On the asymptotic formula for Goldbach numbers in short intervals

Let $R(k)=\sum\limits_{l+m=k}\Lambda(l)\Lambda(m)$, \Sing(k) = 2 \prod\limits_{p>2}\left(1-\frac{1}{(p-1)^2}\right) \prod\limits_{\substack{ p\mid k\\ p>2 }} \left(\frac{p-1}{p-2}\right) if $k$ is even and \Sing(k) =0 if $k$ is odd. It is known that R(k) \sim k\Sing(k) as $N\to \infty$ for almost all $k\in [N,2N]$ and that \sum_{k\in [n,n+H)}R(k) \sim \sum_{k\in [n,n+H)} k\Sing(k) \quad\hbox{for} \quad n\to \infty \eqno{(1)} uniformly for $H\geq n^{1/6+\epsilon}$. Here we prove, assuming $N^\epsilon\leq H\leq N^{1/6+\epsilon}$ and $N\to\infty$, that (1) holds for almost all $n\in [N,2N]$

Lung metastasis 21 years after initial diagnosis of osteosarcoma: a case report

<p>Abstract</p> <p>Introduction</p> <p>To the best of our knowledge, this case report describes the longest disease-free interval between primary diagnosis and metastatic recurrence of an osteosarcoma.</p> <p>Case presentation</p> <p>A 35-year-old Caucasian American man presented with asymptomatic lung metastases 21 years after being diagnosed and treated for lower extremity osteosarcoma. He underwent curative lung resection, but 2 years thereafter developed metastatic disease in the scapula and tibia and, after resection and chemotherapy, is in remission 1 year later.</p> <p>Conclusion</p> <p>This case highlights the importance of long follow-up periods and continued surveillance of osteosarcoma patients after initial curative treatment.</p

Improved Classical Cryptanalysis of SIKE in Practice

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The AIB1 glutamine repeat polymorphism is not associated with risk of breast cancer before age 40 years in Australian women

INTRODUCTION: AIB1, located at 20q12, is a member of the steroid hormone coactivator family. It contains a glutamine repeat (CAG/CAA) polymorphism at its carboxyl-terminal region that may alter the transcriptional activation of the receptor and affect susceptibility to breast cancer through altered sensitivity to hormones. METHODS: We evaluated this repeat polymorphism in the context of early-onset disease by conducting a case-control study of 432 Australian women diagnosed with breast cancer before the age of 40 years and 393 population-based control individuals who were frequency matched for age. Genotyping was performed using a scanning laser fluorescence imager. RESULTS: There were no differences in genotype frequencies between cases and control individuals, or between cases categorized by family history or by BRCA1 and BRCA2 germline mutation status. There was no evidence that the presence of one or two alleles of 26 glutamine repeats or fewer was associated with breast cancer (odds ratio = 1.03, 95% confidence interval = 0.73–1.44), or that women with alleles greater than 29 repeats were at increased risk of breast cancer. Exclusion of women who carried a BRCA1 or BRCA2 mutation (24 cases) and non-Caucasian women (44 cases) did not alter the risk estimates or inferences. We present raw data, including that on mutation carriers, to allow pooling with other studies. CONCLUSION: There was no evidence that risk of breast cancer depends on AIB1 CAG/CAA polymorphism status, even if affected women carry a mutation in BRCA1 or BRCA2

UNC2025, a MERTK Small-Molecule Inhibitor, Is Therapeutically Effective Alone and in Combination with Methotrexate in Leukemia Models

MERTK tyrosine kinase is ectopically expressed in 30–50% of acute lymphoblastic leukemias (ALL) and over 80% of acute myeloid leukemias (AML) and is a potential therapeutic target. Here, we evaluated the utility of UNC2025, a MERTK tyrosine kinase inhibitor, for treatment of acute leukemia

A Quasi-Model-Independent Search for New Physics at Large Transverse Momentum

We apply a quasi-model-independent strategy ("Sleuth") to search for new high p_T physics in approximately 100 pb^-1 of ppbar collisions at sqrt(s) = 1.8 TeV collected by the DZero experiment during 1992-1996 at the Fermilab Tevatron. Over thirty-two e mu X, W+jets-like, Z+jets-like, and 3(lepton/photon)X exclusive final states are systematically analyzed for hints of physics beyond the standard model. Simultaneous sensitivity to a variety of models predicting new phenomena at the electroweak scale is demonstrated by testing the method on a particular signature in each set of final states. No evidence of new high p_T physics is observed in the course of this search, and we find that 89% of an ensemble of hypothetical similar experimental runs would have produced a final state with a candidate signal more interesting than the most interesting observed in these data.Comment: 28 pages, 17 figures. Submitted to Physical Review

