Quadratic Fields Admitting Elliptic Curves with Rational jj-Invariant and Good Reduction Everywhere

Clemm and Trebat-Leder (2014) proved that the number of quadratic number fields with absolute discriminant bounded by $x$ over which there exist elliptic curves with good reduction everywhere and rational $j$-invariant is $\gg x\log^{-1/2}(x)$. In this paper, we assume the $abc$-conjecture to show the sharp asymptotic $\sim cx\log^{-1/2}(x)$ for this number, obtaining formulae for $c$ in both the real and imaginary cases. Our method has three ingredients: (1) We make progress towards a conjecture of Granville: Given a fixed elliptic curve $E/\mathbb{Q}$ with short Weierstrass equation $y^2 = f(x)$ for reducible $f \in \mathbb{Z}[x]$, we show that the number of integers $d$, $|d| \leq D$, for which the quadratic twist $dy^2 = f(x)$ has an integral non-$2$-torsion point is at most $D^{2/3+o(1)}$, assuming the $abc$-conjecture. (2) We apply the Selberg--Delange method to obtain a Tauberian theorem which allows us to count integers satisfying certain congruences while also being divisible only by certain primes. (3) We show that for a polynomially sparse subset of the natural numbers, the number of pairs of elements with least common multiple at most $x$ is $O(x^{1-\epsilon})$ for some $\epsilon > 0$. We also exhibit a matching lower bound. If instead of the $abc$-conjecture we assume a particular tail bound, we can prove all the aforementioned results and that the coefficient $c$ above is greater in the real quadratic case than in the imaginary quadratic case, in agreement with an experimentally observed bias.Comment: 35 pages, 1 figur

Characteristics of two different locking compression plates in the volar fixation of complex articular distal radius fractures

Objectives: To investigate the differences of open reduction and internal fixation (ORIF) of complex AO Type C distal radius fractures between two different models of a single implant type. Methods: A total of 136 patients who received either a 2.4 mm (n = 61) or 3.5 mm (n = 75) distal radius locking compression plate (LCP DR) using a volar approach were followed over two years. The main outcome measurements included motion, grip strength, pain, and the scores of Gartland and Werley, the Short-Form 36 (SF-36) and the Disabilities of the Arm, Shoulder, and Hand (DASH). Differences between the treatment groups were evaluated using regression analysis and the likelihood ratio test with significance based on the Bonferroni corrected p-value of 0.052) and grip strength measurements relative to the contralateral healthy side (p = 0.583). In addition, DASH and SF-36 component scores as well as pain were not significantly different between the treatment groups throughout the two-year period (all p ≥ 0.005). No patient from either treatment group had a step-off > 2 mm. Conclusions: Differences in plate design do not influence the overall final outcome of fracture fixation using LCP

Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

Immune Activation in Amyloid-β-Related Angiitis Correlates with Decreased Parenchymal Amyloid-β Plaque Load

Background: Primary angiitis of the central nervous system (PACNS) is a rare but serious condition. A fraction of patients suffering from PACNS concurrently exhibit pronounced cerebral amyloid angiopathy (CAA) which is characterized by deposits of amyloid-β (Aβ) in and around the walls of small and medium-sized arteries of the brain. PACNS with CAA has been identified as a distinct disease entity, termed Aβ-related angiitis (ABRA). Evidence points to an immune reaction to vessel wall Aβ as the trigger of vasculitis. Objective: To investigate whether the inflammatory response to Aβ has (1) any effect on the status of immune activation in the brain parenchyma and (2) leads to clearance of Aβ from brain parenchyma. Methods: We studied immune activation and Aβ load by quantitative immunohistochemical analysis in brain parenchyma adjacent to affected vessels in 11 ABRA patients and 10 matched CAA controls. Results: ABRA patients showed significantly increased immune activation and decreased Aβ loads in the brain parenchyma adjacent to affected vessels. Conclusion: Our results are in line with the hypothesis of ABRA being the result of an excessive immune response to Aβ and show that this can lead to enhanced clearance of Aβ from the brain parenchyma by immune-mediated mechanisms

Effects of trade barriers on development and growth

A basic definition of trade barriers could be ‘all factors that influence the amount of goods and services shipped across international borders’ (Feenstra and Taylor, 2017a). This definition is quite neutral, and it needs to be understood that the word ‘barrier’ has a negative connotation, which means that a trade barrier would be any instrument that limits or restrict trade between countries, as opposed to free trade. It is generally accepted that free trade is good for productivity and economic growth, but it is also true that most countries apply some sort of trade restriction, for different reasons

