19,422 research outputs found

    Fractal functions on the real projective plane

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    Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then we consider an iterated function system giving rise to a fractal interpolation function of a set of data.Comment: 25 pages, 18 figure

    An exploration of the language within Ofsted reports and their influence on primary school performance in mathematics: a mixed methods critical discourse analysis

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    This thesis contributes to the understanding of the language of Ofsted reports, their similarity to one another and associations between different terms used within ‘areas for improvement’ sections and subsequent outcomes for pupils. The research responds to concerns from serving headteachers that Ofsted reports are overly similar, do not capture the unique story of their school, and are unhelpful for improvement. In seeking to answer ‘how similar are Ofsted reports’ the study uses two tools, a plagiarism detection software (Turnitin) and a discourse analysis tool (NVivo) to identify trends within and across a large corpus of reports. The approach is based on critical discourse analysis (Van Dijk, 2009; Fairclough, 1989) but shaped in the form of practitioner enquiry seeking power in the form of impact on pupils and practitioners, rather than a more traditional, sociological application of the method. The research found that in 2017, primary school section 5 Ofsted reports had more than half of their content exactly duplicated within other primary school inspection reports published that same year. Discourse analysis showed the quality assurance process overrode variables such as inspector designation, gender, or team size, leading to three distinct patterns of duplication: block duplication, self-referencing, and template writing. The most unique part of a report was found to be the ‘area for improvement’ section, which was tracked to externally verified outcomes for pupils using terms linked to ‘mathematics’. Those required to improve mathematics in their areas for improvement improved progress and attainment in mathematics significantly more than national rates. These findings indicate that there was a positive correlation between the inspection reporting process and a beneficial impact on pupil outcomes in mathematics, and that the significant similarity of one report to another had no bearing on the usefulness of the report for school improvement purposes within this corpus

    An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal

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    Nonsinusoidal oscillatory signals are everywhere. In practice, the nonsinusoidal oscillatory pattern, modeled as a 1-periodic wave-shape function (WSF), might vary from cycle to cycle. When there are finite different WSFs, s1,…,sKs_1,\ldots,s_K, so that the WSF jumps from one to another suddenly, the different WSFs and jumps encode useful information. We present an iterative warping and clustering algorithm to estimate s1,…,sKs_1,\ldots,s_K from a nonstationary oscillatory signal with time-varying amplitude and frequency, and hence the change points of the WSFs. The algorithm is a novel combination of time-frequency analysis, singular value decomposition entropy and vector spectral clustering. We demonstrate the efficiency of the proposed algorithm with simulated and real signals, including the voice signal, arterial blood pressure, electrocardiogram and accelerometer signal. Moreover, we provide a mathematical justification of the algorithm under the assumption that the amplitude and frequency of the signal are slowly time-varying and there are finite change points that model sudden changes from one wave-shape function to another one.Comment: 39 pages, 11 figure

    Barren plateaus in quantum tensor network optimization

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    We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider as the cost function the expectation value of a Hamiltonian that is a sum of local terms. For randomly chosen variational parameters we show that the variance of the cost function gradient decreases exponentially with the distance of a Hamiltonian term from the canonical centre in the quantum tensor network. Therefore, as a function of qubit count, for qMPS most gradient variances decrease exponentially and for qTTN as well as qMERA they decrease polynomially. We also show that the calculation of these gradients is exponentially more efficient on a classical computer than on a quantum computer

    Technical Dimensions of Programming Systems

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    Programming requires much more than just writing code in a programming language. It is usually done in the context of a stateful environment, by interacting with a system through a graphical user interface. Yet, this wide space of possibilities lacks a common structure for navigation. Work on programming systems fails to form a coherent body of research, making it hard to improve on past work and advance the state of the art. In computer science, much has been said and done to allow comparison of programming languages, yet no similar theory exists for programming systems; we believe that programming systems deserve a theory too. We present a framework of technical dimensions which capture the underlying characteristics of programming systems and provide a means for conceptualizing and comparing them. We identify technical dimensions by examining past influential programming systems and reviewing their design principles, technical capabilities, and styles of user interaction. Technical dimensions capture characteristics that may be studied, compared and advanced independently. This makes it possible to talk about programming systems in a way that can be shared and constructively debated rather than relying solely on personal impressions. Our framework is derived using a qualitative analysis of past programming systems. We outline two concrete ways of using our framework. First, we show how it can analyze a recently developed novel programming system. Then, we use it to identify an interesting unexplored point in the design space of programming systems. Much research effort focuses on building programming systems that are easier to use, accessible to non-experts, moldable and/or powerful, but such efforts are disconnected. They are informal, guided by the personal vision of their authors and thus are only evaluable and comparable on the basis of individual experience using them. By providing foundations for more systematic research, we can help programming systems researchers to stand, at last, on the shoulders of giants

