Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

On restricted families of projections in ℝ3

We study projections onto non-degenerate one-dimensional families of lines and planes in R 3 . Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most 12 -dimensional sets [Math Processing Error] is typically preserved under one-dimensional families of projections onto lines. We improve the result by an ε , proving that if [Math Processing Error], then the packing dimension of the projections is almost surely at least [Math Processing Error]. For projections onto planes, we obtain a similar bound, with the threshold 12 replaced by 1 . In the special case of self-similar sets [Math Processing Error] without rotations, we obtain a full Marstrand-type projection theorem for 1-parameter families of projections onto lines. The [Math Processing Error] case of the result follows from recent work of M. Hochman, but the [Math Processing Error] part is new: with this assumption, we prove that the projections have positive length almost surely.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

A numerical model for inert gas transport in the lung based on fractal airway morphology

Patients suffering from cystic fibrosis (CF) show thick secretions, mucus plugging and bronchiectasis in bronchial and alveolar ducts. This results in substantial structural changes of the airway morphology and heterogeneous ventilation. Disease progression and treatment effects are monitored by so-called gas washout tests, where the change in concentration of an inert gas is measured over a single or multiple breaths. The result of the tests based on the profile of the measured concentration is a marker for the severity of the ventilation inhomogeneity strongly affected by the airway morphology. However, it is hard to localize underlying obstructions to specific parts of the airways, especially if occurring in the lung periphery. In order to support the analysis of lung function tests (e.g. multi-breath washout), we developed a numerical model of the entire airway tree, coupling a lumped parameter model for the lung ventilation with a 4th-order accurate finite difference model of a 1D advection-diffusion equation for the transport of an inert gas. The boundary conditions for the flow problem comprise the pressure and flow profile at the mouth, which is typically known from clinical washout tests. The natural asymmetry of the lung morphology is approximated by a generic, fractal, asymmetric branching scheme which we applied for the conducting airways. A conducting airway ends when its dimension falls below a predefined limit. A model acinus is then connected to each terminal airway. The morphology of an acinus unit comprises a network of expandable cells. A regional, linear constitutive law describes the pressure-volume relation between the pleural gap and the acinus. The cyclic expansion (breathing) of each acinus unit depends on the resistance of the feeding airway and on the flow resistance and stiffness of the cells themselves. Special care was taken in the development of a conservative numerical scheme for the gas transport across bifurcations, handling spatially and temporally varying advective and diffusive fluxes over a wide range of scales. Implicit time integration was applied to account for the numerical stiffness resulting from the discretized transport equation. Local or regional modification of the airway dimension, resistance or tissue stiffness are introduced to mimic pathological airway restrictions typical for CF. This leads to a more heterogeneous ventilation of the model lung. As a result the concentration in some distal parts of the lung model remains increased for a longer duration. The inert gas concentration at the mouth towards the end of the expirations is composed of gas from regions with very different washout efficiency. This results in a steeper slope of the corresponding part of the washout profile.

The sense of the body in individuals with spinal cord injury

Increasing evidence suggests that the basic foundations of the self lie in the brain systems that represent the body. Specific sensorimotor stimulation has been shown to alter the bodily self. However, little is known about how disconnection of the brain from the body affects the phenomenological sense of the body and the self. Spinal cord injury (SCI) patients who exhibit massively reduced somatomotor processes below the lesion in the absence of brain damage are suitable for testing the influence of body signals on two important components of the self-the sense of disembodiment and body ownership. We recruited 30 SCI patients and 16 healthy participants, and evaluated the following parameters: (i) depersonalization symptoms, using the Cambridge Depersonalization Scale (CDS), and (ii) measures of body ownership, as quantified by the rubber hand illusion (RHI) paradigm. We found higher CDS scores in SCI patients, which show increased detachment from their body and internal bodily sensations and decreasing global body ownership with higher lesion level. The RHI paradigm reveals no alterations in the illusory ownership of the hand between SCI patients and controls. Yet, there was no typical proprioceptive drift in SCI patients with intact tactile sensation on the hand, which might be related to cortical reorganization in these patients. These results suggest that disconnection of somatomotor inputs to the brain due to spinal cord lesions resulted in a disturbed sense of an embodied self. Furthermore, plasticity-related cortical changes might influence the dynamics of the bodily self.

