Externally definable sets and dependent pairs

We prove that externally definable sets in first order NIP theories have honest definitions, giving a new proof of Shelah's expansion theorem. Also we discuss a weak notion of stable embeddedness true in this context. Those results are then used to prove a general theorem on dependent pairs, which in particular answers a question of Baldwin and Benedikt on naming an indiscernible sequence.Comment: 17 pages, some typos and mistakes corrected, overall presentation improved, more details for the examples are give

External definability and groups in NIP theories

We prove that many properties and invariants of definable groups in NIP theories, such as definable amenability, G/G^{00}, etc., are preserved when passing to the theory of the Shelah expansion by externally definable sets, M^{ext}, of a model M. In the light of these results we continue the study of the "definable topological dynamics" of groups in NIP theories. In particular we prove the Ellis group conjecture relating the Ellis group to G/G^{00} in some new cases, including definably amenable groups in o-minimal structures.Comment: 28 pages. Introduction was expanded and some minor mistakes were corrected. Journal of the London Mathematical Society, accepte

A notion of geometric complexity and its application to topological rigidity

We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is homotopy equivalent to M, then M x R^n is homeomorphic to N x R^n, for n large enough. This statement is known as the stable Borel conjecture. On the other hand, we show that the class of FDC groups includes all countable subgroups of GL(n,K), for any field K, all elementary amenable groups, and is closed under taking subgroups, extensions, free amalgamated products, HNN extensions, and direct unions.Comment: 58 pages, 5 figure

ASTRA 3.0: Test Case Report

In the context of activities related to the application of system analysis to safety and security of critical installations a new logical and probabilistic fault tree analysis procedure was developed and implemented in the software package ASTRA, version 3.0. This report contains the results of the logical and probabilistic analysis for a limited, but significant, subset of test cases considered during the test campaign performed at the JRC. Most of the described test cases come from the open literature, for which results are available to the reader. For more complex test cases ASTRA 3.0 was compared with other available tools, such as ASTRA 2.0 and XS-MKA, a Markovian analysis package. The experience gained with the testing activity also allowed the identification of a set of recommendations for future improvements.JRC.DG.G.7-Traceability and vulnerability assessmen

Take one

This item contains two issues of the Take One newsletter: September 3, and 17, 1981Take One was published every two weeks and focused on short news items and announcements "for the people of University Hospital.

ASTRA 3.0: Logical and Probabilistic Analysis Methods

This report contains the description of the main methods, implemented in ASTRA 3.0, to analyse coherent and non-coherent fault trees. ASTRA 3.0 is fully based on the Binary Decision Diagrams (BDD) approach. In case of non-coherent fault trees ASTRA 3.0 dynamically assigns to each node of the graph a label that identifies the type of the associated variable in order to drive the application of the most suitable analysis algorithms. The resulting BDD is referred to as Labelled BDD (LBDD). Exact values of the unavailability, expected number of failure and repair are calculated; the unreliability upper bound is automatically determined under given conditions. Five different importance measures of basic events are also provided. From the LBDD a ZBDD embedding all the MCS is obtained from which a subset of Significant Minimal Cut Sets (SMCS) is determined through the application of the cut-off techniques. With very complex trees it may happen that the working memory is not sufficient to store the large LBDD structure. In these cases ASTRA 3.0 completes the analysis by constructing a Reduced ZBDD embedding the SMCS - using cut-off techniques - thus by-passing the construction of the LBDD. The report also contains few tutorials on the usefulness of non-coherent fault trees, on the BDD approach, and on the determination of failure and repair frequencies.JRC.DG.G.7-Traceability and vulnerability assessmen

Hubungan antara Ukuran-ukuran Tubuh dengan Bobot Badan pada Kambing Kacang di Kabupaten Grobogan, Jawa Tengah

Morphological performance can be used to characterize and to select livestock. Body weight can be estimated by body measurements. The objective of this study was to analyze the correlation between body measurements and body weight of Kacang goats in Grobogan Regency. Fourty one Kacang goats were used as materials. Kacang goats were grouped into different group of sex. Variable observed were body weight, face length, ear length, chest circumference, chest width, chest depth, body length, height at wither, height at hip, hip width, front leg length, hind leg length and tail length. Data observed were analyzed by using Statistical Analysis System (SAS ver 6.12). Results showed regression equation models of body measurements can be used to estimate the body weight of Kacang goat with coeffisient of determination of 81.4%-97.8%. Variable of body measurements used to estimate body weight of Kacang goat were face length, ear length, chest circumference, chest width, body length, height at wither and hind leg length

Components' IMportance Measures for Initiating and Enabling events in Fault Tree Analysis

This report deals with the problem of determining the exact values of the importance indexes of basic events in case of both unavailability and frequency analysis of coherent and non-coherent fault trees. In particular a new method is described for determining the importance of enabling events in case of frequency analysis. Insights are given into the importance analysis implemented in the new software ASTRA 3.0 based on the Binary Decision Diagram approach with Labelled variables (LBDD). The analysis methods are also described with reference to modularised fault trees. Simple numerical examples are provided to clarify how the methods work. Proofs of the implemented equations are provided in Appendixes.JRC.DG.G.7-Traceability and vulnerability assessmen