Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs

General upper tail estimates are given for counting edges in a random induced subhypergraph of a fixed hypergraph H, with an easy proof by estimating the moments. As an application we consider the numbers of arithmetic progressions and Schur triples in random subsets of integers. In the second part of the paper we return to the subgraph counts in random graphs and provide upper tail estimates in the rooted case.Comment: 15 page

Proximal humerus reconstruction after tumour resection: biological versus endoprosthetic reconstruction

The purpose of this study was to compare the outcome, complications and survival of the three most commonly used surgical reconstructions of the proximal humerus after transarticular tumour resection. Between 1985 and 2005, 38 consecutive proximal humeral reconstructions using allograft-prosthesis composite (n = 10), osteoarticular allograft (n = 13) or a modular tumour prosthesis (n = 14) were performed in our clinic. The mean follow-up was ten years (1–25). Of these, 27 were disease free at latest follow-up (mean 16.8 years) and ten had died of disease. The endoprosthetic group presented the smallest complication rate of 21% (n = 1), compared to 40% (n = 4) in the allograft-prosthesis composite and 62% (n = 8) in the osteoarticular allograft group. Only one revision was performed in the endoprosthetic group, in a case of shoulder instability. Infection after revision (n = 3), pseudoarthrosis (n = 2), fracture of the allograft (n = 3) and shoulder instability (n = 4) were the major complications of allograft use in general. Kaplan-Meier analysis showed a significantly better implant survival for the endoprosthetic group (log-rank p = 0.002). At final follow-up the Musculoskeletal Tumour Society scores were an average of 72% for the allograft-prosthetic composite (n = 7, median follow-up 17 years), 76% for the osteoarticular allograft (n = 3, 19 years) and 77% for the endoprosthetic reconstruction (n = 10, 5 years) groups. An endoprosthetic reconstruction after transarticular proximal humeral resection resulted in the lowest complication rate, highest implant survival and comparable functional results when compared to allograft-prosthesis composite and osteoarticular allograft use. We believe that the surgical approach that best preserves the abductor mechanism and provides sufficient surgical exposure for tumour resection contributed to better functional results and glenohumeral stability in the endoprosthetic group

Dynamical mean-field approach to materials with strong electronic correlations

We review recent results on the properties of materials with correlated electrons obtained within the LDA+DMFT approach, a combination of a conventional band structure approach based on the local density approximation (LDA) and the dynamical mean-field theory (DMFT). The application to four outstanding problems in this field is discussed: (i) we compute the full valence band structure of the charge-transfer insulator NiO by explicitly including the p-d hybridization, (ii) we explain the origin for the simultaneously occuring metal-insulator transition and collapse of the magnetic moment in MnO and Fe2O3, (iii) we describe a novel GGA+DMFT scheme in terms of plane-wave pseudopotentials which allows us to compute the orbital order and cooperative Jahn-Teller distortion in KCuF3 and LaMnO3, and (iv) we provide a general explanation for the appearance of kinks in the effective dispersion of correlated electrons in systems with a pronounced three-peak spectral function without having to resort to the coupling of electrons to bosonic excitations. These results provide a considerable progress in the fully microscopic investigations of correlated electron materials.Comment: 24 pages, 14 figures, final version, submitted to Eur. Phys. J. for publication in the Special Topics volume "Cooperative Phenomena in Solids: Metal-Insulator Transitions and Ordering of Microscopic Degrees of Freedom

"I am NN": A Reconstruction of Anscombe's "The First Person"

This paper develops a way of understanding G.E.M. Anscombe’s essay “The First Person”, at the heart of which are the following two ideas: first, that the point of her essay is to show that it is not possible for anyone to understand what they express with “I” as an Art des Gegebenseins—a way of thinking of an object that constitutes identifying knowledge of which object is being thought of; and second, that the argument through which her essay seeks to show this is itself first personal in character. Understanding Anscombe’s essay in this light has the merit of showing much of what it says to be correct. But it sets us the task of saying what it is that we understand ourselves to express with “I” if not an Art des Gegebenseins, and in particular what it is that we understand ourselves to express with sentences with “I” as subject that might seem to express identity-judgments, such as “I am NN”, and “I am this body”