Functional Liftings of Vectorial Variational Problems with Laplacian Regularization

We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration method as well as from sublabel-accurate continuous multilabeling approaches, and makes these approaches amenable for variational problems with vectorial data and higher-order regularization, as is common in image processing applications. We motivate the approach in the function space setting and prove that, in the special case of absolute Laplacian regularization, it encompasses the discretization-first sublabel-accurate continuous multilabeling approach as a special case. We present a mathematical connection between the lifted and original functional and discuss possible interpretations of minimizers in the lifted function space. Finally, we exemplarily apply the proposed approach to 2D image registration problems.Comment: 12 pages, 3 figures; accepted at the conference "Scale Space and Variational Methods" in Hofgeismar, Germany 201

Catalysis in non--local quantum operations

We show how entanglement can be used, without being consumed, to accomplish unitary operations that could not be performed with out it. When applied to infinitesimal transformations our method makes equivalent, in the sense of Hamiltonian simulation, a whole class of otherwise inequivalent two-qubit interactions. The new catalysis effect also implies the asymptotic equivalence of all such interactions.Comment: 4 pages, revte

Low levels of cardiovascular risk factors and coronary heart disease in a UK Chinese population.

OBJECTIVE: To compare the prevalence of cardiovascular risk factors and coronary heart disease in Chinese and Europid adults. DESIGN: Population based, cross sectional survey. SETTING: Newcastle upon Tyne, UK, 1991-93. SUBJECTS: Altogether 380 Chinese and 625 Europid adults, aged 25-64 years. MAIN OUTCOME MEASURES: Fasting lipid levels, blood pressure, body mass index (BMI), the proportions who smoked, and the prevalence of coronary heart disease based on the Rose angina questionnaire and major electrocardiographic abnormalities on resting 12 lead electrocardiogram (Minnesota codes 1.1-1.2). All figures were age adjusted to the 1991 England and Wales population. RESULTS: Altogether 183 and 197 Chinese, and 310 and 315 Europid men and women respectively were seen. Compared with Europid men, Chinese men had a lower mean total cholesterol concentration (5.1 versus 5.6 mmol/l, p 0.05) and diastolic (75 versus 68 mmHg, p < 0.001) blood pressures. The prevalence of coronary heart disease was significantly lower in Chinese than Europid men (4.9% versus 16.6%, p < 0.001) but not significantly different in women (7.3% versus 11.1%, p = 0.16). CONCLUSION: Strategies for UK Chinese are needed to maintain this favourable risk factor profile and prevent any potential increase in the risk of coronary heart disease associated with increasing acculturation

Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure

Froth-like minimizers of a non local free energy functional with competing interactions

We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.Comment: 38 pages, 2 figure

The fate of the homoctenids (Tentaculitoidea) during the Frasnian-Famennian mass extinction (Late Devonian)

The homoctenids (Tentaculitoidea) are small, conical-shelled marine animals which are amongst the most abundant and widespread of all Late Devonian fossils. They were a principal casualty of the Frasnian-Famennian (F-F, Late Devonian) mass extinction, and thus provide an insight into the extinction dynamics. Despite their abundance during the Late Devonian, they have been largely neglected by extinction studies. A number of Frasnian-Famennian boundary sections have been studied, in Poland, Germany, France, and the United States. These sections have yielded homoctenids, which allow precise recognition of the timing of the mass extinction. It is clear that the homoctenids almost disappear from the fossil record during the latest Frasnian “Upper Kellwasser Event”. The coincident extinction of this pelagic group, and the widespread development of intense marine anoxia within the water column, provides a causal link between anoxia and the F-F extinction. Most notable is the sudden demise of a group, which had been present in rock-forming densities, during this anoxic event. One new species, belonging to Homoctenus is described, but is not formally named here

Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical Physics on Probabilistic Methods in Statistical Physic

Pathogenic role of delta 2 tubulin in bortezomib-induced peripheral neuropathy

The pathogenesis of chemotherapy-induced peripheral neuropathy (CIPN) is poorly understood. Here, we report that the CIPN-causing drug bortezomib (Bort) promotes delta 2 tubulin (D2) accumulation while affecting microtubule stability and dynamics in sensory neurons in vitro and in vivo and that the accumulation of D2 is predominant in unmyelinated fibers and a hallmark of bortezomib-induced peripheral neuropathy (BIPN) in humans. Furthermore, while D2 overexpression was sufficient to cause axonopathy and inhibit mitochondria motility, reduction of D2 levels alleviated both axonal degeneration and the loss of mitochondria motility induced by Bort. Together, our data demonstrate that Bort, a compound structurally unrelated to tubulin poisons, affects the tubulin cytoskeleton in sensory neurons in vitro, in vivo, and in human tissue, indicating that the pathogenic mechanisms of seemingly unrelated CIPN drugs may converge on tubulin damage. The results reveal a previously unrecognized pathogenic role for D2 in BIPN that may occur through altered regulation of mitochondria motility

Modeling and Simulation of Multi-Lane Traffic Flow

A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity fluctuations, overtaking and lane-changing maneuvers is systematically deduced from a gas-kinetic (Boltzmann-like) approach. The resulting equations contain corrections with respect to previous models. For efficient computer simulations, a reduced model delineating the coarse-grained temporal behavior is derived and applied to bottleneck situations.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm