Symmetry-Based Search Space Reduction For Grid Maps

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles, removing from each rectangle all interior nodes and possibly some from along the perimeter. We then add a series of macro-edges between selected pairs of remaining perimeter nodes to facilitate provably optimal traversal through each rectangle. We also develop a novel online pruning technique to further speed up search. Our algorithm is fast, memory efficient and retains the same optimality and completeness guarantees as searching on an unmodified grid map

The FastMap Algorithm for Shortest Path Computations

We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph. Later, at runtime, a shortest path between any two nodes can be computed with A* search using the Euclidean distances as heuristic. Our preprocessing algorithm, called FastMap, is inspired by the data mining algorithm of the same name and runs in near-linear time. Hence, FastMap is orders of magnitude faster than competing approaches that produce a Euclidean embedding using Semidefinite Programming. FastMap also produces admissible and consistent heuristics and therefore guarantees the generation of shortest paths. Moreover, FastMap applies to general undirected graphs for which many traditional heuristics, such as the Manhattan Distance heuristic, are not well defined. Empirically, we demonstrate that A* search using the FastMap heuristic is competitive with A* search using other state-of-the-art heuristics, such as the Differential heuristic

The behavioural function of pheromones in crayfish

Pacifastacus leniusculus and Procambarus clarkii are highly invasive freshwater crayfish and are having detrimental impacts on native species and habitats throughout Europe. The application of pheromone baits have been proposed as a way of increasing trap efficiency for population control, however the chemical identity of crayfish pheromones is unknown. An incomplete understanding of chemical communication has delayed progress in the development of appropriate bioassays. This thesis therefore focused on researching the natural context of chemical signalling by crayfish, including signal delivery and receiver response.Urine release by male and female crayfish was found to coincide with aggressive behaviours rather than reproductive behaviours. Female urine release was essential for initiating mating, with males detecting female receptivity by spying on hormones and metabolites released with threat signals. Physiological indicators of reception included a brief cardiac and ventilatory arrest followed by an increase in rate. Both behavioural and physiological responses formed the basis of a novel assay design.During courtship male crayfish do not appear to advertise by urine signals. This raised the question of whether chemical signals were important for female assessment of the quality of size-matched males. When given a free choice, females could not distinguish dominant and subordinate males through chemical signals alone. This suggests that females either use other criteria (e.g. size) for mate choice or perform cryptic postcopulatory mate choice.Blocking natural urine release of crayfish, which had previously fought to establish dominance, and artificially introducing urinary signals proved an effective bioassay for investigating the mechanisms of dominance hierarchy formation. Urine from the dominant male was the key factor in establishing dominance relationships. In the absence of dominant urine, subordinate males were less likely to retreat from aggressive bouts and fights were more intense.The mechanisms of signal delivery during agonistic encounters were investigated by measuring ventilatory activity. Increased ventilation rate was associated with highly aggressive behaviours and urinary signalling. This indicated crayfish create gill currents to disperse signals and increase transfer efficiency from sender to receiver.This thesis sheds light into the mechanism of chemical communication in crayfish and provides the basis for future bioassay guided purification of crayfish pheromones

Performance Trade‐Offs Among Tropical Tree Seedlings In Contrasting Microhabitats

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/117031/1/ecy20058692461.pd

Competitive coexistence of coral-dwelling fishes: the lottery hypothesis revisited

Evidence for competitive lotteries among reef fishes has remained elusive despite this being the group of organisms for which the lottery model was first developed. I used a combination of laboratory and field experiments to test the mechanisms of coexistence between two closely related species of coral-dwelling goby, Gobiodon histrio and G. erythrospilus, that occur in similar abundance at Lizard Island on the Great Barrier Reef. These two species exhibited similar patterns of habitat use and nearly identical ability to compete for vacant corals. Furthermore, there was a priority effect where the first species to occupy a vacant coral excluded an interspecific intruder of similar body size. The relative abundance of recruit and juvenile G. histrio and G. erythrospilus in the field matched the relative abundance of adults, as expected where there is no post-recruitment displacement by a competitive hierarchy. Finally, a reciprocal competitor-reduction experiment confirmed that G. histrio and G. erythrospilus compete for vacant space, with the removal of either species leading to an increase in the abundance of the other species. Therefore these two species are nearly ecologically equivalent and appear to coexist by means of a competitive lottery for vacant space

Modelling socio-spatial movement behaviour of orangutans (Pongo abelii) in Suaq (Sumatra Utara)

