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Ecumenical Modal Logic 1

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3rd International Workshop on Dynamic Logic, DaLí 2020

作者： Marin, Sonia Pereira, Luiz Carlos Pimentel, Elaine Sales, Emerson Department of Computer Science University College London London United Kingdom Philosophy Department PUC-Rio Rio de Janeiro Brazil Department of Mathematics UFRN Natal Brazil Graduate Program in Applied Mathematics and Statistics UFRN Natal Brazil

ISBN: (数字)9783030658403

ISBN: (纸本)9783030658397

The discussion about how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system is back in fashion. Indeed, recently Prawitz and others have been discussing the so called ecumenical Systems, where connectives from these logics can co-exist in peace. In Prawitz’ system, the classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation, and the constant for the absurd, but they would each have their own existential quantifier, disjunction, and implication, with different meanings. Prawitz’ main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. In this work we extend Prawitz’ ecumenical idea to alethic K -modalities. © 2020, Springer Nature Switzerland AG.

关键词： computer circuits

The Role of Heterogeneity in Autonomous Perimeter Defense Problems

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arXiv 2022年

作者： Adler, Aviv Mickelin, Oscar Ramachandran, K. Sukhatme, Gaurav S. Karaman, Sertac Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA United States Program in Applied and Computational Mathematics Princeton University Princeton NJ08544 United States Department of Computer Science University of Southern California Los AngelesCA90089 United States Department of Aeronautics and Astronautics Massachusetts Institute of Technology CambridgeMA02139 United States

When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant. Copyright © 2022, The Authors. All rights reserved.

关键词： Dynamic programming

Unbiased Estimation using a Class of Diffusion Processes

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arXiv 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 KSA Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (d, B(d)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}tϵ[0,1]on d, d ϵ 0. This latter process is constructed such that, starting at X0= 0, one has X1∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 16] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(ϵ2), for arbitrary ϵ > 0, the associated cost is O(ϵ-5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(ϵ2), the associated cost (which is random) is, with high probability, O(ϵ-2| log(ϵ)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse *** Codes 60J60, 62D05, 65C40 © 2022, CC BY.

关键词： Diffusion

Learning shared neural manifolds from multi-subject FMRI data

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arXiv 2021年

作者： Huang, Jessie Busch, Erica L. Wallenstein, Tom Gerasimiuk, Michal Benz, Andrew Lajoie, Guillaume Wolf, Guy Turk-Browne, Nicholas B. Krishnaswamy, Smita Department Of Computer Science Department Of Psychology Department Of Mathematics Department Of Genetics Program In Applied Mathematics Wu Tsai Institute Yale University United States Department Of Mathematics And Statistics Université De Montréal Canada Mila Quebec AI Institute Canada

Functional magnetic resonance imaging (fMRI) is a notoriously noisy measurement of brain activity because of the large variations between individuals, signals marred by environmental differences during collection, and spatiotemporal averaging required by the measurement resolution. In addition, the data is extremely high dimensional, with the space of the activity typically having much lower intrinsic dimension. In order to understand the connection between stimuli of interest and brain activity, and analyze differences and commonalities between subjects, it becomes important to learn a meaningful embedding of the data that denoises, and reveals its intrinsic structure. Specifically, we assume that while noise varies significantly between individuals, true responses to stimuli will share common, low-dimensional features between subjects which are jointly discoverable. Similar approaches have been exploited previously but they have mainly used linear methods such as PCA and shared response modeling (SRM). In contrast, we propose a neural network called MRMD-AE (manifold-regularized multiple decoder, autoencoder), that learns a common embedding from multiple subjects in an experiment while retaining the ability to decode to individual raw fMRI signals. We show that our learned common space represents an extensible manifold (where new points not seen during training can be mapped), improves the classification accuracy of stimulus features of unseen timepoints, as well as improves cross-subject translation of fMRI signals. We believe this framework can be used for many downstream applications such as guided brain-computer interface (BCI) training in the future. Copyright © 2021, The Authors. All rights reserved.

关键词： Magnetic resonance imaging

Correction: Unbiased and multilevel methods for a class of diffusions partially observed via marked point processes

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Statistics and Computing 2024年第6期34卷 1-1页

作者： Alvarez, Miguel Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal Saudi Arabia School of Data Science The Chinese University of Hong Kong Shenzhen China

Developing a medical artificial intelligence course for high school students

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Developing a medical artificial intelligence course for high...

International Forum on Medical Imaging in Asia 2021, IFMIA 2021

作者： Huang, Chao-Jung Wu, Tinghui Lu, Jui-Ting Lin, Beatrice Chang, Dawei Wang, Pochuan Wang, Mei-Chi Lee, Peijung Wang, Weichung National Taiwan University-Stanford Joint Program Office of AI in Biotechnology Ministry of Science and Technology Joint Research Center for Artificial Intelligence Technology and All Vista Healthcare Taipei Taiwan Institute of Applied Mathematical Sciences National Taiwan University Taipei Taiwan Department of Mathematics Ecole Normale Supérieure de Lyon Lyon France Department of Computer Science and Information Engineering National Taiwan University Taipei Taiwan Department of Electronic and Computer Engineering National Taiwan University of Science and Technology Taipei Taiwan Department of Mathematics National Taiwan University Taipei Taiwan

