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Pilot-wave dynamics: Using dynamic mode decomposition to characterize bifurcations, routes to chaos, and emergent statistics

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Physical Review E 2023年第3期108卷 034213-034213页

作者： J. Nathan Kutz André Nachbin Peter J. Baddoo John W. M. Bush Department of Applied Mathematics and Electrical and Computer Engineering University of Washington Seattle Washington 98195 USA Department of Mathematical Sciences Worcester Polytechnic Institute Worcester Massachusetts 01742 USA Department of Mathematics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA

We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry and apply the dynamic mode decomposition (DMD) in order to characterize the evolution of the wave field as the bath's vibrational acceleration is increased progressively. Dynamic mode decomposition provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatiotemporal data. Thus, DMD reduces the complex nonlinear interactions between pilot waves and droplet to a low-dimensional linear superposition of DMD modes characterizing the wave field. In particular, it provides a low-dimensional characterization of the bifurcation structure of the pilot-wave physics, wherein the excitation and recruitment of additional modes in the linear superposition models the bifurcation sequence. This DMD characterization yields a fresh perspective on the bouncing-droplet problem that forges valuable new links with the mathematical machinery of quantum mechanics. Specifically, the analysis shows that as the vibrational acceleration is increased, the pilot-wave field undergoes a series of Hopf bifurcations that ultimately lead to a chaotic wave field. The established relation between the mean pilot-wave field and the droplet statistics allows us to characterize the evolution of the emergent statistics with increased vibrational forcing from the evolution of the pilot-wave field. We thus develop a numerical framework with the same basic structure as quantum mechanics, specifically a wave theory that predicts particle statistics.

关键词： Dynamical systems

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Mental Health Analysis using Deep Learning of Social Media Data gathered using Chrome Extension

Mental Health Analysis using Deep Learning of Social Media D...

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Emerging technology (INCET), International Conference for

作者： Manvita Joshi Chetashri Mahajan Traividya Korgaonkar Nataasha Raul Meghana Naik Computer Engineering Department Sardar Patel Institute of Technology Mumbai India Applied Sciences Mathematics and Humanities Department Sardar Patel Institute of Technology Mumbai India

Recently the topic of ’mental health’ has gained high awareness, especially among younger generations. The age group that mostly gets affected by mental disorders is between 15-49 years of age. Research conducted on different social media data has found that a person with mental disorders (such as depression, anxiety, etc) tends to use social media more as compared to a mentally healthy person. Most users convey their emotional states through posting on public platforms, tweeting and accordingly watching related videos on YouTube that best describes their current mental state. It is also found that there is a difference in users’ social media activities (on Facebook, Twitter, and YouTube) with a healthy mind and one with an unhealthy mind. A study conducted in 2018 found that 45% of teenagers worldwide are constantly using the internet. According to research, teenagers use the internet on average for about nine hours each day. The internet can prove to be the easiest medium to monitor a person’s online activities (such as posting on social media, writing emails, watching or liking YouTube videos, commenting on YouTube videos, etc). The aforementioned activities and the internet usage time of a person can help to understand his/her mental state. The user’s social media activity can be analysed for finding potential patterns in his emotions/mood. These patterns can be helpful in uncovering underlying mental health issues such as depression, stress disorders, PTSD, schizophrenia etc. These findings can be reported to the user’s therapist for their monitoring record. To predict the mental state of the user by analysing their social media activities, an initiative was taken to develop an application with the objective to forewarn its users of any negative patterns regarding the state of mind that they exhibit. This application makes use of the Bidirectional LSTM algorithm, a deep learning method to identify a user’s emotions (one among the 6 defined emotions) and stores

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CLASSICAL SOLUTIONS TO THE THIN-FILM EQUATION WITH GENERAL MOBILITY IN THE PERFECT-WETTING REGIME

arXiv

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arXiv 2023年

作者： Gnann, Manuel V. Wisse, Anouk C. Delft Institute of Applied Mathematics Faculty of Electrical Engineering Mathematics and Computer Science Delft University of Technology Mekelweg 4 Delft2628 CD Netherlands

