Geometric continuity and compatibility conditions for 4-patch surfaces

When considering regularity of surfaces, it is its geometry that is of interest. Thus, the concept of geometric regularity or geometric continuity of a specific order is a relevant concept. In this paper we discuss necessary and sufficient conditions for a 4-patch surface to be geometrically continuous of order one and two or, in other words, being tangent plane continuous and curvature continuous respectively. The focus is on the regularity at the point where the four patches meet and the compatibility conditions that must appear in this case. In this article the compatibility conditions are proved to be independent of the patch parametrization, i.e., the compatibility conditions are universal. In the end of the paper these results are applied to a specific parametrization such as Bezier representation in order to generalize a 4-patch surface result by Sarraga.Comment: 25 pages, 6 figure

Finite-time Convergent Gossiping

Gossip algorithms are widely used in modern distributed systems, with applications ranging from sensor networks and peer-to-peer networks to mobile vehicle networks and social networks. A tremendous research effort has been devoted to analyzing and improving the asymptotic rate of convergence for gossip algorithms. In this work we study finite-time convergence of deterministic gossiping. We show that there exists a symmetric gossip algorithm that converges in finite time if and only if the number of network nodes is a power of two, while there always exists an asymmetric gossip algorithm with finite-time convergence, independent of the number of nodes. For $n=2^m$ nodes, we prove that a fastest convergence can be reached in $nm=n\log_2 n$ node updates via symmetric gossiping. On the other hand, under asymmetric gossip among $n=2^m+r$ nodes with $0\leq r<2^m$, it takes at least $mn+2r$ node updates for achieving finite-time convergence. It is also shown that the existence of finite-time convergent gossiping often imposes strong structural requirements on the underlying interaction graph. Finally, we apply our results to gossip algorithms in quantum networks, where the goal is to control the state of a quantum system via pairwise interactions. We show that finite-time convergence is never possible for such systems.Comment: IEEE/ACM Transactions on Networking, In Pres

What is the Effect of Operational Managerial Practices on Dairy Farm Efficiency? Some Results from Sweden

The article aims to investigate how operational managerial practices can contribute to improved farm level efficiency at dairy farms. Operational managerial practices are defined as animal health, breeding, and feeding practices. The main contribution of the article is that it investigates aspects that can be adjusted every day to improve farm efficiency. Aspects describing each of the considered managerial practices are regressed on farm level data envelopment efficiency scores based on farm level data from Sweden. The results show that changes in breeding and feeding practices can lead to improved efficiency. Breeding exactly the number of heifers that is needed for replacement of the dairy cows negatively affects long-run technical efficiency. On the other hand, analyzing forage positively affects long-run allocative efficiency and analyzing fodder grain positively affects short-run economic efficiency. Feeding the cows hay instead of only silage, reduces long-run economic efficiency. No significant effects of animal health practices were found. These results suggest that the farms in the sample are homogeneous in terms of animal health practices and that inefficient farms cannot become more efficient by adapting to the animal health practices of more efficient farms.allocative efficiency, dairy farms, data envelopment analysis, economic efficiency, operational managerial practices, technical efficiency, tobit regression, Sweden, Livestock Production/Industries, Productivity Analysis,

Control Problems at the European Spallation Source

A background on the Europan Spallation Source is given, and our work on three control problems important for the design of its linear accelerator are presented

A note on approximating bond returns allowing for both yield change and time passage

A number of papers through the years have addressed the price-yield relationship, the approximation of bond returns and the associated components of price sensitivity. Typically, the research has been focused around the concept of duration and convexity to explain the price sensitivity of a bond to changes in its yield. Fixed income portfolio managers, however, are also interested in what happens to bond prices over a certain investment horizon, i.e. how time passage affect bond returns together with yield changes. Chance and Jordan [1996] examines this in a very neat way by a second order Taylor series expansion around the current market yiel

A note on approximating bond returns allowing for both yield change and time passage

A number of papers through the years have addressed the price-yield relationship, the approximation of bond returns and the associated components of price sensitivity. Typically, the research has been focused around the concept of duration and convexity to explain the price sensitivity of a bond to changes in its yield. Fixed income portfolio managers, however, are also interested in what happens to bond prices over a certain investment horizon, i.e. how time passage affect bond returns together with yield changes. Chance and Jordan [1996] examines this in a very neat way by a second order Taylor series expansion around the current market yiel

Temperature Stabilization of the Phase-Reference Line at the European Spallation Source

We consider temperature stabilization of the phase-reference line at the European Spallation Source, a facility for neutron spallation currently under construction. Based on extensive modeling of the heat dynamics, a prototype model-based control system with associated hardware architecture is developed and experimentally evaluated on a small-scale setup. The results indicate that temperature stability within ±0.1°C is possible to achieve, also with significant disturbances in the ambient temperature expected during operation

An algorithm for correction of atmospheric scattering dilution effects in volcanic gas emission measurements using skylight differential optical absorption spectroscopy

Differential Optical Absorption Spectroscopy (DOAS) is commonly used to measure gas emissions from volcanoes. DOAS instruments measure the absorption of solar ultraviolet (UV) radiation scattered in the atmosphere by sulfur dioxide (SO2) and other trace gases contained in volcanic plumes. The standard spectral retrieval methods assume that all measured light comes from behind the plume and has passed through the plume along a straight line. However, a fraction of the light that reaches the instrument may have been scattered beneath the plume and thus has passed around it. Since this component does not contain the absorption signatures of gases in the plume, it effectively “dilutes” the measurements and causes underestimation of the gas abundance in the plume. This dilution effect is small for clean-air conditions and short distances between instrument and plume. However, plume measurements made at long distance and/or in conditions with significant atmospheric aerosol, haze, or clouds may be severely affected. Thus, light dilution is regarded as a major error source in DOAS measurements of volcanic degassing. Several attempts have been made to model the phenomena and the physical mechanisms are today relatively well understood. However, these models require knowledge of the local atmospheric aerosol composition and distribution, parameters that are almost always unknown. Thus, a practical algorithm to quantitatively correct for the dilution effect is still lacking. Here, we propose such an algorithm focused specifically on SO2 measurements. The method relies on the fact that light absorption becomes non-linear for high SO2 loads, and that strong and weak SO2 absorption bands are unequally affected by the diluting signal. These differences can be used to identify when dilution is occurring. Moreover, if we assume that the spectral radiance of the diluting light is identical to the spectrum of light measured away from the plume, a measured clean air spectrum can be used to represent the dilution component. A correction can then be implemented by iteratively subtracting fractions of this clean air spectrum from the measured spectrum until the respective absorption signals on strong and weak SO2 absorption bands are consistent with a single overhead SO2 abundance. In this manner, we can quantify the magnitude of light dilution in each individual measurement spectrum as well as obtaining a dilution-corrected value for the SO2 column density along the line of sight of the instrument. This paper first presents the theory behind the method, then discusses validation experiments using a radiative transfer model, as well as applications to field data obtained under different measurement conditions at three different locations; Fagradalsfjall located on the Reykjanaes peninsula in south Island, Manam located off the northeast coast of mainland Papua New Guinea and Holuhraun located in the inland of north east Island