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A study of genome-wide gene expression in major depressive disorder (MDD) was undertaken in a large population-based sample to determine whether altered expression levels of genes and pathways could provide insights into biological mechanisms that are relevant to this disorder. Gene expression studies have the potential to detect changes that may be because of differences in common or rare genomic sequence variation, environmental factors or their interaction. We recruited a European ancestry sample of 463 individuals with recurrent MDD and 459 controls, obtained self-report and semi-structured interview data about psychiatric and medical history and other environmental variables, sequenced RNA from whole blood and genotyped a genome-wide panel of common single-nucleotide polymorphisms. We used analytical methods to identify MDD-related genes and pathways using all of these sources of information. In analyses of association between MDD and expression levels of 13 857 single autosomal genes, accounting for multiple technical, physiological and environmental covariates, a significant excess of low P -values was observed, but there was no significant single-gene association after genome-wide correction. Pathway-based analyses of expression data detected significant association of MDD with increased expression of genes in the interferon α/β signaling pathway. This finding could not be explained by potentially confounding diseases and medications (including antidepressants) or by computationally estimated proportions of white blood cell types. Although cause–effect relationships cannot be determined from these data, the results support the hypothesis that altered immune signaling has a role in the pathogenesis, manifestation, and/or the persistence and progression of MDD.

Co-morbidity of mood and anxiety disorders is common and often associated with greater illness severity. This study investigates clinical correlates and familiality of four anxiety disorders in a large sample of bipolar disorder (BP) and major depressive disorder (MDD) pedigrees. The sample comprised 566 BP families with 1416 affected subjects and 675 MDD families with 1726 affected subjects. Clinical characteristics and familiality of panic disorder, social phobia, specific phobia and obsessive-compulsive disorder (OCD) were examined in BP and MDD pedigrees with multivariate modeling using generalized estimating equations. Co-morbidity between mood and anxiety disorders was associated with several markers of clinical severity, including earlier age of onset, greater number of depressive episodes and higher prevalence of attempted suicide, when compared with mood disorder without co-morbid anxiety. Familial aggregation was found with co-morbid panic and OCD in both BP and MDD pedigrees. Specific phobia showed familial aggregation in both MDD and BP families, although the findings in BP were just short of statistical significance after adjusting for other anxiety co-morbidities. We found no evidence for familiality of social phobia. Our findings suggest that co-morbidity of MDD and BP with specific anxiety disorders (OCD, panic disorder and specific phobia) is at least partly due to familial factors, which may be of relevance to both phenotypic and genetic studies of co-morbidity.

We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\\mathbb{R}^n$, $n\\in\\{1,2,3\\}$. Standard homogenization theory provides, for the limit of a small periodicity length $\\varepsilon>0$, an effective second order wave equation that describes solutions on time intervals $[0,T]$. In order to approximate solutions on large time intervals $[0,T\\varepsilon^{-2}]$, one has to use a dispersive, higher order wave equation. In this work, we provide a well-posed, weakly dispersive effective equation and an estimate for errors between the solution of the original heterogeneous problem and the solution of the dispersive wave equation. We use Bloch-wave analysis to identify a family of relevant limit models and introduce an approach to select a well-posed effective model under symmetry assumptions on the periodic structure. The analytical results are confirmed and illustrated by numerical tests. [PUBLICATION ABSTRACT]

