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Optimal Second-Order Rates for Quantum Soft Covering and Privacy Amplification

IEEE Transactions on Information Theory 2024年第7期70卷 5077-5091页

作者： Shen, Yu-Chen Gao, Li Cheng, Hao-Chung National Taiwan University Department of Electrical Engineering Taipei10617 Taiwan University of Houston Department of Mathematics HoustonTX77204 United States Graduate Institute of Communication Engineering Department of Mathematics Institute of Applied Mathematical Sciences Center for Quantum Science and Engineering National Taiwan University Department of Electrical Engineering Taipei10617 Taiwan Physics Division National Center for Theoretical Sciences Taipei10617 Taiwan Quantum Computing Center New Taipei City23678 Taiwan

We study quantum soft covering and privacy amplification against quantum side information. The former task aims to approximate a quantum state by sampling from a prior distribution and querying a quantum channel. The latter task aims to extract uniform and independent randomness against quantum adversaries. For both tasks, we use trace distance to measure the closeness between the processed state and the ideal target state. We show that the minimal amount of samples for achieving an \varepsilon -covering is given by the (1-\varepsilon ) -hypothesis testing information (with additional logarithmic additive terms), while the maximal extractable randomness for an \varepsilon -secret extractor is characterized by the conditional (1-\varepsilon ) -hypothesis testing entropy. When performing independent and identical repetitions of the tasks, our one-shot characterizations lead to tight asymptotic expansions of the above-mentioned operational quantities. We establish their second-order rates given by the quantum mutual information variance and the quantum conditional information variance, respectively. Moreover, our results extend to the moderate deviation regime, which are the optimal asymptotic rates when the trace distances vanish at sub-exponential speed. Our proof technique is direct analysis of trace distance without smoothing. © 1963-2012 IEEE.

关键词： Hash functions

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An inexact augmented lagrangian algorithm for training leaky ReLU neural network with group sparsity

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2023年第1期24卷 10097-10139页

作者： Wei Liu Xin Liu Xiaojun Chen Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong

The leaky ReLU network with a group sparse regularization term has been widely used in the recent years. However, training such network yields a nonsmooth nonconvex optimization problem and there exists a lack of approaches to compute a stationary point deterministically. In this paper, we first resolve the multi-layer composite term in the original optimization problem by introducing auxiliary variables and additional constraints. We show the new model has a nonempty and bounded solution set and its feasible set satisfies the Mangasarian-Fromovitz constraint qualification. Moreover, we show the relationship between the new model and the original problem. Remarkably, we propose an inexact augmented Lagrangian algorithm for solving the new model, and show the convergence of the algorithm to a KKT point. Numerical experiments demonstrate that our algorithm is more efficient for training sparse leaky ReLU neural networks than some well-known algorithms.

关键词： sparse neural network leaky ReLU group sparsity penalty method inexact augmented Lagrangian method

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A Coupled Graph Theoric and Deep Learning Approaches for Nonrigid Image Registration 1

引用

International Conference on Artificial Intelligence and Smart Environment, ICAISE 2022

作者： El Bahi, Omaima Qaraai, Youssef El Allaoui, Ahmad Mathematical and Computer Modelling of Systems Team Applied Mathematics Computing and Systems Laboratory Faculty of Sciences and Techniques Errachidia Moulay Ismail University of Meknes Meknes Morocco Decisional Computing and Systems Modelling Team Engineering Sciences and Techniques Laboratory Faculty of Sciences and Techniques Errachidia Moulay Ismail University of Meknes Meknes Morocco

ISBN: (数字)9783031262548

ISBN: (纸本)9783031262531

Image registration is one of the essential elements in computer vision and several practical domains. Its objective is to recover a spatial transformation that aligns images. This is frequently formulated as an optimization problem based on an objective function that measures the quality of transformation with respect to the picture data and some prior information. This article revisits the concept of graph cuts as an effective optimization technique for image registration. We present a combination of graph cuts with superpixels segmentation via convolutional neural network (CNN), which produces a meaningful graph representation that can overcame the high computation cost. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Image registration

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No Black Holes from Light

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Physical Review Letters 2024年第4期133卷 041401-041401页

作者： Álvaro Álvarez-Domínguez Luis J. Garay Eduardo Martín-Martínez José Polo-Gómez Departamento de Física Teórica and IPARCOS Department of Applied Mathematics Institute for Quantum Computing Waterloo Ontario N2L 2Y5 Canada

We show that it is not possible to concentrate enough light to precipitate the formation of an event horizon. We argue that the dissipative quantum effects coming from the self-interaction of light (such as vacuum polarization) are enough to prevent any meaningful buildup of energy that could create a black hole in any realistic scenario.

