IA Scholar Query: Linear manifolds analysis: theory and algorithm.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgTue, 01 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440The impact of the interactive mobile learning environment on developing the adaptive multimedia production skills of educational technology students
https://scholar.archive.org/work/mogovpee5vhwnjctqeeuh5rmve
The aim of the current research is to develop an interactive Mlearning environment and reveal its impact on the development of adaptive multimedia production skills for students of the fourth year, Instruction Technology Dept., Faculty of Specific Education, Minia University in the second semester of the academic year (2020/ 2021 AD). The research followed the experimental method, and the semi-experimental design The experimental design with two groups: the experimental group consisting of (30) students who studied in an interactive m-learning environment, and the control group consisting of (30) students who studied in the traditional method, in order to develop the skills of multimedia production. The adaptive media and the measurement tools, namely: the cognitive test and the multimedia assessment card, and the results showed a difference between the scores of the experimental group and the control group in the cognitive and performance aspect of the adaptive multimedia production skills.اسماء محمود سید عبد الرحمنwork_mogovpee5vhwnjctqeeuh5rmveTue, 01 Nov 2022 00:00:00 GMTTransmutation Method and Boundary-Value Problems for Singular Elliptic Equations
https://scholar.archive.org/work/olnpiila7fbvziwoqnex233gh4
The main content of this text is composed from the two doctoral dissertations of V.\,V.~Katrakhov (1989) and S.\,M.~Sitnik (2016). Apart from a detailed review and bibliography the book contains original results of the authors. The text is concluded with brief biographic essay of Valeriy Vyacheslavovich Katrakhov and a detailed bibliography.Valeriy V. Katrakhov, Sergey M. Sitnikwork_olnpiila7fbvziwoqnex233gh4Wed, 05 Oct 2022 00:00:00 GMTEquivalence of Nondifferentiable Metrics
https://scholar.archive.org/work/rbasigswkbb2leymh6myisjuoy
We study nondifferentiable metrics occuring in general relativity via the method of equivalence of Cartan adapted to the Courant algebroids. We derive new local differential invariants naturally associated with the loci of nondifferentiability and rank deficiency of the metric. As an application, we utilize the newfangled invariants to resolve the problem of causality in the interior of the black holes that contain closed timelike geodesics. Also, a no-go type theorem limits the evolution scenarios for gravitational collapse.Alexander Golubevwork_rbasigswkbb2leymh6myisjuoyWed, 05 Oct 2022 00:00:00 GMTAnomaly of (2+1)-Dimensional Symmetry-Enriched Topological Order from (3+1)-Dimensional Topological Quantum Field Theory
https://scholar.archive.org/work/cxm3ab3favfc3l2xbcvucnze3i
Symmetry acting on a (2+1)D topological order can be anomalous in the sense that they possess an obstruction to being realized as a purely (2+1)D on-site symmetry. In this paper, we develop a (3+1)D topological quantum field theory to calculate the anomaly indicators of a (2+1)D topological order with a general finite group symmetry G, which may contain anti-unitary elements and/or permute anyons. These anomaly indicators are partition functions of the (3+1)D topological quantum field theory on a specific manifold equipped with some G-bundle, and they are expressed using the data characterizing the topological order and the symmetry actions. Combined with the relative anomaly formalism, our framework actually enables us to calculate the anomaly of a given topological order with a fully general symmetry. Our framework is applied to derive the anomaly indicators for various symmetry groups, including ℤ_2×ℤ_2, ℤ_2^T×ℤ_2^T, etc, where ℤ_2 and ℤ_2^T denote a unitary and anti-unitary order-2 group, respectively.Weicheng Ye, Liujun Zouwork_cxm3ab3favfc3l2xbcvucnze3iWed, 05 Oct 2022 00:00:00 GMTOn the Trade-Off between Actionable Explanations and the Right to be Forgotten
https://scholar.archive.org/work/5nlxwgzoibgvppdemi42bpfjda
