Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

An integral conservative gridding--algorithm using Hermitian curve interpolation

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

Expression of human cathepsin L or human cathepsin V in mouse thymus mediates positive selection of T helper cells in cathepsin L knock-out mice

A genetic deficiency of the cysteine protease cathepsin L (Ctsl) in mice results in impaired positive selection of conventional CD4+ T helper cells as a result of an incomplete processing of the MHC class II associated invariant chain or incomplete proteolytic generation of positively selecting peptide ligands. The human genome encodes, in contrast to the mouse genome, for two cathepsin L proteases, namely cathepsin L (CTSL) and cathepsin V (CTSV; alternatively cathepsin L2). In the human thymic cortex, CTSV is the predominately expressed protease as compared to CTSL or other cysteine cathepsins. In order to analyze the functions of CTSL and CTSV in the positive selection of CD4+ T cells we employed Ctsl knock-out mice crossed either with transgenic mice expressing CTSL under the control of its genuine human promoter or with transgenic mice expressing CTSV under the control of the keratin 14 (K14) promoter, which drives expression to the cortical epithelium. Both human proteases are expressed in the thymus of the transgenic mice, and independent expression of both CTSL and CTSV rescues the reduced frequency of CD4+ T cells in Ctsl-deficient mice. Moreover, the expression of the human cathepsins does not change the number of CD4+CD25+Foxp3+ regulatory T cells, but the normalization of the frequency of conventional CD4+ T cell in the transgenic mice results in a rebalancing of conventional T cells and regulatory T cells. We conclude that the functional differences of CTSL and CTSV in vivo are not mainly determined by their inherent biochemical properties, but rather by their tissue specific expression pattern.

Bone morphogenetic protein-7 is a MYC target with prosurvival functions in childhood medulloblastoma

Medulloblastoma (MB) is the most common malignant brain tumor in children. It is known that overexpression and/or amplification of the MYC oncogene is associated with poor clinical outcome, but the molecular mechanisms and the MYC downstream effectors in MB remain still elusive. Besides contributing to elucidate how progression of MB takes place, most importantly, the identification of novel MYC-target genes will suggest novel candidates for targeted therapy in MB. A group of 209 MYC-responsive genes was obtained from a complementary DNA microarray analysis of a MB-derived cell line, following MYC overexpression and silencing. Among the MYC-responsive genes, we identified the members of the bone morphogenetic protein (BMP) signaling pathway, which have a crucial role during the development of the cerebellum. In particular, the gene BMP7 was identified as a direct target of MYC. A positive correlation between MYC and BMP7 expression was documented by analyzing two distinct sets of primary MB samples. Functional studies in vitro using a small-molecule inhibitor of the BMP/SMAD signaling pathway reproduced the effect of the small interfering RNA-mediated silencing of BMP7. Both approaches led to a block of proliferation in a panel of MB cells and to inhibition of SMAD phosphorylation. Altogether, our findings indicate that high MYC levels drive BMP7 overexpression, promoting cell survival in MB cells. This observation suggests the potential relevance of targeting the BMP/SMAD pathway as a novel therapeutic approach for the treatment of childhood MB.

Sleep-disordered breathing in acute ischemic stroke and transient ischemic attack: effects on short- and long-term outcome and efficacy of treatment with continuous positive airways pressure - rationale and design of the SAS CARE study

Sleep-disordered breathing represents a risk factor for cardiovascular morbidity and mortality and negatively affects short-term and long-term outcome after an ischemic stroke or transient ischemic attack. The effect of continuous positive airways pressure in patients with sleep-disordered breathing and acute cerebrovascular event is poorly known. The SAS CARE 1 study assesses the effects of sleep-disordered breathing on clinical evolution, vascular functions, and markers within the first three-months after an acute cerebrovascular event. The SAS CARE 2 assesses the effect of continuous positive airways pressure on clinical evolution, cardiovascular events, and mortality as well as vascular functions and markers at 12 and 24 months after acute cerebrovascular event.

Putative functions of extracellular matrix glycoproteins in secondary palate morphogenesis

