Interpretations of Presburger Arithmetic in Itself

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

Randomisation and Derandomisation in Descriptive Complexity Theory

We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the complexity class BPP, bounded error probabilistic polynomial time, is defined from PTIME. Our main focus lies on questions of derandomisation, and we prove that there is a query which is definable in BPFO, the probabilistic version of first-order logic, but not in Cinf, finite variable infinitary logic with counting. This implies that many of the standard logics of finite model theory, like transitive closure logic and fixed-point logic, both with and without counting, cannot be derandomised. Similarly, we present a query on ordered structures which is definable in BPFO but not in monadic second-order logic, and a query on additive structures which is definable in BPFO but not in FO. The latter of these queries shows that certain uniform variants of AC0 (bounded-depth polynomial sized circuits) cannot be derandomised. These results are in contrast to the general belief that most standard complexity classes can be derandomised. Finally, we note that BPIFP+C, the probabilistic version of fixed-point logic with counting, captures the complexity class BPP, even on unordered structures

Neurolymphomatosis mimicking neurosarcoidosis: a case report

<p>Abstract</p> <p>Introduction</p> <p>Both neurosarcoidosis and central nervous system lymphoma can be very difficult to diagnose. We describe the case of a patient in whom neurosarcoidosis was strongly suspected, but who was eventually found to have lymphoma. We believe the case to be of interest and practical value to neurologists, oncologists and internists with an interest in inflammatory diseases.</p> <p>Case presentation</p> <p>A diagnosis of neurosarcoidosis was considered in a 49-year-old Caucasian man on the basis of the following symptoms and indications: a cough, bilateral hilar lymphadenopathy confirmed by thoracic computed tomography, the development of an S1 radiculopathy, cerebrospinal fluid abnormalities (raised protein level), bilateral lung hilar and lachrymal gland uptake on a gallium scan, and erythema nodosum confirmed with skin biopsy. These were followed by the development of multiple cranial neuropathies, including seventh nerve palsy. Exhaustive further investigations yielded no evidence for an alternative diagnosis. Treatments with steroids, cyclophosphamide, intravenous immunoglobulin and finally infliximab were of no benefit. He eventually developed cutaneous nodules, a biopsy of which revealed lymphoma that proved resistant to therapy.</p> <p>Conclusion</p> <p>Constant diagnostic vigilance is required in disorders such as neurosarcoidosis.</p

Remote Field Induced Response of Polymer Nanocomposites Embedded with Sur face-functionalised Dielectric Nanoparticles

Matrix toughening is one of the most popular approaches to improve the overall fracture toughness of polymer composite materials. The most widely known approach for matrix toughening is the addition of a second phase such as rigid or/and rubber particles to dissipate the fracture energy, and vessels that containing healing agents that prevent further crack propagation when ruptured. Only a few studies have shown an alternative ‘active toughening’ by introducing an internal compressive stress field in the matrix via the mismatch in filler/matrix thermal expansion under heating. In this study, epoxy composite materials with embedded ferroelectric barium titanate nanoparticles are fabricated with the aid of silane surface functionalisation. Surface-bonded fibre grating sensors are employed to investigate the strain and temperature change of the epoxy nanocomposite materials under microwave exposure, as an attempt to introduce such field aided strain tailoring of the epoxy matrix as an active toughening mechanism

Electromagnetic Field Controlled Domain Wall Displacement for Induced Strain Tailoring in BaTiO3-Epoxy Nanocomposite

