21,313 research outputs found

    The Metaverse: Survey, Trends, Novel Pipeline Ecosystem & Future Directions

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    The Metaverse offers a second world beyond reality, where boundaries are non-existent, and possibilities are endless through engagement and immersive experiences using the virtual reality (VR) technology. Many disciplines can benefit from the advancement of the Metaverse when accurately developed, including the fields of technology, gaming, education, art, and culture. Nevertheless, developing the Metaverse environment to its full potential is an ambiguous task that needs proper guidance and directions. Existing surveys on the Metaverse focus only on a specific aspect and discipline of the Metaverse and lack a holistic view of the entire process. To this end, a more holistic, multi-disciplinary, in-depth, and academic and industry-oriented review is required to provide a thorough study of the Metaverse development pipeline. To address these issues, we present in this survey a novel multi-layered pipeline ecosystem composed of (1) the Metaverse computing, networking, communications and hardware infrastructure, (2) environment digitization, and (3) user interactions. For every layer, we discuss the components that detail the steps of its development. Also, for each of these components, we examine the impact of a set of enabling technologies and empowering domains (e.g., Artificial Intelligence, Security & Privacy, Blockchain, Business, Ethics, and Social) on its advancement. In addition, we explain the importance of these technologies to support decentralization, interoperability, user experiences, interactions, and monetization. Our presented study highlights the existing challenges for each component, followed by research directions and potential solutions. To the best of our knowledge, this survey is the most comprehensive and allows users, scholars, and entrepreneurs to get an in-depth understanding of the Metaverse ecosystem to find their opportunities and potentials for contribution

    Computational approach to the Schottky problem

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    We present a computational approach to the classical Schottky problem based on Fay's trisecant identity for genus g≥4g\geq 4. For a given Riemann matrix B∈Hg\mathbb{B}\in\mathbb{H}^{g}, the Fay identity establishes linear dependence of secants in the Kummer variety if and only if the Riemann matrix corresponds to a Jacobian variety as shown by Krichever. The theta functions in terms of which these secants are expressed depend on the Abel maps of four arbitrary points on a Riemann surface. However, there is no concept of an Abel map for general B∈Hg\mathbb{B} \in \mathbb{H}^{g}. To establish linear dependence of the secants, four components of the vectors entering the theta functions can be chosen freely. The remaining components are determined by a Newton iteration to minimize the residual of the Fay identity. Krichever's theorem assures that if this residual vanishes within the finite numerical precision for a generic choice of input data, then the Riemann matrix is with this numerical precision the period matrix of a Riemann surface. The algorithm is compared in genus 4 for some examples to the Schottky-Igusa modular form, known to give the Jacobi locus in this case. It is shown that the same residuals are achieved by the Schottky-Igusa form and the approach based on the Fay identity in this case. In genera 5, 6 and 7, we discuss known examples of Riemann matrices and perturbations thereof for which the Fay identity is not satisfied

    Bayesian Optimization with Conformal Prediction Sets

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    Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency.Comment: For code, see https://www.github.com/samuelstanton/conformal-bayesopt.gi

    Patching Weak Convolutional Neural Network Models through Modularization and Composition

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    Despite great success in many applications, deep neural networks are not always robust in practice. For instance, a convolutional neuron network (CNN) model for classification tasks often performs unsatisfactorily in classifying some particular classes of objects. In this work, we are concerned with patching the weak part of a CNN model instead of improving it through the costly retraining of the entire model. Inspired by the fundamental concepts of modularization and composition in software engineering, we propose a compressed modularization approach, CNNSplitter, which decomposes a strong CNN model for NN-class classification into NN smaller CNN modules. Each module is a sub-model containing a part of the convolution kernels of the strong model. To patch a weak CNN model that performs unsatisfactorily on a target class (TC), we compose the weak CNN model with the corresponding module obtained from a strong CNN model. The ability of the weak CNN model to recognize the TC can thus be improved through patching. Moreover, the ability to recognize non-TCs is also improved, as the samples misclassified as TC could be classified as non-TCs correctly. Experimental results with two representative CNNs on three widely-used datasets show that the averaged improvement on the TC in terms of precision and recall are 12.54% and 2.14%, respectively. Moreover, patching improves the accuracy of non-TCs by 1.18%. The results demonstrate that CNNSplitter can patch a weak CNN model through modularization and composition, thus providing a new solution for developing robust CNN models.Comment: Accepted at ASE'2

