3,079 research outputs found

    Symmetries of Riemann surfaces and magnetic monopoles

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    This thesis studies, broadly, the role of symmetry in elucidating structure. In particular, I investigate the role that automorphisms of algebraic curves play in three specific contexts; determining the orbits of theta characteristics, influencing the geometry of the highly-symmetric Bring’s curve, and in constructing magnetic monopole solutions. On theta characteristics, I show how to turn questions on the existence of invariant characteristics into questions of group cohomology, compute comprehensive tables of orbit decompositions for curves of genus 9 or less, and prove results on the existence of infinite families of curves with invariant characteristics. On Bring’s curve, I identify key points with geometric significance on the curve, completely determine the structure of the quotients by subgroups of automorphisms, finding new elliptic curves in the process, and identify the unique invariant theta characteristic on the curve. With respect to monopoles, I elucidate the role that the Hitchin conditions play in determining monopole spectral curves, the relation between these conditions and the automorphism group of the curve, and I develop the theory of computing Nahm data of symmetric monopoles. As such I classify all 3-monopoles whose Nahm data may be solved for in terms of elliptic functions

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    The Application of Data Analytics Technologies for the Predictive Maintenance of Industrial Facilities in Internet of Things (IoT) Environments

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    In industrial production environments, the maintenance of equipment has a decisive influence on costs and on the plannability of production capacities. In particular, unplanned failures during production times cause high costs, unplanned downtimes and possibly additional collateral damage. Predictive Maintenance starts here and tries to predict a possible failure and its cause so early that its prevention can be prepared and carried out in time. In order to be able to predict malfunctions and failures, the industrial plant with its characteristics, as well as wear and ageing processes, must be modelled. Such modelling can be done by replicating its physical properties. However, this is very complex and requires enormous expert knowledge about the plant and about wear and ageing processes of each individual component. Neural networks and machine learning make it possible to train such models using data and offer an alternative, especially when very complex and non-linear behaviour is evident. In order for models to make predictions, as much data as possible about the condition of a plant and its environment and production planning data is needed. In Industrial Internet of Things (IIoT) environments, the amount of available data is constantly increasing. Intelligent sensors and highly interconnected production facilities produce a steady stream of data. The sheer volume of data, but also the steady stream in which data is transmitted, place high demands on the data processing systems. If a participating system wants to perform live analyses on the incoming data streams, it must be able to process the incoming data at least as fast as the continuous data stream delivers it. If this is not the case, the system falls further and further behind in processing and thus in its analyses. This also applies to Predictive Maintenance systems, especially if they use complex and computationally intensive machine learning models. If sufficiently scalable hardware resources are available, this may not be a problem at first. However, if this is not the case or if the processing takes place on decentralised units with limited hardware resources (e.g. edge devices), the runtime behaviour and resource requirements of the type of neural network used can become an important criterion. This thesis addresses Predictive Maintenance systems in IIoT environments using neural networks and Deep Learning, where the runtime behaviour and the resource requirements are relevant. The question is whether it is possible to achieve better runtimes with similarly result quality using a new type of neural network. The focus is on reducing the complexity of the network and improving its parallelisability. Inspired by projects in which complexity was distributed to less complex neural subnetworks by upstream measures, two hypotheses presented in this thesis emerged: a) the distribution of complexity into simpler subnetworks leads to faster processing overall, despite the overhead this creates, and b) if a neural cell has a deeper internal structure, this leads to a less complex network. Within the framework of a qualitative study, an overall impression of Predictive Maintenance applications in IIoT environments using neural networks was developed. Based on the findings, a novel model layout was developed named Sliced Long Short-Term Memory Neural Network (SlicedLSTM). The SlicedLSTM implements the assumptions made in the aforementioned hypotheses in its inner model architecture. Within the framework of a quantitative study, the runtime behaviour of the SlicedLSTM was compared with that of a reference model in the form of laboratory tests. The study uses synthetically generated data from a NASA project to predict failures of modules of aircraft gas turbines. The dataset contains 1,414 multivariate time series with 104,897 samples of test data and 160,360 samples of training data. As a result, it could be proven for the specific application and the data used that the SlicedLSTM delivers faster processing times with similar result accuracy and thus clearly outperforms the reference model in this respect. The hypotheses about the influence of complexity in the internal structure of the neuronal cells were confirmed by the study carried out in the context of this thesis

