17,635 research outputs found

    Implicit Loss of Surjectivity and Facial Reduction: Theory and Applications

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    Facial reduction, pioneered by Borwein and Wolkowicz, is a preprocessing method that is commonly used to obtain strict feasibility in the reformulated, reduced constraint system. The importance of strict feasibility is often addressed in the context of the convergence results for interior point methods. Beyond the theoretical properties that the facial reduction conveys, we show that facial reduction, not only limited to interior point methods, leads to strong numerical performances in different classes of algorithms. In this thesis we study various consequences and the broad applicability of facial reduction. The thesis is organized in two parts. In the first part, we show the instabilities accompanied by the absence of strict feasibility through the lens of facially reduced systems. In particular, we exploit the implicit redundancies, revealed by each nontrivial facial reduction step, resulting in the implicit loss of surjectivity. This leads to the two-step facial reduction and two novel related notions of singularity. For the area of semidefinite programming, we use these singularities to strengthen a known bound on the solution rank, the Barvinok-Pataki bound. For the area of linear programming, we reveal degeneracies caused by the implicit redundancies. Furthermore, we propose a preprocessing tool that uses the simplex method. In the second part of this thesis, we continue with the semidefinite programs that do not have strictly feasible points. We focus on the doubly-nonnegative relaxation of the binary quadratic program and a semidefinite program with a nonlinear objective function. We closely work with two classes of algorithms, the splitting method and the Gauss-Newton interior point method. We elaborate on the advantages in building models from facial reduction. Moreover, we develop algorithms for real-world problems including the quadratic assignment problem, the protein side-chain positioning problem, and the key rate computation for quantum key distribution. Facial reduction continues to play an important role for providing robust reformulated models in both the theoretical and the practical aspects, resulting in successful numerical performances

    Interpretable and explainable machine learning for ultrasonic defect sizing

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    Despite its popularity in literature, there are few examples of machine learning (ML) being used for industrial nondestructive evaluation (NDE) applications. A significant barrier is the ‘black box’ nature of most ML algorithms. This paper aims to improve the interpretability and explainability of ML for ultrasonic NDE by presenting a novel dimensionality reduction method: Gaussian feature approximation (GFA). GFA involves fitting a 2D elliptical Gaussian function an ultrasonic image and storing the seven parameters that describe each Gaussian. These seven parameters can then be used as inputs to data analysis methods such as the defect sizing neural network presented in this paper. GFA is applied to ultrasonic defect sizing for inline pipe inspection as an example application. This approach is compared to sizing with the same neural network, and two other dimensionality reduction methods (the parameters of 6 dB drop boxes and principal component analysis), as well as a convolutional neural network applied to raw ultrasonic images. Of the dimensionality reduction methods tested, GFA features produce the closest sizing accuracy to sizing from the raw images, with only a 23% increase in RMSE, despite a 96.5% reduction in the dimensionality of the input data. Implementing ML with GFA is implicitly more interpretable than doing so with principal component analysis or raw images as inputs, and gives significantly more sizing accuracy than 6 dB drop boxes. Shapley additive explanations (SHAP) are used to calculate how each feature contributes to the prediction of an individual defect’s length. Analysis of SHAP values demonstrates that the GFA-based neural network proposed displays many of the same relationships between defect indications and their predicted size as occur in traditional NDE sizing methods

    Fast emulation of anisotropies induced in the cosmic microwave background by cosmic strings

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    Cosmic strings are linear topological defects that may have been produced during symmetry-breaking phase transitions in the very early Universe. In an expanding Universe the existence of causally separate regions prevents such symmetries from being broken uniformly, with a network of cosmic string inevitably forming as a result. To faithfully generate observables of such processes requires computationally expensive numerical simulations, which prohibits many types of analyses. We propose a technique to instead rapidly emulate observables, thus circumventing simulation. Emulation is a form of generative modelling, often built upon a machine learning backbone. End-to-end emulation often fails due to high dimensionality and insufficient training data. Consequently, it is common to instead emulate a latent representation from which observables may readily be synthesised. Wavelet phase harmonics are an excellent latent representations for cosmological fields, both as a summary statistic and for emulation, since they do not require training and are highly sensitive to non-Gaussian information. Leveraging wavelet phase harmonics as a latent representation, we develop techniques to emulate string induced CMB anisotropies over a 7.2 degree field of view, with sub-arcminute resolution, in under a minute on a single GPU. Beyond generating high fidelity emulations, we provide a technique to ensure these observables are distributed correctly, providing a more representative ensemble of samples. The statistics of our emulations are commensurate with those calculated on comprehensive Nambu-Goto simulations. Our findings indicate these fast emulation approaches may be suitable for wide use in, e.g., simulation based inference pipelines. We make our code available to the community so that researchers may rapidly emulate cosmic string induced CMB anisotropies for their own analysis

