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arXiv 2024年

作者： Basmajian, Ara Valli, Robert Suzzi PhD Program in Mathematics The Graduate Center CUNY 365 Fifth ave. New YorkNY10016 United States Department of Mathematics and Statistics Hunter College CUNY 695 Park ave. New YorkNY10065 United States Department of Mathematics Manhattan College 4513 Manhattan College Pkwy. RiverdaleNY10471 United States

For a fixed cusp neighborhood (determined by depth D) of the modular surface, we investigate the class of reciprocal geodesics that enter this neighborhood (called a cusp excursion) a fixed number of times. Since reciprocal geodesics traverse their image an even number of times such a geodesic only has an even number of cusp excursions, say 2n. Denoting this class of geodesics as (formula presented), we derive several growth rate results for (formula presented), where |γ| is the word length of γ in Z2 ∗ Z3 with respect to the generators of the factors. © 2024, CC BY.

关键词： Geodesy

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On the Characteristics of Natural Hydraulic Dampers: An Image-Based Approach to Study the Fluid Flow Behaviour Inside the Human Meniscal Tissue

SSRN

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SSRN 2023年

作者： Waghorne, J. Bonomo, F.P. Rabbani, Arash Bell, Daniel Barrera, Olga School of Engineering Computing and Mathematics Oxford Brookes University Oxford United Kingdom Università degli Studi di Palermo Palermo90128 Italy School of Mathematics and Statistics Department of Engineering Science University of Oxford United Kingdom

The meniscal tissue is a layered material with varying properties influenced by collagen content and arrangement. Understanding the relationship between structure and properties is crucial for disease management, treatment development, and biomaterial design. The internal layer of the meniscus is softer and more deformable than the outer layers, thanks to interconnected collagen channels that guide fluid flow. To investigate these relationships, we propose a novel approach that combines Computational Fluid Dynamics (CFD) with Image Analysis (CFD-IA). We analyze fluid flow in the internal architecture of the human meniscus across a range of inlet velocities (0.1mm/s to 1.6m/s) using high-resolution 3D micro-computed tomography scans. Statistical correlations are observed between architectural parameters (tortuosity, connectivity, porosity, pore size) and fluid flow parameters (Re number distribution, permeability). Some channels exhibit Re values of 1400 at an inlet velocity of 1.6m/s, and a transition from Darcy’s regime to a non-Darcian regime occurs around an inlet velocity of 0.02m/s. Location-dependent permeability ranges from 20-32 Darcy. Regression modelling reveals a strong correlation between fluid velocity and tortuosity at high inlet velocities, as well as with channel diameter at low inlet velocities. At higher inlet velocities, flow paths deviate more from the preferential direction, resulting in a decrease in the concentration parameter by an average of 0.4. This research provides valuable insights into the fluid flow behaviour within the meniscus and its structural influences. © 2023, The Authors. All rights reserved.

关键词： Computational fluid dynamics

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A Scalable Platform to Collect, Store, Visualize and Analyze Big Data in Real- Time 3

A Scalable Platform to Collect, Store, Visualize and Analyze...

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3rd International Conference on Innovative Practices in Technology and Management, ICIPTM 2023

作者： Kshirsagar, Pravin Ramdas Reddy, Dhoma Harshavardhan Dhingra, Mallika Dhabliya, Dharmesh Gupta, Ankur S B Jain College of Engineering and Technology Department of Artificial Intelligence Maharashtra Nagpur India Trainee Security Analyst JunoClinic Davman Technology Services Private Limited Maharashtra Mumbai India Manipal University Jaipur Department of Mathematics and Statistics Rajasthan Jaipur India Vishwakarma Institute of Information Technology Department of Information Technology Maharashtra Pune India Vaish College of Engineering Department of Computer Science and Engineering Haryana Rohtak India

ISBN: (纸本)9798350336238

Examination and evaluation of sentiment The most popular area for dissecting and extracting knowledge from communication data from many sources, such as Facebook, Instagram, Twitter, Amazon, and so on, is known as mining. It plays a fundamental role in enabling the organizations to work productively on advancing the business system and gaining the most comprehensive understanding of the buyer's feedback on their product. It entails calculating a person's behavior in terms of his buying preferences and then placing yourself in his shoes about the commercial aspect of a relationship. You may think of this component as a situation, person, blog post, or tangible experience. Appraisals, checks, and Reflections created by customers may be divided into smaller, more notable pieces for usage by large businesses. The analysis of comparable purchasing behavior may be used to understand the needs of the customer and foresee future opportunities to assist them. E-business Associations may track the uses and passions associated with their Particulars via this internal assessment and adopt better marketing mechanism to give a tailored shopping experience for their customers, so improving their hierarchical advantage. By using the programming interface key, Twitter data for this article was collected from Twitter. Similarly, we really want to finish setting up the systems. Additionally, the system supported NLP approaches, thus we wish to implement the calculation as a crucial backslide. The exploratory problems exhibit perfection. © 2023 IEEE.

