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LIMIT DISTRIBUTION THEORY FOR SMOOTH p-WASSERSTEIN DISTANCES

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arXiv 2022年

作者： Goldfeld, Ziv Kato, Kengo Nietert, Sloan Rioux, Gabriel School of Electrical and Computer Engineering Cornell University United States Department of Statistics and Data Science Cornell University United States Department of Computer Science Cornell Universty United States Center for Applied Mathematics Cornell University United States

The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked by the curse of dimensionality, whereby the number of data points needed to accurately estimate them grows exponentially with dimension. Gaussian smoothing was recently introduced as a means to alleviate the curse of dimensionality, giving rise to a parametric convergence rate in any dimension, while preserving the Wasserstein metric and topological structure. To facilitate valid statistical inference, in this work, we develop a comprehensive limit distribution theory for the empirical smooth Wasserstein distance. The limit distribution results leverage the functional delta method after embedding the domain of the Wasserstein distance into a certain dual Sobolev space, characterizing its Hadamard directional derivative for the dual Sobolev norm, and establishing weak convergence of the smooth empirical process in the dual space. To estimate the distributional limits, we also establish consistency of the nonparametric bootstrap. Finally, we use the limit distribution theory to study applications to generative modeling via minimum distance estimation with the smooth Wasserstein distance, showing asymptotic normality of optimal solutions for the quadratic cost. Copyright © 2022, The Authors. All rights reserved.

关键词： Sobolev spaces

Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion

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arXiv 2022年

作者： Maama, Mohamed Jasra, Ajay Ombao, Hernando Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC) algorithms to sample from the posterior density on the parameters given data. We rely on a novel representation of the time discretization, which seeks to sample from an approximation of the posterior and then corrects via importance sampling;the approximation reduces the time (in terms of total observation time T) by O(T). This method is extended by using a multilevel MCMC method which can reduce the computational cost to achieve a given mean square error (MSE) versus using a single time discretization. Our methods are illustrated on simulated and real data. Copyright © 2022, The Authors. All rights reserved.

关键词： Mean square error

ON THE SIZE DISTRIBUTION OF THE FIXED-LENGTH LEVENSHTEIN BALLS WITH RADIUS ONE

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arXiv 2022年

作者： Wang, Geyang Wang, Qi Department of Electronic and Computer Engineering Institute for Systems Research University of Maryland College ParkMD20742 United States Department of Computer Science and Engineering National Center for Applied Mathematics Shenzhen Southern University of Science and Technology Nanshan District Guangdong Shenzhen518055 China

The fixed-length Levenshtein (FLL) distance between two words x, y ∈ Znm is the smallest integer t such that x can be transformed to y by t insertions and t deletions. The size of a ball in the FLL metric is a fundamental yet challenging problem. Very recently, Bar-Lev, Etzion, and Yaakobi explicitly determined the minimum, maximum and average sizes of the FLL balls with radius one, respectively. In this paper, based on these results, we further prove that the size of the FLL balls with radius one is highly concentrated around its mean by Azuma's *** Codes 94B50, 05D40 © 2022, CC BY.

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MedTsLLM: Leveraging LLMs for Multimodal Medical Time Series Analysis

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arXiv 2024年

作者： Chan, Nimeesha Parker, Felix Bennett, William Wu, Tianyi Jia, Mung Yao Fackler, James Ghobadi, Kimia Department of Civil and Systems Engineering Johns Hopkins University United States Department of Anesthesiology and Critical Care Medicine Johns Hopkins University United States Department of Applied Mathematics and Statistics Johns Hopkins University United States Department of Computer Science Johns Hopkins University United States

The complexity and heterogeneity of data in many real-world applications pose significant challenges for traditional machine learning and signal processing techniques. For instance, in medicine, effective analysis of diverse physiological signals is crucial for patient monitoring and clinical decision-making and yet highly challenging. We introduce MedTsLLM, a general multimodal large language model (LLM) framework that effectively integrates time series data and rich contextual information in the form of text to analyze physiological signals, performing three tasks with clinical relevance: semantic segmentation, boundary detection, and anomaly detection in time series. These critical tasks enable deeper analysis of physiological signals and can provide actionable insights for clinicians. We utilize a reprogramming layer to align embeddings of time series patches with a pretrained LLM's embedding space and make effective use of raw time series, in conjunction with textual context. Given the multivariate nature of medical datasets, we develop methods to handle multiple covariates. We additionally tailor the text prompt to include patient-specific information. Our model outperforms state-of-the-art baselines, including deep learning models, other LLMs, and clinical methods across multiple medical domains, specifically electrocardiograms and respiratory waveforms. MedTsLLM presents a promising step towards harnessing the power of LLMs for medical time series analysis that can elevate data-driven tools for clinicians and improve patient outcomes. © 2024, CC BY-SA.