Cleft palate is a common birth defect in humans. Elevation and fusion of paired palatal shelves are coordinated by growth and transcription factors, and mutations in these can cause malformations. Among the effector genes for growth factor signaling are extracellular matrix (ECM) glycoproteins. These provide substrates for cell adhesion (e.g., fibronectin, tenascins), but also regulate growth factor availability (e.g., fibrillins). Cleft palate in Bmp7 null mouse embryos is caused by a delay in palatal shelf elevation. In contrast, palatal shelves of Tgf-β3 knockout mice elevate normally, but a cleft develops due to their failure to fuse. However, nothing is known about a possible functional interaction between specific ECM proteins and Tgf-β/Bmp family members in palatogenesis. To start addressing this question, we studied the mRNA and protein distribution of relevant ECM components during secondary palate development, and compared it to growth factor expression in wildtypewild type and mutant mice. We found that fibrillin-2 (but not fibrillin-1) mRNA appeared in the mesenchyme of elevated palatal shelves adjacent to the midline epithelial cells, which were positive for Tgf-β3 mRNA. Moreover, midline epithelial cells started expressing fibronectin upon contact of the two palatal shelves. These findings support the hypothesis that fibrillin-2 and fibronectin are involved in regulating the activity of Tgf-β3 at the fusing midline. In addition, we observed that tenascin-W (but not tenascin-C) was misexpressed in palatal shelves of Bmp7-deficient mouse embryos. In contrast to tenascin-C, tenascin-W secretion was strongly induced by Bmp7 in embryonic cranial fibroblasts in vitro. These results are consistent with a putative function for tenascin-W as a target of Bmp7 signaling during palate elevation. Our results indicate that distinct ECM proteins are important for morphogenesis of the secondary palate, both as downstream effectors and as regulators of Tgf-β/Bmp activity.

Strengthening of laterality of verbal and visuospatial functions during childhood and adolescence

Cognitive functions in the child's brain develop in the context of complex adaptive processes, determined by genetic and environmental factors. Little is known about the cerebral representation of cognitive functions during development. In particular, knowledge about the development of right hemispheric (RH) functions is scarce. Considering the dynamics of brain development, localization and lateralization of cognitive functions must be expected to change with age. Twenty healthy subjects (8.6-20.5 years) were examined with fMRI and neuropsychological tests. All participants completed two fMRI tasks known to activate left hemispheric (LH) regions (language tasks) and two tasks known to involve predominantly RH areas (visual search tasks). A laterality index (LI) was computed to determine the asymmetry of activation. Group analysis revealed unilateral activation of the LH language circuitry during language tasks while visual search tasks induced a more widespread RH activation pattern in frontal, superior temporal, and occipital areas. Laterality of language increased between the ages of 8-20 in frontal (r = 0.392, P = 0.049) and temporal (r = 0.387, P = 0.051) areas. The asymmetry of visual search functions increased in frontal (r = -0.525, P = 0.009) and parietal (r = -0.439, P = 0.027) regions. A positive correlation was found between Verbal-IQ and the LI during a language task (r = 0.585, P = 0.028), while visuospatial skills correlated with LIs of visual search (r = -0.621, P = 0.018). To summarize, cognitive development is accompanied by changes in the functional representation of neuronal circuitries, with a strengthening of lateralization not only for LH but also for RH functions. Our data show that age and performance, independently, account for the increases of laterality with age.

Functions and effects of creatine in the central nervous system

Creatine kinase catalyses the reversible transphosphorylation of creatine by ATP. In the cell, creatine kinase isoenzymes are specifically localized at strategic sites of ATP consumption to efficiently regenerate ATP in situ via phosphocreatine or at sites of ATP generation to build-up a phosphocreatine pool. Accordingly, the creatine kinase/phosphocreatine system plays a key role in cellular energy buffering and energy transport, particularly in cells with high and fluctuating energy requirements like neurons. Creatine kinases are expressed in the adult and developing human brain and spinal cord, suggesting that the creatine kinase/phosphocreatine system plays a significant role in the central nervous system. Functional impairment of this system leads to a deterioration in energy metabolism, which is phenotypic for many neurodegenerative and age-related diseases. Exogenous creatine supplementation has been shown to reduce neuronal cell loss in experimental paradigms of acute and chronic neurological diseases. In line with these findings, first clinical trials have shown beneficial effects of therapeutic creatine supplementation. Furthermore, creatine was reported to promote differentiation of neuronal precursor cells that might be of importance for improving neuronal cell replacement strategies. Based on these observations there is growing interest on the effects and functions of this compound in the central nervous system. This review gives a short excursion into the basics of the creatine kinase/phosphocreatine system and aims at summarizing findings and concepts on the role of creatine kinase and creatine in the central nervous system with special emphasis on pathological conditions and the positive effects of creatine supplementation.

Expressing and Amplifying Positive Emotions Facilitate Goal Attainment in Workplace Interactions

Expressing emotions has social functions; it provides information, affects social interactions, and shapes relationships with others. Expressing positive emotions could be a strategic tool for improving goal attainment during social interactions at work. Such effects have been found in research on social contagion, impression management, and emotion work. However, expressing emotions one does not feel entails the risk of being perceived as inauthentic. This risk may well be worth taking when the emotions felt are negative, as expressing negative emotions usually has negative effects. When experiencing positive emotions, however, expressing them authentically promises benefits, and the advantage of amplifying them is not so obvious. We postulated that expressing, and amplifying, positive emotions would foster goal attainment in social interactions at work, particularly when dealing with superiors. Analyses are based on 494 interactions involving the pursuit of a goal by 113 employes. Multilevel analyses, including polynomial analyses, show that authentic display of positive emotions supported goal attainment throughout. However, amplifying felt positive emotions promoted goal attainment only in interactions with superiors, but not with colleagues. Results are discussed with regard to the importance of hierarchy for detecting, and interpreting, signs of strategic display of positive emotions.