    Composing games into complex institutions

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    Game theory is used by all behavioral sciences, but its development has long centered around tools for relatively simple games and toy systems, such as the economic interpretation of equilibrium outcomes. Our contribution, compositional game theory, permits another approach of equally general appeal: the high-level design of large games for expressing complex architectures and representing real-world institutions faithfully. Compositional game theory, grounded in the mathematics underlying programming languages, and introduced here as a general computational framework, increases the parsimony of game representations with abstraction and modularity, accelerates search and design, and helps theorists across disciplines express real-world institutional complexity in well-defined ways. Relative to existing approaches in game theory, compositional game theory is especially promising for solving game systems with long-range dependencies, for comparing large numbers of structurally related games, and for nesting games into the larger logical or strategic flows typical of real world policy or institutional systems.Comment: ~4000 words, 6 figure

    A Design Science Research Approach to Smart and Collaborative Urban Supply Networks

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    Urban supply networks are facing increasing demands and challenges and thus constitute a relevant field for research and practical development. Supply chain management holds enormous potential and relevance for society and everyday life as the flow of goods and information are important economic functions. Being a heterogeneous field, the literature base of supply chain management research is difficult to manage and navigate. Disruptive digital technologies and the implementation of cross-network information analysis and sharing drive the need for new organisational and technological approaches. Practical issues are manifold and include mega trends such as digital transformation, urbanisation, and environmental awareness. A promising approach to solving these problems is the realisation of smart and collaborative supply networks. The growth of artificial intelligence applications in recent years has led to a wide range of applications in a variety of domains. However, the potential of artificial intelligence utilisation in supply chain management has not yet been fully exploited. Similarly, value creation increasingly takes place in networked value creation cycles that have become continuously more collaborative, complex, and dynamic as interactions in business processes involving information technologies have become more intense. Following a design science research approach this cumulative thesis comprises the development and discussion of four artefacts for the analysis and advancement of smart and collaborative urban supply networks. This thesis aims to highlight the potential of artificial intelligence-based supply networks, to advance data-driven inter-organisational collaboration, and to improve last mile supply network sustainability. Based on thorough machine learning and systematic literature reviews, reference and system dynamics modelling, simulation, and qualitative empirical research, the artefacts provide a valuable contribution to research and practice

    Corporate Social Responsibility: the institutionalization of ESG

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    Understanding the impact of Corporate Social Responsibility (CSR) on firm performance as it relates to industries reliant on technological innovation is a complex and perpetually evolving challenge. To thoroughly investigate this topic, this dissertation will adopt an economics-based structure to address three primary hypotheses. This structure allows for each hypothesis to essentially be a standalone empirical paper, unified by an overall analysis of the nature of impact that ESG has on firm performance. The first hypothesis explores the evolution of CSR to the modern quantified iteration of ESG has led to the institutionalization and standardization of the CSR concept. The second hypothesis fills gaps in existing literature testing the relationship between firm performance and ESG by finding that the relationship is significantly positive in long-term, strategic metrics (ROA and ROIC) and that there is no correlation in short-term metrics (ROE and ROS). Finally, the third hypothesis states that if a firm has a long-term strategic ESG plan, as proxied by the publication of CSR reports, then it is more resilience to damage from controversies. This is supported by the finding that pro-ESG firms consistently fared better than their counterparts in both financial and ESG performance, even in the event of a controversy. However, firms with consistent reporting are also held to a higher standard than their nonreporting peers, suggesting a higher risk and higher reward dynamic. These findings support the theory of good management, in that long-term strategic planning is both immediately economically beneficial and serves as a means of risk management and social impact mitigation. Overall, this contributes to the literature by fillings gaps in the nature of impact that ESG has on firm performance, particularly from a management perspective

    High-Dimensional Private Empirical Risk Minimization by Greedy Coordinate Descent

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    In this paper, we study differentially private empirical risk minimization (DP-ERM). It has been shown that the worst-case utility of DP-ERM reduces polynomially as the dimension increases. This is a major obstacle to privately learning large machine learning models. In high dimension, it is common for some model's parameters to carry more information than others. To exploit this, we propose a differentially private greedy coordinate descent (DP-GCD) algorithm. At each iteration, DP-GCD privately performs a coordinate-wise gradient step along the gradients' (approximately) greatest entry. We show theoretically that DP-GCD can achieve a logarithmic dependence on the dimension for a wide range of problems by naturally exploiting their structural properties (such as quasi-sparse solutions). We illustrate this behavior numerically, both on synthetic and real datasets
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