Failure in an epoxy polymer composite material is prone to initiate by the coalescence of microcracks in its polymer matrix. As such, matrix toughening via addition of a second phase as rigid or/and rubber nano/micro-particles is one of the most popular approaches to improve the fracture toughness across multiple scales in a polymer composite, which dissipates fracture energy via deformation mechanisms and microcracks arrest. Few studies have focused on tailorable and variable toughening, so-called ‘active toughening’, mainly suggesting thermally induced strains which offer slow and irreversible toughening due to polymer’s poor thermal conductivity. The research presented in the current article has developed an instantaneous, reversible extrinsic strain field via remote electromagnetic radiation. Quantification of the extrinsic strain evolving in the composite with the microwave energy has been conducted using in-situ real-time fibre optic sensing. A theoretical constitutive equation correlating the exposure energy to micro-strains has been developed, with its solution validating the experimental data and describing their underlying physics. The research has utilised functionalised dielectric ferroelectric nanomaterials, barium titanate (BaTiO3), as a second phase dispersed in an epoxy matrix, able to introduce microscopic electro-strains to their surrounding rigid epoxy subjected to an external electric field (microwaves, herein), as result of their domain walls dipole displacements. Epoxy Araldite LY1564, a diglycidyl ether of bisphenol A associated with the curing agent Aradur 3487 were embedded with the BaTiO3 nanoparticles. The silane coupling agent for the nanoparticles’ surface functionalisation was 3-glycidoxypropyl trimethoxysilane (3-GPS). Hydrogen peroxide (H2O2, 30%) and acetic acid (C2H4O2, 99.9%) used as functionalisation aids, and the ethanol (C2H6O, 99.9%) used for BaTiO3 dispersion. Firstly, the crystal microstructure of the functionalised nanoparticles and the thermal and dielectric properties of the achieved epoxy composite materials have been characterised. It has been observed that the addition of the dielectric nanoparticles has a slight impact on the curing extent of the epoxy. Secondly, the surface-bonded fibre Bragg grating (FBG) sensors have been employed to investigate the real-time variation of strain and temperature in the epoxy composites exposed to microwaves at 2.45 GHz and at different exposure energy. The strains developed due to the in-situ exposure at composite, adhesive and their holding fixture material were evaluated using the FBG. The domain wall induced extrinsic strains were distinguished from the thermally induced strains, and found that the increasing exposure energy has an instantaneously increasing effect on the development of such strains. Post-exposure Raman spectra showed no residual field in the composite indicating no remnant strain field examined under microwave powers < 1000 W, thus suggesting a reversible strain introduction mechanism, i.e. the composite retaining its nominal properties post exposure. The dielectric composite development and quantifications presented in this article proposes a novel active toughening technology for high-performance composite applications in numerous sectors

A Randomised Controlled Trial Assessing the Effect of Oral Diazepam on F-18-FDG Uptake in the Neck and Upper Chest Region

A distinctive pattern of physiological symmetrical uptake of F-18-fluorodeoxyglucose (F-18-FDG) in the neck and upper chest region is a phenomenon that is sometimes observed on positron emission tomography (PET) scans of some oncologic patients. Initially, it was assumed to be muscle uptake secondary to patient anxiety or tension, which could be prevented by diazepam treatment. However, PET-computed tomography data have shown that F-18-FDG uptake is not restricted to the musculature but is also localised within the non-muscular soft tissue, such as brown adipose tissue. The efficacy of benzodiazepine treatment to reduce this uptake has not been well established. Therefore, a randomised controlled trial was conducted to decide whether diazepam would decrease physiological F-18-FDG uptake in the neck and upper chest region (FDG-NUC). A randomised, double-blind, placebo-controlled trial was conducted to assess the effect on FDG-NUC of 5 mg diazepam, given orally 1 h before F-18-FDG injection. Patients younger than 40 years, having or suspected to have a malignancy, were eligible for inclusion. The primary endpoint was FDG-NUC, as assessed by visual analysis of whole-body PET scans by two independent observers. The secondary endpoint was clinical relevance of FDG-NUC. Fifty-two patients were included between September 2003 and January 2005. Twenty-eight patients (54%) received placebo; 24 (46%) received diazepam. FDG-NUC was seen in 25% of the patients in the diazepam group versus 29% in the placebo group. This difference was not statistically significant. No beneficial effect of administration of diazepam could be established. Pre-medication with benzodiazepines to diminish physiological uptake of F-18-FDG in the neck and upper chest region is not indicate

Role of Imaging in the Staging and Response Assessment of Lymphoma:Consensus of the International Conference on Malignant Lymphomas Imaging Working Group

This article comprises the consensus reached to update guidance on the use of PET-CT for staging and response assessment for 18F FDG-avid lymphomas in clinical practice and late-phase trials