Description of the inelastic collision of two solitary waves for the BBM equation

We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves).Comment: submitted for publication. Corrected typo in Theorem 1.

Asymptotic stability of breathers in some Hamiltonian networks of weakly coupled oscillators

We consider a Hamiltonian chain of weakly coupled anharmonic oscillators. It is well known that if the coupling is weak enough then the system admits families of periodic solutions exponentially localized in space (breathers). In this paper we prove asymptotic stability in energy space of such solutions. The proof is based on two steps: first we use canonical perturbation theory to put the system in a suitable normal form in a neighborhood of the breather, second we use dispersion in order to prove asymptotic stability. The main limitation of the result rests in the fact that the nonlinear part of the on site potential is required to have a zero of order 8 at the origin. From a technical point of view the theory differs from that developed for Hamiltonian PDEs due to the fact that the breather is not a relative equilibrium of the system

Long time dynamics and coherent states in nonlinear wave equations

We discuss recent progress in finding all coherent states supported by nonlinear wave equations, their stability and the long time behavior of nearby solutions.Comment: bases on the authors presentation at 2015 AMMCS-CAIMS Congress, to appear in Fields Institute Communications: Advances in Applied Mathematics, Modeling, and Computational Science 201

Search for Lorentz and CPT Violation Effects in Muon Spin Precession

The spin precession frequency of muons stored in the $(g-2)$ storage ring has been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT violation signatures were searched for: a nonzero $\Delta\omega_{a}$ (=$\omega_{a}^{\mu^{+}}-\omega_{a}^{\mu^{-}}$); and a sidereal variation of $\omega_{a}^{\mu^{\pm}}$. No significant effect is found, and the following limits on the standard-model extension parameters are obtained: $b_{Z} =-(1.0 \pm 1.1)\times 10^{-23}$ GeV; $(m_{\mu}d_{Z0}+H_{XY}) = (1.8 \pm 6.0 \times 10^{-23})$ GeV; and the 95% confidence level limits $\check{b}_{\perp}^{\mu^{+}}< 1.4 \times 10^{-24}$ GeV and $\check{b}_{\perp}^{\mu^{-}} < 2.6 \times 10^{-24}$ GeV.Comment: 5 pages, 3 figures, submitted to Physical Review Letters, Modified to answer the referees suggestion

An Improved Limit on the Muon Electric Dipole Moment

Three independent searches for an electric dipole moment (EDM) of the positive and negative muons have been performed, using spin precession data from the muon g-2 storage ring at Brookhaven National Laboratory. Details on the experimental apparatus and the three analyses are presented. Since the individual results on the positive and negative muon, as well as the combined result, d=-0.1(0.9)E-19 e-cm, are all consistent with zero, we set a new muon EDM limit, |d| < 1.9E-19 e-cm (95% C.L.). This represents a factor of 5 improvement over the previous best limit on the muon EDM.Comment: 19 pages, 15 figures, 7 table

Search for Lorentz and CPT Violation Effects in Muon Spin Precession

The spin precession frequency of muons stored in the $(g-2)$ storage ring has been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT violation signatures were searched for: a nonzero $\Delta\omega_{a}$ (=$\omega_{a}^{\mu^{+}}-\omega_{a}^{\mu^{-}}$); and a sidereal variation of $\omega_{a}^{\mu^{\pm}}$. No significant effect is found, and the following limits on the standard-model extension parameters are obtained: $b_{Z} =-(1.0 \pm 1.1)\times 10^{-23}$ GeV; $(m_{\mu}d_{Z0}+H_{XY}) = (1.8 \pm 6.0 \times 10^{-23})$ GeV; and the 95% confidence level limits $\check{b}_{\perp}^{\mu^{+}}< 1.4 \times 10^{-24}$ GeV and $\check{b}_{\perp}^{\mu^{-}} < 2.6 \times 10^{-24}$ GeV.Comment: 5 pages, 3 figures, submitted to Physical Review Letters, Modified to answer the referees suggestion

Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL

We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a_mu = (g-2)/2. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce a_mu(Expt) = 11 659 208.0(5.4)(3.3) x 10^-10, where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for a_mu includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, ~0.55 ppm, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on e+e- hadronic cross sections, lie 2.2 - 2.7 standard deviations below the experimental result.Comment: Summary paper of E821 Collaboration measurements of the muon anomalous magnetic moment, each reported earlier in Letters or Brief Reports; 96 pages, 41 figures, 16 tables. Revised version submitted to PR

