Practical Distance Functions for Path-Planning in Planar Domains

Path planning is an important problem in robotics. One way to plan a path between two points $x,y$ within a (not necessarily simply-connected) planar domain $\Omega$, is to define a non-negative distance function $d(x,y)$ on $\Omega\times\Omega$ such that following the (descending) gradient of this distance function traces such a path. This presents two equally important challenges: A mathematical challenge -- to define $d$ such that $d(x,y)$ has a single minimum for any fixed $y$ (and this is when $x=y$), since a local minimum is in effect a "dead end", A computational challenge -- to define $d$ such that it may be computed efficiently. In this paper, given a description of $\Omega$, we show how to assign coordinates to each point of $\Omega$ and define a family of distance functions between points using these coordinates, such that both the mathematical and the computational challenges are met. This is done using the concepts of \emph{harmonic measure} and \emph{$f$-divergences}. In practice, path planning is done on a discrete network defined on a finite set of \emph{sites} sampled from $\Omega$, so any method that works well on the continuous domain must be adapted so that it still works well on the discrete domain. Given a set of sites sampled from $\Omega$, we show how to define a network connecting these sites such that a \emph{greedy routing} algorithm (which is the discrete equivalent of continuous gradient descent) based on the distance function mentioned above is guaranteed to generate a path in the network between any two such sites. In many cases, this network is close to a (desirable) planar graph, especially if the set of sites is dense

Consumer satisfaction with water, wastewater and waste services in Portugal

While the concept of consumer satisfaction is a central topic in modern marketing theory and practice, citizens' satisfaction with public services, and especially water and waste services, is a eld that still remains empirically rather unexplored. The following study aims to contribute to this area by analysing the determinants of user satisfaction in the water, wastewater and waste sector in Portugal, using a unique survey of 1070 consumers undertaken by the Portuguese Water and Waste Regulator ERSAR. I perform an analysis of the relation between overall service satisfaction and attributespeci c service satisfaction with an ordered logit model. I then explore if subjective consumer satisfaction can be re ected by ERSAR's technical performance indicators. The results suggest that overall consumer satisfaction is driven by consumer's satisfaction with speci c service aspects but unrelated to socioeconomic and demographic characteristics. Furthermore, I show that there is no monotonic association between ERSAR's technical performance indicators and consumers' levels of satisfaction

Upper equatorial Atlantic circulation and cold tongue variability

The eastern equatorial Atlantic, with its characteristic cold tongue during boreal summer, is a region where upper ocean variability is reflected in the most obvious way through sea surface temperature (SST) anomalies. This region is of high interest for a better understanding of climate fluctuations in the tropical Atlantic sector because its SST variability is significantly correlated with rainfall variability over the tropical ocean and adjacent land regions. The heat budget in the eastern equatorial Atlantic is largely determined by non-local exchanges, and this study focuses on the role of horizontal advection via zonal currents as well as equatorial waves for SST variability. The Equatorial Undercurrent (EUC) is studied using a simulation for the period 1990−2002 with a high-resolution ocean general circulation model of the Atlantic Ocean. Simulated transports of the EUC (19.2 Sv across 35°W and 13.7 Sv across 23°W) which supplies the annual mean upwelling in the central and eastern equatorial Atlantic agree well with new transport estimates derived from shipboard observations. Although the observations are not conclusive concerning the seasonal cycle of EUC transports, the simulated seasonal cycles fit largely in the observed range. The analysis of the EUC variability associated with interannual boreal summer variability of the equatorial cold tongue indicates that the supply of cold thermocline waters by the EUC weakens (increases) during warm (cold) events. Additionally, the cold tongue region is found to be affected by equatorial waves. Moored observations as 20°C-isotherm depth anomalies and dynamic height anomalies at the equator, 35°W and 23°W also indicate the presence of equatorial Kelvin waves during both a warm event in 2002 and a cold event in 2005, with relaxed (intensified) winds in the west and the EUC embedded in a shallower (deeper) thermocline at 23°W during boreal summer 2002 (2005). Basinwide satellite sea surface height anomalies are used to derive an equatorial Kelvin wave mode. The time evolution of this mode represents the basis for a regression analysis to investigate related oceanic variability with respect to differences in upper equatorial Atlantic variability during 2002 and 2005: Compared to the exceptionally strong wave activity in 2002, equatorial Kelvin waves were generally weaker during 2005. The main effect of equatorial Kelvin waves on zonal velocity anomalies at 23°W, 0° is evident well below the EUC core, with a secondary maximum near the surface. Their direct influence on cold tongue SST is small, but they are found to affect the equatorial thermocline slope. Prior to the cold tongue onset in 2002 (2005), the presence of equatorial Kelvin waves results in a flat (inclined) thermocline that is crucial for the shallowing (deepening) of the EUC core at 23°W during boreal summer 2002 (2005) and that might precondition the development of the warm (cold) event. The present study shows that knowledge about the input from the west and thus about the preconditioning of the upper layer stratification in the eastern equatorial Atlantic by equatorial waves as well as horizontal advection via the zonal currents may be of prime importance for the prediction of Atlantic extreme events