Topological obstructions for vertex numbers of Minkowski sums

We show that for polytopes P_1, P_2, ..., P_r \subset \R^d, each having n_i \ge d+1 vertices, the Minkowski sum P_1 + P_2 + ... + P_r cannot achieve the maximum of \prod_i n_i vertices if r \ge d. This complements a recent result of Fukuda & Weibel (2006), who show that this is possible for up to d-1 summands. The result is obtained by combining methods from discrete geometry (Gale transforms) and topological combinatorics (van Kampen--type obstructions) as developed in R\"{o}rig, Sanyal, and Ziegler (2007).Comment: 13 pages, 2 figures; Improved exposition and less typos. Construction/example and remarks adde

Comparison of spatial downscaling methods of general circulation model results to study climate variability during the last glacial maximum

The extent to which climate conditions influenced the spatial distribution of hominin populations in the past is highly debated. General circulation models (GCMs) and archaeological data have been used to address this issue. Most GCMs are not currently capable of simulating past surface climate conditions with sufficiently detailed spatial resolution to distinguish areas of potential hominin habitat, however. In this paper, we propose a statistical downscaling method (SDM) for increasing the resolution of climate model outputs in a computationally efficient way. Our method uses a generalised additive model (GAM), calibrated over present-day climatology data, to statistically downscale temperature and precipitation time series from the outputs of a GCM simulating the climate of the Last Glacial Maximum (19 000–23 000 BP) over western Europe. Once the SDM is calibrated, we first interpolate the coarse-scale GCM outputs to the final resolution and then use the GAM to compute surface air temperature and precipitation levels using these interpolated GCM outputs and fine-resolution geographical variables such as topography and distance from an ocean. The GAM acts as a transfer function, capturing non-linear relationships between variables at different spatial scales and correcting for the GCM biases. We tested three different techniques for the first interpolation of GCM output: bilinear, bicubic and kriging. The resulting SDMs were evaluated by comparing downscaled temperature and precipitation at local sites with paleoclimate reconstructions based on paleoclimate archives (archaeozoological and palynological data) and the impact of the interpolation technique on patterns of variability was explored. The SDM based on kriging interpolation, providing the best accuracy, was then validated on present-day data outside of the calibration period. Our results show that the downscaled temperature and precipitation values are in good agreement with paleoclimate reconstructions at local sites, and that our method for producing fine-grained paleoclimate simulations is therefore suitable for conducting paleo-anthropological research. It is nonetheless important to calibrate the GAM on a range of data encompassing the data to be downscaled. Otherwise, the SDM is likely to overcorrect the coarse-grain data. In addition, the bilinear and bicubic interpolation techniques were shown to distort either the temporal variability or the values of the response variables, while the kriging method offered the best compromise. Since climate variability is an aspect of the environment to which human populations may have responded in the past, the choice of interpolation technique is therefore an important consideration.</p

Characterizing Protein Conformation Space

In this work, we propose a radical approach for exploring the space of all possible protein structures. We present techniques to explore the clash-free conformation space, which comprises all protein structures whose atoms are not in self-collision. Unlike energy based methods, this approach allows efficient exploration and remains general -- the benefits of characterization of the space apply to all proteins. We hypothesize that this conformation space branches into many small funnels as we sample compact conformations. We develop a compact representation the conformation space, and give experimental results that support our hypothesis. Potential applications of our method include protein folding as well as observing structural relationships between proteins.Singapore-MIT Alliance (SMA

Similar compositional turnover but distinct insular environmental and geographical drivers of native and exotic ants in two oceans

Aim This study aims to quantify the patterns in compositional turnover of native and exotic ants on small islands in two oceans, and to explore whether such patterns are driven by similar environmental, geographical and potentially biotic variables. Location Pacific and Atlantic islands. Time period Present. Major taxa studied Ants. Methods We applied Multi‐Site Generalised Dissimilarity Modelling (MS‐GDM), which relates zeta diversity, the number of species shared by a given number of islands, to differences in environmental, geographical and biotic drivers. The use of zeta diversity enabled us to differentiate the contribution of rare species (shared by few islands) from those of widespread ones (shared by multiple islands) to compositional turnover. For completion, we also related species richness of insular ants per island with the same set of explanatory variables using Generalised Additive Models (GAM). Results Pacific and Atlantic islands have similar patterns of ant species turnover and richness, albeit partly driven by different drivers. Native and exotic species turnover are mostly explained by the same set of variables in the Pacific (annual precipitation and distance to the nearest island), but not in the Atlantic (annual precipitation is a good predictor of native species turnover, but none of the variables considered in our study explained exotic species turnover). No signal of biotic interactions was detected at the insular community level. Main conclusions Successful invasion strategies may depend on a combination of factors specific to the region in question. In the Pacific, milder environments and the absence of natives on certain islands enable exotic ants to select the same types of environment as native ants. In the harsher Atlantic Ocean, however, native ant species are likely to be well adapted to local environmental conditions, making it harder for exotics to become established. Exotic ant species, therefore, potentially rely on other attributes to establish, such as a combination of tolerance to a wide range of environmental conditions and human‐mediated colonization