As machine learning (ML) models are increasingly being deployed in high-stakes applications, policymakers have suggested tighter data protection regulations (e.g., GDPR, CCPA). One key principle is the "right to be forgotten" which gives users the right to have their data deleted. Another key principle is the right to an actionable explanation, also known as algorithmic recourse, allowing users to reverse unfavorable decisions. To date, it is unknown whether these two principles can be operationalized simultaneously. Therefore, we introduce and study the problem of recourse invalidation in the context of data deletion requests. More specifically, we theoretically and empirically analyze the behavior of popular state-of-the-art algorithms and demonstrate that the recourses generated by these algorithms are likely to be invalidated if a small number of data deletion requests (e.g., 1 or 2) warrant updates of the predictive model. For the setting of linear models and overparameterized neural networks -- studied through the lens of neural tangent kernels (NTKs) -- we suggest a framework to identify a minimal subset of critical training points which, when removed, maximize the fraction of invalidated recourses. Using our framework, we empirically show that the removal of as little as 2 data instances from the training set can invalidate up to 95 percent of all recourses output by popular state-of-the-art algorithms. Thus, our work raises fundamental questions about the compatibility of "the right to an actionable explanation" in the context of the "right to be forgotten" while also providing constructive insights on the determining factors of recourse robustness.Martin Pawelczyk and Tobias Leemann and Asia Biega and Gjergji Kasneciwork_5nlxwgzoibgvppdemi42bpfjdaWed, 05 Oct 2022 00:00:00 GMTA kernel-based quantum random forest for improved classification
https://scholar.archive.org/work/7kpncbf3kvhsdjxka7n3ychgue
The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to attain expressional and computational advantage. In this work we extend the linear quantum support vector machine (QSVM) with kernel function computed through quantum kernel estimation (QKE), to form a decision tree classifier constructed from a decision directed acyclic graph of QSVM nodes - the ensemble of which we term the quantum random forest (QRF). To limit overfitting, we further extend the model to employ a low-rank Nyström approximation to the kernel matrix. We provide generalisation error bounds on the model and theoretical guarantees to limit errors due to finite sampling on the Nyström-QKE strategy. In doing so, we show that we can achieve lower sampling complexity when compared to QKE. We numerically illustrate the effect of varying model hyperparameters and finally demonstrate that the QRF is able obtain superior performance over QSVMs, while also requiring fewer kernel estimations.Maiyuren Srikumar, Charles D. Hill, Lloyd C.L. Hollenbergwork_7kpncbf3kvhsdjxka7n3ychgueWed, 05 Oct 2022 00:00:00 GMTAnalog Quantum Simulation of the Dynamics of Open Quantum Systems with Quantum Dots and Microelectronic Circuits
https://scholar.archive.org/work/t4pfk65vbnchtlmi4oumjbzkru
We introduce a general setup for the analog quantum simulation of the dynamics of open quantum systems based on semiconductor quantum dots electrically connected to a chain of quantum RLC electronic circuits. The dots are chosen to be in the regime of spin-charge hybridization to enhance their sensitivity to the RLC circuits while mitigating the detrimental effects of unwanted noise. In this context, we establish an experimentally realizable map between the hybrid system and a qubit coupled to thermal harmonic environments of arbitrary complexity that enables the analog quantum simulation of open quantum systems. We assess the utility of the simulator by numerically exact emulations that indicate that the experimental setup can faithfully mimic the intended target even in the presence of its natural inherent noise. We further provide a detailed analysis of the physical requirements on the quantum dots and the RLC circuits needed to experimentally realize this proposal that indicates that the simulator can be created with existing technology. The approach can exactly capture the effects of highly structured non-Markovian quantum environments typical of photosynthesis and chemical dynamics, and offer clear potential advantages over conventional and even quantum computation. The proposal opens a general path for effective quantum dynamics simulations based on semiconductor quantum dots.Chang Woo Kim, John M. Nichol, Andrew N. Jordan, Ignacio Francowork_t4pfk65vbnchtlmi4oumjbzkruWed, 05 Oct 2022 00:00:00 GMTGlossary of terms in the SPHERE project environment
https://scholar.archive.org/work/3rottguedfgpbcdv6fd76os4u4
"The Glossary of terms in the SPHERE project environment" is a 206 pages document that presents 1287 terms used during the project. It can help you identify the acronyms presented in the Acronyms document and consult the terms and their definition.Antoni Quintana, Enric Ortega Fontwork_3rottguedfgpbcdv6fd76os4u4Wed, 05 Oct 2022 00:00:00 GMTLearnable latent embeddings for joint behavioral and neural analysis
https://scholar.archive.org/work/5eexr6itxjam7oebf6ynn22cla
