a b s t r a c tLet f be a univariate polynomial with real coefficients, f ∈ R[X ].Subdivision algorithms based on algebraic techniques (e.g., Sturm or Descartes methods) are widely used for isolating the real roots of f in a given interval. In this paper, we consider a simple subdivision algorithm whose primitives are purely numerical (e.g., function evaluation). The complexity of this algorithm is adaptive because the algorithm makes decisions based on local data. The complexity analysis of adaptive algorithms (and this algorithm in particular) is a new challenge for computer science. In this paper, we compute the size of the subdivision tree for the SqFreeEVAL algorithm.The SqFreeEVAL algorithm is an evaluation-based numerical algorithm which is well-known in several communities. The algorithm itself is simple, but prior attempts to compute its complexity have proven to be quite technical and have yielded sub-optimal results. Our main result is a simple O(d (L +ln d)) bound on the size of the subdivision tree for the SqFreeEVAL algorithm on the benchmark problem of isolating all real roots of an integer polynomial f of degree d and whose coefficients can be written with at most L bits. Our proof uses two amortization-based techniques: first, we use the algebraic amortization technique of the standard Mahler-Davenport root bounds to interpret the integral in terms of d and L. Second, we use a continuous amortization technique based on an integral to bound the size of the subdivision tree. This paper is the first to use the novel analysis technique of continuous amortization to derive state of the art complexity bounds.

Ungulate populations exhibiting partial migration present a unique opportunity to explore the causes of the general phenomenon of migration. The European roe deer Capreolus capreolus is particularly suited for such studies due to a wide distribution range and a high level of ecological plasticity. In this study we undertook a comparative analysis of roe deer GPS location data from a representative set of European ecosystems available within the EURODEER collaborative project. We aimed at evaluating the ecological factors affecting migration tactic (i.e. occurrence) and pattern (i.e. timing, residence time, number of migratory trips). Migration occurrence varied between and within populations and depended on winter severity and topographic variability. Spring migrations were highly synchronous, while the timing of autumn migrations varied widely between regions, individuals and sexes. Overall, roe deer were faithful to their summer ranges, especially males. In the absence of extreme and predictable winter conditions, roe deer seemed to migrate opportunistically, in response to a tradeoff between the costs of residence in spatially separated ranges and the costs of migratory movements. Animals performed numerous trips between winter and summer ranges which depended on factors influencing the costs of movement such as between‐range distance, slope and habitat openness. Our results support the idea that migration encompasses a behavioural continuum, with one‐trip migration and residence as its end points, while commuting and multi‐trip migration with short residence times in seasonal ranges are intermediate tactics. We believe that a full understanding of the variation in tactics of temporal separation in habitat use will provide important insights on migration and the factors that influence its prevalence.

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Continuous monitoring of extreme environments, such as the European Alps, is hampered by the sparse and/or irregular distribution of meteorological stations, the difficulties in performing ground surveys and the complexity of interpolating existing station data. Remotely sensed Land Surface Temperature (LST) is therefore of major interest for a variety of environmental and ecological applications. But while MODIS LST data from the Terra and Aqua satellites are aimed at closing the gap between data demand and availability, clouds and other atmospheric disturbances often obscure parts or even the entirety of these satellite images. A novel algorithm is presented in this paper, which is able to reconstruct incomplete MODIS LST maps. All nine years of the available daily LST data (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008) have been processed, allowing the original LST map resolution of 1,000 m to be improved to 200 m, which means the resulting LST maps can be applied at a regional level. Extracted time series and aggregated data are shown as examples and are compared to meteorological station time series as an indication of the quality obtained.

BackgroundThe tiger mosquito (Aedes albopictus), vector of several emerging diseases, is expanding into more northerly latitudes as well as into higher altitudes in northern Italy. Changes in the pattern of distribution of the tiger mosquito may affect the potential spread of infectious diseases transmitted by this species in Europe. Therefore, predicting suitable areas of future establishment and spread is essential for planning early prevention and control strategies.Methodology/Principal FindingsTo identify the areas currently most suitable for the occurrence of the tiger mosquito in the Province of Trento, we combined field entomological observations with analyses of satellite temperature data (MODIS Land Surface Temperature: LST) and human population data. We determine threshold conditions for the survival of overwintering eggs and for adult survival using both January mean temperatures and annual mean temperatures. We show that the 0°C LST threshold for January mean temperatures and the 11°C threshold for annual mean temperatures provide the best predictors for identifying the areas that could potentially support populations of this mosquito. In fact, human population density and distance to human settlements appear to be less important variables affecting mosquito distribution in this area. Finally, we evaluated the future establishment and spread of this species in relation to predicted climate warming by considering the A2 scenario for 2050 statistically downscaled at regional level in which winter and annual temperatures increase by 1.5 and 1°C, respectively.Conclusions/SignificanceMODIS satellite LST data are useful for accurately predicting potential areas of tiger mosquito distribution and for revealing the range limits of this species in mountainous areas, predictions which could be extended to an European scale. We show that the observed trend of increasing temperatures due to climate change could facilitate further invasion of Ae. albopictus into new areas.