814 research outputs found

    On the locality of indistinguishable quantum systems

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    This thesis investigates local realism in quantum indistinguishable particle systems, focusing on bosonic, fermionic, and 2D non-abelian anyonic systems. The local realism of quantum indistinguishable particle systems is asserted. It proves annihilation operators represent the local ontic states in these systems. It closes the literature gap on obtaining Deutsch-Hayden descriptors in indistinguishable particle systems. The prima facie paradox of action at a distance using fermionic annihilation operators as descriptors is resolved. The work provides examples of using and interpreting the annihilation operators as local ontic states. It contains the novel construction and characterisation of the annihilation operators for 2 D non-abelian anyonic systems. The explicit form of Fibonacci anyon annihilation operators is provided, and their usefulness is shown in expressing the anyonic Hubbard model Hamiltonian algebraically. By studying the indistinguishable particle systems’ local realistic structure, the thesis showcases the relevance of the choice of subsystem lattice and exotic possible compositions of subsystems

    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

    Audio-visual multi-modality driven hybrid feature learning model for crowd analysis and classification

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    The high pace emergence in advanced software systems, low-cost hardware and decentralized cloud computing technologies have broadened the horizon for vision-based surveillance, monitoring and control. However, complex and inferior feature learning over visual artefacts or video streams, especially under extreme conditions confine majority of the at-hand vision-based crowd analysis and classification systems. Retrieving event-sensitive or crowd-type sensitive spatio-temporal features for the different crowd types under extreme conditions is a highly complex task. Consequently, it results in lower accuracy and hence low reliability that confines existing methods for real-time crowd analysis. Despite numerous efforts in vision-based approaches, the lack of acoustic cues often creates ambiguity in crowd classification. On the other hand, the strategic amalgamation of audio-visual features can enable accurate and reliable crowd analysis and classification. Considering it as motivation, in this research a novel audio-visual multi-modality driven hybrid feature learning model is developed for crowd analysis and classification. In this work, a hybrid feature extraction model was applied to extract deep spatio-temporal features by using Gray-Level Co-occurrence Metrics (GLCM) and AlexNet transferrable learning model. Once extracting the different GLCM features and AlexNet deep features, horizontal concatenation was done to fuse the different feature sets. Similarly, for acoustic feature extraction, the audio samples (from the input video) were processed for static (fixed size) sampling, pre-emphasis, block framing and Hann windowing, followed by acoustic feature extraction like GTCC, GTCC-Delta, GTCC-Delta-Delta, MFCC, Spectral Entropy, Spectral Flux, Spectral Slope and Harmonics to Noise Ratio (HNR). Finally, the extracted audio-visual features were fused to yield a composite multi-modal feature set, which is processed for classification using the random forest ensemble classifier. The multi-class classification yields a crowd-classification accurac12529y of (98.26%), precision (98.89%), sensitivity (94.82%), specificity (95.57%), and F-Measure of 98.84%. The robustness of the proposed multi-modality-based crowd analysis model confirms its suitability towards real-world crowd detection and classification tasks

    Beam scanning by liquid-crystal biasing in a modified SIW structure

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    A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium

    Fuzzy Natural Logic in IFSA-EUSFLAT 2021

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    The present book contains five papers accepted and published in the Special Issue, “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”, of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference “The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences”, which took place in Bratislava (Slovakia) from September 19 to September 24, 2021. Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF–THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented. This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications

    A Comparison Study of the Differential Functioning of Tests Statistic and a New Mahalanobis Distance-Based Statistic For Pre-Screening Item Response Theory Models

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    The Differential Test Functioning (DTF) statistic, with the Item Parameter Replication (IPR) procedure, can measure Differential Item Functioning (DIF) within the Differential Functioning of Items and Tests (DFIT) framework for Item Response Theory (IRT) models. However, it comes with many practical costs and theoretical assumptions. In some reasonably anticipated circumstances, the DTF statistic cannot be evaluated easily, and DFIT analysis consequentially remains beyond the scope of impacted IRT models. A straightforward, diagnostic statistic would add value to typical IRT model fitting. It was hypothesized that a statistic based on Mahalanobis distances and standard errors of an IRT model could perform as a reliable flag for likely DIF. To test this hypothesis, a Monte Carlo simulation study compared the performance of the traditional DTF measure to the new statistic. Although easy to calculate, the statistic proved unproductive in flagging models with DIF present. Related performance analysis and recommendations were provided

    Modeling and Simulation in Engineering

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    The Special Issue Modeling and Simulation in Engineering, belonging to the section Engineering Mathematics of the Journal Mathematics, publishes original research papers dealing with advanced simulation and modeling techniques. The present book, “Modeling and Simulation in Engineering I, 2022”, contains 14 papers accepted after peer review by recognized specialists in the field. The papers address different topics occurring in engineering, such as ferrofluid transport in magnetic fields, non-fractal signal analysis, fractional derivatives, applications of swarm algorithms and evolutionary algorithms (genetic algorithms), inverse methods for inverse problems, numerical analysis of heat and mass transfer, numerical solutions for fractional differential equations, Kriging modelling, theory of the modelling methodology, and artificial neural networks for fault diagnosis in electric circuits. It is hoped that the papers selected for this issue will attract a significant audience in the scientific community and will further stimulate research involving modelling and simulation in mathematical physics and in engineering
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