    Mirror symmetry for Dubrovin-Zhang Frobenius manifolds

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    Frobenius manifolds were formally defined by Boris Dubrovin in the early 1990s, and serve as a bridge between a priori very different fields of mathematics such as integrable systems theory, enumerative geometry, singularity theory, and mathematical physics. This thesis concerns, in particular, a specific class of Frobenius manifolds constructed on the orbit space of an extension of the affine Weyl group defined by Dubrovin together with Youjin Zhang. Here, we find Landau-Ginzburg superpotentials, or B-model mirrors, for these Frobenius structures by considering the characteristic equation for Lax operators of relativistic Toda chains as proposed by Andrea Brini. As a bonus, the results open up various applications in topology, integrable hierarchies, and Gromov-Witten theory, making interesting research questions in these areas more accessible. Some such applications are considered in this thesis. The form of the determinant of the Saito metric on discriminant strata is investigated, applications to the combinatorics of Lyashko-Looijenga maps are given, and investigations into the integrable systems theoretic and enumerative geometric applications are commenced

    Variational quantum eigensolver for causal loop Feynman diagrams and acyclic directed graphs

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    We present a variational quantum eigensolver (VQE) algorithm for the efficient bootstrapping of the causal representation of multiloop Feynman diagrams in the Loop-Tree Duality (LTD) or, equivalently, the selection of acyclic configurations in directed graphs. A loop Hamiltonian based on the adjacency matrix describing a multiloop topology, and whose different energy levels correspond to the number of cycles, is minimized by VQE to identify the causal or acyclic configurations. The algorithm has been adapted to select multiple degenerated minima and thus achieves higher detection rates. A performance comparison with a Grover's based algorithm is discussed in detail. The VQE approach requires, in general, fewer qubits and shorter circuits for its implementation, albeit with lesser success rates.Comment: 32 pages, 7 figures. Improved discussion and success rates of multi-run VQ

    Mining Butterflies in Streaming Graphs

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    This thesis introduces two main-memory systems sGrapp and sGradd for performing the fundamental analytic tasks of biclique counting and concept drift detection over a streaming graph. A data-driven heuristic is used to architect the systems. To this end, initially, the growth patterns of bipartite streaming graphs are mined and the emergence principles of streaming motifs are discovered. Next, the discovered principles are (a) explained by a graph generator called sGrow; and (b) utilized to establish the requirements for efficient, effective, explainable, and interpretable management and processing of streams. sGrow is used to benchmark stream analytics, particularly in the case of concept drift detection. sGrow displays robust realization of streaming growth patterns independent of initial conditions, scale and temporal characteristics, and model configurations. Extensive evaluations confirm the simultaneous effectiveness and efficiency of sGrapp and sGradd. sGrapp achieves mean absolute percentage error up to 0.05/0.14 for the cumulative butterfly count in streaming graphs with uniform/non-uniform temporal distribution and a processing throughput of 1.5 million data records per second. The throughput and estimation error of sGrapp are 160x higher and 0.02x lower than baselines. sGradd demonstrates an improving performance over time, achieves zero false detection rates when there is not any drift and when drift is already detected, and detects sequential drifts in zero to a few seconds after their occurrence regardless of drift intervals

    Advances and Applications of DSmT for Information Fusion. Collected Works, Volume 5

