Evolution of size-dependent flowering in a variable environment: construction and analysis of a stochastic integral projection model

Understanding why individuals delay reproduction is a classic problem in evolutionary biology. In plants, the study of reproductive delays is complicated because growth and survival can be size and age dependent, individuals of the same size can grow by different amounts and there is temporal variation in the environment. We extend the recently developed integral projection approach to include size- and age-dependent demography and temporal variation. The technique is then applied to a long-term individually structured dataset for Carlina vulgaris, a monocarpic thistle. The parameterized model has excellent descriptive properties in terms of both the population size and the distributions of sizes within each age class. In Carlina, the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy approach. Considering each year separately, we show that both the direction and the magnitude of selection on the flowering strategy vary from year to year. Provided the flowering strategy is constrained, so it cannot be a step function, the model accurately predicts the average size at flowering. Elasticity analysis is used to partition the size- and age-specific contributions to the stochastic growth rate, λs. We use λs to construct fitness landscapes and show how different forms of stochasticity influence its topography. We prove the existence of a unique stochastic growth rate, λs, which is independent of the initial population vector, and show that Tuljapurkar's perturbation analysis for log(λs) can be used to calculate elasticities

The Ariadne's Clew Algorithm

We present a new approach to path planning, called the "Ariadne's clew algorithm". It is designed to find paths in high-dimensional continuous spaces and applies to robots with many degrees of freedom in static, as well as dynamic environments - ones where obstacles may move. The Ariadne's clew algorithm comprises two sub-algorithms, called Search and Explore, applied in an interleaved manner. Explore builds a representation of the accessible space while Search looks for the target. Both are posed as optimization problems. We describe a real implementation of the algorithm to plan paths for a six degrees of freedom arm in a dynamic environment where another six degrees of freedom arm is used as a moving obstacle. Experimental results show that a path is found in about one second without any pre-processing

Towards the Formal Specification and Verification of Maple Programs

In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors in such programs w.r.t. their specifications by static analysis. This task is more complex for widely used computer algebra languages like Maple as these are fundamentally different from classical languages: they support non-standard types of objects such as symbols, unevaluated expressions and polynomials and require abstract computer algebraic concepts and objects such as rings and orderings etc. As a starting point we have defined and formalized a syntax, semantics, type system and specification language for MiniMaple

Minimum-time trajectory generation for quadrotors in constrained environments

In this paper, we present a novel strategy to compute minimum-time trajectories for quadrotors in constrained environments. In particular, we consider the motion in a given flying region with obstacles and take into account the physical limitations of the vehicle. Instead of approaching the optimization problem in its standard time-parameterized formulation, the proposed strategy is based on an appealing re-formulation. Transverse coordinates, expressing the distance from a frame path, are used to parameterise the vehicle position and a spatial parameter is used as independent variable. This re-formulation allows us to (i) obtain a fixed horizon problem and (ii) easily formulate (fairly complex) position constraints. The effectiveness of the proposed strategy is proven by numerical computations on two different illustrative scenarios. Moreover, the optimal trajectory generated in the second scenario is experimentally executed with a real nano-quadrotor in order to show its feasibility.Comment: arXiv admin note: text overlap with arXiv:1702.0427