Mapping behavioral actions to neural activity is a fundamental goal of neuroscience. As our ability to record large neural and behavioral data increases, there is growing interest in modeling neural dynamics during adaptive behaviors to probe neural representations. In particular, neural latent embeddings can reveal underlying correlates of behavior, yet, we lack non-linear techniques that can explicitly and flexibly leverage joint behavior and neural data. Here, we fill this gap with a novel method, CEBRA, that jointly uses behavioral and neural data in a hypothesis- or discovery-driven manner to produce consistent, high-performance latent spaces. We validate its accuracy and demonstrate our tool's utility for both calcium and electrophysiology datasets, across sensory and motor tasks, and in simple or complex behaviors across species. It allows for single and multi-session datasets to be leveraged for hypothesis testing or can be used label-free. Lastly, we show that CEBRA can be used for the mapping of space, uncovering complex kinematic features, and rapid, high-accuracy decoding of natural movies from visual cortex.Steffen Schneider, Jin Hwa Lee, Mackenzie Weygandt Mathiswork_5eexr6itxjam7oebf6ynn22claWed, 05 Oct 2022 00:00:00 GMTMulticlass Learnability Beyond the PAC Framework: Universal Rates and Partial Concept Classes
https://scholar.archive.org/work/qde3vhsypbboleksmoygfx36mi
In this paper we study the problem of multiclass classification with a bounded number of different labels k, in the realizable setting. We extend the traditional PAC model to a) distribution-dependent learning rates, and b) learning rates under data-dependent assumptions. First, we consider the universal learning setting (Bousquet, Hanneke, Moran, van Handel and Yehudayoff, STOC '21), for which we provide a complete characterization of the achievable learning rates that holds for every fixed distribution. In particular, we show the following trichotomy: for any concept class, the optimal learning rate is either exponential, linear or arbitrarily slow. Additionally, we provide complexity measures of the underlying hypothesis class that characterize when these rates occur. Second, we consider the problem of multiclass classification with structured data (such as data lying on a low dimensional manifold or satisfying margin conditions), a setting which is captured by partial concept classes (Alon, Hanneke, Holzman and Moran, FOCS '21). Partial concepts are functions that can be undefined in certain parts of the input space. We extend the traditional PAC learnability of total concept classes to partial concept classes in the multiclass setting and investigate differences between partial and total concepts.Alkis Kalavasis, Grigoris Velegkas, Amin Karbasiwork_qde3vhsypbboleksmoygfx36miWed, 05 Oct 2022 00:00:00 GMTStochastic coordinate transformations with applications to robust machine learning
https://scholar.archive.org/work/o3dsxrtrivdfxmdrq4rryzdwt4
In this paper we introduce a set of novel features for identifying underlying stochastic behavior of input data using the Karhunen-Loeve expansion. These novel features are constructed by applying a coordinate transformation based on the recent Functional Data Analysis theory for anomaly detection. The associated signal decomposition is an exact hierarchical tensor product expansion with known optimality properties for approximating stochastic processes (random fields) with finite dimensional function spaces. In principle these low dimensional spaces can capture most of the stochastic behavior of 'underlying signals' in a given nominal class, and can reject signals in alternative classes as stochastic anomalies. Using a hierarchical finite dimensional expansion of the nominal class, a series of orthogonal nested subspaces is constructed for detecting anomalous signal components. Projection coefficients of input data in these subspaces are then used to train a Machine Learning (ML) classifier. However, due to the split of the signal into nominal and anomalous projection components, clearer separation surfaces of the classes arise. In fact we show that with a sufficiently accurate estimation of the covariance structure of the nominal class, a sharp classification can be obtained. This is particularly advantageous for situations with large unbalanced datasets. We formulate this concept and demonstrate it on a number of high-dimensional datasets in cancer diagnostics. This approach yields significant increases in accuracy over ML methods that use the original feature data. This method leads to a significant increase in precision and accuracy over the current top benchmarks for the Global Cancer Map (GCM) gene expression network dataset. Furthermore, tests from unbalanced semi-synthetic datasets created from the GCM data confirmed increased accuracy as the dataset becomes more unbalanced.Julio Enrique Castrillon-Candas, Dingning Liu, Mark Konwork_o3dsxrtrivdfxmdrq4rryzdwt4Wed, 05 Oct 2022 00:00:00 GMTMaximum likelihood for high-noise group orbit estimation and single-particle cryo-EM
