Parsimonious Segmentation of Time Series' by Potts Models

Typical problems in the analysis of data sets like time-series or images crucially rely on the extraction of primitive features based on segmentation. Variational approaches are a popular and convenient framework in which such problems can be studied. We focus on Potts models as simple nontrivial instances. The discussion proceeds along two data sets from brain mapping and functional genomics

Scale space consistency of piecewise constant least squares estimators -- another look at the regressogram

We study the asymptotic behavior of piecewise constant least squares regression estimates, when the number of partitions of the estimate is penalized. We show that the estimator is consistent in the relevant metric if the signal is in $L^2([0,1])$, the space of c\`{a}dl\`{a}g functions equipped with the Skorokhod metric or $C([0,1])$ equipped with the supremum metric. Moreover, we consider the family of estimates under a varying smoothing parameter, also called scale space. We prove convergence of the empirical scale space towards its deterministic target.Comment: Published at http://dx.doi.org/10.1214/074921707000000274 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

The Electrostatics of Einstein's Unified Field Theory

When sources are added at their right-hand sides, and g_{(ik)} is a priori assumed to be the metric, the equations of Einstein's Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_{(ik)} in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_{(ik)}, however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by H\'ely. In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when H\'ely's physically correct metric is adopted.Comment: 15 pages. Misprints corrected. To appear in General Relativity and Gravitatio

Time-Varying Fine-Structure Constant Requires Cosmological Constant

Webb et al. presented preliminary evidence for a time-varying fine-structure constant. We show Teller's formula for this variation to be ruled out within the Einstein-de Sitter universe, however, it is compatible with cosmologies which require a large cosmological constant.Comment: 3 pages, no figures, revtex, to be published in Mod. Phys. Lett.

Multidimensional perfect fluid cosmology with stable compactified internal dimensions

Multidimensional cosmological models in the presence of a bare cosmological constant and a perfect fluid are investigated under dimensional reduction to 4-dimensional effective models. Stable compactification of the internal spaces is achieved for a special class of perfect fluids. The external space behaves in accordance with the standard Friedmann model. Necessary restrictions on the parameters of the models are found to ensure dynamical behavior of the external (our) universe in agreement with observations.Comment: 11 pages, Latex2e, uses IOP packages, submitted to Class.Quant.Gra

Breathing synchronized electrical stimulation of the abdominal muscles in patients with acute tetraplegia

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively

Triptolide exhibits anti-inflammatory, anti-catabolic as well as anabolic effects and suppresses TLR expression and MAPK activity in IL-1β treated human intervertebral disc cells

Introduction: Increased levels of proinflammatory cytokines seem to play a pivotal role in the development of back pain in a subpopulation of patients with degenerative intervertebral disc (IVD) disease. As current treatment options are mostly limited to surgical interventions or conservative treatment, anti-inflammatory substances might offer a novel, more target-orientated therapeutic approach. Triptolide (TPL), a natural substance found in the Chinese medicinal herb Tripterygium wilfordii Hook, has been demonstrated to possess anti-inflammatory effects in various cells, but no studies exist so far for the IVD. Therefore, the aim of this study was to determine the effects of TPL on human IVD cells by analyzing changes in gene expression and underlying molecular mechanisms. Materials and methods: In order to investigate the anti-inflammatory, anabolic and anti-catabolic effect of TPL, dose-dependency experiments (n=5) and time course experiments (n=5) were performed on IL-1β prestimulated human IVD cells and changes in gene expression of IL-6/-8, TNF-α, PGE2S, MMP1/2/3/13, aggrecan and collagen-I/-II were analyzed by real-time RT-PCR. The molecular mechanisms underlying the effects observed upon TPL treatment were investigated by analyzing involvement of Toll-like receptors TLR2/4 (real-time RT-PCR, n=5), NF-κB, MAP kinases p38, ERK and JNK (immunoblotting and immunocytochemistry, n=4) as well as RNA polymerase II (immunoblotting, n=3). Results: Results showed that 50nM TPL exhibited an anti-inflammatory, anti-catabolic and anabolic effect on the mRNA level for IL-6/-8, PGE2S, MMP1/2/3/13, aggrecan, collagen-II and TLR2/4, with most pronounced changes after 18h for proinflammatory cytokines and MMPs or 30h for TLRs and matrix proteins. However, we also observed an up-regulation of TNF-α at higher concentrations. The effects of TPL did not seem to be mediated via an inhibition of NF-κB or a decrease of RNA polymerase II levels, but TPL influenced activity of MAP kinases p38 and ERK (but not JNK) and expression of TLR2/4. Conclusions: In conclusion, TPL may possess promising potential for the treatment of inflammation-related discogenic back pain in vitro, but its analgetic effect will need to be confirmed in an appropriate in vivo animal mode

An optical mechanism for aberration of starlight

We present a physical-optics based theory of the physical mechanism for aberration of starlight. We apply non-relativistic and relativistic theories for wavefront image formation and include the effects of optically transmitting media within the sensor. We show that the sensors imaging properties combined with finite velocity of light fully accounts for aberration. That is, the influence of the moving sensor on the incident wavefront from the star fully explains aberration. Our treatment differs from all previous derivations because we include wavefront-imaging physics within the sensor model. Our predictions match Earth-sensor based measurements, but differ at larger sensor speeds from predictions of the special relativistic-based theory. While experimental uncertainty resulting from the low Earth-orbital velocity prevents experimental confirmation of the special relativistic model of aberration, we find that Earth-based sensors containing refractive optical media could experimentally differentiate between these competing descriptions and, in addition, yield an independent test of time dilation. We derive and present the details of such an experiment

Assessing the stress-transfer capability of mineral impregnated PBO yarns in a limestone calcined clay cement-based (LC3) matrix

Technical textiles made of poly(p-phenylene-2,6-benzobisoxazole) (PBO) represent attractive candidates for strengthening and repairing damaged concrete and masonry structures, due to the outstanding durability and mechanical performance of PBO fibres. Similarly to their aramid counterparts, PBO fibres have proved very effective against dynamic and impact loading. In this contribution, the pull-out behaviour of PBO multifilament yarns embedded into a blended cement-based matrix is investigated, with particular reference to its stress-transfer capacity. In addition to the as-received PBO yarns, impregnation with a cement-based suspension, which can fully preserve the inorganic nature of the composite system, is also evaluated. Experimental results are presented and interpreted using a one-dimensional mechanical model. The findings indicate that mineral impregnation of the yarns provides a 40% increase in the stress-transfer capacity with the matrix, corresponding to a halving of the anchoring length. These performance gains are also supported by a transition in the failure mechanism which shifts from friction-based pull-out to fibre rupture