Distinguishing bipolar disorder (BP) from major depressive disorder (MDD) has important relevance for prognosis and treatment. Prior studies have identified clinical features that differ between these two diseases but have been limited by heterogeneity and lack of replication. We sought to identify depression-related features that distinguish BP from MDD in large samples with replication. Using a large, opportunistically ascertained collection of subjects with BP and MDD we selected 34 depression-related clinical features to test across the diagnostic categories in an initial discovery dataset consisting of 1228 subjects (386 BPI, 158 BPII and 684 MDD). Features significantly associated with BP were tested in an independent sample of 1000 BPI cases and 1000 MDD cases for classifying ability in receiver operating characteristic (ROC) analysis. Seven clinical features showed significant association with BPI compared with MDD: delusions, psychomotor retardation, incapacitation, greater number of mixed symptoms, greater number of episodes, shorter episode length, and a history of experiencing a high after depression treatment. ROC analyses of a model including these seven factors showed significant evidence for discrimination between BPI and MDD in an independent dataset (area under the curve = 0.83). Only two features (number of mixed symptoms, and feeling high after an antidepressant) showed an association with BPII versus MDD. Our study suggests that clinical features distinguishing depression in BPI versus MDD have important classification potential for clinical practice, and should also be incorporated as 'baseline' features in the evaluation of novel diagnostic biomarkers.

The functional equation of associativity is the topic of Abel's first contribution to Crelle's Journal. Seventy years later, it was featured as the second part of Hilbert's Fifth Problem, and it was solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel (1949). In 1958, B Schweizer and A Sklar showed that the “triangular norms” introduced by Menger in his definition of a probabilistic metric space should be associative; and in their book Probabilistic Metric Spaces, they presented the basic properties of such triangular norms and the closely related copulas. Since then, the study of these two classes of functions has been evolving at an ever-increasing pace and the results have been applied in fields such as statistics, information theory, fuzzy set theory, multi-valued and quantum logic, hydrology, and economics, in particular, risk analysis. This book presents the foundations of the subject of associative functions on real intervals. It brings together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations.

Objective The Gamma Knife Icon (Elekta AB, Stockholm, Sweden) allows frameless stereotactic treatment using a combination of cone beam computer tomography (CBCT), a thermoplastic mask system, and an infrared-based high-definition motion management (HDMM) camera system for patient tracking during treatment. We report on the first patient with meningioma at the left petrous bone treated with adaptive fractionated stereotactic radiotherapy (a-gkFSRT). Methods The first patient treated with Gamma Knife Icon at our institute received MR imaging for preplanning before treatment. For each treatment fraction, a daily CBCT was performed to verify the actual scull/tumor position. The system automatically adapted the planned shot positions to the daily position and recalculated the dose distribution (online adaptive planning). During treatment, the HDMM system recorded the intrafractional patient motion. Furthermore, the required times were recorded to define a clinical treatment slot. Results Total treatment time was around 20 min. Patient positioning needed 0.8 min, CBCT positioning plus acquisition 1.65 min, CT data processing and adaptive planning 2.66 min, and treatment 15.6 min. The differences for the five daily CBCTs compared to the reference are for rotation: −0.59 ± 0.49°/0.18 ± 0.20°/0.05 ± 0.36° and for translation: 0.94 ± 0.52 mm/−0.08 ± 0.08 mm/−1.13 ± 0.89 mm. Over all fractions, an intrafractional movement of 0.13 ± 0.04 mm was observed. Conclusion The Gamma Knife Icon allows combining the accuracy of the stereotactic Gamma Knife system with the flexibility of fractionated treatment with the mask system and CBCT. Furthermore, the Icon system introduces a new online patient tracking system to the clinical routine. The interfractional accuracy of patient positioning was controlled with a thermoplastic mask and CBCT.

The FKBP5 gene product forms part of a complex with the glucocorticoid receptor and can modulate cortisol-binding affinity. Variations in the gene have been associated with increased recurrence of depression and with rapid response to antidepressant treatment. We sought to determine whether common FKBP5 variants confer risk for bipolar disorder. We genotyped seven tag single-nucleotide polymorphisms (SNPs) in FKBP5, plus two SNPs previously associated with illness, in 317 families with 554 bipolar offspring, derived primarily from two studies. Single marker and haplotypic analyses were carried out with FBAT and EATDT employing the standard bipolar phenotype. Association analyses were also conducted using 11 disease-related variables as covariates. Under an additive genetic model, rs4713902 showed significant overtransmission of the major allele ( P =0.0001), which was consistent across the two sample sets ( P =0.004 and 0.006). rs7757037 showed evidence of association that was strongest under the dominant model ( P =0.001). This result was consistent across the two datasets ( P =0.017 and 0.019). The dominant model yielded modest evidence for association ( P <0.05) for three additional markers. Covariate-based analyses suggested that genetic variation within FKBP5 may influence attempted suicide and number of depressive episodes in bipolar subjects. Our results are consistent with the well-established relationship between the hypothalamic–pituitary–adrenal (HPA) axis, which mediates the stress response through regulation of cortisol, and mood disorders. Ongoing whole-genome association studies in bipolar disorder and major depression should further clarify the role of FKBP5 and other HPA genes in these illnesses.

