Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Predicting future distributions of mountain plants under climate change: does dispersal capacity matter?

Many studies have investigated the impacts that climate change could potentially have on the distribution of plant species, but few have attempted to constrain projections through plant dispersal limitations. Instead, most studies published so far have been using the simplification of considering dispersal as either unlimited or null. However, depending on a species' dispersal capacity, landscape fragmentation, and the rate of climatic change, these assumptions can lead to serious over- or underestimation of a species' future distribution. To quantify the discrepancies between unlimited, realistic, and no dispersal scenarios, we carried out projections of future distribution over the 21st century for 287 mountain plant species in a study area of the Western Swiss Alps. For each species, simulations were run for four dispersal scenarios (unlimited dispersal, no dispersal, realistic dispersal and realistic dispersal with long-distance dispersal events) and under four climate change scenarios. Although simulations accounting for realistic dispersal limitations did significantly differ from those considering dispersal as unlimited or null in terms of projected future distribution, using the unlimited dispersal simplification nevertheless provided good approximations for species extinctions under more moderate climate change scenarios. Overall, simulations accounting for dispersal limitations produced, for our mountainous study area, results that were significantly closer to unlimited dispersal than to no dispersal. Finally, analyzing the temporal pattern of species extinctions over the entire 21st century showed that, due to the possibility of a large number of species shifting their distribution to higher elevation, important species extinctions for our study area might not occur before the 2080-2100 time periods.

Can we disentangle predator-prey interactions from species distributions at a macro-scale? A case study with a raptor species.

There is a debate on whether an influence of biotic interactions on species distributions can be reflected at macro-scale levels. Whereas the influence of biotic interactions on spatial arrangements is beginning to be studied at local scales, similar studies at macro-scale levels are scarce. There is no example disentangling, from other similarities with related species, the influence of predator-prey interactions on species distributions at macro-scale levels. In this study we aimed to disentangle predator-prey interactions from species distribution data following an experimental approach including a factorial design. As a case of study we selected the short-toed eagle because of its known specialization on certain prey reptiles. We used presence-absence data at a 100 Km2 spatial resolution to extract the explanatory capacity of different environmental predictors (five abiotic and two biotic predictors) on the short-toed eagle species distribution in Peninsular Spain. Abiotic predictors were relevant climatic and topographic variables, and relevant biotic predictors were prey richness and forest density. In addition to the short-toed eagle, we also obtained the predictor's explanatory capacities for i) species of the same family Accipitridae (as a reference), ii) for other birds of different families (as controls) and iii) species with randomly selected presences (as null models). We run 650 models to test for similarities of the short-toed eagle, controls and null models with reference species, assessed by regressions of explanatory capacities. We found higher similarities between the short-toed eagle and other species of the family Accipitridae than for the other two groups. Once corrected by the family effect, our analyses revealed a signal of predator-prey interaction embedded in species distribution data. This result was corroborated with additional analyses testing for differences in the concordance between the distributions of different bird categories and the distributions of either prey or non-prey species of the short-toed eagle. Our analyses were useful to disentangle a signal of predator-prey interactions from species distribution data at a macro-scale. This study highlights the importance of disentangling specific features from the variation shared with a given taxonomic level.

On the relationship between connections and the asymptotic properties of predictive distributions

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

Random assignment of intervention points in two phase single-case designs: data-division-specific distributions

The present study explores the statistical properties of a randomization test based on the random assignment of the intervention point in a two-phase (AB) single-case design. The focus is on randomization distributions constructed with the values of the test statistic for all possible random assignments and used to obtain p-values. The shape of those distributions is investigated for each specific data division defined by the moment in which the intervention is introduced. Another aim of the study consisted in testing the detection of inexistent effects (i.e., production of false alarms) in autocorrelated data series, in which the assumption of exchangeability between observations may be untenable. In this way, it was possible to compare nominal and empirical Type I error rates in order to obtain evidence on the statistical validity of the randomization test for each individual data division. The results suggest that when either of the two phases has considerably less measurement times, Type I errors may be too probable and, hence, the decision making process to be carried out by applied researchers may be jeopardized.

Photoreceptor types and distributions in the retinae of insectivores.

The retinae of insectivores have been rarely studied, and their photoreceptor arrangements and expression patterns of visual pigments are largely unknown. We have determined the presence and distribution of cones in three species of shrews (common shrew Sorex araneus, greater white-toothed shrew Crocidura russula, dark forest shrew Crocidura poensis; Soricidae) and in the lesser hedgehog tenrec Echinops telfairi (Tenrecidae). Special cone types were identified and quantified in flattened whole retinae by antisera/antibodies recognizing the middle-to-long-wavelength-sensitive (M/L-)cone opsin and the short-wavelength-sensitive (S-)cone opsin, respectively. A combination of immunocytochemistry with conventional histology was used to assess rod densities and cone/rod ratios. In all four species the rods dominate at densities of about 230,000-260,000/mm2. M/L- and S-cones are present, comprising between 2% of the photoreceptors in the nocturnal Echinops telfairi and 13% in Sorex araneus that has equal diurnal and nocturnal activity phases. This suggests dichromatic color vision like in many other mammals. A striking feature in all four species are dramatically higher S-cone proportions in ventral than in dorsal retina (0.5% vs. 2.5-12% in Sorex, 5-15% vs. 30-45% in Crocidura poensis, 3-12% vs. 20-50% in Crocidura russula, 10-30% vs. 40-70% in Echinops). The functional and comparative aspects of these structural findings are discussed.

Degree of previous cutting in explaining the differences in diameter distributions between mature managed and natural Norway spruce forests

Abstract

A critical evaluation of secondary cancer risk models applied to Monte Carlo dose distributions of 2-dimensional, 3-dimensional conformal and hybrid intensity-modulated radiation therapy for breast cancer.

The comparison of radiotherapy techniques regarding secondary cancer risk has yielded contradictory results possibly stemming from the many different approaches used to estimate risk. The purpose of this study was to make a comprehensive evaluation of different available risk models applied to detailed whole-body dose distributions computed by Monte Carlo for various breast radiotherapy techniques including conventional open tangents, 3D conformal wedged tangents and hybrid intensity modulated radiation therapy (IMRT). First, organ-specific linear risk models developed by the International Commission on Radiological Protection (ICRP) and the Biological Effects of Ionizing Radiation (BEIR) VII committee were applied to mean doses for remote organs only and all solid organs. Then, different general non-linear risk models were applied to the whole body dose distribution. Finally, organ-specific non-linear risk models for the lung and breast were used to assess the secondary cancer risk for these two specific organs. A total of 32 different calculated absolute risks resulted in a broad range of values (between 0.1% and 48.5%) underlying the large uncertainties in absolute risk calculation. The ratio of risk between two techniques has often been proposed as a more robust assessment of risk than the absolute risk. We found that the ratio of risk between two techniques could also vary substantially considering the different approaches to risk estimation. Sometimes the ratio of risk between two techniques would range between values smaller and larger than one, which then translates into inconsistent results on the potential higher risk of one technique compared to another. We found however that the hybrid IMRT technique resulted in a systematic reduction of risk compared to the other techniques investigated even though the magnitude of this reduction varied substantially with the different approaches investigated. Based on the epidemiological data available, a reasonable approach to risk estimation would be to use organ-specific non-linear risk models applied to the dose distributions of organs within or near the treatment fields (lungs and contralateral breast in the case of breast radiotherapy) as the majority of radiation-induced secondary cancers are found in the beam-bordering regions.