The effect of cross-boundary management on the trajectory to commonness in biological invasions

The number of alien species introduced and undergoing range expansion in novel environments is steadily increasing, with important consequences for native ecosystems. The efficacy of management planning and decision making to limit such invasions can be improved by understanding how interventions will impact the population dynamics of recently introduced species. To do so, here we expand on a typological framework that enables the classification of populations over time into 10 categories of commonness, and apply it to a spatially discrete metapopulation with heterogeneous abundance across spatial units (patches). We use this framework to assess the effect of cross-boundary management on the capacity of a metapopulation with different demographic and dispersal characteristics, including time lags in population growth, to become common. We demonstrate this framework by simulating a simple theoretical metapopulation model capable of exploring a range of environments, species characteristics, and management actions. Management can vary in the efficacy of propagule interception between patches, and in the synchronisation of the implementation of these measures across patches (i.e. if management is implemented simultaneously across patches). Simulations show that poor interception efficacy that only modestly reduces the number of propagules entering a given spatial unit cannot be compensated for by strong management synchronisation between spatial units. Management synchronisation will nonetheless result in a reduction in rates of spread once a critical threshold of interception efficacy has been met. Finally, time lags in population growth that may result in delayed spread are an important aspect to be considered in management as they can amplify the efficacy of management. Our results demonstrate how a typological framework of categories of commonness can be used to provide practical insights for the management of biological invasions

Systematic use of models of concurrency in executable domain-specific modelling languages

Language-Oriented Programming (LOP) advocates designing eXecutable Domain-Specific Modeling Languages (xDSMLs) to facilitate the design, development, verification and validation of modern softwareintensive and highly-concurrent systems. These systems place their needs of rich concurrency constructs at the heart of modern software engineering processes. To ease theirdevelopment, theoretical computer science has studied the use of dedicated paradigms for the specification of concurrent systems, called Models of Concurrency (MoCs). They enable the use of concurrencyaware analyses such as detecting deadlocks or starvation situations, but are complex to understand and master. In this thesis, we develop and extend an approach that aims at reconciling LOP and MoCs by designing so-called Concurrencyaware xDSMLs. In these languages, the systematic use of a MoC is specified at the language level, removing from the end-user the burden of understanding or using MoCs. It also allows the refinement of the language for specific execution platforms, and enables the use of concurrency-aware analyses on the systems

Développement d’un modèle centré sur l’individu des déplacements du caribou, du loup et de l’orignal, et de leurs interactions, en forêt boréale aménagée

