Non-self-adjoint graphs

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.

Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law

We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to 1 /| x | 2 . The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius R. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if R is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Skolemization for Substructural Logics

The usual Skolemization procedure, which removes strong quantifiers by introducing new function symbols, is in general unsound for first-order substructural logics defined based on classes of complete residuated lattices. However, it is shown here (following similar ideas of Baaz and Iemhoff for first-order intermediate logics in [1]) that first-order substructural logics with a semantics satisfying certain witnessing conditions admit a “parallel” Skolemization procedure where a strong quantifier is removed by introducing a finite disjunction or conjunction (as appropriate) of formulas with multiple new function symbols. These logics typically lack equivalent prenex forms. Also, semantic consequence does not in general reduce to satisfiability. The Skolemization theorems presented here therefore take various forms, applying to the left or right of the consequence relation, and to all formulas or only prenex formulas.

Impact of body mass index on long-term clinical outcomes after second-generation drug eluting stent implantation: Insights from the international global RESOLUTE program

BACKGROUND An increased body mass index (BMI) is associated with a high risk of cardiovascular disease and reduction in life expectancy. However, several studies reported improved clinical outcomes in obese patients treated for cardiovascular diseases. The aim of the present study is to investigate the impact of BMI on long-term clinical outcomes after implantation of zotarolimus eluting stents. METHODS Individual patient data were pooled from the RESOLUTE Clinical Program comprising five trials worldwide. The study population was sorted according to BMI tertiles and clinical outcomes were evaluated at 2-year follow-up. RESULTS Data from a total of 5,127 patients receiving the R-ZES were included in the present study. BMI tertiles were as follow: I tertile (≤ 25.95 kg/m(2) -Low or normal weight) 1,727 patients; II tertile (>25.95 ≤ 29.74 kg/m(2) -overweight) 1,695 patients, and III tertile (>29.74 kg/m(2) -obese) 1,705 patients. At 2-years follow-up no difference was found for patients with high BMI (III tertile) compared with patients with normal or low BMI (I tertile) in terms of target lesion failure (I-III tertile, HR [95% CI] = 0.89 [0.69, 1.14], P = 0.341; major adverse cardiac events (I-III tertile, HR [95% CI] = 0.90 [0.72, 1.14], P = 0.389; cardiac death (I-III tertile, HR [95% CI] = 1.20 [0.73, 1.99], P = 0.476); myocardial infarction (I-III tertile, HR [95% CI] = 0.86 [0.55, 1.35], P = 0.509; clinically-driven target lesion revascularization (I-III tertile, HR [95% CI] = 0.75 [0.53, 1.08], P = 0.123; definite or probable stent thrombosis (I-III tertile, HR [95% CI] = 0.98 [0.49, 1.99], P = 0.964. CONCLUSIONS In the present study, the patients' body mass index was found to have no impact on long-term clinical outcomes after coronary artery interventions.

Out-of-Body Experiences and Other Complex Dissociation Experiences in a Patient with Unilateral Peripheral Vestibular Damage and Deficient Multisensory Integration

Out-of-body experiences (OBEs) are illusory perceptions of one's body from an elevated disembodied perspective. Recent theories postulate a double disintegration process in the personal (visual, proprioceptive and tactile disintegration) and extrapersonal (visual and vestibular disintegration) space as the basis of OBEs. Here we describe a case which corroborates and extends this hypothesis. The patient suffered from peripheral vestibular damage and presented with OBEs and lucid dreams. Analysis of the patient's behaviour revealed a failure of visuo-vestibular integration and abnormal sensitivity to visuo-tactile conflicts that have previously been shown to experimentally induce out-of-body illusions (in healthy subjects). In light of these experimental findings and the patient's symptomatology we extend an earlier model of the role of vestibular signals in OBEs. Our results advocate the involvement of subcortical bodily mechanisms in the occurrence of OBEs.

Towards mapping the late Quaternary vegetation change of Europe

The number of well-dated pollen diagrams in Europe has increased considerably over the last 30 years and many of them have been submitted to the European Pollen Database (EPD). This allows for the construction of increasingly precise maps of Holocene vegetation change across the continent. Chronological information in the EPD has been expressed in uncalibrated radiocarbon years, and most chronologies to date are based on this time scale. Here we present new chronologies for most of the datasets stored in the EPD based on calibrated radiocarbon years. Age information associated with pollen diagrams is often derived from the pollen stratigraphy itself or from other sedimentological information. We reviewed these chronological tie points and assigned uncertainties to them. The steps taken to generate the new chronologies are described and the rationale for a new classification system for age uncertainties is introduced. The resulting chronologies are fit for most continental-scale questions. They may not provide the best age model for particular sites, but may be viewed as general purpose chronologies. Taxonomic particularities of the data stored in the EPD are explained. An example is given of how the database can be queried to select samples with appropriate age control as well as the suitable taxonomic level to answer a specific research question.

