Beware greedy algorithms

Nestedness – the tendency for specialist species to interact with subsets of the species that generalist species interact with – is a pervasive feature of empirical mutualistic communities (Bascompte, Jordano, Melián, & Olesen, 2003). While theoretical work has discovered important dynamical implications of nestedness, such as enhanced community stability and species coexistence (Bastolla et al., 2009; Rohr, Saavedra, & Bascompte, 2014; Thébault & Fontaine, 2010), there has been less agreement about why networks vary in their levels of nestedness. Answering this question is an important challenge as it has the potential to improve understanding of the mechanisms leading to nested architectures and hence the processes underlying community persistence.Arcadia Cambridge Faculty of Mathematics CMP bursary fund Natural Environment Research Council as part of the Cambridge Earth System Science NERC DTP. Grant Number: NE/L002507/

Optimal control and reinforcement learning for formula one lap simulation

Lap simulation in a Formula One context is a subclass of optimal control problems and describes the computation of optimal trajectories around racing circuits. The results of lap simulation are primarily used for vehicle setup and strategic racing decisions. The optimal lap problem is solved using two classes of algorithms. The first algorithm uses direct collocation to compute optimal trajectories and the second algorithm uses specially constructed reinforcement learning environments and generalised function approximation to compute desirable system inputs. Historically direct collocation methods were considered impractical for minimum lap time simulations, due to their high computational costs. The exponential increase in computational performance has enabled the practical application of these algorithms. These lap time simulations require a vehicle model, as well as a track discretisation. As an example for this, the classical bicycle model along with a curvilinear track model are introduced. To solve the resulting direct collocation problems, algorithms for non-linear optimisation problems are presented and performance critical aspects are discussed. The optimisation algorithm is accelerated by utilising highly parallel computer architectures, such as graphics processing units (GPUs). An analytical gradient approximation is presented to achieve approximations of projection systems which constitute one most performance critical components of the solution process. Mesh refinement algorithms are discussed and a novel mesh refinement heuristic based on optimal polynomial approximation in an $L^1$ sense is discussed. The $L^1$ approximation is improved by detecting singularities and using Clenshaw--Curtis quadrature on intermediary intervals. In Chapter 4 of this work, the lap time optimisation problem is reformulated as a reinforcement learning environments. For this, the relevant background literature on reinforcement learning is discussed and a translation of a training optimisation environment is constructed. Details of this environment are discussed in the form of reward signals, terminal conditions, and observation features. A series of learning models is discussed with increasing feature fidelity leading to an algorithm that can generalise well across representations of circuits from the 2022 Formula One calendar. This work expands on the current literature by providing novel, physically motivated, reinforcement learning environments for lap time optimisation tasks. The results of both approaches are combined by using strategy extraction to initialise the collocation optimisation algorithm and optimise the underlying mesh

maxnodf: An R package for fair and fast comparisons of nestedness between networks

1. Nestedness is a widespread pattern in mutualistic networks that has high ecological and evolutionary importance due to its role in enhancing species persistence and community stability. Nestedness measures tend to be correlated with fundamental properties of networks, such as size and connectance, and so nestedness values must be normalised to enable fair comparisons between different ecological communities. Current approaches, such as using null‐corrected nestedness values and z‐scores, suffer from extensive statistical issues. Thus a new approach called NODFc was recently proposed, where nestedness is expressed relative to network size, connectance and the maximum nestedness that could be achieved in a particular network. While this approach is demonstrably effective in overcoming the issues of collinearity with basic network properties, it is computationally intensive to calculate, and current approaches are too slow to be practical for many types of analysis, or for analysing large networks. 2. We developed three highly‐optimised algorithms, based on greedy, hillclimbing and simulated annealing approaches, for calculation of NODFc, spread along a speed‐quality continuum. Users thus have the choice between a fast algorithm with a less accurate estimate, a slower algorithm with a more accurate estimate, and an intermediate option. 3. We outline the package, and its implementation, as well as provide comparative performance benchmarking and two example analyses. We show that maxnodf enables speed increases of hundreds of times faster than existing approaches, with large networks seeing the biggest improvements. For example, for a large network with 3000 links, computation time was reduced from 50 minutes using the fastest existing algorithm to 11 seconds using maxnodf. 4. maxnodf makes correctly‐normalised nestedness measures feasible for complex analyses of even large networks. Analyses that would previously take weeks to complete can now be finished in hours or even seconds. Given evidence that correctly normalising nestedness values can significantly change the conclusions of ecological studies, we believe this package will usher in necessary widespread use of appropriate comparative nestedness statistics