    On regular copying languages

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    This paper proposes a formal model of regular languages enriched with unbounded copying. We augment finite-state machinery with the ability to recognize copied strings by adding an unbounded memory buffer with a restricted form of first-in-first-out storage. The newly introduced computational device, finite-state buffered machines (FS-BMs), characterizes the class of regular languages and languages de-rived from them through a primitive copying operation. We name this language class regular copying languages (RCLs). We prove a pumping lemma and examine the closure properties of this language class. As suggested by previous literature (Gazdar and Pullum 1985, p.278), regular copying languages should approach the correct characteriza-tion of natural language word sets

    Machine Learning Approaches for the Prioritisation of Cardiovascular Disease Genes Following Genome- wide Association Study

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    Genome-wide association studies (GWAS) have revealed thousands of genetic loci, establishing itself as a valuable method for unravelling the complex biology of many diseases. As GWAS has grown in size and improved in study design to detect effects, identifying real causal signals, disentangling from other highly correlated markers associated by linkage disequilibrium (LD) remains challenging. This has severely limited GWAS findings and brought the method’s value into question. Although thousands of disease susceptibility loci have been reported, causal variants and genes at these loci remain elusive. Post-GWAS analysis aims to dissect the heterogeneity of variant and gene signals. In recent years, machine learning (ML) models have been developed for post-GWAS prioritisation. ML models have ranged from using logistic regression to more complex ensemble models such as random forests and gradient boosting, as well as deep learning models (i.e., neural networks). When combined with functional validation, these methods have shown important translational insights, providing a strong evidence-based approach to direct post-GWAS research. However, ML approaches are in their infancy across biological applications, and as they continue to evolve an evaluation of their robustness for GWAS prioritisation is needed. Here, I investigate the landscape of ML across: selected models, input features, bias risk, and output model performance, with a focus on building a prioritisation framework that is applied to blood pressure GWAS results and tested on re-application to blood lipid traits

    Identifying Design-Build Decision-Making Factors and Providing Future Research Guidelines: Social Network and Association Rule Analysis

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    There is a dire need to rebuild existing infrastructure with strategic and efficient methods. Design-build (DB) becomes a potential solution that provides fast-tracked delivery as a more time and cost-efficient project delivery method. Past research studied factors influencing DB but without providing a holistic analytic approach. This paper fills this knowledge gap. First, a systematic literature review is performed using the preferred reporting items for systematic reviews and meta-analyses techniques, and a set of factors affecting DB projects are then identified and clustered, using k-means clustering, based on the whole literature discussions. Second, a graph theory approach, social network analysis (SNA), is conducted methodically to detect the understudied factors. Third, the clustered factors are analyzed using association rule (AR) analysis to identify factors that have not been cross-examined together. To this end, the findings of this research highlighted the need to investigate a group of important understudied factors that affect DB decision-making and procedures that are related to management, decision-making and executive methods, and stakeholder and team related aspects, among others. Also, while the majority of the existing research focused on theoretical efforts, there is far less work associated with computational/mathematical approaches that develop actual DB frameworks. Accordingly, future research is recommended to tackle this critical need by developing models that can assess DB performance, success, and implementation, among other aspects. Furthermore, since none of the studies evaluated DB while factoring in all 34 identified relevant factors, it is recommended that future research simultaneously incorporates most, if not all, these factors to provide a well-rounded and comprehensive analysis for DB decision-making. In addition, future studies need to tackle broader sectors rather than focusing over and over on the already saturated ones. As such, this study consolidated past literature and critically used it to offer robust support for the advancement of DB knowledge within the construction industry

