Integral points on elliptic curves and explicit valuations of division polynomials

Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant C such that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at most one integral multiple [n]P such that n > C. The proof is a modification of a proof of Ingram giving an unconditional but not uniform bound. The new ingredient is a collection of explicit formulae for the sequence of valuations of the division polynomials. For P of non-singular reduction, such sequences are already well described in most cases, but for P of singular reduction, we are led to define a new class of sequences called elliptic troublemaker sequences, which measure the failure of the Neron local height to be quadratic. As a corollary in the spirit of a conjecture of Lang and Hall, we obtain a uniform upper bound on h(P)/h(E) for integer points having two large integral multiples.Comment: 41 pages; minor corrections and improvements to expositio

Do What I Mean: Online Shopping with a Natural Language Search Agent

Ineffective search engines on e-catalog sites are driving away potential customers. Natural-language querying improves precision and parsing capability, and with advances in the technology, it can also meet these shopping sites\u27 performance demands

Amicable pairs and aliquot cycles for elliptic curves

An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j not 0) have no aliqout cycles of length greater than two. We give conjectural formulas for the frequency of amicable pairs. For CM curves, the derivation of precise conjectural formulas involves a detailed analysis of the values of the Grossencharacter evaluated at a prime ideal P in End(E) having the property that #E(F_P) is prime. This is especially intricate for the family of curves with j = 0.Comment: 53 page

RNase L Mediates Transient Control of The Interferon Response Through Modulation of The Double-stranded RNA-Dependent Protein Kinase PKR

The transient control of diverse biological responses that occurs in response to varied forms of stress is often a highly regulated process. During the interferon (IFN) response, translational repression due to phosphorylation of eukaryotic initiation factor 2α, eIF2α, by the double-stranded RNA-dependent protein kinase, PKR, constitutes a means of inhibiting viral replication. Here we show that the transient nature of the IFN response against acute viral infections is regulated, at least in part, by RNase L. During the IFN antiviral response in RNase L-null cells, PKR mRNA stability was enhanced, PKR induction was increased, and the phosphorylated form of eIF2α appeared with extended kinetics compared with similarly treated wild type cells. An enhanced IFN response in RNase L-null cells was also demonstrated by monitoring inhibition of viral protein synthesis. Furthermore, ectopic expression of RNase L from a plasmid vector prevented the IFN induction of PKR. These results suggest a role for RNase L in the transient control of the IFN response and possibly of other cytokine and stress responses

RNase L Mediates Transient Control of The Interferon Response Through Modulation of The Double-stranded RNA-Dependent Protein Kinase PKR

The transient control of diverse biological responses that occurs in response to varied forms of stress is often a highly regulated process. During the interferon (IFN) response, translational repression due to phosphorylation of eukaryotic initiation factor 2α, eIF2α, by the double-stranded RNA-dependent protein kinase, PKR, constitutes a means of inhibiting viral replication. Here we show that the transient nature of the IFN response against acute viral infections is regulated, at least in part, by RNase L. During the IFN antiviral response in RNase L-null cells, PKR mRNA stability was enhanced, PKR induction was increased, and the phosphorylated form of eIF2α appeared with extended kinetics compared with similarly treated wild type cells. An enhanced IFN response in RNase L-null cells was also demonstrated by monitoring inhibition of viral protein synthesis. Furthermore, ectopic expression of RNase L from a plasmid vector prevented the IFN induction of PKR. These results suggest a role for RNase L in the transient control of the IFN response and possibly of other cytokine and stress responses

Dominant negative variants in KIF5B cause osteogenesis imperfecta via down regulation of mTOR signaling

BACKGROUND: Kinesin motor proteins transport intracellular cargo, including mRNA, proteins, and organelles. Pathogenic variants in kinesin-related genes have been implicated in neurodevelopmental disorders and skeletal dysplasias. We identified de novo, heterozygous variants in KIF5B, encoding a kinesin-1 subunit, in four individuals with osteogenesis imperfecta. The variants cluster within the highly conserved kinesin motor domain and are predicted to interfere with nucleotide binding, although the mechanistic consequences on cell signaling and function are unknown. METHODS: To understand the in vivo genetic mechanism of KIF5B variants, we modeled the p.Thr87Ile variant that was found in two patients in the C. elegans ortholog, unc-116, at the corresponding position (Thr90Ile) by CRISPR/Cas9 editing and performed functional analysis. Next, we studied the cellular and molecular consequences of the recurrent p.Thr87Ile variant by microscopy, RNA and protein analysis in NIH3T3 cells, primary human fibroblasts and bone biopsy. RESULTS: C. elegans heterozygous for the unc-116 Thr90Ile variant displayed abnormal body length and motility phenotypes that were suppressed by additional copies of the wild type allele, consistent with a dominant negative mechanism. Time-lapse imaging of GFP-tagged mitochondria showed defective mitochondria transport in unc-116 Thr90Ile neurons providing strong evidence for disrupted kinesin motor function. Microscopy studies in human cells showed dilated endoplasmic reticulum, multiple intracellular vacuoles, and abnormal distribution of the Golgi complex, supporting an intracellular trafficking defect. RNA sequencing, proteomic analysis, and bone immunohistochemistry demonstrated down regulation of the mTOR signaling pathway that was partially rescued with leucine supplementation in patient cells. CONCLUSION: We report dominant negative variants in the KIF5B kinesin motor domain in individuals with osteogenesis imperfecta. This study expands the spectrum of kinesin-related disorders and identifies dysregulated signaling targets for KIF5B in skeletal development