https://scholar.archive.org/work/gkenykfetfa6pkwu2d3pdp37ta
Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study several problems of function estimation in a high noise regime, where samples are observed after random rotation and possible linear projection of the function domain. We describe a stratification of the Fisher information eigenvalues according to transcendence degrees of graded pieces of the algebra of group invariants, and we relate critical points of the log-likelihood landscape to a sequence of moment optimization problems, extending previous results for a discrete rotation group without projections. We then compute the transcendence degrees and forms of these optimization problems for several examples of function estimation under SO(2) and SO(3) rotations, including a simplified model of cryo-EM as introduced by Bandeira, Blum-Smith, Kileel, Perry, Weed, and Wein. We affirmatively resolve conjectures that 3^rd-order moments are sufficient to locally identify a generic signal up to its rotational orbit in these examples. For low-dimensional approximations of the electric potential maps of two small protein molecules, we empirically verify that the noise-scalings of the Fisher information eigenvalues conform with our theoretical predictions over a range of SNR, in a model of SO(3) rotations without projections.Zhou Fan and Roy R. Lederman and Yi Sun and Tianhao Wang and Sheng Xuwork_gkenykfetfa6pkwu2d3pdp37taWed, 05 Oct 2022 00:00:00 GMTCompressed CPD-Based Channel Estimation and Joint Beamforming for RIS-Assisted Millimeter Wave Communications
https://scholar.archive.org/work/d43hywa4wvbudovgoxrbohjxre
We consider the problem of channel estimation and joint active and passive beamforming for reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. We show that, with a well-designed frame-based training protocol, the received pilot signal can be organized into a low-rank third-order tensor that admits a canonical polyadic decomposition (CPD). Based on this observation, we propose two CPD-based methods for estimating the cascade channels associated with different subcarriers. The proposed methods exploit the intrinsic low-rankness of the CPD formulation, which is a result of the sparse scattering characteristics of mmWave channels, and thus have the potential to achieve a significant training overhead reduction. Specifically, our analysis shows that the proposed methods have a sample complexity that scales quadratically with the sparsity of the cascade channel. Also, by utilizing the singular value decomposition-like structure of the effective channel, this paper develops a joint active and passive beamforming method based on the estimated cascade channels. Simulation results show that the proposed CPD-based channel estimation methods attain mean square errors that are close to the Cramer-Rao bound (CRB) and present a clear advantage over the compressed sensing-based method. In addition, the proposed joint beamforming method can effectively utilize the estimated channel parameters to achieve superior beamforming performance.Xi Zheng, Jun Fang, Hongwei Wang, Peilan Wang, Hongbin Liwork_d43hywa4wvbudovgoxrbohjxreTue, 04 Oct 2022 00:00:00 GMTDetecting asset price bubbles using deep learning
https://scholar.archive.org/work/w56piy42cfes3jqyk6gmcifpou
In this paper we employ deep learning techniques to detect financial asset bubbles by using observed call option prices. The proposed algorithm is widely applicable and model-independent. We test the accuracy of our methodology in numerical experiments within a wide range of models and apply it to market data of tech stocks in order to assess if asset price bubbles are present. In addition, we provide a theoretical foundation of our approach in the framework of local volatility models. To this purpose, we give a new necessary and sufficient condition for a process with time-dependent local volatility function to be a strict local martingale.Francesca Biagini, Lukas Gonon, Andrea Mazzon, Thilo Meyer-Brandiswork_w56piy42cfes3jqyk6gmcifpouTue, 04 Oct 2022 00:00:00 GMTSample Complexity of Nonparametric Off-Policy Evaluation on Low-Dimensional Manifolds using Deep Networks
https://scholar.archive.org/work/oq5tws7ngjdt7bk4ukdrdfw6mi