Agrarian learning processes in Switzerland 1918–1939

This paper examines the social impacts of weather extremes and the processes of social and communicative learning a society undertakes to find alternative ways to deal with the consequences of a crisis. In the beginning of the 20th Century hunger seemed to be expelled from Europe. Switzerland – like many other European countries – was involved in a global interdependent trade system, which provided necessary goods. But at the end of World War I very cold and wet summers in 1916/17 (causing crop failure) and the difficulties in war-trade led to malnutrition and enormous price risings of general living-standards in Switzerland, which shocked the people and caused revolutionary uprisings in 1918. The experience of malnutrition during the last two years of war made clear that the traditional ways of food supply in Switzerland lacked crisis stability. Therefore various agents in the field of food production, distribution and consumption searched for alternative ways of food supply. In that sense politicians, industrialists, consumer-groups, left-wing communitarians and farmers developed several strategies for new ways in food production. Traditionally there were political conflicts in Switzerland between farmers and consumers regarding price policies, which led mainly to the conflict in 1918. Consumers accused famers of holding back food to control extortionate prices while the farmers pointed to the bad harvest causing the price rising. The collaboration of these groups in search for new forms of food-stability made social integration possible again. In addition to other crisis-factors, weather extremes can have disastrous impacts and destroy a society’s self-confidence to its core. But even such crisis can lead to processes of substantial learning that allows a regeneration of confidence and show positive influence on political stabilization. The paper focuses on the process of learning and the alternative methods of food production that were suggested by various agents working in the field during the Interwar period. To achieve that goal documents of the various associations are analyzed and newspapers have been taken into consideration. Through the method of discourse-analysis of food-production during the Interwar period, possible solutions that crossed the minds of the agents should be brought to light.

Observations of the northern seasonal polar cap on Mars: I. Spring sublimation activity and processes

Spring sublimation of the seasonal CO2 northern polar cap is a dynamic process in the current Mars climate. Phenomena include dark fans of dune material propelled out onto the seasonal ice layer, polygonal cracks in the seasonal ice, sand flow down slipfaces, and outbreaks of gas and sand around the dune margins. These phenomena are concentrated on the north polar erg that encircles the northern residual polar cap. The Mars Reconnaissance Orbiter has been in orbit for three Mars years, allowing us to observe three northern spring seasons. Activity is consistent with and well described by the Kieffer model of basal sublimation of the seasonal layer of ice applied originally in the southern hemisphere. Three typical weak spots have been identified on the dunes for escape of gas sublimed from the bottom of the seasonal ice layer: the crest of the dune, the interface of the dune with the interdune substrate, and through polygonal cracks in the ice. Pressurized gas flows through these vents and carries out material entrained from the dune. Furrows in the dunes channel gas to outbreak points and may be the northern equivalent of southern radially-organized channels ("araneiform" terrain), albeit not permanent. Properties of the seasonal CO2 ice layer are derived from timing of seasonal events such as when final sublimation occurs. Modification of dune morphology shows that landscape evolution is occurring on Mars today, driven by seasonal activity associated with sublimation of the seasonal CO2 polar cap.