关键词： Semantics

Ultra-Low-Loss Silicon Nitride Photonics Based on Deposited Films Compatible with Foundries

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arXiv 2023年

作者： Ji, Xingchen Okawachi, Yoshitomo Gil-Molina, Andres Corato-Zanarella, Mateus Roberts, Samantha Gaeta, Alexander L. Lipson, Michal Department of Electrical Engineering Columbia University New YorkNY10027 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Currently at John Hopcroft Center for Computer Science School of Electronic Information and Electrical Engineering Shanghai Jiao Tong University Shanghai200240 China

The fabrication processes of silicon nitride (Si3N4) photonic devices used in foundries require low temperature deposition, which typically leads to high propagation losses. Here, we show that propagation loss as low as 0.42 dB/cm can be achieved using foundry compatible processes by solely reducing waveguide surface roughness. By post-processing the fabricated devices using rapid thermal anneal (RTA) and furnace anneal, we achieve propagation losses down to 0.28 dB/cm and 0.06 dB/cm, respectively. These low losses are comparable to the conventional devices using high temperature, high-stress LPCVD films. We also tune the dispersion of the devices, and proved that these devices can be used for linear and nonlinear applications. Low threshold parametric oscillation, broadband frequency combs and narrow-linewidth laser are demonstrated. Our work demonstrates the feasibility of scalable photonic systems based on foundries. Copyright © 2023, The Authors. All rights reserved.

关键词： Silicon nitride

Compiling for time-predictability with dual-issue single-path code

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Journal of Systems Architecture 2021年 118卷 102230-102230页

作者： Maroun, Emad Jacob Schoeberl, Martin Puschner, Peter Institute of Computer Engineering Vienna University of Technology Vienna Austria Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby Denmark

Designed for real-time systems, the Patmos instruction-set architecture's features ensure a high degree of predictability. One such feature is its dual-issue pipeline, which can issue and execute bundles of up to two instructions at a time. Executing instructions in the second issue slot is a predictable way to increase the throughput of a processor, but without dedicated support from the compiler, this benefit cannot be unlocked. A compiler generates highly predictable programs by generating single-path code. This technique produces code that always follows the same trace of instructions. While Patmos’ compiler can already produce single-path code, it does not assign any instructions to the second issue-slot. This limitation is unfortunate, as single-path code inherently possesses a high degree of instruction-level parallelism. In this paper, we present a single-path code generation technique with support for dual-issue pipelines. It can also support different bundling algorithms, which allows changing algorithms without having to edit other parts of the compiler. We present a simple bundling algorithm plugged into the single-path code generator. It looks for branches and bundles the basic blocks on each path of the branch. While this specific bundling algorithm is too simple to provide a real-world benefit, it highlights the potential that further work on bundling algorithms can unlock. © 2021 The Authors

关键词： Real time systems

Comparison of two maintenance models to quantify unavailability of systems with components with dormant failures 29

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Comparison of two maintenance models to quantify unavailabil...

29th European Safety and Reliability Conference, ESREL 2019

作者： Briš, Radim Tran, Nuong Thi Thuy Department of Applied Mathematics Faculty of Electrical Engineering and Computer Science VŠB - Technical University of Ostrava Czech Republic

ISBN: (纸本)9789811127243

Repairable systems with latent failures are systems when a failure is identified only at special inspection times, appearing with a given fixed period. In the case of its occurrence the restoration process is launched at the earliest follow-up inspection time. Maintenance policies for such systems can be categorized into two main categories: calendar based and age based policies. In the calendar based policy, the system testing and maintenance is realized at a fixed date, whereas in the age based policy we suppose that maintenance actions are realized at a fixed time interval from the latest time of maintenance. In the age based policy, a real calendar time of inspection or preventive maintenance is random in fact, due to random occurrences of failures and random duration of restorations. Relevant issue of the paper is to recognize differences between both kinds of maintenance policies. The paper summarizes innovative stochastic reliability models, recently developed and used for unavailability quantification of repairable and maintained systems with latent failures. Models are transformed into numerical codes to answer the relevant matter: to what extent is affected unavailability in context with age-based versus calendar-based maintenance policy? The differences of unavailability, computed in the course of time, between age-based and calendar-based maintenance policies are demonstrated on examples selected from both references and practice. © 2019 European Safety and Reliability Association. Published by Research Publishing, Singapore.