We prove well-posedness, partial regularity, and stability of the thin-film equation ht+(m(h)hzzz)z = 0 with general mobility m(h) = hn and mobility exponent n ∈ (1, 3/2)∪(3/2,3) in the regime of perfect wetting (zero contact angle). After a suitable coordinate transformation to fix the free boundary (the contact line where liquid, air, and solid coalesce), the thin-film equation is rewritten as an abstract Cauchy problem and we obtain maximal Lpt-regularity for the linearized evolution. Partial regularity close to the free boundary is obtained by studying the elliptic regularity of the spatial part of the linearization. This yields solutions that are non-smooth in the distance to the free boundary, in line with previous findings for source-type self-similar solutions. In a scaling-wise quasi-minimal norm for the initial data, we obtain a well-posedness and asymptotic stability result for perturbations of traveling waves. The novelty of this work lies in the usage of Lp-estimates in time, where 1 2t-estimates, well-posedness, and stability for 1.8384 ≈ 3/17 (15 − √21) MSC Codes 35K65, 35K25, 35R35, 76A20, 76D08 Copyright © 2023, The Authors. All rights reserved.

关键词： Asymptotic stability

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Exact soft analytical side-channel attacks using tractable circuits 24

Exact soft analytical side-channel attacks using tractable c...

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Proceedings of the 41st International Conference on Machine Learning

作者： Thomas Wedenig Rishub Nagpal Gaëtan Cassiers Stefan Mangard Robert Peharz Institute of Theoretical Computer Science Graz University of Technology Graz Austria Institute of Applied Information Processing and Communications Graz University of Technology Graz Austria Institute of Information and Communication Technologies Electronics and Applied Mathematics (ICTM) UCLouvain Ottignies-Louvain-la-Neuve Belgium

Detecting weaknesses in cryptographic algorithms is of utmost importance for designing secure information systems. The state-of-the-art soft analytical side-channel attack (SASCA) uses physical leakage information to make probabilistic predictions about intermediate computations and combines these "guesses" with the known algorithmic logic to compute the posterior distribution over the key. This attack is commonly performed via loopy belief propagation, which, however, lacks guarantees in terms of convergence and inference quality. In this paper, we develop a fast and exact inference method for SASCA, denoted as ExSASCA, by leveraging knowledge compilation and tractable probabilistic circuits. When attacking the Advanced Encryption Standard (AES), the most widely used encryption algorithm to date, ExSASCA outperforms SASCA by more than 31% top-1 success rate absolute. By leveraging sparse belief messages, this performance is achieved with little more computational cost than SASCA, and about 3 orders of magnitude less than exact inference via exhaustive enumeration. Even with dense belief messages, ExSASCA still uses 6 times less computations than exhaustive inference.

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A comparison of Krylov methods for Shifted Skew-Symmetric Systems

arXiv

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arXiv 2023年

作者： Idema, R. Vuik, C. Delft University of Technology Faculty of Electrical Engineering Mathematics and Computer Science Delft Institute of Applied Mathematics Mekelweg 4 Delft2628 CD Netherlands

It is well known that for general linear systems, only optimal Krylov methods with long recurrences exist. For special classes of linear systems it is possible to find optimal Krylov methods with short recurrences. In this paper we consider the important class of linear systems with a shifted skew-symmetric coefficient matrix. We present the MRS3 solver, a minimal residual method that solves these problems using short vector recurrences. We give an overview of existing Krylov solvers that can be used to solve these problems, and compare them with the MRS3 method, both theoretically and by numerical experiments. From this comparison we argue that the MRS3 solver is the fastest and most robust of these Krylov method for systems with a shifted skew-symmetric coefficient matrix. © 2023, CC BY.

关键词： Linear systems

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Optimizing Fresh Food Supply Chains: Leveraging 3PL for Carbon Reduction and Profit Maximization - A Game-Theoretic Analysis

Optimizing Fresh Food Supply Chains: Leveraging 3PL for Carb...