Influences of porcine circo-, arteriviruses and cathelicidins in plasmacytoid dendritic cell-derived interferon-alpha responses

Type I interferons (IFNs), mainly IFN-α/β play a crucial role in innate defense against viruses. In addition to their direct antiviral activity, type I IFNs have antitumoral and immunomodulatory effects. Although all cells are virtually able to induce IFN-α, the plasmacytoid dendritic cell (pDC) subset represents the ultimate producers of IFN-α as well as other proinflammatory cytokines. Due to the specific expression of TLR7 and TLR9 recognizing single-stranded (ss) RNA and unmethylated CpG motifs respectively, pDCs can secrete up to 1000 times more IFN-α than any cellular types. Additionally, it is well known that several cytokines including type I and II IFNs, Flt3-L, IL-4 and GM-CSF favor pDC-derived IFN-α responses to unmethylated CpG motifs. In a first step, we aimed to characterize and clarify the interactions of two porcine viruses with pDCs. The double-stranded DNA replicative forms of porcine circovirus type 2 (PCV2) were demonstrated to inhibit CpG-induced IFN- α by pDCs. Our study showed that none of the cytokines known to enhance pDC responsiveness can counter-regulate the PCV2-mediated inhibition of IFN-α induced by CpG, albeit IFN-γ significantly reduced the level of inhibition. Interestingly, the presence of IFN-γ enabled pDCs to induce IFN-α to low doses of PCV2. We also noted that after DNase treatment, PCV2 preparations were still able to stimulate pDCs. These data suggest that encapsulated viral ssDNA promotes the induction of IFN-α in pDCs treated with IFN-γ whereas free DNA, presumably as double-stranded forms, was responsible for inhibiting pDC responses. Regarding PRRSV, it has been reported that North American isolates did not induce and even inhibited IFN-α response in pDCs. However, PRRSV infection was also shown to lead to an induction of IFN-α in the serum and in the lungs suggesting that certain cells are responsive to the virus. Contrasting to previous reports we found that numerous PRRSV isolates directly induced IFN-α in pDCs. This response was still observed after UV-inactivation of viruses and required TLR7 signaling. The inhibition of CpG-induced IFN-α was weak and strain dependent, again contrasting with a previous report. We also observed that IFN-γ and IL-4 enhanced IFN-α response to two prototype strains, VR-2332 and LVP23. In summary, we demonstrated that both PCV2 and PRRSV promote IFN-α secretion in pDCs in vitro suggesting that IFN-α detected in PCV2- or PRRSV-infected animal might originate from pDCs. On the other hand, PRRSV replication is restricted to the macrophage (MΦ) lineage. These innate immune cells represent a heterogeneous population which can be induce to “classical” (M1) and “alternative” (M2) activated MΦ acquiring inflammatory or “wound-healing” functional properties, respectively. Nonetheless, little is known about the effect of polarization into M1 or M2 and the susceptibility of these cells to PRRSV. Thus, we examined the impact of cytokine on MΦ polarization into M1 or M2. Infections of these cells by several PRRSV isolates enabled the discrimination of PRRSV isolate in a genotype- and irulencedependent manner in M1 and IFN-β-activated MΦ. In contrast, the expression of PRRSV nucleocapsid in M2 or inactivated MΦ was indistinguishable among the PRRSV isolates tested. In the last part of my Thesis, we investigated the influence of three synthetic porcine cathelicidin peptides for their ability to deliver nucleic acid to pDCs. We reported that all cathelicidins tested can complex and quickly deliver nucleic acids resulting in IFN-α induction. Moreover, we show that the typical α- helical amphipathic conformation is required to mediate killing of bacteria but not for inducing IFN-α secretion by pDCs. Furthermore, we found that E.coli treated with one of these cathelicidins is able to induce significantly higher levels of IFN-α compared to a non-sense version of the peptide. These data suggest that cathelicidins could influence the immune response in a two-step process. First, these peptides target bacteria leading to cell lysis. In turn, cathelicidins form complexes and deliver extracellular microbial nucleic acids released into pDCs. These pDC-derived IFN-α responses could be of particular relevance in driving the adaptive immune responses against microbial infections.

