The omega-limit sets of quadratic Julia sets

In this paper we characterize \w-limit sets of dendritic Julia sets for quadratic maps. We use Baldwin's symbolic representation of these spaces as a non-Hausdorff itinerary space and prove that quadratic maps with dendritic Julia sets have shadowing, and also that for all such maps, a closed invariant set is an \w-limit set of a point if, and only if, it is internally chain transitive.Comment: 24 page

On the omega-limit sets of tent maps

For a continuous map f on a compact metric space (X,d), a subset D of X is internally chain transitive if for every x and y in D and every delta > 0 there is a sequence of points {x=x_0,x_1, ...,x_n=y} such that d(f(x_i),x_{i+1}) < delta for i=0,1, ...,n-1. It is known that every omega-limit set is internally chain transitive; in earlier work it was shown that for X a shift of finite type, a closed subset D of X is internally chain transitive if and only if D is an omega-limit set for some point in X, and that the same is also true for the tent map with slope equal to 2. In this paper, we prove that for tent maps whose critical point c=1/2 is periodic, every closed, internally chain transitive set is necessarily an omega-limit set. Furthermore, we show that there are at least countably many tent maps with non-recurrent critical point for which there is a closed, internally chain transitive set which is not an omega-limit set. Together, these results lead us to conjecture that for those tent maps with shadowing (or pseudo-orbit tracing), the omega-limit sets are precisely those sets having internal chain transitivity.Comment: 17 page

Shadowing and Expansivity in Sub-Spaces

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval, in which context some of our results can be extended.Comment: 18 page

The Angelina Jolie effect : how high celebrity profile can have a major impact on provision of cancer related services

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Acknowledgements We acknowledge the support of the Genesis Breast Cancer Prevention Appeal and Breast Cancer Campaign, which funds the FH02 study. DGE is a NIHR Senior investigator. FH02 Study Group, Family History Clinics providing data is as follows, Edinburgh: Lynda Luke, Lesley Smart; St Barts, London: Vian Salih, Ilyena Froud; Grantham: Nicky Turner, Natarajan Vaithilingam; Leighton Hospital Crewe: Tracey Hales, Samantha Bennion; LondonDerry: Celia Diver-Hall, Jackie McGee; Nottingham: Douglas MacMillan; Nicky Scott; Bath: Diana Dalgleish, Alison Smith; Coventry: Celia Lewis; Royal Marsden Hospital, London: Janet self, Gerald Gui; Derby: Mark Sibbering, Samantha Crockett; City Hospital, Birmingham: Simerjit Rai, Harriet Goddard; Genesis Prevention Centre, Manchester: Lorraine Roberts, Jayne Beesley. RGC teams are as follows, Nottingham RGC: Gareth Cross; Guys Hospital: Adam Shaw; Manchester RGC: Andrew Wallace.Peer reviewedPublisher PD

Beliefs About Medication and Uptake of Preventive Therapy in Women at Increased Risk of Breast Cancer: Results From a Multicenter Prospective Study

Introduction Uptake of preventive therapies for breast cancer is low. We examined whether women at increased risk of breast cancer can be categorized into groups with similar medication beliefs, and whether belief group membership was prospectively associated with uptake of preventive therapy. Patients and Methods Women (n = 732) attending an appointment to discuss breast cancer risk were approached; 408 (55.7%) completed the Beliefs About Medicines and the Perceived Sensitivity to Medicines questionnaires. Uptake of tamoxifen at 3 months was reported in 258 (63.2%). The optimal number of belief groups were identified using latent profile analysis. Results Uptake of tamoxifen was 14.7% (38/258). One in 5 women (19.4%; 78/402) reported a strong need for tamoxifen. The model fit statistics supported a 2-group model. Both groups held weak beliefs about their need for tamoxifen for current and future health. Group 2 (38%; 154/406 of the sample) reported stronger concerns about tamoxifen and medicines in general, and stronger perceived sensitivity to the negative effects of medicines compared with group 1 (62%; 252/406). Women with low necessity and lower concerns (group 1) were more likely to initiate tamoxifen (18.3%; 33/180) than those with low necessity and higher concerns (group 2) (6.4%; 5/78). After adjusting for demographic and clinical factors, the odds ratio was 3.37 (95% confidence interval, 1.08-10.51; P = .036). Conclusion Uptake of breast cancer preventive therapy was low. A subgroup of women reported low need for preventive therapy and strong medication concerns. These women were less likely to initiate tamoxifen. Medication beliefs are targets for supporting informed decision-making

Identification and characterisation of a rare MTTP variant underlying hereditary non-alcoholic fatty liver disease

Background and aimsNon-alcoholic fatty liver disease (NAFLD) is a complex trait with an estimated prevalence of 25% globally. We aimed to identify the genetic variant underlying a four-generation family with progressive NAFLD leading to cirrhosis, decompensation and development of hepatocellular carcinoma in the absence of common risk factors such as obesity and type 2 diabetes.MethodsExome sequencing and genome comparisons were used to identify the likely causal variant. We extensively characterised the clinical phenotype and post-prandial metabolic responses of family members with the identified novel variant in comparison to healthy non-carriers and wild-type patients with NAFLD. Variant-expressing hepatocyte-like cells (HLCs) were derived from human induced pluripotent stem cells generated from homozygous donor skin fibroblasts and restored to wild-type using CRISPR-Cas9. The phenotype was assessed using imaging, targeted RNA analysis and molecular expression arrays.ResultsWe identified a rare causal variant c.1691T>C p.I564T (rs745447480) in MTTP, encoding microsomal triglyceride transfer protein (MTP), associated with progressive NAFLD, unrelated to metabolic syndrome and without characteristic features of abetalipoproteinemia. HLCs derived from a homozygote donor had significantly lower MTP activity and lower lipoprotein ApoB secretion compared to wild-type cells, while having similar levels of MTP mRNA and protein. Cytoplasmic triglyceride accumulation in HLCs triggered endoplasmic reticulum stress, secretion of pro-inflammatory mediators and production of reactive oxygen species.ConclusionWe have identified and characterized a rare causal variant in MTTP and homozygosity for MTTP p.I564T is associated with progressive NAFLD without any other manifestations of abetalipoproteinemia. Our findings provide insights into mechanisms driving progressive NAFLD

Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans

Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in 25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16 regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP, while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium (LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region. Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa, an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent signals within the same regio

Associations of common breast cancer susceptibility alleles with risk of breast cancer subtypes in BRCA1 and BRCA2 mutation carriers

Introduction: More than 70 common alleles are known to be involved in breast cancer (BC) susceptibility, and several exhibit significant heterogeneity in their associations with different BC subtypes. Although there are differences in the association patterns between BRCA1 and BRCA2 mutation carriers and the general population for several loci, no study has comprehensively evaluated the associations of all known BC susceptibility alleles with risk of BC subtypes in BRCA1 and BRCA2 carriers. Methods: We used data from 15,252 BRCA1 and 8,211 BRCA2 carriers to analyze the associations between approximately 200,000 genetic variants on the iCOGS array and risk of BC subtypes defined by estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER2) and triple-negative- (TN) status; morphologic subtypes; histological grade; and nodal involvement. Results: The estimated BC hazard ratios (HRs) for the 74 known BC alleles in BRCA1 carriers exhibited moderate correlations with the corresponding odds ratios from the general population. However, their associations with ER-positive BC in BRCA1 carriers were more consistent with the ER-positive as