The Sumatran orangutan (pongo abelii ) is a flagship species for its valuable tropical rainforest habitat, but they are critically endangered. Habitat loss and wildlife trade can bring this close relative of ours to the brink of extinction. As humans continue to remove land from its natural habitat, the spatial behavior and needs of orangutans are of particular interest. The spatial behaviour and ecology of orangutans and their ecological needs are still poorly understood. By looking at different habitats and populations, the influence of external and internal factors on orangutans can be analysed. A data set from Suaq (Sumatra Utara, Indonesia) was compared to the available literature of a second research site in Tuanan (Borneo, Indonesia). The habitats and their topography are very similar, but fruit productivity, density, and sociability are much higher in Suaq which allows us to compare the underlying ecological differences. Three spatio-temporal levels of analysis were defined: Level 1 - distance patterns, Level 2 - daily movement patterns and Level 3 - momentary movement behaviour. In the context of this work, mainly level 1 and level 2 were analysed. For the first level, the focus was on ten adult females, while for the second level results for all age and sex classes were included. For all further analyses, external and internal predictors were used to see how they influenced the movement patterns found. External factors were Fruit Availability Index, average temperature, daytime and nighttime rainfall, and a derived density of fruit tree value. Internal factors for all individuals were age-sex classes. Whereas for adult females – which were the focus of this thesis – dominance rank, age, age of current offspring and relatedness were considered. On level one, the ranging pattern over the full study period and some user-defined periods were analysed with four home range algorithms (Minimum Convex Polygon, Kernel Distance Estimation, Biased Random Bridge, Autocorrelated Kernel Density Estimation. KDE and BRB gave similar estimates and proved to be the most useful. They did not over-smooth or under-smooth the distribution and were of high quality with respect to the defined quality descriptors (e.g. number of polygons, compactness, number of holes and Area Under the Curve). The AKDE was useful to access the absolute home range sizes for smaller sample sizes and the MCP was mainly used to compare the results with other studies. The unbalanced data set in terms of time and size proved to be the main problem in analysing spatial behaviour with the present data set. A conservative approximation of about 100 animals was determined, leading to reliable range estimates. Home ranges were found to be ranging between 1.6 (algorithm: BRB, focal: Ellie) and 2.4 km2 (algorithm: BRB, focal: Cissy) which is smaller than in recent studies. Likewise were core ranges smaller than expected but seemed more stable and less dependent on sample size. Existing hypotheses that home ranges in Suaq are much bigger based on the patchiness of feeding resources than, e.g. in Tuanan could not be confirmed. Dominance, age and the number of normalised forage trees were found to have no effect on the size of the home ranges. Fruit trees can account for some larger core ranges, but in general, the normalised fruit tree value did not differ between overlaps, core ranges nor complete home ranges. The overlaps of the resulted home ranges were also compared with different algorithms. The Utilization Distribution Overlap Index (UDOI) was especially useful in estimating overlaps based on the uncertainty analysis conducted at the beginning of this thesis. Overlap percentages of home ranges were bigger than for core ranges which may indicate partial range exclusion. The total amount of relatively shared range was found to be on average 84% and for core ranges 96%. However, using the UDOI values ranged between 0.32 (focal: Yulia) and 0.7 (focal: Tiara) where 1 equals 100% overlap. Relatedness explained around 10% higher overlaps and similar dominance levels showed to explain lower values of overlaps. The higher overlap of related females may be the result of female philopatry rather than a sign of active range exclusion. The higher overlap of differing dominance rank groups may result from the enlarged home ranges of young females. On level two, 1314 follows were mainly analysed by deriving the Day-journey-length or daily total-traveled-distance (DJL) and two tortuosity indices namely, the Straightness Index (SI) and the sinuosity index. A preliminary analysis revealed that an underestimation of DJL is present, based on the chosen sampling interval. DJL was around 35% lower when GPS fixes were taken every 30 min instead of every 5 min. The discussion of how much DJL actually reflect real daily movement, which revealed that many uncertainties exist and that further research is needed (e.g. denser sampling interval, inclusion of height changes). Nonetheless, the average DJL of 885 m was found to be higher in Suaq than in Tuanan. The overall higher travel distance is mainly addressed to a more pronounced ”search and find“ strategy compared to a ”sit and wait“ strategy in Tuanan during seasons of low fruit availability. Especially flanged males tended to travel much further in Suaq (+200 m) than in Tuanan, even slightly more than adult females. Flanged males in Suaq may adjust their mating and movement strategies based on habitat productivity and social conditions. The more stable dominance hierarchy between males may be maintained by longer DJL of flanged males. This results in the greater risk of unflanged males becoming flanged males and the greater developmental arrest in Suaq compared to Tuanan can be explained. External factors like day rain and night rain, average temperatures and fruit availability did not show any impact on day journey length. This indicates a ceiling effect where fruit availability is always high enough to support high movement activities, even when variation in FAI occurs. For females, dominance did not impact the movement parameters but the age of the current offspring did. The DJL increased from around 800 m to 1000 m on average over the duration of motherhood (for every year +34 m). A very similar pattern was also found in Tuanan and probably relates to the clinging of young o↵spring at lower ages but also to an adjustment to the offspring’s energy, household and movement competence. The age of the current offspring also influenced both tortuosity indices negatively (negative in the sense of tortuosity) and showed that I actually can detect movement changes with these indices. The only other factor which explained tortuosity was the number of visited fruit trees. This could indicate that feeding tree distribution is actually slightly clumped. Furthermore, this thesis gives various backgrounds and further insights into the available data set and possible future research. E.g. about the movement activity over daytime (level 3). The immense effort of preparing the analysis and the data set is additionally described and the used methods implemented in R are openly available

Relaxion Monodromy and the Weak Gravity Conjecture

The recently proposed relaxion models require extremely large trans-Planckian axion excursions as well as a potential explicitly violating the axion shift symmetry. The latter property is however inconsistent with the axion periodicity, which corresponds to a gauged discrete shift symmetry. A way to make things consistent is to use monodromy, i.e. both the axion and the potential parameters transform under the discrete shift symmetry. The structure is better described in terms of a 3-form field $C_{\mu \nu \rho}$ coupling to the SM Higgs through its field strength $F_4$. The 4-form also couples linearly to the relaxion, in the Kaloper-Sorbo fashion. The extremely small relaxion-Higgs coupling arises in a see-saw fashion as $g\simeq F_4/f$, with $f$ being the axion decay constant. We discuss constraints on this type of constructions from membrane nucleation and the Weak Gravity Conjecture. The latter requires the existence of membranes, whose too fast nucleation could in principle drive the theory out of control, unless the cut-off scale is lowered. This allows to constrain relaxion models on purely theoretical grounds. We also discuss possible avenues to embed this structure into string theory.Comment: 26 pages + appendices, 3 figures; v3: Corrected bounds on relaxion parameter spac