The spectral problem for the dispersionless Camassa-Holm equation

We present a spectral and inverse spectral theory for the zero dispersion spectral problem associated with the Camassa-Holm equation. This is an alternative approach to that in [10] by Eckhardt and Teschl

Observation of individual molecules trapped on a nanostructured insulator

For the first time, ordered polar molecules confined in monolayer-deep rectangular pits produced on an alkali halide surface by electron irradiation have been resolved at room temperature by non-contact atomic force microscopy. Molecules self-assemble in a specific fashion inside pits of width smaller than 15 nm. By contrast no ordered aggregates of molecules are observed on flat terraces. Conclusions regarding nucleation and ordering mechanisms are drawn. Trapping in pits as small as 2 nm opens a route to address single molecules

Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited

We show the David-Jerison construction of big pieces of Lipschitz graphs inside a corkscrew domain does not require its surface measure be upper Ahlfors regular. Thus we can study absolute continuity of harmonic measure and surface measure on NTA domains of locally finite perimeter using Lipschitz approximations. A partial analogue of the F. and M. Riesz Theorem for simply connected planar domains is obtained for NTA domains in space. As a consequence every Wolff snowflake has infinite surface measure.Comment: 22 pages, 6 figure

Human glabrous skin contains crystallized urea dendriform structures in the stratum corneum which affect the hydration levels

Glabrous skin is hair-free skin with a high density of sweat glands, which is found on the palms, and soles of mammalians, covered with a thick stratum corneum. Dry hands are often an occupational problem which deserves attention from dermatologists. Urea is found in the skin as a component of the natural moisturizing factor and of sweat. We report the discovery of dendrimer structures of crystalized urea in the stratum corneum of palmar glabrous skin using laser scanning microscopy. The chemical and structural nature of the urea crystallites was investigated in vivo by non-invasive techniques. The relation of crystallization to skin hydration was explored. We analysed the index finger, small finger and tenar palmar area of 18 study participants using noninvasive optical methods, such as laser scanning microscopy, Raman microspectroscopy and two-photon tomography. Skin hydration was measured using corneometry. Crystalline urea structures were found in the stratum corneum of about two-thirds of the participants. Participants with a higher density of crystallized urea structures exhibited a lower skin hydration. The chemical nature and the crystalline structure of the urea were confirmed by Raman microspectroscopy and by second harmonic generated signals in two-photon tomography. The presence of urea dendrimer crystals in the glabrous skin seems to reduce the water binding capacity leading to dry hands. These findings highlight a new direction in understanding the mechanisms leading to dry hands and open opportunities for the development of better moisturizers and hand disinfection products and for diagnostic of dry skin

Atomic Scale Memory at a Silicon Surface

The limits of pushing storage density to the atomic scale are explored with a memory that stores a bit by the presence or absence of one silicon atom. These atoms are positioned at lattice sites along self-assembled tracks with a pitch of 5 atom rows. The writing process involves removal of Si atoms with the tip of a scanning tunneling microscope. The memory can be reformatted by controlled deposition of silicon. The constraints on speed and reliability are compared with data storage in magnetic hard disks and DNA.Comment: 13 pages, 5 figures, accepted by Nanotechnolog

Genetic analysis of phenotypic indicators for heat tolerance in crossbred dairy cattle

Climate change-induced rise in global temperatures has intensified heat stress on dairy cattle and is contributing to the generally observed low milk productivity. Selective breeding aimed at enhancing animals’ ability to withstand rising temperatures while maintaining optimal performance is crucial for ensuring future access to dairy products. However, phenotypic indicators of heat tolerance are yet to be effectively factored into the objectives of most selective breeding programs. This study investigated the response of milk production to changing heat load as an indication of heat tolerance and the influence of calving season on this response in multibreed dairy cattle performing in three agroecological zones Kenya. First-parity 7-day average milk yield (65 261 milk records) of 1 739 cows were analyzed. Based on routinely recorded weather data that were accessible online, the Temperature-Humidity Index (THI) was calculated and used as a measure of heat load. THI measurements used represented averages of the same 7-day periods corresponding to each 7-day average milk record. Random regression models, including reaction norm functions, were fitted to derive two resilience indicators: slope of the reaction norm (Slope) and its absolute value (Absolute), reflecting changes in milk yield in response to the varying heat loads (THI 50 and THI 80). The genetic parameters of these indicators were estimated, and their associations with average test-day milk yield were examined. There were no substantial differences in the pattern of milk yield response to heat load between cows calving in dry and wet seasons. Animals with ≤50% Bos taurus genes were the most thermotolerant at extremely high heat load levels. Animals performing in semi-arid environments exhibited the highest heat tolerance capacity. Heritability estimates for these indicators ranged from 0.06 to 0.33 and were mostly significantly different from zero (P &lt; 0.05). Slope at THI 80 had high (0.64–0.71) negative correlations with average daily milk yield, revealing that high-producing cows are more vulnerable to heat stress and vice versa. A high (0.63–0.74) positive correlation was observed between Absolute and average milk yield at THI 80. This implied that low milk-producing cows have a more stable milk production under heat-stress conditions and vice versa. The study demonstrated that the slope of the reaction norms and its absolute value can effectively measure the resilience of crossbred dairy cattle to varying heat load conditions. The implications of these findings are valuable in improving the heat tolerance of livestock species through genetic selection.</p

Surviving the surf: The tribomechanical properties of the periostracum of Mytilus sp

We investigated the friction and wear behavior as well as the mechanical properties of the periostracum of Mytilus sp. Tribological properties were determined with a reciprocal sliding microtribometer, while mechanical characterization was performed using a nanoindenter. Measurements were performed in dry and wet conditions. On the dry periostracum we found a low friction coefficient of 0.078 ± 0.007 on the young parts and a higher one of 0.63 ± 0.02 on the old parts of the shell. Under wet, saline, conditions we only observed one average coefficient of friction of 0.37 ± 0.01. Microscopic ex situ analysis indicated that dry periostracum wore rather rapidly by plowing and fatigue, while it exhibited a high wear resistance when immersed in salt water. The Young’s modulus and hardness of the periostracum were also investigated in both dry and wet conditions. Under dry conditions the Young’s modulus of the periostracum was 8 ± 3 GPa, while under wet conditions it was 0.21 ± 0.05 GPa. The hardness of dry periostracum samples was 353 ± 127 MPa, whereas the hardness of wet samples was 5 ± 2 MPa. It was found that, in the wet state, viscous behavior plays a significant role in the mechanical response of the periostracum. Our results strongly indicate that the periostracum can provide an important contribution to the overall wear resistance of Mytilus sp. shell

A bank of unscented Kalman filters for multimodal human perception with mobile service robots

A new generation of mobile service robots could be ready soon to operate in human environments if they can robustly estimate position and identity of surrounding people. Researchers in this field face a number of challenging problems, among which sensor uncertainties and real-time constraints. In this paper, we propose a novel and efficient solution for simultaneous tracking and recognition of people within the observation range of a mobile robot. Multisensor techniques for legs and face detection are fused in a robust probabilistic framework to height, clothes and face recognition algorithms. The system is based on an efficient bank of Unscented Kalman Filters that keeps a multi-hypothesis estimate of the person being tracked, including the case where the latter is unknown to the robot. Several experiments with real mobile robots are presented to validate the proposed approach. They show that our solutions can improve the robot's perception and recognition of humans, providing a useful contribution for the future application of service robotics

Inverse Scattering Transform for the Camassa-Holm equation

An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asymptotic expansions.Comment: 17 pages, LaTe