An Algorithm for Group Formation and Maximal Independent Set in an Amorphous Computer

Amorphous computing is the study of programming ultra-scale computing environments of smart sensors and actuators cite{white-paper}. The individual elements are identical, asynchronous, randomly placed, embedded and communicate locally via wireless broadcast. Aggregating the processors into groups is a useful paradigm for programming an amorphous computer because groups can be used for specialization, increased robustness, and efficient resource allocation. This paper presents a new algorithm, called the clubs algorithm, for efficiently aggregating processors into groups in an amorphous computer, in time proportional to the local density of processors. The clubs algorithm is well-suited to the unique characteristics of an amorphous computer. In addition, the algorithm derives two properties from the physical embedding of the amorphous computer: an upper bound on the number of groups formed and a constant upper bound on the density of groups. The clubs algorithm can also be extended to find the maximal independent set (MIS) and $Delta + 1$ vertex coloring in an amorphous computer in $O(log N)$ rounds, where $N$ is the total number of elements and $Delta$ is the maximum degree.

Maximal L p -regularity for the Laplacian on Lipschitz domains

I.Wood: Maximal Lp-regularity for the Laplacian on Lipschitz domains, Math. Z., 255, 4 (2007), 855-875.

A 3-min all-out test to determine peak oxygen uptake and the maximal steady state

Burnley, M., Doust, J., Vanhatalo, A., A 3-min all-out test to determine peak oxygen uptake and the maximal steady state, Medicine & Science in Sports & Exercise. 38(11):1995-2003, November 2006. RAE2008

Maximal strength and cortisol responses to psyching-up during the squat exercise

McGuigan, M. R., Ghiagiarelli, J., Tod, D. (2005). Maximal strength and cortisol responses to psyching-up during the squat exercise. Journal of Sports Sciences, 23 (7), 687-692. RAE2008

Problems of maximal mean resistance on the plane

Plakhov, A.Y.; Gouveia, P.D.F., (2007) 'Problems of maximal mean resistance on the plane', Nonlinearity 20(9) pp.2271-2287 RAE2008

Entropy Loss is Maximal for Uniform Inputs

A secure sketch (defined by Dodis et al.) is an algorithm that on an input w produces an output s such that w can be reconstructed given its noisy version w' and s. Security is defined in terms of two parameters m and m˜ : if w comes from a distribution of entropy m, then a secure sketch guarantees that the distribution of w conditioned on s has entropy m˜ , where λ = m−m˜ is called the entropy loss. In this note we show that the entropy loss of any secure sketch (or, more generally, any randomized algorithm) on any distribution is no more than it is on the uniform distribution.

The inverse limit of GIT quotients of Grassmannians by the maximal torus

There are finitely many GIT quotients of

Estimating the magnitude of trastuzumab effects within patient subgroups in the HERA trial.

BACKGROUND: Trastuzumab (Herceptin(R)) improves disease-free survival (DFS) and overall survival for patients with human epidermal growth factor receptor 2 (HER2)-positive early breast cancer. We aimed to assess the magnitude of its clinical benefit for subpopulations defined by nodal and steroid hormone receptor status using data from the Herceptin Adjuvant (HERA) study. PATIENTS AND METHODS: HERA is an international multicenter randomized trial comparing 1 or 2 years of trastuzumab treatment with observation after standard chemotherapy in women with HER2-positive breast cancer. In total, 1703 women randomized to 1-year trastuzumab and 1698 women randomized to observation were included in these analyses. Median follow-up was 23.5 months. The primary endpoint was DFS. RESULTS: The overall hazard ratio (HR) for trastuzumab versus observation was 0.64 [95% confidence interval (CI) 0.54-0.76; P < 0.0001], ranging from 0.46 to 0.82 for subgroups. Estimated improvement in 3-year DFS in subgroups ranged from +11.3% to +0.6%. Patients with the best prognosis (those with node-negative disease and tumors 1.1-2.0 cm) had benefit similar to the overall cohort (HR 0.53, 95% CI 0.26-1.07; 3-year DFS improvement +4.6%, 95% CI -4.0% to 13.2%). CONCLUSIONS: Adjuvant trastuzumab therapy reduces the risk of relapse similarly across subgroups defined by nodal status and steroid hormone receptor status, even those at relatively low risk for relapse.

Finite groups and geometries: a view on the present state and on the future

The model: groups of Lie-Chevalley type and buildingsThis paper is not the presentation of a completed theory but rather a report on a search progressing as in the natural sciences in order to better understand the relationship between groups and incidence geometry, in some future sought-after theory Τ. The search is based on assumptions and on wishes some of which are time-dependent, variations being forced, in particular, by the search itself.A major historical reference for this subject is, needless to say, Klein's Erlangen Programme. Klein's views were raised to a powerful theory thanks to the geometric interpretation of the simple Lie groups due to Tits (see for instance), particularly his theory of buildings and of groups with a BN-pair (or Tits systems). Let us briefly recall some striking features of this.Let G be a group of Lie-Chevalley type of rank r, denned over GF(q), q = pn, p prime. Let Xr denote the Dynkin diagram of G. To these data corresponds a unique thick building B(G) of rank r over the Coxeter diagram Xr (assuming we forget arrows provided by the Dynkin diagram). It turns out that B(G) can be constructed in a uniform way for all G, from a fixed p-Sylow subgroup U of G, its normalizer NG(U) and the r maximal subgroups of G containing NG(U).

Search for maximal flavor violating scalars in same-charge lepton pairs in pp̄ collisions at s=1.96TeV

Models of maximal flavor violation (MxFV) in elementary particle physics may contain at least one new scalar SU(2) doublet field ΦFV=(η0,η+) that couples the first and third generation quarks (q1, q3) via a Lagrangian term LFV=ξ13ΦFVq1q3. These models have a distinctive signature of same-charge top-quark pairs and evade flavor-changing limits from meson mixing measurements. Data corresponding to 2fb-1 collected by the Collider Dectector at Fermilab II detector in pp̄ collisions at s=1.96TeV are analyzed for evidence of the MxFV signature. For a neutral scalar η0 with mη0=200GeV/c2 and coupling ξ13=1, ∼11 signal events are expected over a background of 2.1±1.8 events. Three events are observed in the data, consistent with background expectations, and limits are set on the coupling ξ13 for mη0=180-300GeV/c2. © 2009 The American Physical Society.