8,594 research outputs found

    A Unifying Theory for Graph Transformation

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    The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO

    A Phenomenological Study Exploring the Factors That Contribute to Persistence in Online Doctoral Programs for Students With Learning Disabilities or ADHD

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    The purpose of this transcendental phenomenological study was to discover the factors that contributed to persistence in online doctoral programs for students with learning disabilities (LD) and attention deficit hyperactivity disorder (ADHD). The theory guiding this study was Tinto’s theory of student persistence, as it suggested the more students were academically and socially integrated into their institution, the more likely they were to persist in their studies. The Central research question of this study is, “What are the factors that contribute to persistence in online doctoral programs for students with LD and ADHD?” Participants in this study consisted of seven individuals with learning disabilities or ADHD who had completed all of their required coursework in their current online doctoral program and had started the dissertation phase of their program, and four who had graduated from their online doctoral programs within the last two years. Candidates were selected using purposive sampling. Perspectives of students with LD and ADHD as they related to their academic persistence were shared. The lived experiences of online doctoral students with LD and ADHD were studied using online discussion board prompts, individual interviews, and focus groups. The data were collected and analyzed using Moustakas’ transcendental phenomenology approach and generated six themes and commonalities among the participants in this study. The themes were Overcoming Challenges and Barriers, Adaptation and Coping Strategies, Motivation, Self-Efficacy, Support Systems, and Personal Determination and Perseverance. The data analysis revealed empirical, practical, and theoretical implications along with recommendations for future research

    Classical and quantum algorithms for scaling problems

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    This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size

    Language integrated relational lenses

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    Relational databases are ubiquitous. Such monolithic databases accumulate large amounts of data, yet applications typically only work on small portions of the data at a time. A subset of the database defined as a computation on the underlying tables is called a view. Querying views is helpful, but it is also desirable to update them and have these changes be applied to the underlying database. This view update problem has been the subject of much previous work before, but support by database servers is limited and only rarely available. Lenses are a popular approach to bidirectional transformations, a generalization of the view update problem in databases to arbitrary data. However, perhaps surprisingly, lenses have seldom actually been used to implement updatable views in databases. Bohannon, Pierce and Vaughan propose an approach to updatable views called relational lenses. However, to the best of our knowledge this proposal has not been implemented or evaluated prior to the work reported in this thesis. This thesis proposes programming language support for relational lenses. Language integrated relational lenses support expressive and efficient view updates, without relying on updatable view support from the database server. By integrating relational lenses into the programming language, application development becomes easier and less error-prone, avoiding the impedance mismatch of having two programming languages. Integrating relational lenses into the language poses additional challenges. As defined by Bohannon et al. relational lenses completely recompute the database, making them inefficient as the database scales. The other challenge is that some parts of the well-formedness conditions are too general for implementation. Bohannon et al. specify predicates using possibly infinite abstract sets and define the type checking rules using relational algebra. Incremental relational lenses equip relational lenses with change-propagating semantics that map small changes to the view into (potentially) small changes to the source tables. We prove that our incremental semantics are functionally equivalent to the non-incremental semantics, and our experimental results show orders of magnitude improvement over the non-incremental approach. This thesis introduces a concrete predicate syntax and shows how the required checks are performed on these predicates and show that they satisfy the abstract predicate specifications. We discuss trade-offs between static predicates that are fully known at compile time vs dynamic predicates that are only known during execution and introduce hybrid predicates taking inspiration from both approaches. This thesis adapts the typing rules for relational lenses from sequential composition to a functional style of sub-expressions. We prove that any well-typed functional relational lens expression can derive a well-typed sequential lens. We use these additions to relational lenses as the foundation for two practical implementations: an extension of the Links functional language and a library written in Haskell. The second implementation demonstrates how type-level computation can be used to implement relational lenses without changes to the compiler. These two implementations attest to the possibility of turning relational lenses into a practical language feature

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Algebraic solutions of linear differential equations: an arithmetic approach

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    Given a linear differential equation with coefficients in Q(x)\mathbb{Q}(x), an important question is to know whether its full space of solutions consists of algebraic functions, or at least if one of its specific solutions is algebraic. After presenting motivating examples coming from various branches of mathematics, we advertise in an elementary way a beautiful local-global arithmetic approach to these questions, initiated by Grothendieck in the late sixties. This approach has deep ramifications and leads to the still unsolved Grothendieck-Katz pp-curvature conjecture.Comment: 47 page

    Machine learning applications in search algorithms for gravitational waves from compact binary mergers