关键词： Big data

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Characterization of elastic topological states using dynamic mode decomposition

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Physical Review B 2023年第18期107卷 184308-184308页

作者： Shuaifeng Li Panayotis G. Kevrekidis Jinkyu Yang Department of Aeronautics and Astronautics University of Washington Seattle Washington 98195 USA Department of Mathematics and Statistics University of Massachusetts Amherst Massachusetts 01003 USA Department of Mechanical Engineering Seoul National University Seoul 08826 Republic of Korea

Elastic topological states have been receiving increased attention in numerous scientific and engineering fields due to their defect-immune nature, resulting in applications of vibration control and information processing. Here, we present the data-driven discovery of elastic topological states using dynamic mode decomposition (DMD). The DMD spectrum and DMD modes are retrieved from the propagation of the relevant states along the topological boundary, where their nature is learned by DMD. Applications such as classification and synthesis of wave propagation can be achieved by the underlying characteristics from DMD. We demonstrate the classification between topological and traditional metamaterials using DMD modes. Moreover, the model enabled by the DMD modes realizes the synthesis of topological state propagation along the given interface. Our approach to characterizing topological states using DMD can pave the way towards data-driven discovery of topological phenomena in material physics and more broadly lattice systems.

关键词： Topological insulators Topological materials Machine learning

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Signaling Games for Log-Concave Distributions: Number of Bins and Properties of Equilibria

Signaling Games for Log-Concave Distributions: Number of Bin...

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作者： Kazikli, Ertan Saritas, Serkan Gezici, Sinan Linder, Tamas Yuksel, Serdar Department of Mathematics and Statistics Queen's University KingstonONK7L 3N6 Canada Ankara06800 Turkey Department of Electrical and Electronics Engineering Bilkent University Ankara06800 Turkey

We investigate the equilibrium behavior for the decentralized cheap talk problem for real random variables and quadratic cost criteria in which an encoder and a decoder have misaligned objective functions. In prior work, it has been shown that the number of bins in any equilibrium has to be countable, generalizing a classical result due to Crawford and Sobel who considered sources with density supported on [0, 1]. In this paper, we first refine this result in the context of log-concave sources. For sources with two-sided unbounded support, we prove that, for any finite number of bins, there exists a unique equilibrium. In contrast, for sources with semi-unbounded support, there may be a finite upper bound on the number of bins in equilibrium depending on certain conditions stated explicitly. Moreover, we prove that for log-concave sources, the expected costs of the encoder and the decoder in equilibrium decrease as the number of bins increases. Furthermore, for strictly log-concave sources with two-sided unbounded support, we prove convergence to the unique equilibrium under best response dynamics which starts with a given number of bins, making a connection with the classical theory of optimal quantization and convergence results of Lloyd's method. In addition, we consider more general sources which satisfy certain assumptions on the tail(s) of the distribution and we show that there exist equilibria with infinitely many bins for sources with two-sided unbounded support. Further explicit characterizations are provided for sources with exponential, Gaussian, and compactly-supported probability distributions. © 1963-2012 IEEE.

关键词： Signal encoding

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QUANTITATIVE CLTS IN DEEP NEURAL NETWORKS

arXiv

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arXiv 2023年

作者： Favaro, S. Hanin, Boris Marinucci, D. Nourdin, I. Peccati, G. Department of Economics and Statistics University of Torino and Collegio Carlo Alberto Italy Department of Operations Research and Financial Engineering Princeton University United States Department of Mathematics University of Rome Tor Vergata Italy Department of Mathematics Luxembourg University Luxembourg

We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant n. Under mild assumptions on the non-linearity, we obtain quantitative bounds on normal approximations valid at large but finite n and any fixed network depth. Our theorems show both for the finite-dimensional distributions and the entire process, that the distance between a random fully connected network (and its derivatives) to the corresponding infinite width Gaussian process scales like n−γ for γ > 0, with the exponent depending on the metric used to measure discrepancy. Our bounds are strictly stronger in terms of their dependence on network width than any previously available in the literature;in the one-dimensional case, we also prove that they are optimal, i.e., we establish matching lower bounds. © 2023, CC BY.

关键词： Deep neural networks

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Taming "data-hungry" reinforcement learning? stability in continuous state-action spaces 24

Taming "data-hungry" reinforcement learning? stability in co...