We consider the off-policy evaluation problem of reinforcement learning using deep convolutional neural networks. We analyze the deep fitted Q-evaluation method for estimating the expected cumulative reward of a target policy, when the data are generated from an unknown behavior policy. We show that, by choosing network size appropriately, one can leverage any low-dimensional manifold structure in the Markov decision process and obtain a sample-efficient estimator without suffering from the curse of high data ambient dimensionality. Specifically, we establish a sharp error bound for fitted Q-evaluation, which depends on the intrinsic dimension of the state-action space, the smoothness of Bellman operator, and a function class-restricted χ^2-divergence. It is noteworthy that the restricted χ^2-divergence measures the behavior and target policies' mismatch in the function space, which can be small even if the two policies are not close to each other in their tabular forms. We also develop a novel approximation result for convolutional neural networks in Q-function estimation. Numerical experiments are provided to support our theoretical analysis.Xiang Ji, Minshuo Chen, Mengdi Wang, Tuo Zhaowork_oq5tws7ngjdt7bk4ukdrdfw6miTue, 04 Oct 2022 00:00:00 GMTThe connected wedge theorem and its consequences
https://scholar.archive.org/work/ixivavv3avaa3opq6s6atduwfu
In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of these statements, and their relationship, with a number of new results. Centrally, we present and prove a new theorem, the n-to-n connected wedge theorem, which considers n input and n output locations at the boundary of an asymptotically AdS_2+1 spacetime described by AdS/CFT. When a sufficiently strong set of causal connections exists among these points in the bulk, a set of n associated regions in the boundary will have extensive-in-N mutual information across any bipartition of the regions. The proof holds in three bulk dimensions for classical spacetimes satisfying the null curvature condition and for semiclassical spacetimes satisfying standard conjectures. The n-to-n connected wedge theorem gives a precise example of how causal connections in a bulk state can emerge from large-N entanglement features of its boundary dual. It also has consequences for quantum information theory: it reveals one pattern of entanglement which is sufficient for information processing in a particular class of causal networks. We argue this pattern is also necessary, and give an AdS/CFT inspired protocol for information processing in this setting. Our theorem generalizes the 2-to-2 connected wedge theorem proven in arXiv:1912.05649. We also correct some errors in the proof presented there, in particular a false claim that existing proof techniques work above three bulk dimensions.Alex May, Jonathan Sorce, Beni Yoshidawork_ixivavv3avaa3opq6s6atduwfuTue, 04 Oct 2022 00:00:00 GMTThe black hole interior from non-isometric codes and complexity
https://scholar.archive.org/work/uurupxz57rbwno7cfokdtkgauq
Quantum error correction has given us a natural language for the emergence of spacetime, but the black hole interior poses a challenge for this framework: at late times the apparent number of interior degrees of freedom in effective field theory can vastly exceed the true number of fundamental degrees of freedom, so there can be no isometric (i.e. inner-product preserving) encoding of the former into the latter. In this paper we explain how quantum error correction nonetheless can be used to explain the emergence of the black hole interior, via the idea of "non-isometric codes protected by computational complexity". We show that many previous ideas, such as the existence of a large number of "null states", a breakdown of effective field theory for operations of exponential complexity, the quantum extremal surface calculation of the Page curve, post-selection, "state-dependent/state-specific" operator reconstruction, and the "simple entropy" approach to complexity coarse-graining, all fit naturally into this framework, and we illustrate all of these phenomena simultaneously in a soluble model.Chris Akers, Netta Engelhardt, Daniel Harlow, Geoff Penington, Shreya Vardhanwork_uurupxz57rbwno7cfokdtkgauqTue, 04 Oct 2022 00:00:00 GMTDetection and Evaluation of Clusters within Sequential Data
https://scholar.archive.org/work/bue3nywa3nbqffglua55yjgbd4