ISBN: (数字)9781510644212

ISBN: (纸本)9781510644205

Artificial intelligence (AI) training courses often require prerequisites such as calculus or statistics. It is hence challenging to design and develop an introductory AI course for students of secondary education. This research intends to develop a medical AI course, provide high school students with an overview of deep learning applications in medical image analysis, and inspire them to pursue careers in the field of medical AI. We designed a 20-hour course, including lectures and two hands-on projects based on medical image classification. The proposed courses provided medical AI disciplines and built up their knowledge from basic to advanced levels. During the ten-day online courses, all the students were fully engaged and gave us positive feedback. The students endeavored to complete the experimental study in training, testing, and hypothesis of medical images application in the course. Their performance exceeded all expectations, for they did further analysis by tuning different hyperparameters. We designed a course evaluation form, which suggested that the students found it essential and expected to interact with the instructors. The results indicate that combining lectures with hands-on sessions would lead to evidently better achievement in terms of high school students' medical AI knowledge and positive attitudes while addressing real-world problems in the projects. Through this innovative education model, high school students regained their enthusiasm and were encouraged to cultivate their medical AI skills through self-learning while finishing the project. We conclude that this course could be successfully applied to interdisciplinary education in high school. © 2021 SPIE.

关键词： Students

Autonomous Electron Tomography Reconstruction with Machine Learning

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arXiv 2023年

作者： Millsaps, William Schwartz, Jonathan Di, Zichao Wendy Jiang, Yi Hovden, Robert Department of Nuclear Engineering & Radiological Sciences University of Michigan Ann ArborMI United States Department of Materials Science and Engineering University of Michigan Ann ArborMI United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL United States Advanced Photon Source Facility Argonne National Laboratory LemontIL United States Applied Physics Program University of Michigan Ann ArborMI United States

This manuscript is published in Microscopy and Microanalysis (DOI: 10.1093/micmic/ozad083). Modern electron tomography has progressed to higher resolution at lower doses by leveraging compressed sensing methods that minimize total variation (TV). However, these sparsity-emphasized reconstruction algorithms introduce tunable parameters that greatly influence the reconstruction quality. Here, Pareto front analysis shows that high-quality tomograms are reproducibly achieved when TV minimization is heavily weighted. However, in excess, compressed sensing tomography creates overly smoothed 3D reconstructions. Adding momentum to the gradient descent during reconstruction reduces the risk of over-smoothing and better ensures that compressed sensing is well behaved. For simulated data, the tedious process of tomography parameter selection is efficiently solved using Bayesian optimization with Gaussian processes. In combination, Bayesian optimization with momentum-based compressed sensing greatly reduces the required compute time-an 80% reduction was observed for the 3D reconstruction of SrTiO3 nanocubes. Automated parameter selection is necessary for large scale tomographic simulations that enable the 3D characterization of a wider range of inorganic and biological materials. © 2023, CC BY.

关键词： Compressed sensing

Utilizing probabilistic entanglement between sensors in quantum networks

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arXiv 2024年

作者： Van Milligen, Emily A. Gagatsos, Christos N. Kaur, Eneet Towsley, Don Guha, Saikat Department of Physics The University of Arizona 1630 East University Boulevard TucsonAZ85721 United States Department of Electrical and Computer Engineering The University of Arizona 1630 East University Boulevard TucsonAZ85721 United States Wyant College of Optical Sciences The University of Arizona 1630 East University Boulevard TucsonAZ85721 United States Program in Applied Mathematics The University of Arizona TucsonAZ85721 United States Cisco Quantum Lab Los Angeles United States College of Computer Science University of Massachusetts AmherstMA United States

One of the most promising applications of quantum networks is entanglement assisted sensing. The field of quantum metrology exploits quantum correlations to improve the precision bound for applications such as precision timekeeping, field sensing, and biological imaging. When measuring multiple spatially distributed parameters, current literature focuses on quantum entanglement in the discrete variable case—and quantum squeezing in the continuous variable case distributed amongst all of the sensors in a given network. However, it can be difficult to ensure all sensors pre-share entanglement of sufficiently high fidelity. This work probes the space between fully entangled and fully classical sensing networks by modeling a star network with probabilistic entanglement generation that is attempting to estimate the average of local parameters. The quantum Fisher information is used to determine which protocols best utilize entanglement as a resource for different network conditions. It is shown that without entanglement distillation there is a threshold fidelity below which classical sensing is preferable. For a network with a given number of sensors and links characterized by a certain initial fidelity and probability of success, this work outlines when and how to use entanglement, when to store it, and when it needs to be distilled. © 2024, CC BY.

关键词： Quantum entanglement

Adaptive tikhonov strategies for stochastic ensemble Kalman inversion

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arXiv 2021年

作者： Weissmann, Simon Chada, Neil K. Schillings, Claudia Tong, Xin T. Interdisciplinary Center for Scientific Computing University of Heidelberg Heidelberg69120 Germany Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal KSA 23955 Saudi Arabia Mannheim School of Computer Science and Mathematics University of Mannheim Mannheim68131 Germany Department of Mathematics National University of Singapore Singapore119077 Singapore

Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov strategies for EKI. This work builds upon Tikhonov EKI (TEKI) which was proposed for a fixed regularization constant. By adaptively learning the regularization parameter, this procedure is known to improve the recovery of the underlying unknown. For the analysis, we consider a continuous-time setting where we extend known results such as well-posdeness and convergence of various loss functions, but with the addition of noisy observations. Furthermore, we allow a time-varying noise and regularization covariance in our presented convergence result which mimic adaptive regularization schemes. In turn we present three adaptive regularization schemes, which are highlighted from both the deterministic and Bayesian approaches for inverse problems, which include bilevel optimization, the MAP formulation and covariance learning. We numerically test these schemes and the theory on linear and nonlinear partial differential equations, where they outperform the non-adaptive TEKI and *** Codes 65M32, 60G35, 65C35, 70F17 Copyright © 2021, The Authors. All rights reserved.

关键词： Continuous time systems