On the convergence of EM-like algorithms for image segmentation using Markov random fields.

Inference of Markov random field images segmentation models is usually performed using iterative methods which adapt the well-known expectation-maximization (EM) algorithm for independent mixture models. However, some of these adaptations are ad hoc and may turn out numerically unstable. In this paper, we review three EM-like variants for Markov random field segmentation and compare their convergence properties both at the theoretical and practical levels. We specifically advocate a numerical scheme involving asynchronous voxel updating, for which general convergence results can be established. Our experiments on brain tissue classification in magnetic resonance images provide evidence that this algorithm may achieve significantly faster convergence than its competitors while yielding at least as good segmentation results.

A random linear functional approach to efficiency bounds

This paper suggests a method for obtaining efficiency bounds in models containing either only infinite-dimensional parameters or both finite- and infinite-dimensional parameters (semiparametric models). The method is based on a theory of random linear functionals applied to the gradient of the log-likelihood functional and is illustrated by computing the lower bound for Cox's regression model

Spatial predictions of land-use transitions and associated threats to biodiversity: the case of forest regrowth in mountain grasslands

Question Can we predict where forest regrowth caused by abandonment of agricultural activities is likely to occur? Can we assess how it may conflict with grassland diversity hotspots? Location Western Swiss Alps (4003210m a.s.l.). Methods We used statistical models to predict the location of land abandonment by farmers that is followed by forest regrowth in semi-natural grasslands of the Western Swiss Alps. Six modelling methods (GAM, GBM, GLM, RF, MDA, MARS) allowing binomial distribution were tested on two successive transitions occurring between three time periods. Models were calibrated using data on land-use change occurring between 1979 and 1992 as response, and environmental, accessibility and socio-economic variables as predictors, and these were validated for their capacity to predict the changes observed from 1992 to 2004. Projected probabilities of land-use change from an ensemble forecast of the six models were combined with a model of plant species richness based on a field inventory, allowing identification of critical grassland areas for the preservation of biodiversity. Results Models calibrated over the first land-use transition period predicted the second transition with reasonable accuracy. Forest regrowth occurs where cultivation costs are high and yield potential is low, i.e. on steeper slopes and at higher elevations. Overlaying species richness with land-use change predictions, we identified priority areas for the management and conservation of biodiversity at intermediate elevations. Conclusions Combining land-use change and biodiversity projections, we propose applied management measures for targeted/identified locations to limit the loss of biodiversity that could otherwise occur through loss of open habitats. The same approach could be applied to other types of land-use changes occurring in other ecosystems.

Insights into the biogeographical history of the Lower Guinea Forest Domain: evidence for the role of refugia in the intraspecific differentiation of Aucoumea klaineana.

Determining the biogeographical histories of rainforests is central to our understanding of the present distribution of tropical biodiversity. Ice age fragmentation of central African rainforests strongly influenced species distributions. Elevated areas characterized by higher species richness and endemism have been postulated to be Pleistocene forest refugia. However, it is often difficult to separate the effects of history and of present-day ecological conditions on diversity patterns at the interspecific level. Intraspecific genetic variation could yield new insights into history, because refugia hypotheses predict patterns not expected on the basis of contemporary environmental dynamics. Here, we test geographically explicit hypotheses of vicariance associated with the presence of putative refugia and provide clues about their location. We intensively sampled populations of Aucoumea klaineana, a forest tree sensitive to forest fragmentation, throughout its geographical range. Characterizing variation at 10 nuclear microsatellite loci, we were able to obtain phylogeographic data of unprecedented detail for this region. Using Bayesian clustering approaches, we demonstrated the presence of four differentiated genetic units. Their distribution matched that of forest refugia postulated from patterns of species richness and endemism. Our data also show differences in diversity dynamics at leading and trailing edges of the species' shifting distribution. Our results confirm predictions based on refugia hypotheses and cannot be explained on the basis of present-day ecological conditions.

Self-avoiding random walks and Olbers' paradox

In this paper, we prove that a self-avoiding walk of infinite length provides a structure that would resolve Olbers' paradox. That is, if the stars of a universe were distributed like the vertices of an infinite random walk with each segment length of about a parsec, then the night sky could be as dark as actually observed on the Earth. Self-avoiding random walk structure can therefore resolve the Olbers' paradox even in a static universe.

Scaling behavior of random knots.

Using numerical simulations we investigate how overall dimensions of random knots scale with their length. We demonstrate that when closed non-self-avoiding random trajectories are divided into groups consisting of individual knot types, then each such group shows the scaling exponent of approximately 0.588 that is typical for self-avoiding walks. However, when all generated knots are grouped together, their scaling exponent becomes equal to 0.5 (as in non-self-avoiding random walks). We explain here this apparent paradox. We introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots. We also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots.

Correlated genetic effects on reproduction define a domestication syndrome in a forest tree.