Performance of mitochondrial DNA mutations detecting early stage cancer

<p>Abstract</p> <p>Background</p> <p>Mutations in the mitochondrial genome (mtgenome) have been associated with cancer and many other disorders. These mutations can be point mutations or deletions, or admixtures (heteroplasmy). The detection of mtDNA mutations in body fluids using resequencing microarrays, which are more sensitive than other sequencing methods, could provide a strategy to measure mutation loads in remote anatomical sites.</p> <p>Methods</p> <p>We determined the mtDNA mutation load in the entire mitochondrial genome of 26 individuals with different early stage cancers (lung, bladder, kidney) and 12 heavy smokers without cancer. MtDNA was sequenced from three matched specimens (blood, tumor and body fluid) from each cancer patient and two matched specimens (blood and sputum) from smokers without cancer. The inherited wildtype sequence in the blood was compared to the sequences present in the tumor and body fluid, detected using the Affymetrix Genechip^®Human Mitochondrial Resequencing Array 1.0 and supplemented by capillary sequencing for noncoding region.</p> <p>Results</p> <p>Using this high-throughput method, 75% of the tumors were found to contain mtDNA mutations, higher than in our previous studies, and 36% of the body fluids from these cancer patients contained mtDNA mutations. Most of the mutations detected were heteroplasmic. A statistically significantly higher heteroplasmy rate occurred in tumor specimens when compared to both body fluid of cancer patients and sputum of controls, and in patient blood compared to blood of controls. Only 2 of the 12 sputum specimens from heavy smokers without cancer (17%) contained mtDNA mutations. Although patient mutations were spread throughout the mtDNA genome in the lung, bladder and kidney series, a statistically significant elevation of tRNA and ND complex mutations was detected in tumors.</p> <p>Conclusion</p> <p>Our findings indicate comprehensive mtDNA resequencing can be a high-throughput tool for detecting mutations in clinical samples with potential applications for cancer detection, but it is unclear the biological relevance of these detected mitochondrial mutations. Whether the detection of tumor-specific mtDNA mutations in body fluidsy this method will be useful for diagnosis and monitoring applications requires further investigation.</p

Impact of primary kidney disease on the effects of empagliflozin in patients with chronic kidney disease: secondary analyses of the EMPA-KIDNEY trial

Background: The EMPA KIDNEY trial showed that empagliflozin reduced the risk of the primary composite outcome of kidney disease progression or cardiovascular death in patients with chronic kidney disease mainly through slowing progression. We aimed to assess how effects of empagliflozin might differ by primary kidney disease across its broad population. Methods: EMPA-KIDNEY, a randomised, controlled, phase 3 trial, was conducted at 241 centres in eight countries (Canada, China, Germany, Italy, Japan, Malaysia, the UK, and the USA). Patients were eligible if their estimated glomerular filtration rate (eGFR) was 20 to less than 45 mL/min per 1·73 m2, or 45 to less than 90 mL/min per 1·73 m2 with a urinary albumin-to-creatinine ratio (uACR) of 200 mg/g or higher at screening. They were randomly assigned (1:1) to 10 mg oral empagliflozin once daily or matching placebo. Effects on kidney disease progression (defined as a sustained ≥40% eGFR decline from randomisation, end-stage kidney disease, a sustained eGFR below 10 mL/min per 1·73 m2, or death from kidney failure) were assessed using prespecified Cox models, and eGFR slope analyses used shared parameter models. Subgroup comparisons were performed by including relevant interaction terms in models. EMPA-KIDNEY is registered with ClinicalTrials.gov, NCT03594110. Findings: Between May 15, 2019, and April 16, 2021, 6609 participants were randomly assigned and followed up for a median of 2·0 years (IQR 1·5–2·4). Prespecified subgroupings by primary kidney disease included 2057 (31·1%) participants with diabetic kidney disease, 1669 (25·3%) with glomerular disease, 1445 (21·9%) with hypertensive or renovascular disease, and 1438 (21·8%) with other or unknown causes. Kidney disease progression occurred in 384 (11·6%) of 3304 patients in the empagliflozin group and 504 (15·2%) of 3305 patients in the placebo group (hazard ratio 0·71 [95% CI 0·62–0·81]), with no evidence that the relative effect size varied significantly by primary kidney disease (pheterogeneity=0·62). The between-group difference in chronic eGFR slopes (ie, from 2 months to final follow-up) was 1·37 mL/min per 1·73 m2 per year (95% CI 1·16–1·59), representing a 50% (42–58) reduction in the rate of chronic eGFR decline. This relative effect of empagliflozin on chronic eGFR slope was similar in analyses by different primary kidney diseases, including in explorations by type of glomerular disease and diabetes (p values for heterogeneity all &gt;0·1). Interpretation: In a broad range of patients with chronic kidney disease at risk of progression, including a wide range of non-diabetic causes of chronic kidney disease, empagliflozin reduced risk of kidney disease progression. Relative effect sizes were broadly similar irrespective of the cause of primary kidney disease, suggesting that SGLT2 inhibitors should be part of a standard of care to minimise risk of kidney failure in chronic kidney disease. Funding: Boehringer Ingelheim, Eli Lilly, and UK Medical Research Council