Stability and Convergence of Product Formulas for Operator Matrices

We present easy to verify conditions implying stability estimates for operator matrix splittings which ensure convergence of the associated Trotter, Strang and weighted product formulas. The results are applied to inhomogeneous abstract Cauchy problems and to boundary feedback systems.Comment: to appear in Integral Equations and Operator Theory (ISSN: 1420-8989

Limiting absorption principle for the dissipative Helmholtz equation

Adapting Mourre's commutator method to the dissipative setting, we prove a limiting absorption principle for a class of abstract dissipative operators. A consequence is the resolvent estimates for the high frequency Helmholtz equation when trapped trajectories meet the set where the imaginary part of the potential is non-zero. We also give the resolvent estimates in Besov spaces

Childbirth after adolescent and young adult cancer: a population-based study

Purpose: Annually, > 45,000 US women are diagnosed with cancer during adolescence and young adulthood (AYA). Since 2006, national guidelines have recommended fertility counseling for cancer patients. We examined childbirth after AYA cancer by calendar period, cancer diagnosis, and maternal characteristics. Methods: We identified a cohort of women with an incident invasive AYA cancer diagnosis at ages 15–39 during 2000–2013 in North Carolina. Cancer records were linked with statewide birth certificates through 2014. Hazard ratios (HR) and 95% confidence intervals (CI) for first post-diagnosis live birth were calculated using Cox proportional hazards regression. Results: Among 17,564 AYA cancer survivors, 1989 had ≥ 1 birth after diagnosis during 98,397 person-years. The 5- and 10-year cumulative incidence of live birth after cancer was 10 and 15%, respectively. AYA survivors with a post-diagnosis birth were younger at diagnosis, had lower stage disease, and had less often received chemotherapy than those without a birth. The 5-year cumulative incidence of post-diagnosis birth was 10.0% for women diagnosed during 2007–2012, compared to 9.4% during 2000–2005 (HR = 1.01; 0.91, 1.12), corresponding to periods before and after publication of American Society of Clinical Oncology fertility counseling guidelines in 2006. Conclusions: Despite advances in fertility preservation options and recognition of fertility counseling as a part of high-quality cancer care, the incidence of post-diagnosis childbirth has remained stable over the last 15 years. Implications for Cancer Survivors: Our study uses statewide data to provide recent, population-based estimates of how often AYA women have biological children after a cancer diagnosis

Influence of uncorrelated overlayers on the magnetism in thin itinerant-electron films

The influence of uncorrelated (nonmagnetic) overlayers on the magnetic properties of thin itinerant-electron films is investigated within the single-band Hubbard model. The Coulomb correlation between the electrons in the ferromagnetic layers is treated by using the spectral density approach (SDA). It is found that the presence of nonmagnetic layers has a strong effect on the magnetic properties of thin films. The Curie temperatures of very thin films are modified by the uncorrelated overlayers. The quasiparticle density of states is used to analyze the results. In addition, the coupling between the ferromagnetic layers and the nonmagnetic layers is discussed in detail. The coupling depends on the band occupation of the nonmagnetic layers, while it is almost independent of the number of the nonmagnetic layers. The induced polarization in the nonmagnetic layers shows a long-range decreasing oscillatory behavior and it depends on the coupling between ferromagnetic and nonmagnetic layers.Comment: 9 pages, RevTex, 6 figures, for related work see: http://orion.physik.hu-berlin.d

A model for net-baryon rapidity distribution

In nuclear collisions, a sizable fraction of the available energy is carried away by baryons. As the baryon number is conserved, the net-baryon $B-\bar{B}$ retains information on the energy-momentum carried by the incoming nuclei. A simple and consistent model for net-baryon production in high energy proton-proton and nucleus-nucleus collisions is presented. The basic ingredients of the model are valence string formation based on standard PDFs with QCD evolution and string fragmentation via the Schwinger mechanism. The results of the model are presented and compared with data at different centre-of-mass energies and centralities, as well as with existing models. These results show that a good description of the main features of net-baryon data is possible in the framework of a simplistic model, with the advantage of making the fundamental production mechanisms manifest.Comment: 9 pages, 12 figures; in fig. 11 a) the vertical scale was correcte