We analyse the spectrum of the Laplace operator in a complex geometry, representing a small Helmholtz resonator. The domain is obtained from a bounded set Ω ⊂ ℝn by removing a small obstacle Σε ⊂ Ω of size ε > 0. The set Σε essentially separates an interior domain ${\\mathrm{\\Omega }}_{\\mathrm{\\varepsilon }}^{\\mathrm{i}\\mathrm{n}\\mathrm{n}}$ (the resonator volume) from an exterior domain ${\\mathrm{\\Omega }}_{\\mathrm{\\varepsilon }}^{\\mathrm{o}\\mathrm{u}\\mathrm{t}}$, but the two domains are connected by a thin channel. For an appropriate choice of the geometry, we identify the spectrum of the Laplace operator: it coincides with the spectrum of the Laplace operator on Ω, but contains an additional eigenvalue ${\\mathrm{\\mu }}_{\\mathrm{\\epsilon }}^{-1}$. We prove that this eigenvalue has the behaviour με ≈ VεLε/Aε, where Vε is the volume of the resonator, Lε is the length of the channel and Aε is the area of the cross section of the channel. This justifies the well-known frequency formula ${\\mathrm{\\omega }}_{\\mathrm{H}\\mathrm{R}}={\\mathrm{c}}_{0}\\sqrt{\\mathrm{A}/\\left(\\mathrm{L}\\mathrm{V}\\right)}$ for Helmholtz resonators, where c0 is the speed of sound.

The Helmholtz equation$-\\nabla\\cdot (a\\nabla u) - \\omega^2 u = f$is considered in an unbounded wave guide$\\Omega := \\mathbb{R} \\times S \\subset \\mathbb{R}^d$,$S\\subset \\mathbb{R}^{d-1}$a bounded domain. The coefficient a is strictly elliptic and either periodic in the unbounded direction$x_1 \\in \\mathbb{R}$or periodic outside a compact subset; in the latter case, two different periodic media can be used in the two unbounded directions. For non-singular frequencies$\\omega$, we show the existence of a solution u . While previous proofs of such results were based on analyticity arguments within operator theory, here, only energy methods are used.

Poly(phenylene methylene) (PPM) is a thermally stable, hydrophobic, fluorescent hydrocarbon polymer. Recently, blended PPM has been proposed as a valuable anti-corrosion coating material, and, in particular, rheological additives such as external plasticizers resulted crucial to prevent crack formation. Accordingly, to avoid common problems related to the use of external plasticizers, the development of PPM-related copolymer-based coatings containing n-octyloxy side chains and their anti-corrosion behavior were explored in this study. The aluminum alloy AA2024, widely employed for corrosion studies, was selected as a substrate, covered with a thin layer of a polybenzylsiloxane in order to improve adhesion between the underlying hydrophilic substrate and the top hydrophobic coating. Gratifyingly, coatings with those copolymers were free of bubbles and cracks. The n-octyloxy side-chains may be regarded to adopt the role of a bound plasticizer, as the glass transition temperature of the copolymers decreases with increasing content of alkoxy side-chains. Electrochemical corrosion tests on PPM-substituted coatings exhibited good corrosion protection of the metal surface towards a naturally aerated near-neutrally 3.5% wt.% NaCl neutral solution, providing comparable results to blended PPM formulations, previously reported. Hence, the application of rheological additives can be avoided by use of proper design copolymers.