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IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT)

作者： Anil Dhanda Divya Aggarwal Lovely Jain Priyansh Tyagi Mandeep Mittal Abhay Bansal Department of Mathematics Amity Institute of Applied Sciences Amity University Noida Uttar Pradesh India Department of Mathematics School of Computer Science Engineering and Technology Bennett University Greater Noida India

ISBN: (数字)9798350385922

ISBN: (纸本)9798350385939

Mounting pressure on governments to reduce carbon emissions has forced them to impose regulations on supply chain members. Carbon cap-and-trade regulation has been widely adopted as a means to reduce carbon emissions. A fresh food supply chain involving a Manufacturer, 3PL, and a retailer is introduced. The 3PL is used by the manufacturer for its logistics because of its expertise, resources, and sustainable practices, Also many third-party logistics companies(3PL) offer refrigerated logistics services to the retailer and the 3PL has an overabundance of carbon permits. Trading of permits occurs and the impact on the retail price, the price of refrigerated logistics services in different carbon trading options, without carbon trade, inner carbon trade, and inner and outer carbon trade is studied. The prices are optimized through a game-theoretic approach, we model the trading of carbon permits as a leader-follower game with the 3PL as leader and Retailer as followers. The items are assumed to be of imperfect quality when delivered to the retailer by the 3PL.

关键词： Costs Supply chains Government Carbon dioxide Emissions trading Games Regulation

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FMC-CEE: A Collaborative Execution Environment with Flash Memory Controllers in IoT

FMC-CEE: A Collaborative Execution Environment with Flash Me...

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IEEE Annual Conference on Pervasive Computing and Communications Workshops (PerCom)

作者： Zheng Zhang Jingfeng Xue Thar Baker Tian Chen Yuhang Zhao Weizhi Meng School of Computer Science and Technology Beijing Institute of Technology Beijing China School of Architecture Technology and Engineering University of Brighton Brighton UK School of Cyberspace Science and Technology Beijing Institute of Technology Beijing China Department of Applied Mathematics and Computer Science Technical University of Denmark Copenhagen Denmark

Applications running on an Internet of Things (IoT) device are usually deployed in an untrusted environment. This introduces risks of vulnerability to malware, and loss of intellectual property associated with security sensitive code. Trusted execution environments (TEEs) and TEE-based applications have been widely adopted to run security sensitive workloads and protect the security of applications. However, existing approaches require specialized CPU support or hardware peripherals equipped with co-processors, precluding widely deployment on low-cost IoT devices. In this paper, we propose a flash memory controller-based collaborative execution environment (FMC-CEE), a lightweight security solution constructed on the target flash device to provide code confidentiality and basic security primitives for low-cost IoT devices and embedded devices. FMC-CEE leverages the microprocessor of the target flash device as a co-processor that executes security-sensitive workloads collaboratively with the target system. We implemented a prototype of FMC-CEE on a Trans-Flash (TF) card and executed security-sensitive tasks of the target host. The experimental results show that FMC-CEE takes $590.748 \mu \mathrm{s}$ to execute the remote code (512 bytes), thus incurring very little overhead on the host system.

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Predicting ground state properties: constant sample complexity and deep learning algorithms 24

Predicting ground state properties: constant sample complexi...

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Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Marc Wanner Laura Lewis Chiranjib Bhattacharyya Devdatt Dubhashi Alexandru Gheorghiu Computer Science and Engineering Chalmers University of Technology and University of Gothenburg Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Computer Science and Automation Indian Institute of Science Bangalore India

