Bat habitat requirements : implications for land use planning

Knowledge of the habitat requirements of bat species is needed in decision making in land use planning. Bats' hibernation requirements were studied both in Estonia and in southern Finland. In both countries, the northern bat and the brown long-eared bat hibernated in colder and drier locations, whereas Daubenton's bat and Brandt's/whiskered bats hibernated in warmer and more humid locations. In Estonia, the pond bat hibernated in the warmest and most humid conditions, whereas Natterer's bat hibernated in the coldest and driest conditions. Hibernacula were at their coldest in mid-season and became warmer towards the end of the season. The results suggest that bats made an active choice of colder hibernation temperatures at the seasons end. They minimised the negative effects of hibernation early in the hibernation season by hibernating in warmer locations and energy expenditure late in the hibernation season by hibernating in colder locations. The use of foraging habitats was studied in northern and southern Finland. The northern bat used foraging sites opportunistically. Daubenton's bat foraged mainly in water habitats, whereas Brandt's/whiskered bats and the brown long-eared bat foraged mainly in forest habitats. In northern Finland, Daubenton's bats foraged almost exclusively on rivers and typically together with the northern bat. Daubenton's bats and Brandt's/whiskered bats were found only where there were lower ambient light levels. One of the most important things in the management of foraging areas for them is to keep them shady. Hibernacula in Finland typically housed few bats, suggesting that hibernation sites used by even a small number of bats are important. Bats typically used natural stone for hibernation suggesting that natural underground sites in rocks or cliffs or man-made underground sites built using natural stone are important for them. The results suggest that appropriate timing of surveys may vary according to the species and latitude.

Kalman Filter Algorithm for Rating and Prediction in Basketball

The Thesis presents a state-space model for a basketball league and a Kalman filter algorithm for the estimation of the state of the league. In the state-space model, each of the basketball teams is associated with a rating that represents its strength compared to the other teams. The ratings are assumed to evolve in time following a stochastic process with independent Gaussian increments. The estimation of the team ratings is based on the observed game scores that are assumed to depend linearly on the true strengths of the teams and independent Gaussian noise. The team ratings are estimated using a recursive Kalman filter algorithm that produces least squares optimal estimates for the team strengths and predictions for the scores of the future games. Additionally, if the Gaussianity assumption holds, the predictions given by the Kalman filter maximize the likelihood of the observed scores. The team ratings allow probabilistic inference about the ranking of the teams and their relative strengths as well as about the teams’ winning probabilities in future games. The predictions about the winners of the games are correct 65-70% of the time. The team ratings explain 16% of the random variation observed in the game scores. Furthermore, the winning probabilities given by the model are concurrent with the observed scores. The state-space model includes four independent parameters that involve the variances of noise terms and the home court advantage observed in the scores. The Thesis presents the estimation of these parameters using the maximum likelihood method as well as using other techniques. The Thesis also gives various example analyses related to the American professional basketball league, i.e., National Basketball Association (NBA), and regular seasons played in year 2005 through 2010. Additionally, the season 2009-2010 is discussed in full detail, including the playoffs.

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds. We apply our results to give a distributed (2 + ε)-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating the size of a stable matching.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

A simple local 3-approximation algorithm for vertex cover

We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required. (c) 2009 Elsevier B.V. All rights reserved.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

An optimal local approximation algorithm for max-min linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0 for nonnegative matrices A and C. We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The approximation ratio of our algorithm is the best possible for any local algorithm; there is a matching unconditional lower bound.