Clonality of circulating tumor cells in breast cancer brain metastasis patients

BACKGROUND: The incidence of brain metastases in breast cancer (BCBM) patients is increasing. These patients have a very poor prognosis, and therefore, identification of blood-based biomarkers, such as circulating tumor cells (CTCs), and understanding the genomic heterogeneity could help to personalize treatment options. METHODS: Both EpCAM-dependent (CellSearch® System) and EpCAM-independent Ficoll-based density centrifugation methods were used to detect CTCs from 57 BCBM patients. DNA from individual CTCs and corresponding primary tumors and brain metastases were analyzed by next-generation sequencing (NGS) in order to evaluate copy number aberrations and single nucleotide variations (SNVs). RESULTS: CTCs were detected after EpCAM-dependent enrichment in 47.7% of the patients (≥ 5 CTCs/7.5 ml blood in 20.5%). The CTC count was associated with ERBB2 status (p = 0.029) of the primary tumor as well as with the prevalence of bone metastases (p = 0.021). EpCAM-independent enrichment revealed CTCs in 32.6% of the patients, especially among triple-negative breast cancer (TNBC) patients (70.0%). A positive CTC status after enrichment of either method was significantly associated with decreased overall survival time (p < 0.05). Combining the results of both enrichment methods, 63.6% of the patients were classified as CTC positive. In three patients, the matched tumor tissue and single CTCs were analyzed by NGS showing chromosomal aberrations with a high genomic clonality and mutations in pathways potentially important in brain metastasis formation. CONCLUSION: The detection of CTCs, regardless of the enrichment method, is of prognostic relevance in BCBM patients and in combination with molecular analysis of CTCs can help defining patients with higher risk of early relapse and suitability for targeted treatment

Projective center point and Tverberg theorems

We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called "dual" center point and Tverberg theorems. Furthermore we give a common generalization of these and many other known (transversal, constraint, dual, and colorful) Tverberg type results in a single theorem, as well as some essentially new results about partitioning measures in projective space.Comment: 10 page

Characterization of Ku702–NLS as Bipartite Nuclear Localization Sequence for Non-Viral Gene Delivery

Several barriers have to be overcome in order to achieve gene expression in target cells, e.g. cellular uptake, endosomal release and translocation to the nucleus. Nuclear localization sequences (NLS) enhance gene delivery by increasing the uptake of plasmid DNA (pDNA) to the nucleus. So far, only monopartite NLS were analysed for non-viral gene delivery. In this study, we examined the characteristics of a novel bipartite NLS like construct, namely NLS Ku70. We synthesized a dimeric structure of a modified NLS from the Ku70 protein (Ku702-NLS), a nuclear transport active mutant of Ku702-NLS (s1Ku702-NLS) and a nuclear transport deficient mutant of Ku702-NLS (s2Ku702). We examined the transfection efficiency of binary Ku702-NLS/DNA and ternary Ku702-NLS/PEI/DNA gene vector complexes in vitro by using standard transfection protocols as well as the magnetofection method. The application of Ku702-NLS and s1Ku702-NLS increased gene transfer efficiency in vitro and in vivo. This study shows for the first time that the use of bipartite NLS compounds alone or in combination with cationic polymers is a promising strategy to enhance the efficiency of non-viral gene transfer

Non-secreting pituitary tumours characterised by enhanced expression of YAP/TAZ

Tumours of the anterior pituitary can manifest from all endocrine cell types but the mechanisms for determining their specification are not known. The Hippo kinase cascade is a crucial signalling pathway regulating growth and cell fate in numerous organs. There is mounting evidence implicating this in tumour formation, where it is emerging as an anti-cancer target. We previously demonstrated activity of the Hippo kinase cascade in the mouse pituitary and nuclear association of its effectors YAP/TAZ with SOX2-expressing pituitary stem cells. Here we sought to investigate whether these components are expressed in the human pituitary and if they are deregulated in human pituitary tumours. Analysis of pathway components by immunofluorescence reveals pathway activity during normal human pituitary development and in the adult gland. Poorly differentiated pituitary tumours (null cell adenomas, adamantinomatous craniopharyngiomas (ΑCPs) and papillary craniopharyngiomas (PCPs)), displayed enhanced expression of pathway effectors YAP/TAZ. In contrast, differentiated adenomas displayed lower or absent levels. Knock-down of the kinase-encoding Lats1 in GH3 rat mammosomatotropinoma cells suppressed Prl and Gh promoter activity following an increase in YAP/TAZ levels. In conclusion, we have demonstrated activity of the Hippo kinase cascade in the human pituitary and association of high YAP/TAZ with repression of the differentiated state both in vitro and in vivo. Characterisation of this pathway in pituitary tumours is of potential prognostic value, opening up putative avenues for treatments

Application of the RIMARC algorithm to a large data set of action potentials and clinical parameters for risk prediction of atrial fibrillation

Ex vivo recorded action potentials (APs) in human right atrial tissue from patients in sinus rhythm (SR) or atrial fibrillation (AF) display a characteristic spike-and-dome or triangular shape, respectively, but variability is huge within each rhythm group. The aim of our study was to apply the machine-learning algorithm ranking instances by maximizing the area under the ROC curve (RIMARC) to a large data set of 480 APs combined with retrospectively collected general clinical parameters and to test whether the rules learned by the RIMARC algorithm can be used for accurately classifying the preoperative rhythm status. APs were included from 221 SR and 158 AF patients. During a learning phase, the RIMARC algorithm established a ranking order of 62 features by predictive value for SR or AF. The model was then challenged with an additional test set of features from 28 patients in whom rhythm status was blinded. The accuracy of the risk prediction for AF by the model was very good (0.93) when all features were used. Without the seven AP features, accuracy still reached 0.71. In conclusion, we have shown that training the machine-learning algorithm RIMARC with an experimental and clinical data set allows predicting a classification in a test data set with high accuracy. In a clinical setting, this approach may prove useful for finding hypothesis-generating associations between different parameters. © 2014, International Federation for Medical and Biological Engineering