The TREAT-NMD DMD Global Database: analysis of more than 7,000 Duchenne muscular dystrophy mutations.

Analyzing the type and frequency of patient-specific mutations that give rise to Duchenne muscular dystrophy (DMD) is an invaluable tool for diagnostics, basic scientific research, trial planning, and improved clinical care. Locus-specific databases allow for the collection, organization, storage, and analysis of genetic variants of disease. Here, we describe the development and analysis of the TREAT-NMD DMD Global database (http://umd.be/TREAT_DMD/). We analyzed genetic data for 7,149 DMD mutations held within the database. A total of 5,682 large mutations were observed (80% of total mutations), of which 4,894 (86%) were deletions (1 exon or larger) and 784 (14%) were duplications (1 exon or larger). There were 1,445 small mutations (smaller than 1 exon, 20% of all mutations), of which 358 (25%) were small deletions and 132 (9%) small insertions and 199 (14%) affected the splice sites. Point mutations totalled 756 (52% of small mutations) with 726 (50%) nonsense mutations and 30 (2%) missense mutations. Finally, 22 (0.3%) mid-intronic mutations were observed. In addition, mutations were identified within the database that would potentially benefit from novel genetic therapies for DMD including stop codon read-through therapies (10% of total mutations) and exon skipping therapy (80% of deletions and 55% of total mutations).

Holocene palaeoclimate and palaeovegetation on the islands of Flores and Pico

Palaeoclimatic stability is regarded as an important factor in explaining patterns of endemism in the Azorean flora. However, modelling simulations and quantitative reconstructions for the last 6000 years suggest considerable palaeoclimatic variability. Here we explore the link between Holocene palaeoclimate and palaeovegetation on the islands of Flores and Pico. Modern pollen assemblages indicate that most major plant communities can be detected using pollen analysis and that, in some cases, the pre-colonisation vegetation was quite similar to present-day relict vegetation. A 200–500-year pollen record from Alagoinha, a low-elevation mire in western Flores, shows that Juniperus brevifolia-dominated communities were widespread at lower elevations prior to large-scale deforestation. Today these communities are generally restricted to higher elevations. While our results are preliminary, there appears to be a weak link between palaeovegetation (which was primarily influenced by volcanism, soil formation and human impact) and palaeoclimatic changes detected through geochemical proxies. Even if the Azorean palaeoclimate varied substantially, its impact on the pristine vegetation, at least in terms of pollen production, was relatively small.

Phenotypic plasticity is a negative, though weak, predictor of the commonness of 105 grassland species

Aim The usual hypothesis about the relationship between niche breadth and range size posits that species with the capacity to use a wider range of resources or to tolerate a greater range of environmental conditions should be more widespread. In plants, broader niches are often hypothesized to be due to pronounced phenotypic plasticity, and more plastic species are therefore predicted to be more common. We examined the relationship between the magnitude of phenotypic plasticity in five functional traits, mainly related to leaves, and several measures of abundance in 105 Central European grassland species. We further tested whether mean values of traits, rather than their plasticity, better explain the commonness of species, possibly because they are pre-adapted to exploiting the most common resources. Location Central Europe. Methods In a multispecies experiment with 105 species we measured leaf thickness, leaf greenness, specific leaf area, leaf dry matter content and plant height, and the plasticity of these traits in response to fertilization, waterlogging and shading. For the same species we also obtained five measures of commonness, ranging from plot-level abundance to range size in Europe. We then examined whether these measures of commonness were associated with the magnitude of phenotypic plasticity, expressed as composite plasticity of all traits across the experimental treatments. We further estimated the relative importance of trait plasticity and trait means for abundance and geographical range size. Results More abundant species were less plastic. This negative relationship was fairly consistent across several spatial scales of commonness, but it was weak. Indeed, compared with trait means, plasticity was relatively unimportant for explaining differences in species commonness. Main conclusions Our results do not indicate that larger phenotypic plasticity of leaf morphological traits enhances species abundance. Furthermore, possession of a particular trait value, rather than of trait plasticity, is a more important determinant of species commonness.