Compared to natural selection, domestication implies a dramatic change in traits linked to fitness. A number of traits conferring fitness in the wild might be detrimental under domestication, and domesticated species typically differ from their ancestors in a set of traits known as the domestication syndrome. Specifically, trade-offs between growth and reproduction are well established across the tree of life. According to allocation theory, selection for growth rate is expected to indirectly alter life-history reproductive traits, diverting resources from reproduction to growth. Here we tested this hypothesis by examining the genetic change and correlated responses of reproductive traits as a result of selection for timber yield in the tree Pinus pinaster. Phenotypic selection was carried out in a natural population, and progenies from selected trees were compared with those of control trees in a common garden experiment. According to expectations, we detected a genetic change in important life-history traits due to selection. Specifically, threshold sizes for reproduction were much higher and reproductive investment relative to size significantly lower in the selected progenies just after a single artificial selection event. Our study helps to define the domestication syndrome in exploited forest trees and shows that changes affecting developmental pathways are relevant in domestication processes of long-lived plants.

Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

We study discrete-time models in which death benefits can depend on a stock price index, the logarithm of which is modeled as a random walk. Examples of such benefit payments include put and call options, barrier options, and lookback options. Because the distribution of the curtate-future-lifetime can be approximated by a linear combination of geometric distributions, it suffices to consider curtate-future-lifetimes with a geometric distribution. In binomial and trinomial tree models, closed-form expressions for the expectations of the discounted benefit payment are obtained for a series of options. They are based on results concerning geometric stopping of a random walk, in particular also on a version of the Wiener-Hopf factorization.

Priming psychic and conjuring abilities of a magic demonstration influences event interpretation and random number generation biases

Magical ideation and belief in the paranormal is considered to represent a trait-like character; people either believe in it or not. Yet, anecdotes indicate that exposure to an anomalous event can turn skeptics into believers. This transformation is likely to be accompanied by altered cognitive functioning such as impaired judgments of event likelihood. Here, we investigated whether the exposure to an anomalous event changes individuals' explicit traditional (religious) and non-traditional (e.g., paranormal) beliefs as well as cognitive biases that have previously been associated with non-traditional beliefs, e.g., repetition avoidance when producing random numbers in a mental dice task. In a classroom, 91 students saw a magic demonstration after their psychology lecture. Before the demonstration, half of the students were told that the performance was done respectively by a conjuror (magician group) or a psychic (psychic group). The instruction influenced participants' explanations of the anomalous event. Participants in the magician, as compared to the psychic group, were more likely to explain the event through conjuring abilities while the reverse was true for psychic abilities. Moreover, these explanations correlated positively with their prior traditional and non-traditional beliefs. Finally, we observed that the psychic group showed more repetition avoidance than the magician group, and this effect remained the same regardless of whether assessed before or after the magic demonstration. We conclude that pre-existing beliefs and contextual suggestions both influence people's interpretations of anomalous events and associated cognitive biases. Beliefs and associated cognitive biases are likely flexible well into adulthood and change with actual life events.

Water availability predicts forest canopy height at the global scale.

The tendency of trees to grow taller with increasing water availability is common knowledge. Yet a robust, universal relationship between the spatial distribution of water availability and forest canopy height (H) is lacking. Here, we created a global water availability map by calculating an annual budget as the difference between precipitation (P) and potential evapotranspiration (PET) at a 1-km spatial resolution, and in turn correlated it with a global H map of the same resolution. Across forested areas over the globe, Hmean increased with P-PET, roughly: Hmean (m) = 19.3 + 0.077*(P-PET). Maximum forest canopy height also increased gradually from ~ 5 to ~ 50 m, saturating at ~ 45 m for P-PET > 500 mm. Forests were far from their maximum height potential in cold, boreal regions and in disturbed areas. The strong association between forest height and P-PET provides a useful tool when studying future forest dynamics under climate change, and in quantifying anthropogenic forest disturbance.

Forest Transition in Madagascar's Highlands: Initial Evidence and Implications

Madagascar is renowned for the loss of the forested habitat of lemurs and other species endemic to the island. Less well known is that in the highlands, a region often described as an environmental "basket-case" of fire-degraded, eroded grasslands, woody cover has been increasing for decades. Using information derived from publically available high- and medium-resolution satellites, this study characterizes tree cover dynamics in the highlands of Madagascar over the past two decades. Our results reveal heterogeneous patterns of increased tree cover on smallholder farms and village lands, spurred by a mix of endogenous and exogenous forces. The new trees play important roles in rural livelihoods, providing renewable supplies of firewood, charcoal, timber and other products and services, as well as defensible claims to land tenure in the context of a decline in the use of hillside commons for grazing. This study documents this nascent forest transition through Land Change Science techniques, and provides a prologue to political ecological analysis by setting these changes in their social and environmental context and interrogating the costs and benefits of the shift in rural livelihood strategies.