On Osgood theorem in Banach spaces

Let $X$ be a real Banach space, $\omega:[0,+\infty)\to\R$ be an increasing continuous function such that $\omega(0)=0$ and $\omega(t+s)\leq\omega(t)+\omega(s)$ for all $t,s\in[0,+\infty)$. By the Osgood theorem, if $\int_{0}^1\frac{dt}{\omega(t)}=\infty$, then for any $(t_0,x_0)\in R\times X$ and any continuous map $f: R\times X\to X$ and such that $\|f(t,x)-f(t,y)\|\leq\omega(\|x-y\|)$ for all $t\in R$, $x,y\in X$, the Cauchy problem $\dot x(t)=f(t,x(t))$, $(t_0)=x_0$ has a unique solution in a neighborhood of $t_0$ . We prove that if $X$ has a complemented subspace with an unconditional Schauder basis and $\int_{0}^1\frac{dt}{\omega(t)}

Counterexample to Peano's theorem in infinite-dimensional F '-spaces

Let $E$ be a nonnormable Frechet space, and let $E'$ be the space of all continuous linear functionals on $E$ in the strong topology. A continuous mapping $f : E' \to E'$ such that for any $t_0\in R$ and $x_0\in E'$, the Cauchy problem $\dot x= f(x)$, x(t_0) = x_0$ has no solutions is constructed.

Lymphocytic gastritis-like T cell lymphoma: molecular evidence of an unusual recurrence

This report describes a patient with a gastric biopsy specimen showing histomorphological and immunohistochemical appearances indistinguishable from those usually present in lymphocytic gastritis, a rare condition of unknown aetiology with a distinctive phenotype. The patient had a history of a biopsy confirmed T cell non-Hodgkin lymphoma at two anatomical sites ( bladder and stomach), which was subsequently treated. Molecular analysis of the T cell receptor (TCR) gamma chain gene rearrangements showed a distinct monoclonal T cell population in the bladder and gastric biopsies. The same analysis in the lymphocytic gastritis-like biopsy sample showed a monoclonal population with identical base pair size to that identified in the other specimens. This report highlights the importance of TCR gene rearrangement analysis in the diagnosis of unusual gastric inflammation, and the use of capillary electrophoresis based polymerase chain reaction in the follow up of lymphoproliferative disorders.

Effect of radiotherapy after breast-conserving surgery on 10-year recurrence and 15-year breast cancer death: meta-analysis of individual patient data for 10,801 women in 17 randomised trials

Background: After breast-conserving surgery, radiotherapy reduces recurrence and breast cancer death, but it may do so more for some groups of women than for others. We describe the absolute magnitude of these reductions according to various prognostic and other patient characteristics, and relate the absolute reduction in 15-year risk of breast cancer death to the absolute reduction in 10-year recurrence risk.
Methods: We undertook a meta-analysis of individual patient data for 10?801 women in 17 randomised trials of radiotherapy versus no radiotherapy after breast-conserving surgery, 8337 of whom had pathologically confirmed node-negative (pN0) or node-positive (pN+) disease.
Findings: Overall, radiotherapy reduced the 10-year risk of any (ie, locoregional or distant) first recurrence from 35·0% to 19·3% (absolute reduction 15·7%, 95% CI 13·7–17·7, 2p<0·00001) and reduced the 15-year risk of breast cancer death from 25·2% to 21·4% (absolute reduction 3·8%, 1·6–6·0, 2p=0·00005). In women with pN0 disease (n=7287), radiotherapy reduced these risks from 31·0% to 15·6% (absolute recurrence reduction 15·4%, 13·2–17·6, 2p<0·00001) and from 20·5% to 17·2% (absolute mortality reduction 3·3%, 0·8–5·8, 2p=0·005), respectively. In these women with pN0 disease, the absolute recurrence reduction varied according to age, grade, oestrogen-receptor status, tamoxifen use, and extent of surgery, and these characteristics were used to predict large (=20%), intermediate (10–19%), or lower (<10%) absolute reductions in the 10-year recurrence risk. Absolute reductions in 15-year risk of breast cancer death in these three prediction categories were 7·8% (95% CI 3·1–12·5), 1·1% (–2·0 to 4·2), and 0·1% (–7·5 to 7·7) respectively (trend in absolute mortality reduction 2p=0·03). In the few women with pN+ disease (n=1050), radiotherapy reduced the 10-year recurrence risk from 63·7% to 42·5% (absolute reduction 21·2%, 95% CI 14·5–27·9, 2p<0·00001) and the 15-year risk of breast cancer death from 51·3% to 42·8% (absolute reduction 8·5%, 1·8–15·2, 2p=0·01). Overall, about one breast cancer death was avoided by year 15 for every four recurrences avoided by year 10, and the mortality reduction did not differ significantly from this overall relationship in any of the three prediction categories for pN0 disease or for pN+ disease.
Interpretation: After breast-conserving surgery, radiotherapy to the conserved breast halves the rate at which the disease recurs and reduces the breast cancer death rate by about a sixth. These proportional benefits vary little between different groups of women. By contrast, the absolute benefits from radiotherapy vary substantially according to the characteristics of the patient and they can be predicted at the time when treatment decisions need to be made.
Funding: Cancer Research UK, British Heart Foundation, and UK Medical Research Council.