On the signature of positive braids and adjacency for torus knots

The objects of study in this thesis are knots. More precisely, positive braid knots, which include algebraic knots and torus knots. In the first part of this thesis, we compare two classical knot invariants - the genus g and the signature σ - for positive braid knots. Our main result on positive braid knots establishes a linear lower bound for the signature in terms of the genus. In the second part of the thesis, a positive braid approach is applied to the study of the local behavior of polynomial functions from the complex affine plane to the complex numbers. After endowing polynomial function germs with a suitable topology, the adjacency problem arises: for a fixed germ f, what classes of germs g can be found arbitrarily close to f? We introduce two purely topological notions of adjacency for knots and discuss connections to algebraic notions of adjacency and the adjacency problem.

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Patterns of positive selection in seven ant genomes

The evolution of ants is marked by remarkable adaptations that allowed the development of very complex social systems. To identify how ant-specific adaptations are associated with patterns of molecular evolution, we searched for signs of positive selection on amino-acid changes in proteins. We identified 24 functional categories of genes which were enriched for positively selected genes in the ant lineage. We also reanalyzed genome-wide datasets in bees and flies with the same methodology, to check whether positive selection was specific to ants or also present in other insects. Notably, genes implicated in immunity were enriched for positively selected genes in the three lineages, ruling out the hypothesis that the evolution of hygienic behaviors in social insects caused a major relaxation of selective pressure on immune genes. Our scan also indicated that genes implicated in neurogenesis and olfaction started to undergo increased positive selection before the evolution of sociality in Hymenoptera. Finally, the comparison between these three lineages allowed us to pinpoint molecular evolution patterns that were specific to the ant lineage. In particular, there was ant-specific recurrent positive selection on genes with mitochondrial functions, suggesting that mitochondrial activity was improved during the evolution of this lineage. This might have been an important step toward the evolution of extreme lifespan that is a hallmark of ants.

The effects of qualitatively different acute physical activity interventions in real-world settings on executive functions in preadolescent children

There is growing evidence indicating a positive effect of acute physical activity on cognitive performance in children. Most of the evidence originates, however, from studies in highly controlled laboratory settings. The aim of the present study was to investigate whether the same effects can be found in more real-world settings. We examined the effects of qualitatively different acute physical activity interventions on the three core dimensions of executive functions (updating, inhibition, shifting). In an experimental between-subject design, 219 ten to twelve year-olds were assigned to one of four conditions which varied systematically in physical activation and cognitive engagement. Executive functions were measured before and immediately after the intervention. Contrary to the hypothesis, no effects of acute physical activity with and without cognitive engagement were found on executive functions in the overall sample. Only children with higher fitness and/or higher academic achievement benefitted from the interventions in terms of their updating performance. Thus, the results indicate that it may be more difficult to attain positive effects through acute physical activity in real-world settings than in laboratory settings and that physiological and cognitive requirements may have to be adjusted to individual capacity to make an intervention effective.

Melanoma Cell-Intrinsic PD-1 Receptor Functions Promote Tumor Growth.

Therapeutic antibodies targeting programmed cell death 1 (PD-1) activate tumor-specific immunity and have shown remarkable efficacy in the treatment of melanoma. Yet, little is known about tumor cell-intrinsic PD-1 pathway effects. Here, we show that murine and human melanomas contain PD-1-expressing cancer subpopulations and demonstrate that melanoma cell-intrinsic PD-1 promotes tumorigenesis, even in mice lacking adaptive immunity. PD-1 inhibition on melanoma cells by RNAi, blocking antibodies, or mutagenesis of melanoma-PD-1 signaling motifs suppresses tumor growth in immunocompetent, immunocompromised, and PD-1-deficient tumor graft recipient mice. Conversely, melanoma-specific PD-1 overexpression enhances tumorigenicity, as does engagement of melanoma-PD-1 by its ligand, PD-L1, whereas melanoma-PD-L1 inhibition or knockout of host-PD-L1 attenuate growth of PD-1-positive melanomas. Mechanistically, the melanoma-PD-1 receptor modulates downstream effectors of mTOR signaling. Our results identify melanoma cell-intrinsic functions of the PD-1:PD-L1 axis in tumor growth and suggest that blocking melanoma-PD-1 might contribute to the striking clinical efficacy of anti-PD-1 therapy.