Interpretation of fluid inclusions in quartz deformed by weak ductile shearing: reconstruction of differential stress magnitudes and pre-deformation fluid properties

A well developed theoretical framework is available in which paleofluid properties, such as chemical composition and density, can be reconstructed from fluid inclusions in minerals that have undergone no ductile deformation. The present study extends this framework to encompass fluid inclusions hosted by quartz that has undergone weak ductile deformation following fluid entrapment. Recent experiments have shown that such deformation causes inclusions to become dismembered into clusters of irregularly shaped relict inclusions surrounded by planar arrays of tiny, new-formed (neonate) inclusions. Comparison of the experimental samples with a naturally sheared quartz vein from Grimsel Pass, Aar Massif, Central Alps, Switzerland, reveals striking similarities. This strong concordance justifies applying the experimentally derived rules of fluid inclusion behaviour to nature. Thus, planar arrays of dismembered inclusions defining cleavage planes in quartz may be taken as diagnostic of small amounts of intracrystalline strain. Deformed inclusions preserve their pre-deformation concentration ratios of gases to electrolytes, but their H2O contents typically have changed. Morphologically intact inclusions, in contrast, preserve the pre-deformation composition and density of their originally trapped fluid. The orientation of the maximum principal compressive stress (σ1σ1) at the time of shear deformation can be derived from the pole to the cleavage plane within which the dismembered inclusions are aligned. Finally, the density of neonate inclusions is commensurate with the pressure value of σ1σ1 at the temperature and time of deformation. This last rule offers a means to estimate magnitudes of shear stresses from fluid inclusion studies. Application of this new paleopiezometer approach to the Grimsel vein yields a differential stress (σ1–σ3σ1–σ3) of ∼300 MPa∼300 MPa at View the MathML source390±30°C during late Miocene NNW–SSE orogenic shortening and regional uplift of the Aar Massif. This differential stress resulted in strain-hardening of the quartz at very low total strain (<5%<5%) while nearby shear zones were accommodating significant displacements. Further implementation of these experimentally derived rules should provide new insight into processes of fluid–rock interaction in the ductile regime within the Earth's crust.

Continuous eclogite melting and variable refertilisation in upwelling heterogeneous mantle

Large-scale tectonic processes introduce a range of crustal lithologies into the Earth's mantle. These lithologies have been implicated as sources of compositional heterogeneity in mantle-derived magmas. The model being explored here assumes the presence of widely dispersed fragments of residual eclogite (derived from recycled oceanic crust), stretched and stirred by convection in the mantle. Here we show with an experimental study that these residual eclogites continuously melt during upwelling of such heterogeneous mantle and we characterize the melting reactions and compositional changes in the residue minerals. The chemical exchange between these partial melts and more refractory peridotite leads to a variably metasomatised mantle. Re-melting of these metasomatised peridotite lithologies at given pressures and temperatures results in diverse melt compositions, which may contribute to the observed heterogeneity of oceanic basalt suites. We also show that heterogeneous upwelling mantle is subject to diverse local freezing, hybridization and carbonate-carbon-silicate redox reactions along a mantle adiabat.

Updated Next-to-Next-to-Leading-Order QCD Predictions for the Weak Radiative B -Meson Decays

Weak radiative decays of the B mesons belong to the most important flavor changing processes that provide constraints on physics at the TeV scale. In the derivation of such constraints, accurate standard model predictions for the inclusive branching ratios play a crucial role. In the current Letter we present an update of these predictions, incorporating all our results for the O(α2s) and lower-order perturbative corrections that have been calculated after 2006. New estimates of nonperturbative effects are taken into account, too. For the CP- and isospin-averaged branching ratios, we find Bsγ=(3.36±0.23)×10−4 and Bdγ=(1.73+0.12−0.22)×10−5, for Eγ>1.6  GeV. Both results remain in agreement with the current experimental averages. Normalizing their sum to the inclusive semileptonic branching ratio, we obtain Rγ≡(Bsγ+Bdγ)/Bcℓν=(3.31±0.22)×10−3. A new bound from Bsγ on the charged Higgs boson mass in the two-Higgs-doublet-model II reads MH±>480  GeV at 95% C.L.

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.