Motivated by theoretical advancements in dimensionality reduction techniques we use a recent model, called Block Markov Chains, to conduct a practical study of clustering in real-world sequential data. Clustering algorithms for Block Markov Chains possess theoretical optimality guarantees and can be deployed in sparse data regimes. Despite these favorable theoretical properties, a thorough evaluation of these algorithms in realistic settings has been lacking. We address this issue and investigate the suitability of these clustering algorithms in exploratory data analysis of real-world sequential data. In particular, our sequential data is derived from human DNA, written text, animal movement data and financial markets. In order to evaluate the determined clusters, and the associated Block Markov Chain model, we further develop a set of evaluation tools. These tools include benchmarking, spectral noise analysis and statistical model selection tools. An efficient implementation of the clustering algorithm and the new evaluation tools is made available together with this paper. Practical challenges associated to real-world data are encountered and discussed. It is ultimately found that the Block Markov Chain model assumption, together with the tools developed here, can indeed produce meaningful insights in exploratory data analyses despite the complexity and sparsity of real-world data.Alexander Van Werde, Albert Senen-Cerda, Gianluca Kosmella, Jaron Sanderswork_bue3nywa3nbqffglua55yjgbd4Tue, 04 Oct 2022 00:00:00 GMTStructural stability of invasion graphs for generalized Lotka–Volterra systems
https://scholar.archive.org/work/4opok5ubivelzm2rrtpmd2meti
In this paper we study in detail the structure of the global attractor for a generalized Lotka-Volterra system with Volterra--Lyapunov stable structural matrix. We provide the full characterization of this structure and we show that it coincides with the invasion graph as recently introduced in [15]. We also study the stability of the structure with respect to the perturbation of the problem parameters. This allows us to introduce a definition of structural stability in Ecology in coherence with the classical mathematical concept where there exists a detailed geometrical structure, governing the transient and asymptotic dynamics, which is robust under perturbation.Pablo Almaraz, José A. Langa, Piotr Kalitawork_4opok5ubivelzm2rrtpmd2metiTue, 04 Oct 2022 00:00:00 GMTMore than the sum of its parts – pattern mining, neural networks, and how they complement each other
https://scholar.archive.org/work/cs6gkif3vrdw3avvup2mv54vfy
In this thesis we explore pattern mining and deep learning. Often seen as orthogonal, we show that these fields complement each other and propose to combine them to gain from each other's strengths. We, first, show how to efficiently discover succinct and non-redundant sets of patterns that provide insight into data beyond conjunctive statements. We leverage the interpretability of such patterns to unveil how and which information flows through neural networks, as well as what characterizes their decisions. Conversely, we show how to combine continuous optimization with pattern discovery, proposing a neural network that directly encodes discrete patterns, which allows us to apply pattern mining at a scale orders of magnitude larger than previously possible. Large neural networks are, however, exceedingly expensive to train for which 'lottery tickets' -small, well-trainable sub-networks in randomly initialized neural networks -offer a remedy. We identify theoretical limitations of strong tickets and overcome them by equipping these tickets with the property of universal approximation. To analyze whether limitations in ticket sparsity are algorithmic or fundamental, we propose a framework to plant and hide lottery tickets. With novel ticket benchmarks we then conclude that the limitation is likely algorithmic, encouraging further developments for which our framework offers means to measure progress. the way for their great contributions which served for outstanding joint projects bridging different fields. I further want to thank my parents, my sister, and my girlfriend, for their constant moral support and genuine interest in what I am doing. Finally, special thanks go out to my supervisor Jilles. It was a great journey and, as we say in german, "Der Weg ist das Ziel", it was indeed the journey itself that provided for all the fun. Yet, I am also more than happy with where it ended: this thesis. All of this would not have been possible without you, the freedom you gave me to follow my own ideas, and your trust in me. Thank you! lations or differential between diseased and healthy individuals. Those patterns can then be leveraged for further investigation by a domain expert as potential biomarkers, drug targets, or to improve the foundational understanding of gene regulation as a whole. In machine learning the data is instead exploited with a different goal, that is, to learn predictive models. In the last decade artificial neural networks stood at the forefront of machine learning, solving complex tasks in e.g. image recognition and natural language processing often at human-like performance or even surpassing it (Jonas Fischer, Universität Des Saarlandeswork_cs6gkif3vrdw3avvup2mv54vfyTue, 04 Oct 2022 00:00:00 GMT