Search for Electroweak Production of Single Top Quarks in ppbar Collisions

We present a search for electroweak production of single top quarks in the electron+jets and muon+jets decay channels. The measurements use ~90 pb^-1 of data from Run 1 of the Fermilab Tevatron collider, collected at 1.8 TeV with the DZero detector between 1992 and 1995. We use events that include a tagging muon, implying the presence of a b jet, to set an upper limit at the 95% confidence level on the cross section for the s-channel process ppbar->tb+X of 39 pb. The upper limit for the t-channel process ppbar->tqb+X is 58 pb.Comment: 11 pages, 2 figures. This is the published versio

Search for R-parity Violating Supersymmetry in Dimuon and Four-Jets Channel

We present results of a search for R-parity-violating decay of the neutralino chi_1^0, taken to be the Lightest Supersymmetric Particle. It is assumed that this decay proceeds through one of the lepton-number violating couplings lambda-prime_2jk (j=1,2; k=1,2,3). This search is based on 77.5 pb-1 of data, collected by the D0 experiment at the Fermilab Tevatron in ppbar collisions at a center of mass energy of 1.8 TeV in 1992-1995.Comment: 10 pages, 3 figure

Search for Large Extra Dimensions in Dielectron and Diphoton Production

We report a search for effects of large extra spatial dimensions in ppbar collisions at a center-of-mass energy of 1.8 TeV with the DZero detector, using events containing a pair of electrons or photons. The data are in good agreement with the expected background and do not exhibit evidence for large extra dimensions. We set the most restrictive lower limits to date, at the 95% confidence level, on the effective Planck scale between 1.0 TeV and 1.4 TeV for several formalisms and numbers of extra dimensions.Comment: 6 pages, 2 figures, submitted to Phys. Rev. Let

Antiplatelet therapy with aspirin, clopidogrel, and dipyridamole versus clopidogrel alone or aspirin and dipyridamole in patients with acute cerebral ischaemia (TARDIS): a randomised, open-label, phase 3 superiority trial

Background: Intensive antiplatelet therapy with three agents might be more effective than guideline treatment for preventing recurrent events in patients with acute cerebral ischaemia. We aimed to compare the safety and efficacy of intensive antiplatelet therapy (combined aspirin, clopidogrel, and dipyridamole) with that of guideline-based antiplatelet therapy. Methods: We did an international, prospective, randomised, open-label, blinded-endpoint trial in adult participants with ischaemic stroke or transient ischaemic attack (TIA) within 48 h of onset. Participants were assigned in a 1:1 ratio using computer randomisation to receive loading doses and then 30 days of intensive antiplatelet therapy (combined aspirin 75 mg, clopidogrel 75 mg, and dipyridamole 200 mg twice daily) or guideline-based therapy (comprising either clopidogrel alone or combined aspirin and dipyridamole). Randomisation was stratified by country and index event, and minimised with prognostic baseline factors, medication use, time to randomisation, stroke-related factors, and thrombolysis. The ordinal primary outcome was the combined incidence and severity of any recurrent stroke (ischaemic or haemorrhagic; assessed using the modified Rankin Scale) or TIA within 90 days, as assessed by central telephone follow-up with masking to treatment assignment, and analysed by intention to treat. This trial is registered with the ISRCTN registry, number ISRCTN47823388. Findings: 3096 participants (1556 in the intensive antiplatelet therapy group, 1540 in the guideline antiplatelet therapy group) were recruited from 106 hospitals in four countries between April 7, 2009, and March 18, 2016. The trial was stopped early on the recommendation of the data monitoring committee. The incidence and severity of recurrent stroke or TIA did not differ between intensive and guideline therapy (93 [6%] participants vs 105 [7%]; adjusted common odds ratio [cOR] 0·90, 95% CI 0·67–1·20, p=0·47). By contrast, intensive antiplatelet therapy was associated with more, and more severe, bleeding (adjusted cOR 2·54, 95% CI 2·05–3·16, p<0·0001). Interpretation: Among patients with recent cerebral ischaemia, intensive antiplatelet therapy did not reduce the incidence and severity of recurrent stroke or TIA, but did significantly increase the risk of major bleeding. Triple antiplatelet therapy should not be used in routine clinical practice