Attributing a probability to the shape of a probability density

We discuss properties of two methods for ascribing probabilities to the shape of a probability distribution. One is based on the idea of counting the number of modes of a bootstrap version of a standard kernel density estimator. We argue that the simplest form of that method suffers from the same difficulties that inhibit level accuracy of Silverman's bandwidth-based test for modality: the conditional distribution of the bootstrap form of a density estimator is not a good approximation to the actual distribution of the estimator. This difficulty is less pronounced if the density estimator is oversmoothed, but the problem of selecting the extent of oversmoothing is inherently difficult. It is shown that the optimal bandwidth, in the sense of producing optimally high sensitivity, depends on the widths of putative bumps in the unknown density and is exactly as difficult to determine as those bumps are to detect. We also develop a second approach to ascribing a probability to shape, using Muller and Sawitzki's notion of excess mass. In contrast to the context just discussed, it is shown that the bootstrap distribution of empirical excess mass is a relatively good approximation to its true distribution. This leads to empirical approximations to the likelihoods of different levels of ``modal sharpness,'' or ``delineation,'' of modes of a density. The technique is illustrated numerically.Comment: Published at http://dx.doi.org/10.1214/009053604000000607 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Systematic mutational analysis of the cation-independent mannose 6-phosphate/insulin-like growth factor II receptor cytoplasmic domain - An acidic cluster containing a key aspartate is important for function in lysosomal enzyme sorting

We have used systematic mutational analysis to identify signals in the 166-residue murine cation-independent mannose 6-phosphate/insulin-like growth factor II receptor cytoplasmic domain required for efficient sorting of lysosomal enzymes. Alanine cluster mutagenesis on all conserved residues apart from the endocytosis signal demonstrates that the major sorting determinant is a conserved casein kinase II site followed by a dileucine motif (157DDSDEDLL164). Small deletions or additions outside this region have severe to mild effects, indicating that context is important. Single residue mutagenesis indicates that cycles of serine phosphorylation/dephosphorylation are not obligatory for sorting. In addition, the two leucine residues and four of the five negatively charged residues can readily tolerate conservative substitutions. In contrast, aspartate 160 could not tolerate isoelectric or isosteric substitutions, implicating it as a critical component of the sorting signal

Drawing Big Graphs using Spectral Sparsification

Spectral sparsification is a general technique developed by Spielman et al. to reduce the number of edges in a graph while retaining its structural properties. We investigate the use of spectral sparsification to produce good visual representations of big graphs. We evaluate spectral sparsification approaches on real-world and synthetic graphs. We show that spectral sparsifiers are more effective than random edge sampling. Our results lead to guidelines for using spectral sparsification in big graph visualization.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Influence of aggregate size and fraction on shrinkage induced micro-cracking of mortar and concrete

In this paper, the influence of aggregate size and volume fraction on shrinkage induced micro-cracking and permeability of concrete and mortar was investigated. Nonlinear finite element analyses of model concrete and mortar specimens were performed. The aggregate diameter was varied between 2 and 16 mm. Furthermore, a range of volume fractions between 0.1 and 0.5 was studied. The nonlinear analyses were based on a 2D lattice approach in which aggregates were simplified as monosized cylindrical inclusions. The analysis results were interpreted by means of crack width and change of permeability. The results show that increasing aggregate diameter (at equal volume fraction) and decreasing volume fraction (at equal aggregate diameter) greatly increases permeability.Comment: 12th International Conference on Fracture (ICF 12

Supersymmetry: The Final Countdown

There is hope that the Large Hadron Collider (LHC) at CERN will tell us about the fate of supersymmetry at the TeVscale. Therefore we might try to identify our expectations for the discovery of SUSY, especially in the first years of operation of this machine. In this talk we shall concentrate on the simplest SUSY scheme: the MSSM with SUSY broken in a hidden sector mediated by interactions of gravitational strength (gravity-, modulus and mirage-mediation). Such a situation might be favoured in a large class of string inspired models. There is a good chance to identify such simple schemes by knowing the properties of the gaugino mass spectrum such as the gluino/neutralino mass ratios.Comment: Opening talk at the conference SUSY08, 9 pages, 4 figure

Goal-directed therapy in intraoperative fluid and hemodynamic management.

Intraoperative fluid management is pivotal to the outcome and success of surgery, especially in high-risk procedures. Empirical formula and invasive static monitoring have been traditionally used to guide intraoperative fluid management and assess volume status. With the awareness of the potential complications of invasive procedures and the poor reliability of these methods as indicators of volume status, we present a case scenario of a patient who underwent major abdominal surgery as an example to discuss how the use of minimally invasive dynamic monitoring may guide intraoperative fluid therapy