    3d mirror symmetry of braided tensor categories

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    We study the braided tensor structure of line operators in the topological A and B twists of abelian 3d N=4\mathcal{N}=4 gauge theories, as accessed via boundary vertex operator algebras (VOA's). We focus exclusively on abelian theories. We first find a non-perturbative completion of boundary VOA's in the B twist, which start out as certain affine Lie superalebras; and we construct free-field realizations of both A and B-twist VOA's, finding an interesting interplay with the symmetry fractionalization group of bulk theories. We use the free-field realizations to establish an isomorphism between A and B VOA's related by 3d mirror symmetry. Turning to line operators, we extend previous physical classifications of line operators to include new monodromy defects and bound states. We also outline a mechanism by which continuous global symmetries in a physical theory are promoted to higher symmetries in a topological twist -- in our case, these are infinite one-form symmetries, related to boundary spectral flow, which structure the categories of lines and control abelian gauging. Finally, we establish the existence of braided tensor structure on categories of line operators, viewed as non-semisimple categories of modules for boundary VOA's. In the A twist, we obtain the categories by extending modules of symplectic boson VOA's, corresponding to gauging free hypermultiplets; in the B twist, we instead extend Kazhdan-Lusztig categories for affine Lie superalgebras. We prove braided tensor equivalences among the categories of 3d-mirror theories. All results on VOA's and their module categories are mathematically rigorous; they rely strongly on recently developed techniques to access non-semisimple extensions.Comment: 158 pages, comments welcome

    Explicit spectral gap for Schottky subgroups of SL(2,Z)\mathrm{SL} (2,\mathbb{Z})

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    Let Γ\Gamma be a Schottky subgroup of SL(2,Z)\mathrm{SL} (2,\mathbb{Z}). We establish a uniform and explicit lower bound of the second eigenvalue of the Laplace-Beltrami operator of congruence coverings of the hyperbolic surface Γ\H2\Gamma \backslash \mathbb{H}^2 provided the limit set of Γ\Gamma is thick enough.Comment: 31 page

    A general framework for modelling limit order book dynamics

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    We present a mathematical framework for modelling the dynamics of limit order books, built on the combination of two modelling ingredients: the order flow -modelled as a general spatial point process- and market clearing, modelled via a deterministic ‘mass transport’ operator acting on distributions of buy and sell orders. At the mathematical level, this corresponds to a natural decomposition of the infinitesimal generator describing the evolution of the limit order book into two operators: the generator of the order flow and the clearing operator. Our model provides a flexible framework for modelling and simulating order book dynamics and studying various scaling limits of discrete order book models. We show that our framework includes previous models as special cases and yields insights into the interaction between the order flow and price dynamics, the use of order book data for prediction of intraday price movements. The framework also allows for model comparison and the study of the order flow. The modular structure of the model is well-adapted to simulation and allows the stochastic model for the order flow and the clearing mechanism to be specified independently. Then, as a simple demonstration, models with different assumptions on the order intensities are compared. The simulation result shows that orders of relatively large size also play an essential role in the evolution of the order book process. We further investigate the asymptotic behaviour of the order book processes, including the fluid scaling and the diffusion scaling. The decomposition relation between the order flow and the order book holds when the ask and bid price do not move. In general, the price processes depend on the order flow and the current state of the order book. We prove that as the tick size becomes small, the ask price and bid price converge to the same limiting process.Open Acces

    Image classification over unknown and anomalous domains

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    A longstanding goal in computer vision research is to develop methods that are simultaneously applicable to a broad range of prediction problems. In contrast to this, models often perform best when they are specialized to some task or data type. This thesis investigates the challenges of learning models that generalize well over multiple unknown or anomalous modes and domains in data, and presents new solutions for learning robustly in this setting. Initial investigations focus on normalization for distributions that contain multiple sources (e.g. images in different styles like cartoons or photos). Experiments demonstrate the extent to which existing modules, batch normalization in particular, struggle with such heterogeneous data, and a new solution is proposed that can better handle data from multiple visual modes, using differing sample statistics for each. While ideas to counter the overspecialization of models have been formulated in sub-disciplines of transfer learning, e.g. multi-domain and multi-task learning, these usually rely on the existence of meta information, such as task or domain labels. Relaxing this assumption gives rise to a new transfer learning setting, called latent domain learning in this thesis, in which training and inference are carried out over data from multiple visual domains, without domain-level annotations. Customized solutions are required for this, as the performance of standard models degrades: a new data augmentation technique that interpolates between latent domains in an unsupervised way is presented, alongside a dedicated module that sparsely accounts for hidden domains in data, without requiring domain labels to do so. In addition, the thesis studies the problem of classifying previously unseen or anomalous modes in data, a fundamental problem in one-class learning, and anomaly detection in particular. While recent ideas have been focused on developing self-supervised solutions for the one-class setting, in this thesis new methods based on transfer learning are formulated. Extensive experimental evidence demonstrates that a transfer-based perspective benefits new problems that have recently been proposed in anomaly detection literature, in particular challenging semantic detection tasks
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