关键词： Particle production Schwinger effect Classical black holes Composition of astronomical objects Semiclassical physics

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Smoothers with localized residual computations for geometric multigrid methods

arXiv

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arXiv 2024年

作者： Wichrowski, Michal Munch, Peter Kronbichler, Martin Kanschat, Guido Interdisciplinary Center for Scientifc Computing Heidelberg University Heidelberg Germany High-Performance Scientific Computing University of Augsburg Germany Applied Numerics Faculty of Mathematics Ruhr University Bochum Germany

We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We focus on patch smoothers, which offer robust convergence rates with respect to the finite element degree for various equations, in the setting of multiplicative subspace correction for numerical efficiency. By combining the computation of local residuals with local solvers, we increase the locality of the problem and thus reduce data transfers. The thread-parallel implementation of this algorithm is based on coloring, which contradicts cache efficiency. We improve data locality by rearranging the loop into batches so that more data can be reused. The organization of consecutive batches prioritizes data locality. © 2024, CC BY-NC-ND.

关键词： Finite element method

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Reverse-type Data Processing Inequality

arXiv

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arXiv 2024年

作者： Belzig, Paula Gao, Li Smith, Graeme Wu, Peixue Department of Applied Mathematics University of Waterloo WaterlooON Canada Institute for Quantum Computing University of Waterloo WaterlooON Canada School of Mathematics and Statistics Wuhan University Hubei Wuhan China

The quantum data processing inequality for quantum relative entropy states that two quantum states become harder to distinguish when a noisy channel is applied. On the other hand, a reverse quantum data processing inequality characterizes whether a pair of states remains distinguishable after the application of a noisy channel. In this work, we explore these concepts through contraction and expansion coefficients of quantum channels. We show that many quantum channels do not have a non-zero expansion coefficient, which means that they cannot admit a reverse data-processing inequality. Furthermore, we propose a comparative approach by introducing a relative expansion coefficient to assess how one channel expands relative entropy compared to another. We show that this relative expansion coefficient is positive for various pairs of quantum channels, including depolarizing, generalized dephasing, and amplitude damping channels, allowing us to establish a reverse-type data processing inequality for several settings. As an application, we construct a class of less noisy quantum channels that are non-degradable. This work contributes new mathematical tools for evaluating quantum information preservation across channels. © 2024, CC BY.

关键词： Quantum channel

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Blockchain-based federated learning with checksums to increase security in Internet of Things solutions

引用

Journal of Ambient Intelligence and Humanized computing 2023年第5期14卷 4685-4694页

作者： Prokop, Katarzyna Polap, Dawid Srivastava, Gautam Lin, Jerry Chun-Wei Faculty of Applied Mathematics Silesian University of Technology Kaszubska 23 Gliwice44-100 Poland Dept. of Math and Computer Science Brandon University BrandonMBR7A 6A9 Canada Research Centre for Interneural Computing China Medical University Taichung Taiwan Western Norway University of Applied Sciences Bergen Norway Dept. of Computer Science and Math Lebanese American University Beirut1102 Lebanon

Federated learning is becoming a practical solution for machine learning (ML) in industry. This is due to the possibility of implementing artificial intelligence (AI) systems and training its models on private data sets. However, this is not an ideal solution as it is possible to manipulate or even intercept the model during its transmission between the server and workers. In this paper, we propose a solution to ensure the security of the model transmitted between units in FL. The given model is encrypted with AES, DES, RSA algorithms, then a checksum is determined. This checksum with a private key is stored as a transaction on a blockchain. In the case of sending the model and its modification, the recipient can easily verify whether it is correct. The proposed solution has been described, tested, and compared to indicate its advantages and disadvantages. Conducted experiments were based on analyzing the communication time between participants, the accuracy of machine learning models, and attack detection. In terms of attack detection on the blockchain, we reached 81% thanks to the checksum mechanism. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

关键词： Blockchain

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Finite Difference Approximation with ADI Scheme for Two-dimensional Keller-Segel Equations

arXiv

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arXiv 2023年

作者： Lu, Yubin Chen, Chi-An Li, Xiaofan Liu, Chun Department of Applied Mathematics College of Computing Illinois Institute of Technology ChicagoIL60616 United States