Le caribou forestier est une espèce menacée au Canada, la principale hypothèse au déclin des populations étant l’intensification de la prédation provoquée par les perturbations anthropiques du paysage. Afin de faire face à cette situation, il est nécessaire d’étudier et comprendre l’impact de l’environnement sur les interactions prédateur-proies entre le caribou et le loup, ainsi qu’avec l’orignal, qui est sa principale proie alternative. Pour cela, cette thèse présente la conception d’un modèle centré sur l’individu des déplacements de ces trois espèces en fonction de leur environnement, dont résulteront les interactions prédateur-proies. Afin de permettre l’application de ce modèle sur de longues périodes, et donc pour un environnement changeant, une méthodologie a été développée, qui s’articule atour de deux aspects principaux. Tout d’abord, la notion de niveaux d’émergence est introduite, permettant d’ordonner les comportements observables du système selon leurs interdépendances, afin de choisir comme trait du modèle un com- portement correspondant au domaine d’applicabilité visé. Ordonner les comportements selon leurs niveaux d’émergence permet également d’identifier la redondance entre les patrons, qui peut être à l’origine d’un phénomène de sur-apprentissage lorsqu’ils sont utilisés lors de la calibration. Dans un second temps, un nouveau protocole pour la calibration et la validation du ou des traits choisis à l’aide des niveaux d’émergence, nommé réplication de système basé sur l’individu (Individual Based System Replication - IBSRtion) est également présenté. Ce protocole met l’emphase sur la modélisation directe, contrairement au principal protocole existant, la modélisation orientée patrons (Pattern Oriented Modelling - POM), et permet une approche empirique en générant artificiellement des données non disponibles ou ne pouvant être récoltées par des études de terrains. IBSRtion a également l’avantage de pouvoir être intégrée dans POM, afin de contribuer à la création d’une méthodologie universelle pour la conception de modèles centrés sur l’individu. Le processus de conception de ce modèle aura entre autre permis de faire une synthèse des connaissances et d’identifier certaines lacunes. Une étude visant à palier le manque de connaissances satisfaisantes sur les réponses comportementales à court-terme des proies face au risque de prédation a notamment permis d’observer que celles-ci sont une combinaison de comportements chroniques et éphémères, et que les mécanismes qui en sont à l’origine sont complexes et non-linéaires. Le résultat de ce travail est un modèle complexe utilisant de nombreux sous-modèles, et calibré de façon empirique, applicable à une grande variété d’environnements. Ce modèle a permis de tester l’impact de l’enfeuillement sur les relations prédateur-proies. Des simulations ont été effectuées pour différentes quantités d’enfeuillement, suivant deux configurations spatiales différentes. Les résultats de simulation suggèrent que des plans d’aménagement considérant également l’habitat de l’orignal pourraient être bénéfiques pour le caribou forestier, car ils permettraient d’améliorer la ségrégation spatiale entre les deux espèces, et donc entre le caribou et le loup. En le couplant avec un module de naissances et de morts naturelles ainsi qu’un modèle d’évolution du paysage, ce modèle permettra par la suite d’évaluer l’impact de plans d’aménagement forestier sur la viabilité des populations de caribou forestier.Forest-dwelling woodland caribou are considered threatened in Canada. The main hypothesis to the decrease of populations is the intensification of predation provoked by anthropogenic perturbations in the landscape. To deal with this situation, it is necessary to study and to understand the impact of the environment on the predator-prey interactions between the caribou and the wolf, and with the moose, its main alternative prey. In this perspective, this thesis presents the design of an individual-based model of displacements of these three species with respect to their environment, from which the predator-prey interactions will result. To allow for the application of this model for long periods of time, i.e. for changing environments, a methodology has been developed, which is based on two key points. First, the notion of levels of emergence is introduced, allowing to order the different observable comportments of the system according to their inter-dependencies, to help with choosing a trait of the model corresponding to the intended domain of applicability. Ordering the comportments according to their levels of emergence also permits to identify redundancy between patterns, which can lead to over-fitting when they are used for calibration. Second, a new methodology for calibration and validation of the trait(s) chosen by means of the levels of emergence framework is also presented, named Individual Based System Replication (IBSRtion). This protocol emphasizes forward modelling, contrary to the main existing methodology, Pattern Oriented Modelling (POM), and allows to use an empirical approach by artificially generating data that are unavailable or that cannot be obtained by means of field studies. IBSRtion can also be integrated into POM, to contribute to the establish- ment of a universal methodology for the design of individual based models. The design process of this model allowed for a synthesis of existing knowledge and to point out some gaps. More specifically, a study conducted to deal with the lack of sufficient information on the short-term response of prey to predation risk allowed to observe that their behavioural responses to prior presence of predators are a combination of chronic and ephemeral behaviours, and that the mechanisms that produce them are complex and non-linear. The outcome of this work is a complex model, using many sub-models, and calibrated in an empirical fashion, that can be applied to a wide variety of environments. This model allowed to test the impact of the encroachment of deciduous trees on predator-prey relations. Simulations have been run for different quantities of encroachment, according to two different spatial configurations. Simulation results suggest that management plans taking into account the moose’s habitat might benefit woodland caribou, because they could increase spatial segregation between the two species, and thus between caribou and wolf. Coupling this model with a module of birth and natural death, along with a model of landscape transformation, would allow the assessment of the impact of different forest management plans on the viability of woodland caribou populations

Solving the Direction Field for Discrete Agent Motion

Models for pedestrian dynamics are often based on microscopic approaches allowing for individual agent navigation. To reach a given destination, the agent has to consider environmental obstacles. We propose a direction field calculated on a regular grid with a Moore neighborhood, where obstacles are represented by occupied cells. Our developed algorithm exactly reproduces the shortest path with regard to the Euclidean metric.Comment: 8 pages, 4 figure

A Simple Reactive Obstacle Avoidance Algorithm and Its Application in Singapore Harbor

Autonomous surface craft (ASC) are increasingly attractive as a means for performing harbor operations including monitoring and inspection. However, due to the presence of many fixed and moving structures such as pilings, moorings, and vessels, harbor environments are extremely dynamic and cluttered. In order to move autonomously in such conditions ASC’s must be capable of detecting stationary and moving objects and plan their paths accordingly. We propose a simple and scalable online navigation scheme, wherein the relative motion of surrounding obstacles is estimated by the ASC, and the motion plan is modified accordingly at each time step. Since the approach is model-free and its decisions are made at a high frequency, the system is able to deal with highly dynamic scenarios. We deployed ASC’s in the Selat Pauh region of Singapore Harbor to test the technique using a short-range 2-D laser sensor; detection in the rough waters we encountered was quite poor. Nonetheless, the ASC’s were able to avoid both stationary as well as mobile obstacles, the motions of which were unknown a priori. The successful demonstration of obstacle avoidance in the field validates our fast online approach.Massachusetts Institute of Technology. Singapore-MIT Alliance in Research and Technology (SMART