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    Gravitational waves from compact binary mergers are now routinely observed by Earth-bound detectors. These observations enable exciting new science, as they have opened a new window to the Universe. However, extracting gravitational-wave signals from the noisy detector data is a challenging problem. The most sensitive search algorithms for compact binary mergers use matched filtering, an algorithm that compares the data with a set of expected template signals. As detectors are upgraded and more sophisticated signal models become available, the number of required templates will increase, which can make some sources computationally prohibitive to search for. The computational cost is of particular concern when low-latency alerts should be issued to maximize the time for electromagnetic follow-up observations. One potential solution to reduce computational requirements that has started to be explored in the last decade is machine learning. However, different proposed deep learning searches target varying parameter spaces and use metrics that are not always comparable to existing literature. Consequently, a clear picture of the capabilities of machine learning searches has been sorely missing. In this thesis, we closely examine the sensitivity of various deep learning gravitational-wave search algorithms and introduce new methods to detect signals from binary black hole and binary neutron star mergers at previously untested statistical confidence levels. By using the sensitive distance as our core metric, we allow for a direct comparison of our algorithms to state-of-the-art search pipelines. As part of this thesis, we organized a global mock data challenge to create a benchmark for machine learning search algorithms targeting compact binaries. This way, the tools developed in this thesis are made available to the greater community by publishing them as open source software. Our studies show that, depending on the parameter space, deep learning gravitational-wave search algorithms are already competitive with current production search pipelines. We also find that strategies developed for traditional searches can be effectively adapted to their machine learning counterparts. In regions where matched filtering becomes computationally expensive, available deep learning algorithms are also limited in their capability. We find reduced sensitivity to long duration signals compared to the excellent results for short-duration binary black hole signals

    Modular lifelong machine learning

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    Deep learning has drastically improved the state-of-the-art in many important fields, including computer vision and natural language processing (LeCun et al., 2015). However, it is expensive to train a deep neural network on a machine learning problem. The overall training cost further increases when one wants to solve additional problems. Lifelong machine learning (LML) develops algorithms that aim to efficiently learn to solve a sequence of problems, which become available one at a time. New problems are solved with less resources by transferring previously learned knowledge. At the same time, an LML algorithm needs to retain good performance on all encountered problems, thus avoiding catastrophic forgetting. Current approaches do not possess all the desired properties of an LML algorithm. First, they primarily focus on preventing catastrophic forgetting (Diaz-Rodriguez et al., 2018; Delange et al., 2021). As a result, they neglect some knowledge transfer properties. Furthermore, they assume that all problems in a sequence share the same input space. Finally, scaling these methods to a large sequence of problems remains a challenge. Modular approaches to deep learning decompose a deep neural network into sub-networks, referred to as modules. Each module can then be trained to perform an atomic transformation, specialised in processing a distinct subset of inputs. This modular approach to storing knowledge makes it easy to only reuse the subset of modules which are useful for the task at hand. This thesis introduces a line of research which demonstrates the merits of a modular approach to lifelong machine learning, and its ability to address the aforementioned shortcomings of other methods. Compared to previous work, we show that a modular approach can be used to achieve more LML properties than previously demonstrated. Furthermore, we develop tools which allow modular LML algorithms to scale in order to retain said properties on longer sequences of problems. First, we introduce HOUDINI, a neurosymbolic framework for modular LML. HOUDINI represents modular deep neural networks as functional programs and accumulates a library of pre-trained modules over a sequence of problems. Given a new problem, we use program synthesis to select a suitable neural architecture, as well as a high-performing combination of pre-trained and new modules. We show that our approach has most of the properties desired from an LML algorithm. Notably, it can perform forward transfer, avoid negative transfer and prevent catastrophic forgetting, even across problems with disparate input domains and problems which require different neural architectures. Second, we produce a modular LML algorithm which retains the properties of HOUDINI but can also scale to longer sequences of problems. To this end, we fix the choice of a neural architecture and introduce a probabilistic search framework, PICLE, for searching through different module combinations. To apply PICLE, we introduce two probabilistic models over neural modules which allows us to efficiently identify promising module combinations. Third, we phrase the search over module combinations in modular LML as black-box optimisation, which allows one to make use of methods from the setting of hyperparameter optimisation (HPO). We then develop a new HPO method which marries a multi-fidelity approach with model-based optimisation. We demonstrate that this leads to improvement in anytime performance in the HPO setting and discuss how this can in turn be used to augment modular LML methods. Overall, this thesis identifies a number of important LML properties, which have not all been attained in past methods, and presents an LML algorithm which can achieve all of them, apart from backward transfer

    Towards A Practical High-Assurance Systems Programming Language

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    Writing correct and performant low-level systems code is a notoriously demanding job, even for experienced developers. To make the matter worse, formally reasoning about their correctness properties introduces yet another level of complexity to the task. It requires considerable expertise in both systems programming and formal verification. The development can be extremely costly due to the sheer complexity of the systems and the nuances in them, if not assisted with appropriate tools that provide abstraction and automation. Cogent is designed to alleviate the burden on developers when writing and verifying systems code. It is a high-level functional language with a certifying compiler, which automatically proves the correctness of the compiled code and also provides a purely functional abstraction of the low-level program to the developer. Equational reasoning techniques can then be used to prove functional correctness properties of the program on top of this abstract semantics, which is notably less laborious than directly verifying the C code. To make Cogent a more approachable and effective tool for developing real-world systems, we further strengthen the framework by extending the core language and its ecosystem. Specifically, we enrich the language to allow users to control the memory representation of algebraic data types, while retaining the automatic proof with a data layout refinement calculus. We repurpose existing tools in a novel way and develop an intuitive foreign function interface, which provides users a seamless experience when using Cogent in conjunction with native C. We augment the Cogent ecosystem with a property-based testing framework, which helps developers better understand the impact formal verification has on their programs and enables a progressive approach to producing high-assurance systems. Finally we explore refinement type systems, which we plan to incorporate into Cogent for more expressiveness and better integration of systems programmers with the verification process
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