关键词： Preventive maintenance

The Advanced Encryption Standard with a Dynamic S-Box Using the RC4 Key Schedule

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The Advanced Encryption Standard with a Dynamic S-Box Using ...

Electrical, computer and Energy Technologies (ICECET), International Conference on

作者： Abdelrahman Altigani Muhammad Rukunuddin Ghalib Huwaida T. Elshoush Muawia A. Elsadig Nashat Alrefai Shiraz Naserelden Computer Information Science Higher Colleges of Technology Al Ain UAE School of Engineering & Computing De Monfort University Dubai UAE Computer Science Department Faculty of Mathematical Sciences and Informatics University of Khartoum Khartoum Sudan College of Computer Science and Information Technology Imam Abdulrahman bin Faisal University Dammam KSA Department of Mathematics College of Science Imam Abdulrahman Bin Faisal University Basic and Applied Scientific Research Center Imam Abdulrahman Bin Faisal University Dammam KSA Department of Mathematical Sciences Faculty of Science Universiti Teknologi Malaysia Johor Malaysia

ISBN: (数字)9798350395914

ISBN: (纸本)9798350395921

Since the inception of secure communication, safeguarding data confidentiality has been paramount. With the increased reliance on technology, the need for robust security mechanisms is more critical than ever. This paper explores confidentiality in cybersecurity, focusing on symmetric encryption algorithms. While symmetric encryption, particularly the Advanced Encryption Standard (AES), is in wide use, concerns arise regarding its static nature. Therefore, the paper introduces a dynamic cipher, augmenting AES security by introducing a key-dependent S-Box. By leveraging the RC4 key schedule, the proposed cipher generates unique S-Boxes for each encryption key, significantly increasing security against non-generic attacks. Theoretical analysis demonstrates the proposed cipher is capable of resisting brute force, linear cryptanalysis, and differential cryptanalysis. Furthermore, its adaptability to existing AES implementations ensures practicality and ease of adoption.

关键词： Ciphers Schedules Heuristic algorithms Dynamics Force Dynamic scheduling Encryption computer security Time complexity Standards

A Novel Methodology to Predict Flood and Landslide Disasters using Learning Assisted Artificial Intelligence (AI) Logic

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A Novel Methodology to Predict Flood and Landslide Disasters...

Electronics and Renewable Systems (ICEARS), International Conference on

作者： G. Bhupal Raj Muzeeb Khan Patan Ashwani Kumar Gupta C.Lakshmi Gopinath D Ajay Singh Yadav School of Agriculture SR University Warangal Department of EEE College of Engineering and Technology University of Technology and Applied Sciences Muscat Oman Faculty of Business and Commerce Chandigarh University Unnao Uttar Pradesh Saveetha Engineering College Chennai Department of Computer Science Kristu Jayanti College (Autonomous) Bengaluru Karnataka India Department of Mathematics SRM Institute of Science and Technology Delhi-NCR Campus Ghaziabad U.P

ISBN: (数字)9798331509675

ISBN: (纸本)9798331509682

Comprehending the dynamics of flood and landslide prediction in current and adjacent regions is crucial for the formulation and advancement of effective predictive models, conservation, and management techniques. Conventional forecasting techniques, typically dependent on statistical models and empirical data, may prove inadequate because of the intrinsic complexities and variability of environmental elements. The complex interaction of climatic conditions, hydrological processes, geological attributes, and topographical aspects complicates precise forecasting. The constraints of traditional methods highlight the pressing necessity for more advanced and efficient predictive instruments. Artificial intelligence, especially machine learning (ML) and deep learning (DL), presents a robust paradigm that utilizes sophisticated algorithms to examine extensive datasets, discern intricate patterns, and produce more precise and prompt predictions. This proposed ViT-DL model prediction ability can greatly boost catastrophe preparedness, mitigation strategies, and ultimately, preserve lives and reduce economic damages. This study will comprehensively examine contemporary research trends, emphasizing the methodology used, model efficacy, related problems, and potential future research avenues in AI-based flood and landslide prediction. The experimental results of our proposed model produces 96.6% of Accuracy and 96.31% of Precision, comparision shows our model outperforms the overall accuracy to conventions model techniques.

关键词： Deep learning Accuracy Biological system modeling Prevention and mitigation Disasters Predictive models Market research Terrain factors Floods Forecasting