Bounds for the probability generating functional of a Gibbs point process

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics such as the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity, and higher-order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.

Development and validation of a quantitative method to assess pedicle screw loosening in posterior spine instrumentation on plain radiographs.

PURPOSE Currently, the diagnosis of pedicle screw (PS) loosening is based on a subjectively assessed halo sign, that is, a radiolucent line around the implant wider than 1 mm in plain radiographs. We aimed at development and validation of a quantitative method to diagnose PS loosening on radiographs. METHODS Between 11/2004 and 1/2010 36 consecutive patients treated with thoraco-lumbar spine fusion with PS instrumentation without PS loosening were compared with 37 other patients who developed a clinically manifesting PS loosening. Three different angles were measured and compared regarding their capability to discriminate the loosened PS over the postoperative course. The inter-observer invariance was tested and a receiver operating characteristics curve analysis was performed. RESULTS The angle measured between the PS axis and the cranial endplate was significantly different between the early and all later postoperative images. The Spearman correlation coefficient for the measurements of two observers at each postoperative time point ranged between 0.89 at 2 weeks to 0.94 at 2 months and 1 year postoperative. The angle change of 1.9° between immediate postoperative and 6-month postoperative was 75% sensitive and 89% specific for the identification of loosened screws (AUC = 0.82). DISCUSSION The angle between the PS axis and the cranial endplate showed good ability to change in PS loosening. A change of this angle of at least 2° had a relatively high sensitivity and specificity to diagnose screw loosening.

How expectations affect reference point formation: an experimental investigation

This paper addresses two major topics concerning the role of expectations in the formation of reference points. First, we show that when expectations are present, they have a significant impact on reference point formation. Second, we find that decision-makers employ expected values when forming reference points (integrated mechanism) as opposed to single possible outcomes (segregated mechanism). Despite the importance of reference points in prospect theory, to date, there is no standard method of examining these. We develop a new experimental design that employs an indirect approach and extends an existing direct approach. Our findings are consistent across the two approaches.

Modal interpolation via nested sequents

The main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequent-like proof formalisms, such as hypersequents, nested sequents, and labelled sequents. In this paper, we start closing this gap by presenting an algorithm for proving the CIP for modal logics by induction on a nested-sequent derivation. This algorithm is applied to all the logics of the so-called modal cube.

Critical point and scale setting in SU(3) plasma: An update

We explore a method developed in statistical physics which has been argued to have exponentially small finite-volume effects, in order to determine the critical temperature Tc of pure SU(3) gauge theory close to the continuum limit. The method allows us to estimate the critical coupling βc of the Wilson action for temporal extents up to Nτ∼20 with ≲0.1% uncertainties. Making use of the scale setting parameters r0 and t0−−√ in the same range of β-values, these results lead to the independent continuum extrapolations Tcr0=0.7457(45) and Tct0−−√=0.2489(14), with the latter originating from a more convincing fit. Inserting a conversion of r0 from literature (unfortunately with much larger errors) yields Tc/ΛMS¯¯¯¯¯=1.24(10).

Explication as a Method of Conceptual Re-engineering

Taking Carnap’s classic exposition as a starting point, this paper develops a pragmatic account of the method of explication, defends it against a range of challenges and proposes a detailed recipe for the practice of explicating. It is then argued that confusions are involved in characterizing explications as definitions, and in advocating precising definitions as an alternative to explications. Explication is better characterized as conceptual re-engineering for theoretical purposes, in contrast to conceptual re-engineering for other purposes and improving exactness for purely practical reasons. Finally, three limitations which call for further development of the method of explication are discussed.