Keller-Segel systems are a set of nonlinear partial differential equations used to model chemotaxis in biology. In this paper, we propose two alternating direction implicit (ADI) schemes to solve the 2D Keller-Segel systems directly with minimal computational cost, while preserving positivity, energy dissipation law and mass conservation. One scheme unconditionally preserves positivity, while the other does so conditionally. Both schemes achieve second-order accuracy in space, with the former being first-order accuracy in time and the latter second-order accuracy in time. Besides, the former scheme preserves the energy dissipation law asymptotically. We validate these results through numerical experiments, and also compare the efficiency of our schemes with the standard five-point scheme, demonstrating that our approaches effectively reduce computational costs. Copyright © 2023, The Authors. All rights reserved.

关键词： Energy dissipation

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Influence of Temperature-Dependent Thermophysical Properties of TiO2-SiO2-ZnO-Fe2O3/PAO Tetra-Hybrid Nanofluid along a Vertical Porous Surface with Suction

引用

Open Journal of Fluid Dynamics 2024年第3期14卷 123-146页

作者： Philip Iyiola Farayola Lateefat Olanike Aselebe Kafilat Adebimpe Salaudeen Saheed Dolapo Ogundiran Tajudeen Motunrayo Asiru Department of Mathematics and Computing Science Education Emmanuel Alayande University of Education Oyo Nigeria Department of General Studies Federal School of Surveying Oyo Nigeria Department of Pure and Applied Mathematics Ladoke Akintola University of Technology Ogbomoso Nigeria

The significance of the thermophysical properties of Tetra hybrid nanofluid in enhancing heat transmission in various applications like heat exchangers, automobiles, and solar storage cannot be overstated. These features can be tampered with when nanoparticles are been introduced into the base fluid to produce an improved heat carrier fluid for the system. This study investigates the impact of temperature-dependent properties on the movement of TiO2-SiO2-ZnO-Fe2O3/PAO Tetra hybrid nanofluid along a vertical porous surface with suction. The system of governing Partial Differential Equations (PDEs) was formulated and transformed into the system of coupled nonlinear third-order Ordinary Differential Equations (ODEs) by similarity techniques. The resulting ODEs were solved numerically using the shooting method and fourth order Runge-Kutta method with the aid of Maple 18.0 software. Using numerical and statistical methods, the study analyzes velocity, temperature profiles, skin friction coefficient, and Nusselt number. It was found that as the variable thermal conductivity parameter upsurges both the skin friction coefficient and Nusselt number intensify at the rate of 0.011697519 and 8.043581616 respectively. This study underscores the vital role of Tetra hybrid nanofluid’s thermophysical properties in improving heat transmission for diverse appli cations. By manipulating nanoparticles within the base fluid, the heat carrier fluid’s efficiency can be enhanced, critical for industries like automotive and enewable energy. These insights inform the design of more efficient heat exchange systems, advancing sustainability and performance in real-world scenarios.

关键词： Tetra Hybrid Nanofluid Shooting Technique Numerical Method Skin Friction Nusselt Number Thermophysical Properties

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Artificial Intelligence in Financial Derivatives: A Comparative Analysis of PSO and ACO for American-Style Put Options

Artificial Intelligence in Financial Derivatives: A Comparat...

引用

Advances in Electrical, computing, Communication and Sustainable Technologies (ICAECT), International Conference on

作者： Afroza Akter Salma Parvin A B M Shahadat Hossain MD Morshedul Islam Department of Mathematics Bangladesh University of Engineering and Technology Dhaka Bangladesh Department of Applied Mathematics University of Dhaka Dhaka Bangladesh Mathematical & Computing Sciences Concordia University of Edmonton Edmonton AB Canada

ISBN: (数字)9798350356236

ISBN: (纸本)9798350356243

Artificial Intelligence (AI) enhances option pricing accuracy and risk management, enabling precise valuation of complex derivatives across various market scenarios. This paper compares Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) in valuing American-style put options. We apply these metaheuristic algorithms to tackle the complexity of option pricing due to the early exercise feature, evaluating their performance across various boundary functions. We assess each method's accuracy and computational efficiency through extensive simulations. These simulations are benchmarked against findings from existing literature. Python's Computer Algebra System (CAS) is used for the simulations. The findings highlight AI's potential to enhance option valuation and contribute valuable insights for practitioners in finance.

关键词： Accuracy Computational modeling Metaheuristics Finance Pricing Numerical models Risk management Artificial intelligence Particle swarm optimization Cost accounting

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