    Visual Programming Paradigm for Organizations in Multi-Agent Systems

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    Over the past few years, due to a fast digitalization process, business activities witnessed the adoption of new technologies, such as Multi-Agent Systems, to increase the autonomy of their activities. However, the complexity of these technologies often hinders the capability of domain experts, who do not possess coding skills, to exploit them directly. To take advantage of these individuals' expertise in their field, the idea of a user-friendly and accessible Integrated Development Environment arose. Indeed, efforts have already been made to develop a block-based visual programming language for software agents. Although the latter project represents a huge step forward, it does not provide a solution for addressing complex, real-world use cases where interactions and coordination among single entities are crucial. To address this problem, Multi-Agent Oriented Programming introduces organization as a first-class abstraction for designing and implementing Multi-Agent Systems. Therefore, this thesis aims to provide a solution allowing users to impose an organization on top of the agents easily. Since ease of use and intuitiveness remain the key points for this project, users will be able to define organizations through visual language and an intuitive development environment

    Reinforcement learning in large state action spaces

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    Reinforcement learning (RL) is a promising framework for training intelligent agents which learn to optimize long term utility by directly interacting with the environment. Creating RL methods which scale to large state-action spaces is a critical problem towards ensuring real world deployment of RL systems. However, several challenges limit the applicability of RL to large scale settings. These include difficulties with exploration, low sample efficiency, computational intractability, task constraints like decentralization and lack of guarantees about important properties like performance, generalization and robustness in potentially unseen scenarios. This thesis is motivated towards bridging the aforementioned gap. We propose several principled algorithms and frameworks for studying and addressing the above challenges RL. The proposed methods cover a wide range of RL settings (single and multi-agent systems (MAS) with all the variations in the latter, prediction and control, model-based and model-free methods, value-based and policy-based methods). In this work we propose the first results on several different problems: e.g. tensorization of the Bellman equation which allows exponential sample efficiency gains (Chapter 4), provable suboptimality arising from structural constraints in MAS(Chapter 3), combinatorial generalization results in cooperative MAS(Chapter 5), generalization results on observation shifts(Chapter 7), learning deterministic policies in a probabilistic RL framework(Chapter 6). Our algorithms exhibit provably enhanced performance and sample efficiency along with better scalability. Additionally, we also shed light on generalization aspects of the agents under different frameworks. These properties have been been driven by the use of several advanced tools (e.g. statistical machine learning, state abstraction, variational inference, tensor theory). In summary, the contributions in this thesis significantly advance progress towards making RL agents ready for large scale, real world applications

    Symmetry-based decomposition for optimised parallelisation in 3D printing processes

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    Current research in 3D printing focuses on improving printing performance through various techniques, including decomposition, but targets only single printers. With improved hardware costs increasing printer availability, more situations can arise involving a multitude of printers, which offers substantially more throughput in combination that may not be best utilised by current decomposition approaches. A novel approach to 3D printing is introduced that attempts to exploit this as a means of significantly increasing the speed of printing models. This was approached as a problem akin to the parallel delegation of computation tasks in a multi-core environment, where optimal performance involves computation load being distributed as evenly as possible. To achieve this, a decomposition framework was designed that combines recursive symmetric slicing with a hybrid tree-based analytical and greedy strategy to optimally minimise the maximum volume of subparts assigned to the set of printers. Experimental evaluation of the algorithm was performed to compare our approach to printing models normally (“in serial”) as a control. The algorithm was subjected to a range of models and a varying quantity of printers in parallel, with printer parameters held constant, and yielded mixed results. Larger, simpler, and more symmetric objects exhibited more significant and reliable improvements in fabrication duration at larger amounts of parallelisation than smaller, more complex, or more asymmetric objects

    Modular Cluster Circuits for the Variational Quantum Eigensolver

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    The variational quantum eigensolver (VQE) algorithm recently became a popular method to compute quantum chemical properties of molecules on noisy intermediate scale quantum (NISQ) devices. In order to avoid noise accumulation from the NISQ device in the circuit, it is important to keep the so-called quantum depth of the circuit at a minimum, defined as the minimum number of quantum gates that need to be operated sequentially. In the present work, we introduce a modular 2-qubit cluster circuit that allows for the design of a shallow-depth quantum circuit compared to previously proposed architectures without loss of chemical accuracy. Moreover, by virtue of the simplicity of the cluster circuit, it is possible to assign a valence bond chemical interpretation to the cluster circuit. The design was tested on the H2, (H2)2 and LiH molecules, as well as the finite-size transverse-field Ising model, as the latter provides additional insights in the construction of the circuit in a resonating valence bond picture.Comment: Jupyter Notebook can be found at https://github.com/QuNB-Repo/QCChe
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