Recurrence of Urothelial Carcinoma of the Bladder: A Role for Insulin-Like Growth Factor-II Loss of Imprinting and Cytoplasmic E-Cadherin Immunolocalization

Purpose:This study documents the frequency of insulin-like growth factor-II (IGF-II) loss of imprinting (LOI) in a series of 87 bladder tissues. E-cadherin (CDH1) immunolocalization was also investigated due to the known redistribution of this adherence protein to the cytoplasm following exogenous exposure to IGF-II.
Experimental Design: Informative IGF-II cases were identified following DNA-PCR amplification and subsequent sequencing of the transcribable ApaI RFLP in exon 9 of IGF-II. Similar approaches using primer-specific cDNA templates identified the imprinting status of IGF-II in these informative cases. CDH1cellular localization was assessed on a tissue microarray platform of 114 urothelial carcinoma of the bladder (UCB) cases (70 pTanoninvasive and 44 pT1laminapropria invasive) using the commercially available Novocastra antibody.
Results: IGF-IILOI was evident in 7 of17 (41%) UCB tumors and 4 of11 (36%) tumor-associated normal urothelial samples.Two of four pT1grade 3 tumors, the subject of much debate concerning their suitability for radical cystectomy, showed LOI at the IGF-II locus. In those tumors showing IGF-II LOI, 4 of 7 (57%) displayed concomitant CDH1cytoplasmic staining. In contrast, only 3 of 10 (30%) IGF-IImaintenance ofimprinting tumorshad concomitant CDH1cytoplasmiclocalization. UCB cell lines displaying cytoplasmic CDH1immunolocalization expressed significantly higher levels of IGF-II (CAL29, HT1376, and RT112) compared with RT4, a cell line displaying crisp membranous CDH1staining. Finally, cytoplasmic CDH1staining was an independent predictor of a shorter time to recurrence independent of tumor grade and stage.
Conclusions: We suggest that CDH1 cytoplasmic immunolocalization as a result of increased IGF-II levels identifies those nonmuscle invasive presentations most likely to recur and therefore might benefit from more radical nonconserving bladder surgery

Serial chimerism analyses indicate that mixed haemopoietic chimerism influences the probability of graft rejection and disease recurrence following allogeneic stem cell transplantation (SCT) for severe aplastic anaemia (SAA): indication for routine assessment of chimerism post SCT for SAA

Ninety-one patients were studied serially for chimeric status following allogeneic stem cell transplantation (SCT) for severe aplastic anaemia (SAA) or Fanconi Anaemia (FA). Short tandem repeat polymerase chain reaction (STR-PCR) was used to stratify patients into five groups: (A) complete donor chimeras (n = 39), (B) transient mixed chimeras (n = 15) (C) stable mixed chimeras (n = 18), (D) progressive mixed chimeras (n = 14) (E) recipient chimeras with early graft rejection (n = 5). As serial sampling was not possible in Group E, serial chimerism results for 86 patients were available for analysis. The following factors were analysed for association with chimeric status: age, sex match, donor type, aetiology of aplasia, source of stem cells, number of cells engrafted, conditioning regimen, graft-versus-host disease (GvHD) prophylaxis, occurrence of acute and chronic GvHD and survival. Progressive mixed chimeras (PMCs) were at high risk of late graft rejection (n = 10, P <0.0001). Seven of these patients lost their graft during withdrawal of immunosuppressive therapy. STR-PCR indicated an inverse correlation between detection of recipient cells post-SCT and occurrence of acute GvHD (P = 0.008). PMC was a bad prognostic indicator of survival (P = 0.003). Monitoring of chimeric status during cyclosporin withdrawal may facilitate therapeutic intervention to prevent late graft rejection in patients transplanted for SAA.