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    This ïŹfth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different ïŹelds of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some theoretical advances on DSmT, dealing mainly with modiïŹed Proportional ConïŹ‚ict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classiïŹers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identiïŹcation of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classiïŹcation. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classiïŹcation, and hybrid techniques mixing deep learning with belief functions as well

    On the use of senders for minimal Ramsey theory

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    This thesis investigates problems related to extremal and probabilistic graph theory. Our focus lies on the highly dynamic field of Ramsey theory. The foundational result of this field was proved in 1930 by Franck P. Ramsey. It implies that for every integer t and every sufficiently large complete graph Kn, every colouring of the edges of Kn with colours red and blue contains a red copy or a blue copy of Kt. Let q â©Ÿ 2 represent a number of colours, and let H1,..., Hq be graphs. A graph G is said to be q-Ramsey for the tuple (H1,...,Hq) if, for every colouring of the edges of G with colours {1, . . . , q}, there exists a colour i and a monochromatic copy of Hi in colour i. As we often want to understand the structural properties of the collection of graphs that are q-Ramsey for (H1,..., Hq), we restrict our attention to the graphs that are minimal for this property, with respect to subgraph inclusion. Such graphs are said to be q-Ramsey-minimal for (H1,..., Hq). In 1976, Burr, ErdƑs, and LovĂĄsz determined, for every s, t â©Ÿ 3, the smallest minimum degree of a graph G that is 2-Ramsey-minimal for (Ks, Kt). Significant efforts have been dedicated to generalising this result to a higher number of colours, qâ©Ÿ3, starting with the ‘symmetric’ q-tuple (Kt,..., Kt). In this thesis, we improve on the best known bounds for this parameter, providing state-of-the-art bounds in different (q, t)-regimes. These improvements rely on constructions based on finite geometry, which are then used to prove the existence of extremal graphs with certain key properties. Another crucial ingredient in these proofs is the existence of gadget graphs, called signal senders, that were initially developed by Burr, ErdƑs, and LovĂĄsz in 1976 for pairs of complete graphs. Until now, these senders have been shown to exist only in the two-colour setting, when q = 2, or in the symmetric multicolour setting, when H1,..., Hq are pairwise isomorphic. In this thesis, we then construct similar gadgets for all tuples of complete graphs, providing the first known constructions of these tools in the multicolour asymmetric setting. We use these new senders to prove far-reaching generalisations of several classical results in the area

    Seamless Multimodal Biometrics for Continuous Personalised Wellbeing Monitoring

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    Artificially intelligent perception is increasingly present in the lives of every one of us. Vehicles are no exception, (...) In the near future, pattern recognition will have an even stronger role in vehicles, as self-driving cars will require automated ways to understand what is happening around (and within) them and act accordingly. (...) This doctoral work focused on advancing in-vehicle sensing through the research of novel computer vision and pattern recognition methodologies for both biometrics and wellbeing monitoring. The main focus has been on electrocardiogram (ECG) biometrics, a trait well-known for its potential for seamless driver monitoring. Major efforts were devoted to achieving improved performance in identification and identity verification in off-the-person scenarios, well-known for increased noise and variability. Here, end-to-end deep learning ECG biometric solutions were proposed and important topics were addressed such as cross-database and long-term performance, waveform relevance through explainability, and interlead conversion. Face biometrics, a natural complement to the ECG in seamless unconstrained scenarios, was also studied in this work. The open challenges of masked face recognition and interpretability in biometrics were tackled in an effort to evolve towards algorithms that are more transparent, trustworthy, and robust to significant occlusions. Within the topic of wellbeing monitoring, improved solutions to multimodal emotion recognition in groups of people and activity/violence recognition in in-vehicle scenarios were proposed. At last, we also proposed a novel way to learn template security within end-to-end models, dismissing additional separate encryption processes, and a self-supervised learning approach tailored to sequential data, in order to ensure data security and optimal performance. (...)Comment: Doctoral thesis presented and approved on the 21st of December 2022 to the University of Port
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