for the normal liver than did RapidArc or IMRT. Although the V_{10 Gy}to the normal liver was higher with RapidArc (75.8 ± 13.1%) than with 3DCRT or IMRT (60.5 ± 10.2% and 57.2 ± 10.0%, respectively; <it>p </it>< 0.01), the NTCP did not differ significantly between RapidArc (4.38 ± 2.69) and IMRT (3.98 ± 3.00) and both were better than 3DCRT (7.57 ± 4.36) (<it>p </it>= 0.02).</p> <p>Conclusions</p> <p>RapidArc provided favorable tumor coverage compared with IMRT or 3DCRT, but RapidArc is not superior to IMRT in terms of liver protection. Further studies are needed to establish treatment outcome differences between the three approaches.</p

Association of ORAI1 Haplotypes with the Risk of HLA-B27 Positive Ankylosing Spondylitis

Ankylosing spondylitis (AS) is a chronic inflammation of the sacroiliac joints, spine and peripheral joints. The aetiology of ankylosing spondylitis is still unclear. Previous studies have indicated that genetics factors such as human leukocyte antigen HLA-B27 associates to AS susceptibility. We carried out a case-control study to determine whether the genetic polymorphisms of ORAI1 gene, a major component of store-operated calcium channels that involved the regulation of immune system, is a susceptibility factor to AS in a Taiwanese population. We enrolled 361 AS patients fulfilled the modified New York criteria and 379 controls from community. Five tagging single nucleotides polymorphisms (tSNPs) at ORAI1 were selected from the data of Han Chinese population in HapMap project. Clinical statuses of AS were assessed by the Bath Ankylosing Spondylitis Disease Activity Index (BASDAI), Bath Ankylosing Spondylitis Functional Index (BASFI), and Bath Ankylosing Spondylitis Global Index (BAS-G). Our results indicated that subjects carrying the minor allele homozygote (CC) of the promoter SNP rs12313273 or TT homozygote of the SNP rs7135617 had an increased risk of HLA-B27 positive AS. The minor allele C of 3′UTR SNP rs712853 exerted a protective effect to HLA-B27 positive AS. Furthermore, the rs12313273/rs7135617 pairwise allele analysis found that C-G (OR 1.69, 95% CI 1.27, 2.25; p = 0.0003) and T-T (OR 1.75, 95% CI 1.36, 2.27; p<0.0001) haplotypes had a significantly association with the risk of HLA-B27-positive AS in comparison with the T-G carriers. This is the first study that indicate haplotypes of ORAI1 (rs12313273 and rs7135617) are associated with the risk of HLA-B27 positive AS

Blue Carbon Science, Management and Policy Across a Tropical Urban Landscape

The ability of vegetated coastal ecosystems to sequester high rates of “blue” carbon over millennial time scales has attracted the interest of national and international policy makers as a tool for climate change mitigation. Whereas focus on blue carbon conservation has been mostly on threatened rural seascapes, there is scope to consider blue carbon dynamics along highly fragmented and developed urban coastlines. The tropical city state of Singapore is used as a case study of urban blue carbon knowledge generation, how blue carbon changes over time with urban development, and how such knowledge can be integrated into urban planning alongside municipal and national climate change obligations. A systematic review of blue carbon studies in Singapore was used to support a qualitative review of Singapore’s blue carbon ecosystems, carbon budget, changes through time and urban planning and policy. Habitat loss across all blue carbon ecosystems is coarsely estimated to have resulted in the release of ∼12.6 million tonnes of carbon dioxide since the beginning of the 20th century. However, Singapore’s remaining blue carbon ecosystems still store an estimated 568,971 – 577,227 tonnes of carbon (equivalent to 2.1 million tonnes of carbon dioxide) nationally, with a small proportion of initial loss offset by habitat restoration. Carbon is now a key topic on the urban development and planning agenda, as well as nationally through Singapore’s contributions to the Paris Agreement. The experiences of Singapore show that coastal ecosystems and their blue carbon stocks can be successfully managed along an urban coastline, and can help inform blue carbon science and management along other rapidly urbanizing coastlines throughout the tropics

Anti-Proliferation and Anti-Invasion Effects of Diosgenin on Gastric Cancer BGC-823 Cells with HIF-1α shRNAs

Drug resistance is a major factor for the limited efficacy of chemotherapy in gastric cancer treatment. Hypoxia-inducible factor-1α (HIF-1α), a central transcriptional factor in hypoxia, is suggested to participate in the resistance. Here, we identified a hypoxia-mimic (cobalt chloride) sensitive gastric cell line BGC-823 to explore whether diosgenin, an aglycone of steroidal saponins, can inhibit cancer cell invasion and survival of solid tumor in a hypoxic mimic microenvironment. We have shown that diosgenin is a potent candidate for decreasing the ability of invasion and survival in cobalt chloride treated BGC-823 cells. In addition, when combined with HIF-1α specific short hairpin RNA (shRNA), diosgenin can inhibit BGC-823 cells more effectively. The anti-invasion role of diosgenin may be related to E-cadherin, integrinα5 and integrin β6. These results suggest that diosgenin may be a useful compound in controlling gastric cancer cells in hypoxia condition, especially when combined with down-regulated HIF-1α

Epigenetic response to environmental stress: Assembly of BRG1–G9a/GLP–DNMT3 repressive chromatin complex on Myh6 promoter in pathologically stressed hearts

Chromatin structure is determined by nucleosome positioning, histone modifications, and DNA methylation. How chromatin modifications are coordinately altered under pathological conditions remains elusive. Here we describe a stress-activated mechanism of concerted chromatin modification in the heart. In mice, pathological stress activates cardiomyocytes to express Brg1 (nucleosome-remodeling factor), G9a/Glp (histone methyltransferase), and Dnmt3 (DNA methyltransferase). Once activated, Brg1 recruits G9a and then Dnmt3 to sequentially assemble repressive chromatin—marked by H3K9 and CpG methylation—on a key molecular motor gene (Myh6), thereby silencing Myh6 and impairing cardiac contraction. Disruption of Brg1, G9a or Dnmt3 erases repressive chromatin marks and de-represses Myh6, reducing stress-induced cardiac dysfunction. In human hypertrophic hearts, BRG1–G9a/GLP–DNMT3 complex is also activated; its level correlates with H3K9/CpG methylation, Myh6 repression, and cardiomyopathy. Our studies demonstrate a new mechanism of chromatin assembly in stressed hearts and novel therapeutic targets for restoring Myh6 and ventricular function. The stress-induced Brg1–G9a–Dnmt3 interactions and sequence of repressive chromatin assembly on Myh6 illustrates a molecular mechanism by which the heart epigenetically responds to environmental signals. This article is part of a Special Issue entitled: Cardiomyocyte Biology: Integration of Developmental and Environmental Cues in the Heart edited by Marcus Schaub and Hughes Abriel