Communication issues in requirements elicitation: A content analysis of stakeholder experiences

The gathering of stakeholder requirements comprises an early, but continuous and highly critical stage in system development. This phase in development is subject to a large degree of error, influenced by key factors rooted in communication problems. This pilot study builds upon an existing theory-based categorisation of these problems through presentation of a four-dimensional framework on communication. Its structure is validated through a content analysis of interview data, from which themes emerge, that can be assigned to the dimensional categories, highlighting any problematic areas. The paper concludes with a discussion on the utilisation of the framework for requirements elicitation exercises

Macrocephaly and developmental delay caused by missense variants in RAB5C

Rab GTPases are important regulators of intracellular vesicular trafficking. RAB5C is a member of the Rab GTPase family that plays an important role in the endocytic pathway, membrane protein recycling and signaling. Here we report on 12 individuals with nine different heterozygous de novo variants in RAB5C. All but one patient with missense variants (n = 9) exhibited macrocephaly, combined with mild-to-moderate developmental delay. Patients with loss of function variants (n = 2) had an apparently more severe clinical phenotype with refractory epilepsy and intellectual disability but a normal head circumference. Four missense variants were investigated experimentally. In vitro biochemical studies revealed that all four variants were damaging, resulting in increased nucleotide exchange rate, attenuated responsivity to guanine exchange factors and heterogeneous effects on interactions with effector proteins. Studies in C. elegans confirmed that all four variants were damaging in vivo and showed defects in endocytic pathway function. The variant heterozygotes displayed phenotypes that were not observed in null heterozygotes, with two shown to be through a dominant negative mechanism. Expression of the human RAB5C variants in zebrafish embryos resulted in defective development, further underscoring the damaging effects of the RAB5C variants. Our combined bioinformatic, in vitro and in vivo experimental studies and clinical data support the association of RAB5C missense variants with a neurodevelopmental disorder characterized by macrocephaly and mild-to-moderate developmental delay through disruption of the endocytic pathway

Higher cardiorespiratory fitness predicts long-term survival in patients with heart failure and preserved ejection fraction: the Henry Ford Exercise Testing (FIT) Project

Introduction: Higher cardiorespiratory fitness (CRF) is associated with improved exercise capacity and quality of life in heart failure with preserved ejection fraction (HFpEF), but there are no large studies evaluating the association of HFpEF, CRF, and long-term survival. We therefore aimed to determine the association between CRF and all-cause mortality, in patients with HFpEF. Material and methods: In the Henry Ford Exercise Testing (FIT) Project, 167 patients had baseline HFpEF, defined as a clinical diagnosis of heart failure with ejection fraction ≥ 50% on echocardiogram. The CRF was estimated from the peak workload (in METs) from a clinician-referred treadmill stress test and categorized as poor (1-4 METs), intermediate (5-6 METs), and moderate-high (≥ 7 METs). Additional analyses assessing the effect of HFpEF and CRF on mortality were also conducted, matching HFpEF patients to non-HFpEF patients using propensity scores. Results: Mean age was 64 ±13 years, with 55% women, and 46% Black. Over a median follow-up of 9.7 (5.2-18.9) years, there were 103 deaths. In fully adjusted models, moderate-high CRF was associated with 63% lower mortality risk (HR = 0.37, 95% CI: 0.18-0.73) compared to the poor-CRF group. In the propensity-matched cohort, HFpEF was associated with a HR of 2.3 (95% CI: 1.7-3.2) for mortality compared to non-HFpEF patients, which was attenuated to 1.8 (95% CI: 1.3-2.5) after adjusting for CRF. Conclusions: Moderate-high CRF in patients with HFpEF is associated with improved survival, and differences in CRF partly explain the intrinsic risk of HFpEF. Randomized trials of interventions aimed at improving CRF in HFpEF are needed