Adjoint bi-continuous semigroups and semigroups on the space of measures

For a given bi-continuous semigroup T on a Banach space X we define its adjoint on an appropriate closed subspace X^o of the norm dual X'. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology (X^o,X). An application is the following: For K a Polish space we consider operator semigroups on the space C(K) of bounded, continuous functions (endowed with the compact-open topology) and on the space M(K) of bounded Baire measures (endowed with the weak*-topology). We show that bi-continuous semigroups on M(K) are precisely those that are adjoints of a bi-continuous semigroups on C(K). We also prove that the class of bi-continuous semigroups on C(K) with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict topology. In general, if K is not Polish space this is not the case

Ab initio atomistic thermodynamics and statistical mechanics of surface properties and functions

Previous and present "academic" research aiming at atomic scale understanding is mainly concerned with the study of individual molecular processes possibly underlying materials science applications. Appealing properties of an individual process are then frequently discussed in terms of their direct importance for the envisioned material function, or reciprocally, the function of materials is somehow believed to be understandable by essentially one prominent elementary process only. What is often overlooked in this approach is that in macroscopic systems of technological relevance typically a large number of distinct atomic scale processes take place. Which of them are decisive for observable system properties and functions is then not only determined by the detailed individual properties of each process alone, but in many, if not most cases also the interplay of all processes, i.e. how they act together, plays a crucial role. For a "predictive materials science modeling with microscopic understanding", a description that treats the statistical interplay of a large number of microscopically well-described elementary processes must therefore be applied. Modern electronic structure theory methods such as DFT have become a standard tool for the accurate description of individual molecular processes. Here, we discuss the present status of emerging methodologies which attempt to achieve a (hopefully seamless) match of DFT with concepts from statistical mechanics or thermodynamics, in order to also address the interplay of the various molecular processes. The new quality of, and the novel insights that can be gained by, such techniques is illustrated by how they allow the description of crystal surfaces in contact with realistic gas-phase environments.Comment: 24 pages including 17 figures, related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Time to cancer treatment and reproductive outcomes after fertility preservation among adolescent and young adult women with cancer

Background: Fertility preservation (FP) may be underused after cancer diagnosis because of uncertainty around delays to cancer treatment and subsequent reproductive success. Methods: Women aged 15 to 39 years diagnosed with cancer between 2004 and 2015 were identified from the North Carolina Central Cancer Registry. Use of assisted reproductive technology (ART) after cancer diagnosis between 2004 and 2018 (including FP) was assessed through linkage to the Society for Assisted Reproductive Technology. Linear regression was used to examine time to cancer treatment among women who did (n = 95) or did not (n = 469) use FP. Modified Poisson regression was used to estimate risk ratios (RRs) and 95% CIs for pregnancy and birth based on timing of ART initiation relative to cancer treatment (n = 18 initiated before treatment for FP vs n = 26 initiated after treatment without FP). Results: The median time to cancer treatment was 9 to 33 days longer among women who used FP compared with women who did not, matched on clinical factors. Women who initiated ART before cancer treatment may be more likely to have a live birth given pregnancy compared with women who initiated ART after cancer treatment (age-adjusted RR, 1.47; 95% CI, 0.98-2.23), though this may be affected by the more frequent use of gestational carriers in the former group (47% vs 20% of transfer cycles, respectively). Conclusions: FP delayed gonadotoxic cancer treatment by up to 4.5 weeks, a delay that would not be expected to alter prognosis for many women. Further study of the use of gestational carriers in cancer populations is warranted to better understand its effect on reproductive outcomes

WW Production Cross Section and W Branching Fractions in e+e- Collisions at 189 GeV

From a data sample of 183 pb^-1 recorded at a center-of-mass energy of roots = 189 GeV with the OPAL detector at LEP, 3068 W-pair candidate events are selected. Assuming Standard Model W boson decay branching fractions, the W-pair production cross section is measured to be sigmaWW = 16.30 +- 0.34(stat.) +- 0.18(syst.) pb. When combined with previous OPAL measurements, the W boson branching fraction to hadrons is determined to be 68.32 +- 0.61(stat.) +- 0.28(syst.) % assuming lepton universality. These results are consistent with Standard Model expectations.Comment: 22 pages, 5 figures, submitted to Phys. Lett.

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types