A note on the convergence of parametrised non-resonant invariant manifolds

Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error estimates of analytic parametrisations of non-resonant local invariant manifolds of a saddle of an analytic vector field, from such a truncated series. This enables us to obtain local enclosures, as well as existence results, for the invariant manifolds

Ultrametric Logarithm Laws, II

We prove positive characteristic versions of the logarithm laws of Sullivan and Kleinbock-Margulis and obtain related results in Metric Diophantine Approximation.Comment: submitted to Montasefte Fur Mathemati

Combined kinase inhibitors of MEK1/2 and either PI3K or PDGFR are efficacious in intracranial triple-negative breast cancer

Background: Triple-negative breast cancer (TNBC), lacking expression of hormone and human epidermal growth factor receptor 2 receptors, is an aggressive subtype that frequently metastasizes to the brain and has no FDA-approved systemic therapies. Previous literature demonstrates mitogen-Activated protein kinase kinase (MEK) pathway activation in TNBC brain metastases. Thus, we aimed to discover rational combinatorial therapies with MEK inhibition, hypothesizing that co-inhibition using clinically available brain-penetrant inhibitors would improve survival in preclinical models of TNBC brain metastases. Methods: Using human-derived TNBC cell lines, synthetic lethal small interfering RNA kinase screens were evaluated with brain-penetrant inhibitors against MEK1/2 (selumetinib, AZD6244) or phosphatidylinositol-3 kinase (PI3K; buparlisib, BKM120). Mice bearing intracranial TNBC tumors (SUM149, MDA-MB-231Br, MDA-MB-468, or MDA-MB-436) were treated with MEK, PI3K, or platelet derived growth factor receptor (PDGFR; pazopanib) inhibitors alone or in combination. Tumors were analyzed by western blot and multiplexed kinase inhibitor beads/mass spectrometry to assess treatment effects. Results: Screens identified MEK+PI3K and MEK+PDGFR inhibitors as tractable, rational combinations. Dual treatment of selumetinib with buparlisib or pazopanib was synergistic in TNBC cells in vitro. Both combinations improved survival in intracranial SUM149 and MDA-MB-231Br, but not MDA-MB-468 or MDA-MB-436. Treatments decreased mitogen-Activated protein kinase (MAPK) and PI3K (Akt) signaling in sensitive (SUM149 and 231Br) but not resistant models (MDA-MB-468). Exploratory analysis of kinome reprogramming in SUM149 intracranial tumors after MEK PI3K inhibition demonstrates extensive kinome changes with treatment, especially in MAPK pathway members. Conclusions: Results demonstrate that rational combinations of the clinically available inhibitors selumetinib with buparlisib or pazopanib may prove to be promising therapeutic strategies for the treatment of some TNBC brain metastases. Additionally, effective combination treatments cause widespread alterations in kinase pathways, including targetable potential resistance drivers

Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts

We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for "observed" particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg to gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard MS-bar coupling, alpha_s. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD beta function in the FDH and dimensional reduction schemes.Comment: 44 pages, minor corrections and clarifications include

Radium-223 in women with hormone receptor-positive bone-metastatic breast cancer receiving endocrine therapy: pooled analysis of two international, phase 2, randomized, double-blind, placebo-controlled trials

Background Most women with advanced breast cancer have skeletal metastases. Radium-223 is an alpha-emitting radionuclide that selectively targets areas of bone metastases. Methods Two double-blind, placebo-controlled studies of radium-223 were conducted in women with hormone receptor-positive (HR+), bone-predominant metastatic breast cancer. All patients received endocrine therapy (ET), as a single agent of the investigator’s choice (Study A) or exemestane + everolimus (Study B). Patients were randomized to receive radium-223 (55 kBq/kg) or placebo intravenously every 4 weeks for six doses. Accrual was halted following unblinded interim analyses per protocol amendments, and both studies were terminated. We report pooled analyses of symptomatic skeletal event-free survival (SSE-FS; primary endpoint), radiologic progression-free survival (rPFS) and overall survival (OS; secondary), and time to bone alkaline phosphatase (ALP) progression (exploratory). Results In total, 382 patients were enrolled, and 196 SSE-FS events (70% planned total) were recorded. Hazard ratios (95% confidence intervals) and nominal p values for radium-223 + ET versus placebo + ET were: SSE-FS 0.809 (0.610–1.072), p = 0.1389; rPFS 0.956 (0.759–1.205), p = 0.7039; OS 0.889 (0.660–1.199), p = 0.4410; and time to bone ALP progression 0.593 (0.379–0.926), p = 0.0195. Radium-223- or placebo-related treatment-emergent adverse events were reported in 50.3% versus 35.1% of patients (grade 3/4: 25.7% vs. 8.5%), with fractures/bone-associated events in 23.5% versus 23.9%. Conclusions In patients with HR+ bone-metastatic breast cancer, numeric differences favoring radium-223 + ET over placebo + ET for the primary SSE-FS endpoint were suggestive of efficacy, in line with the primary outcome measure used in the underlying phase 2 studies. No similar evidence of efficacy was observed for secondary progression or survival endpoints. Adverse events were more frequent with radium-223 + ET versus placebo + ET, but the safety profile of the combination was consistent with the safety profiles of the component drugs

The ultra-violet question in maximally supersymmetric field theories

We discuss various approaches to the problem of determining which supersymmetric invariants are permitted as counterterms in maximally supersymmetric super Yang--Mills and supergravity theories in various dimensions. We review the superspace non-renormalisation theorems based on conventional, light-cone, harmonic and certain non-Lorentz covariant superspaces, and we write down explicitly the relevant invariants. While the first two types of superspace admit the possibility of one-half BPS counterterms, of the form $F^4$ and $R^4$ respectively, the last two do not. This suggests that UV divergences begin with one-quarter BPS counterterms, i.e. $d^2 F^4$ and $d^4 R^4$, and this is supported by an entirely different approach based on algebraic renormalisation. The algebraic formalism is discussed for non-renormalisable theories and it is shown how the allowable supersymmetric counterterms can be determined via cohomological methods. These results are in agreement with all the explicit computations that have been carried out to date. In particular, they suggest that maximal supergravity is likely to diverge at four loops in D=5 and at five loops in D=4, unless other infinity suppression mechanisms not involving supersymmetry or gauge invariance are at work.Comment: 56 pages, 1 figure, uses youngtab.sty. Contribution to the proceedings of the W.E. Heraeus Workhop "Quantum Gravity: Challenges and Perspectives", Bad Honnef, 14-16 April 2008. References and clarifying comments adde