Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

Low-threshold monopolar motor mapping for resection of lesions in motor eloquent areas in children and adolescents

Object Resection of lesions close to the primary motor cortex (M1) and the corticospinal tract (CST) is generally regarded as high-risk surgery due to reported rates of postoperative severe deficits of up to 50%. The authors' objective was to determine the feasibility and safety of low-threshold motor mapping and its efficacy for increasing the extent of lesion resection in the proximity of M1 and the CST in children and adolescents. Methods The authors analyzed 8 consecutive pediatric patients in whom they performed 9 resections for lesions within or close (≤ 10 mm) to M1 and/or the CST. Monopolar high-frequency motor mapping with train-of-five stimuli (pulse duration 500 μsec, interstimulus interval 4.0 msec, frequency 250 Hz) was used. The motor threshold was defined as the minimal stimulation intensity that elicited motor evoked potentials (MEPs) from target muscles (amplitude > 30 μV). Resection was performed toward M1 and the CST at sites negative to 1- to 3-mA high-frequency train-of-five stimulation. Results The M1 was identified through high-frequency train-of-five via application of varying low intensities. The lowest motor thresholds after final resection ranged from 1 to 9 mA in 8 cases and up to 18 mA in 1 case, indicating proximity to motor neurons. Intraoperative electroencephalography documented an absence of seizures during all surgeries. Two transient neurological deficits were observed, but there were no permanent deficits. Postoperative imaging revealed complete resection in 8 patients and a very small remnant (< 0.175 cm(3)) in 1 patient. Conclusions High-frequency train-of-five with a minimal threshold of 1-3 mA is a feasible and safe procedure for resections in the proximity of the CST. Thus, low-threshold motor mapping might help to expand the area for safe resection in pediatric patients with lesions located within the precentral gyrus and close to the CST, and may be regarded as a functional navigational tool. The additional use of continuous MEP monitoring serves as a safety feedback for the functional integrity of the CST, especially because the true excitability threshold in children is unknown.

Cardiothoracic ratio in postmortem computed tomography: reliability and threshold for the diagnosis of cardiomegaly

The aim of this study was to evaluate the reliability of the cardiothoracic ratio (CTR) in postmortem computed tomography (PMCT) and to assess a CTR threshold for the diagnosis of cardiomegaly based on the weight of the heart at autopsy. PMCT data of 170 deceased human adults were retrospectively evaluated by two blinded radiologists. The CTR was measured on axial computed tomography images and the actual cardiac weight was weighed at autopsy. Inter-rater reliability, sensitivity, and specificity were calculated. Receiver operating characteristic curves were calculated to assess enlarged heart weight by CTR. The autopsy definition of cardiomegaly was based on normal values of the Zeek method (within a range of both, one or two SD) and the Smith method (within the given range). Intra-class correlation coefficients demonstrated excellent agreements (0.983) regarding CTR measurements. In 105/170 (62 %) cases the CTR in PMCT was >0.5, indicating enlarged heart weight, according to clinical references. The mean heart weight measured in autopsy was 405 ± 105 g. As a result, 114/170 (67 %) cases were interpreted as having enlarged heart weights according to the normal values of Zeek within one SD, while 97/170 (57 %) were within two SD. 100/170 (59 %) were assessed as enlarged according to Smith's normal values. The sensitivity/specificity of the 0.5 cut-off of the CTR for the diagnosis of enlarged heart weight was 78/71 % (Zeek one SD), 74/55 % (Zeek two SD), and 76/59 % (Smith), respectively. The discriminative power between normal heart weight and cardiomegaly was 79, 73, and 74 % for the Zeek (1SD/2SD) and Smith methods respectively. Changing the CTR threshold to 0.57 resulted in a minimum specificity of 95 % for all three definitions of cardiomegaly. With a CTR threshold of 0.57, cardiomegaly can be identified with a very high specificity. This may be useful if PMCT is used by forensic pathologists as a screening tool for medico-legal autopsies.

The transverse-momentum spectrum of Higgs bosons near threshold at NNLO

We give next-to-next-to-leading order (NNLO) predictions for the Higgs production cross section at large transverse momentum in the threshold limit. Near the partonic threshold, all radiation is either soft or collinear to the final state jet which recoils against the Higgs boson. We find that the real emission corrections are of moderate size, but that the virtual corrections are large. We discuss the origin of these corrections and give numerical predictions for the transverse-momentum spectrum. The threshold result is matched to the known NLO result and implemented in the public code PeTeR.

Proof internalization in generalized Frege systems for classical logic

We present a general method for inserting proofs in Frege systems for classical logic that produces systems that can internalize their own proofs.

Censors for Boolean Description Logic

Protecting different kinds of information has become an important area of research. One aspect is to provide effective means to avoid that secrets can be deduced from the answers of legitimate queries. In the context of atomic propositional databases several methods have been developed to achieve this goal. However, in those databases it is not possible to formalize structural information. Also they are quite restrictive with respect to the specification of secrets. In this paper we extend those methods to match the much greater expressive power of Boolean description logics. In addition to the formal framework, we provide a discussion of various kinds of censors and establish different levels of security they can provide.

Systematic analysis of the intravoxel incoherent motion threshold separating perfusion and diffusion effects: Proposal of a standardized algorithm

PURPOSE To systematically evaluate the dependence of intravoxel-incoherent-motion (IVIM) parameters on the b-value threshold separating the perfusion and diffusion compartment, and to implement and test an algorithm for the standardized computation of this threshold. METHODS Diffusion weighted images of the upper abdomen were acquired at 3 Tesla in eleven healthy male volunteers with 10 different b-values and in two healthy male volunteers with 16 different b-values. Region-of-interest IVIM analysis was applied to the abdominal organs and skeletal muscle with a systematic increase of the b-value threshold for computing pseudodiffusion D*, perfusion fraction Fp , diffusion coefficient D, and the sum of squared residuals to the bi-exponential IVIM-fit. RESULTS IVIM parameters strongly depended on the choice of the b-value threshold. The proposed algorithm successfully provided optimal b-value thresholds with the smallest residuals for all evaluated organs [s/mm2]: e.g., right liver lobe 20, spleen 20, right renal cortex 150, skeletal muscle 150. Mean D* [10(-3) mm(2) /s], Fp [%], and D [10(-3) mm(2) /s] values (±standard deviation) were: right liver lobe, 88.7 ± 42.5, 22.6 ± 7.4, 0.73 ± 0.12; right renal cortex: 11.5 ± 1.8, 18.3 ± 2.9, 1.68 ± 0.05; spleen: 41.9 ± 57.9, 8.2 ± 3.4, 0.69 ± 0.07; skeletal muscle: 21.7 ± 19.0; 7.4 ± 3.0; 1.36 ± 0.04. CONCLUSION IVIM parameters strongly depend upon the choice of the b-value threshold used for computation. The proposed algorithm may be used as a robust approach for IVIM analysis without organ-specific adaptation. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.