On two problems in graph Ramsey theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of H. A famous result of Chv\'atal, R\"{o}dl, Szemer\'edi and Trotter states that there exists a constant c(\Delta) such that r(H) \leq c(\Delta) n for every graph H with n vertices and maximum degree \Delta. The important open question is to determine the constant c(\Delta). The best results, both due to Graham, R\"{o}dl and Ruci\'nski, state that there are constants c and c' such that 2^{c' \Delta} \leq c(\Delta) \leq 2^{c \Delta \log^2 \Delta}. We improve this upper bound, showing that there is a constant c for which c(\Delta) \leq 2^{c \Delta \log \Delta}. The induced Ramsey number r_{ind}(H) of a graph H is the least positive integer N for which there exists a graph G on N vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of H. Erd\H{o}s conjectured the existence of a constant c such that, for any graph H on n vertices, r_{ind}(H) \leq 2^{c n}. We move a step closer to proving this conjecture, showing that r_{ind} (H) \leq 2^{c n \log n}. This improves upon an earlier result of Kohayakawa, Pr\"{o}mel and R\"{o}dl by a factor of \log n in the exponent.Comment: 18 page

Modelling of an imaging beamline at the ISIS pulsed neutron source

A combined neutron imaging and neutron diffraction facility, IMAT, is currently being built at the pulsed neutron spallation source ISIS in the U.K. A supermirror neutron guide is required to combine imaging and diffraction modes at the sample position in order to obtain suitable time of flight resolutions for energy selective imaging and diffraction experiments. IMAT will make use of a straight neutron guide and we consider here the optimization of the supermirror guide dimensions and characterisation of the resulting beam characteristics, including the homogeneity of the flux distribution in space and energy and the average and peak neutron fluxes. These investigations take into account some main design criteria: to maximise the neutron flux, to minimise geometrical artefacts in the open beam image at the sample position and to obtain a good energy resolution whilst retaining a large neutron bandwidth. All of these are desirable beam characteristics for the proposed imaging and diffraction analysis modes of IMAT

The Self-Administered Witness Interview Tool (SAW-IT): Enhancing witness recall of workplace incidents

Given the often crucial role of witness evidence in Occupational Health and Safety investigation, statements should be obtained as soon as possible after an incident using best practice methods. The present research systematically tested the efficacy of a novel Self-Administered Witness Interview Tool (SAW-IT); an adapted version of the Self-Administered Interview (SAI©) designed to elicit comprehensive information from witnesses to industrial events. The present study also examined whether completing the SAW-IT mitigated the effect of schematic processing on witness recall. Results indicate that the SAW-IT elicited significantly more correct details, as well as more precise information than a traditional incident report form. Neither the traditional report from, nor the SAW-IT mitigated against biasing effects of contextual information about a worker’s safety history, confirming that witnesses should be shielded from extraneous post-event information prior to reporting. Importantly, these results demonstrate that the SAW-IT can enhance the quality of witness reports

Evaluational adjectives

This paper demarcates a theoretically interesting class of "evaluational adjectives." This class includes predicates expressing various kinds of normative and epistemic evaluation, such as predicates of personal taste, aesthetic adjectives, moral adjectives, and epistemic adjectives, among others. Evaluational adjectives are distinguished, empirically, in exhibiting phenomena such as discourse-oriented use, felicitous embedding under the attitude verb `find', and sorites-susceptibility in the comparative form. A unified degree-based semantics is developed: What distinguishes evaluational adjectives, semantically, is that they denote context-dependent measure functions ("evaluational perspectives")—context-dependent mappings to degrees of taste, beauty, probability, etc., depending on the adjective. This perspective-sensitivity characterizing the class of evaluational adjectives cannot be assimilated to vagueness, sensitivity to an experiencer argument, or multidimensionality; and it cannot be demarcated in terms of pretheoretic notions of subjectivity, common in the literature. I propose that certain diagnostics for "subjective" expressions be analyzed instead in terms of a precisely specified kind of discourse-oriented use of context-sensitive language. I close by applying the account to `find x PRED' ascriptions

The K-theoretic Farrell-Jones Conjecture for hyperbolic groups

We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.Comment: 33 pages; final version; to appear in Invent. Mat

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete