Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term Institutions

Babenyshev and Martins proved that two hidden multi-sorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with substitutions. We show that the -institutions corresponding to the hidden multi-sorted deductive systems studied by Babenyshev and Martins satisfy the multi-term condition of Gil-Férez. This provides a proof of the result of Babenyshev and Martins by appealing to the general result of Gil-Férez pertaining to arbitrary multi-term -institutions. The approach places hidden multi-sorted deductive systems in a more general framework and bypasses the laborious reuse of well-known proof techniques from traditional abstract algebraic logic by using “off the shelf” tools

Capacity and Complexity of HMM Duration Modeling Techniques

The ability of a standard hidden Markov model (HMM) or expanded state HMM (ESHMM) to accurately model duration distributions of phonemes is compared with specific duration-focused approaches such as semi-Markov models or variable transition probabilities. It is demonstrated that either a three-state ESHMM or a standard HMM with an increased number of states is capable of closely matching both Gamma distributions and duration distributions of phonemes from the TIMIT corpus, as measured by Bhattacharyya distance to the true distributions. Standard HMMs are easily implemented with off-the-shelf tools, whereas duration models require substantial algorithmic development and have higher computational costs when implemented, suggesting that a simple adjustment to HMM topologies is perhaps a more efficient solution to the problem of duration than more complex approaches

REFRIGERATOR OPTIMAL SCHEDULING TO MINIMISE THE COST OF OPERATION

The cost optimal scheduling of a household refrigerator is presented in this work. The fundamental approach is the model predictive control methodology applied to the piecewise affine model of the refrigerator. The optimisation could not be solved using off-the-shelf tools, e.g. Multi-Parametric Toolbox, so a binary tree-based optimal scheduling algorithm has been developed for this problem

Profiling a parallel domain specific language using off-the-shelf tools

Profiling tools are essential for understanding and tuning the performance of both parallel programs and parallel language implementations. Assessing the performance of a program in a language with high-level parallel coordination is often complicated by the layers of abstraction present in the language and its implementation. This thesis investigates whether it is possible to profile parallel Domain Specific Languages (DSLs) using existing host language profiling tools. The key challenge is that the host language tools report the performance of the DSL runtime system (RTS) executing the application rather than the performance of the DSL application. The key questions are whether a correct, effective and efficient profiler can be constructed using host language profiling tools; is it possible to effectively profile the DSL implementation, and what capabilities are required of the host language profiling tools? The main contribution of this thesis is the development of an execution profiler for the parallel DSL, Haskell Distributed Parallel Haskell (HdpH) using the host language profiling tools. We show that it is possible to construct a profiler (HdpHProf) to support performance analysis of both the DSL applications and the DSL implementation. The implementation uses several new GHC features, including the GHC-Events Library and ThreadScope, develops two new performance analysis tools for DSL HdpH internals, i.e. Spark Pool Contention Analysis, and Registry Contention Analysis. We present a critical comparative evaluation of the host language profiling tools that we used (GHC-PPS and ThreadScope) with another recent functional profilers, EdenTV, alongside four important imperative profilers. This is the first report on the performance of functional profilers in comparison with well established industrial standard imperative profiling technologies. We systematically compare the profilers for usability and data presentation. We found that the GHC-PPS performs well in terms of overheads and usability so using it to profile the DSL is feasible and would not have significant impact on the DSL performance. We validate HdpHProf for functional correctness and measure its performance using six benchmarks. HdpHProf works correctly and can scale to profile HdpH programs running on up to 192 cores of a 32 nodes Beowulf cluster. We characterise the performance of HdpHProf in terms of profiling data size and profiling execution runtime overhead. It shows that HdpHProf does not alter the behaviour of the GHC-PPS and retains low tracing overheads close to the studied functional profilers; 18% on average. Also, it shows a low ratio of HdpH trace events in GHC-PPS eventlog, less than 3% on average. We show that HdpHProf is effective and efficient to use for performance analysis and tuning of the DSL applications. We use HdpHProf to identify performance issues and to tune the thread granularity of six HdpH benchmarks with different parallel paradigms, e.g. divide and conquer, flat data parallel, and nested data parallel. This include identifying problems such as, too small/large thread granularity, problem size too small for the parallel architecture, and synchronisation bottlenecks. We show that HdpHProf is effective and efficient for tuning the parallel DSL implementation. We use the Spark Pool Contention Analysis tool to examine how the spark pool implementation performs when accessed concurrently. We found that appropriate thread granularity can significantly reduce both conflict ratios, and conflict durations, by more than 90%. We use the Registry Contention Analysis tool to evaluate three alternatives of the registry implementations. We found that the tools can give a better understanding of how different implementations of the HdpH RTS perform

Particle Gibbs for Bayesian Additive Regression Trees

Additive regression trees are flexible non-parametric models and popular off-the-shelf tools for real-world non-linear regression. In application domains, such as bioinformatics, where there is also demand for probabilistic predictions with measures of uncertainty, the Bayesian additive regression trees (BART) model, introduced by Chipman et al. (2010), is increasingly popular. As data sets have grown in size, however, the standard Metropolis-Hastings algorithms used to perform inference in BART are proving inadequate. In particular, these Markov chains make local changes to the trees and suffer from slow mixing when the data are high-dimensional or the best fitting trees are more than a few layers deep. We present a novel sampler for BART based on the Particle Gibbs (PG) algorithm (Andrieu et al., 2010) and a top-down particle filtering algorithm for Bayesian decision trees (Lakshminarayanan et al., 2013). Rather than making local changes to individual trees, the PG sampler proposes a complete tree to fit the residual. Experiments show that the PG sampler outperforms existing samplers in many settings