Empirical Analysis of Schemata in Genetic Programming

Schemata and buiding blocks have been used in Genetic Programming (GP) in several contexts including subroutines, theoretical analysis and for empirical analysis. Of these three the least explored is empirical analysis. This thesis presents a powerful GP empirical analysis technique for analysis of all schemata of a given form occurring in any program of a given population at scales not previously possible for the kinds of global analysis performed. There are many competing GP forms of schema and, rather than choosing one for analysis, the thesis defines the match-tree meta-form of schema as a general language expressing forms of schema for use by the analysis system. This language can express most forms of schema previously used in tree-based GP. The new method can perform wide-ranging analyses on the prohibitively large set of all schemata in the programs by introducing the concepts of maximal schema, maximal program subset, representative set of schemata, and representative program subset. These structures are used to optimize the analysis, shrinking its complexity to a manageable size without sacrificing the result. Characterization experiments analyze GP populations of up to 501 60- node programs, using 11 forms of schema including rooted-hyperschemata and non-rooted fragments. The new method has close to quadratic complexity on population size, and quartic complexity on program size. Efficacy experiments present example analyses using the new method. The experiments offer interesting insights into the dynamics of GP runs including fine-grained analysis of convergence and the visualization of schemata during a GP evolution. Future work will apply the many possible extensions of this new method to understanding how GP operates, including studies of convergence, building blocks and schema fitness. This method provides a much finer-resolution microscope into the inner workings of GP and will be used to provide accessable visualizations of the evolutionary process

Resilience of New Zealand indigenous forest fragments to impacts of livestock and pest mammals

A number of factors have combined to diminish ecosystem integrity in New Zealand indigenous lowland forest fragments surrounded by intensively grazed pasture. Livestock grazing, mammalian pests, adventive weeds and altered nutrient input regimes are important drivers compounding the changes in fragment structure and function due to historical deforestation and fragmentation. We used qualitative systems modelling and empirical data from Beilschmiedia tawa dominated lowland forest fragments in the Waikato Region to explore the relevance of two common resilience paradigms – engineering resilience and ecological resilience – for addressing the conservation management of forest fragments into the future. Grazing by livestock and foraging/predation by introduced mammalian pests both have direct detrimental impacts on key structural and functional attributes of forest fragments. Release from these perturbations through fencing and pest control leads to partial or full recovery of some key indicators (i.e. increased indigenous plant regeneration and cover, increased invertebrate populations and litter mass, decreased soil fertility and increased nesting success) relative to levels seen in larger forest systems over a range of timescales. These changes indicate that forest fragments do show resilience consistent with adopting an engineering resilience paradigm for conservation management, in the landscape context studied. The relevance of the ecological resilience paradigm in these ecosystems is obscured by limited data. We characterise forest fragment dynamics in terms of changes in indigenous species occupancy and functional dominance, and present a conceptual model for the management of forest fragment ecosystems

PhysicsGP: A Genetic Programming Approach to Event Selection

We present a novel multivariate classification technique based on Genetic Programming. The technique is distinct from Genetic Algorithms and offers several advantages compared to Neural Networks and Support Vector Machines. The technique optimizes a set of human-readable classifiers with respect to some user-defined performance measure. We calculate the Vapnik-Chervonenkis dimension of this class of learning machines and consider a practical example: the search for the Standard Model Higgs Boson at the LHC. The resulting classifier is very fast to evaluate, human-readable, and easily portable. The software may be downloaded at: http://cern.ch/~cranmer/PhysicsGP.htmlComment: 16 pages 9 figures, 1 table. Submitted to Comput. Phys. Commu

Transition from connected to fragmented vegetation across an environmental gradient: scaling laws in ecotone geometry

A change in the environmental conditions across space—for example, altitude or latitude—can cause significant changes in the density of a vegetation type and, consequently, in spatial connectivity. We use spatially explicit simulations to study the transition from connected to fragmented vegetation. A static (gradient percolation) model is compared to dynamic (gradient contact process) models. Connectivity is characterized from the perspective of various species that use this vegetation type for habitat and differ in dispersal or migration range, that is, “step length” across the landscape. The boundary of connected vegetation delineated by a particular step length is termed the “ hull edge.” We found that for every step length and for every gradient, the hull edge is a fractal with dimension 7/4. The result is the same for different spatial models, suggesting that there are universal laws in ecotone geometry. To demonstrate that the model is applicable to real data, a hull edge of fractal dimension 7/4 is shown on a satellite image of a piñon‐juniper woodland on a hillside. We propose to use the hull edge to define the boundary of a vegetation type unambiguously. This offers a new tool for detecting a shift of the boundary due to a climate change

Eigenvector Synchronization, Graph Rigidity and the Molecule Problem

The graph realization problem has received a great deal of attention in recent years, due to its importance in applications such as wireless sensor networks and structural biology. In this paper, we extend on previous work and propose the 3D-ASAP algorithm, for the graph realization problem in $\mathbb{R}^3$, given a sparse and noisy set of distance measurements. 3D-ASAP is a divide and conquer, non-incremental and non-iterative algorithm, which integrates local distance information into a global structure determination. Our approach starts with identifying, for every node, a subgraph of its 1-hop neighborhood graph, which can be accurately embedded in its own coordinate system. In the noise-free case, the computed coordinates of the sensors in each patch must agree with their global positioning up to some unknown rigid motion, that is, up to translation, rotation and possibly reflection. In other words, to every patch there corresponds an element of the Euclidean group Euc(3) of rigid transformations in $\mathbb{R}^3$, and the goal is to estimate the group elements that will properly align all the patches in a globally consistent way. Furthermore, 3D-ASAP successfully incorporates information specific to the molecule problem in structural biology, in particular information on known substructures and their orientation. In addition, we also propose 3D-SP-ASAP, a faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a preprocessing step for dividing the initial graph into smaller subgraphs. Our extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very robust to high levels of noise in the measured distances and to sparse connectivity in the measurement graph, and compare favorably to similar state-of-the art localization algorithms.Comment: 49 pages, 8 figure

Learning Structural Kernels for Natural Language Processing

Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting default values for kernel hyperparameters or using grid search, which is slow and coarse-grained. In contrast, Bayesian methods allow efficient model selection by maximizing the evidence on the training data through gradient-based methods. In this paper we show how to perform this in the context of structural kernels by using Gaussian Processes. Experimental results on tree kernels show that this procedure results in better prediction performance compared to hyperparameter optimization via grid search. The framework proposed in this paper can be adapted to other structures besides trees, e.g., strings and graphs, thereby extending the utility of kernel-based methods