Knaster's problem for (Z2)k(Z_2)^k-symmetric subsets of the sphere S2k−1S^{2^k-1}

We prove a Knaster-type result for orbits of the group $(Z_2)^k$ in $S^{2^k-1}$, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$ by $(Z_2)^{k+1}$-symmetric convex fans

The Mathematical Universe

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at http://space.mit.edu/home/tegmark/toe.htm

Care after pancreatic resection according to an algorithm for early detection and minimally invasive management of pancreatic fistula versus current practice (PORSCH-trial): design and rationale of a nationwide stepped-wedge cluster-randomized trial

BACKGROUND: Pancreatic resection is a major abdominal operation with 50% risk of postoperative complications. A common complication is pancreatic fistula, which may have severe clinical consequences such as postoperative bleeding, organ failure and death. The objective of this study is to investigate whether implementation of an algorithm for early detection and minimally invasive management of pancreatic fistula may improve outcomes after pancreatic resection. METHODS: This is a nationwide stepped-wedge, cluster-randomized, superiority trial, designed in adherence to the Consolidated Standards of Reporting Trials (CONSORT) guidelines. During a period of 22 months, all Dutch centers performing pancreatic surgery will cross over in a randomized order from current practice to best practice according to the algorithm. This evidence-based and consensus-based algorithm will provide da

Elliptic flow of identified hadrons in Pb-Pb collisions at 1asNN = 2.76 TeV

The elliptic flow coefficient (v2) of identified particles in Pb-Pb collisions at 1asNN = 2.76 TeV was measured with the ALICE detector at the Large Hadron Collider (LHC). The results were obtained with the Scalar Product method, a two-particle corre- lation technique, using a pseudo-rapidity gap of | 06\u3b7| > 0.9 between the identified hadron under study and the reference particles. The v2 is reported for \u3c0\ub1, K\ub1, K0S, p+p, \u3c6, \u39b+\u39b, \u39e 12+\u39e+ and \u3a9 12+\u3a9+ in several collision centralities. In the low transverse momentum (pT) region, pT 3 GeV/c

"Axillary recurrences after sentinel lymph node biopsy: A multicentre analysis and follow-up of sentinel lymph node negative breast cancer patients"

Item does not contain fulltextINTRODUCTION: The objective of this study was to conduct a multicentre data analysis to identify prognostic factors for developing an axillary recurrence (AR) after negative sentinel lymph node biopsy (SLNB) in a large cohort of breast cancer patients with long follow-up. PATIENTS AND METHODS: The prospective databases from different hospitals of clinically node negative breast cancer patients operated on between, 2000 and 2002 were analyzed. SLNB was performed and pathological analysis done by local pathologists according to national guidelines. Adjuvant treatment was given according to contemporary guidelines. Multivariate analysis was performed using all available variables, a p-value of <0,05 was considered to be significant. RESULTS: A total of 929 patients who did not undergo axillary lymph node dissection were identified. After a median follow up of 77 (range 1-106) months, fifteen patients developed an isolated AR (AR rate 1,6%). Multivariate analysis showed that young age (p = 0.007) and the absence of radiotherapy (p = 0.010) significantly increased the risk of developing an AR. Distant metastasis free survival (DMFS) was significantly worse for patients with an AR compared to all other breast cancer patients (p < 0,0001). CONCLUSION: Even after long-term follow up, the risk of developing an AR after a negative SLN in breast cancer is low. Young age and absence of radiation therapy are highly significant factors for developing an axillary recurrence. DMFS is worse for AR patients compared to patients initially diagnosed with N0 or N1 disease