ISBN: (纸本)9798331314385

A fundamental problem in quantum many-body physics is that of finding ground states of local Hamiltonians. A number of recent works gave provably efficient machine learning (ML) algorithms for learning ground states. Specifically, Huang et al. in [1], introduced an approach for learning properties of the ground state of an n-qubit gapped local Hamiltonian H from only nO(1) data points sampled from Hamiltonians in the same phase of matter. This was subsequently improved by Lewis et al. in [2], to O(log n) samples when the geometry of the n-qubit system is known. In this work, we introduce two approaches that achieve a constant sample complexity, independent of system size n, for learning ground state properties. Our first algorithm consists of a simple modification of the ML model used by Lewis et al. and applies to a property of interest known in advance. Our second algorithm, which applies even if a description of the property is not known, is a deep neural network model. While empirical results showing the performance of neural networks have been demonstrated, to our knowledge, this is the first rigorous sample complexity bound on a neural network model for predicting ground state properties. We also perform numerical experiments on systems of up to 45 qubits that confirm the improved scaling of our approach compared to [1, 2].

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INTERSECTION OF IRREDUCIBLE CURVES AND THE HERMITIAN CURVE

arXiv

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arXiv 2024年

作者： Beelen, Peter Datta, Mrinmoy Montanucci, Maria Niemann, Jonathan Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens LyngbyDK-2800 Denmark Department of Mathematics Indian Institute of Technology Hyderabad Kandi Telangana Sangareddy502285 India

Let Hq denote the Hermitian curve in P2 over Fq2 and Cd be an irreducible plane projective curve in P2 also defined over Fq2 of degree d. Can Hq and Cd intersect in exactly d(q + 1) distinct Fq2-rational points? Bézout's theorem immediately implies that Hq and Cd intersect in at most d(q + 1) points, but equality is not guaranteed over Fq2. In this paper we prove that for many d ≤ q2 − q + 1, the answer to this question is affirmative. The case d = 1 is trivial: it is well known that any secant line of Hq defined over Fq2 intersects Hq in q + 1 rational points. Moreover, all possible intersections of conics and Hq were classified in [9] and their results imply that the answer to the question above is affirmative for d = 2 and q ≥ 4, as well. However, an exhaustive computer search quickly reveals that for (q, d) ∈ {(2, 2), (3, 2), (2, 3)}, the answer is instead negative. We show that for q ≤ d ≤ q2 − q + 1, d = ⌊(q + 1)/2⌋ and d = 3, q ≥ 3 the answer is again affirmative. Various partial results for the case d small compared to q are also *** Codes 11G20, 14G05, 14C17, 14G15 Copyright © 2024, The Authors. All rights reserved.

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Adaptive Trajectory Correction for Underwater Object Tracking

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IEEE Transactions on Circuits and Systems for Video technology 2025年

作者： Luo, Xudong Yuan, Di Shu, Xiu Liu, Qiao Chang, Xiaojun He, Zhenyu Xidian University Guangzhou Institute of Technology Guangzhou510555 China Guangzhou University School of Computer Science and Cyber Engineering Guangzhou510006 China Chongqing Normal University National Center for Applied Mathematics Chongqing401331 China University of Technology Faculty of Engineering and Information Technology Australian Artificial Intelligence Institute Sydney Australia Harbin Institute of Technology School of Computer Science and Technology Shenzhen518055 China

Most extant underwater object tracking (UOT) utilize generic tracking algorithms, which lack applicability to underwater tracking scenarios. Moreover, these algorithms primarily emphasize minimizing interference from various challenging tasks to prevent target drift, but pay less attention to the strategies for mitigating target drift once it occurs. To alleviate the above problems, we propose a simple, effective, and UOT-focused adaptive trajectory correction framework, named ATCTrack. From the perspective of tracking failure, this methodology aims to promptly identify and rectify unreasonable target drift through accurate trajectory coordinate correction and trajectory template updates. Additionally, to mitigate the adverse effects of potential erroneous corrections, we implement an adaptive strategy that corrects only significant target drift, allowing for self-correction within a certain margin. Finally, we introduce an adaptive underwater image enhancement technique to improve the underwater image quality and maintain the trajectory's stability and clarity. Our tracker achieves state-of-the-art performance on the currently prevalent UOT tracking benchmarks compared to other trackers. © 1991-2012 IEEE.

关键词： Object detection

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