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

作者： Yaqi Duan Martin J. Wainwright Department of Technology Operations and Statistics Stern School of Business New York University New York NY Laboratory for Information and Decision Systems Statistics and Data Science Center and Department of Electrical Engineering and Computer Science and Department of Mathematics Massachusetts Institute of Technology Cambridge MA

ISBN: (纸本)9798331314385

We introduce a novel framework for analyzing reinforcement learning (RL) in continuous state-action spaces, and use it to prove fast rates of convergence in both off-line and on-line settings. Our analysis highlights two key stability properties, relating to how changes in value functions and/or policies affect the Bellman operator and occupation measures. We argue that these properties are satisfied in many continuous state-action Markov decision processes. Our analysis also offers fresh perspectives on the roles of pessimism and optimism in off-line and on-line RL.

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Scaling-translation-equivariant networks with decomposed convolutional filters

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2022年第1期23卷 2958-3002页

作者： Wei Zhu Qiang Qiu Robert Calderbank Guillermo Sapiro Xiuyuan Cheng Department of Mathematics and Statistics University of Massachusetts Amherst Amherst MA Department of Electrical and Computer Engineering Purdue University West Lafayette Indiana Department of Electrical and Computer Engineering Duke University Durham NC Department of Mathematics Duke University Durham NC

Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-equivariant (ST -equivariant) CNN with joint convolutions across the space and the scaling group, which is shown to be both sufficient and necessary to achieve equivariance for the regular representation of the scaling-translation group ST. To reduce the model complexity and computational burden, we decompose the convolutional filters under two pre-fixed separable bases and truncate the expansion to low-frequency components. A further benefit of the truncated filter expansion is the improved deformation robustness of the equivariant representation, a property which is theoretically analyzed and empirically verified. Numerical experiments demonstrate that the proposed scaling-translation-equivariant network with decomposed convolutional filters (ScDCFNet) achieves significantly improved performance in multiscale image classification and better interpretability than regular CNNs at a reduced model size.

关键词： convolutional neural network (CNN) computer vision scaling-translation-equivariant decomposed convolutional filters deformation robust equivariant representation

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Smart and Slow Tourism. Evaluation and Challenges in Sardinia (Italy) 1

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11th International Conference on Innovation in Urban and Regional Planning, INPUT 2020

作者： Balletto, Ginevra Borruso, Giuseppe Ladu, Mara Milesi, Alessandra DICAAR - Department of Civil and Environmental Engineering and Architecture University of Cagliari Via Marengo 2 Cagliari Italy DEAMS - Department of Economics Business Mathematics and Statistics Sciences "Bruno de Finetti" University of Trieste Trieste34127 Italy

ISBN: (数字)9783030969851

ISBN: (纸本)9783030969844

Slow tourism is a sustainable way of traveling: it is not based on the consumption of resources and at the same time is linked to the discovery of local places and traditions. Furthermore, it favors a harmonious and responsible development of the territory in contrast with over tourism. Within this scenario and in the wake of a tradition rooted in Europe, the paths have become one of the most successful declinations of slow tourism. In this sense, the paths are increasingly becoming an integral part of the portfolio of tourism products in Sardinia, together with other types of tourism related to boating, culture, archeology, villages, cycling, food and wine, nature. The aim of this work is to investigate the role of slow tourism in Sardinia, with particular reference to the qualitative/quantitative evaluation of the model of the path of Santa Barbara Sulcis-Iglesiente and its exportability in other local contexts to enhance landscapes through the ancient tangible and intangible of mine habitats. Furthermore, the authors analyze the main potentially replicable elements of the path of Santa Barbara also in order to define best practices for the planning of slow tourism associated with smart tourism. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Tourism

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Target Group Influence Maximization using Reinforcement Learning Approach

Target Group Influence Maximization using Reinforcement Lear...

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International Conference on Web Research (ICWR)

作者： Neda Binesh Mahdieh Haddadi Niloofar Arazkhani Faculty of Mathematics Statistics and Computer Science Semnan University Semnan Iran Department of Computer Engineering & Information Technology Amirkabir University of Technology (Tehran Polytechnic) Tehran Iran

ISBN: (数字)9798350394986

ISBN: (纸本)9798350394993

In social networks groups play a crucial role and making decisions based on majority consensus. Which influencer nodes should we select if our goal is to broadcast a subject in a target group and increase the number of active nodes in this group? Here, we study a new influence maximization (IM) problem that focuses on individuals in a target group who are activated by some relevant topic or information. Target Group Influence Maximization (TGIM) aims to select k influencer nodes in such a way that the number of activated nodes in the target group is maximized. In this paper, we study TGIM and focus on activating the majority of nodes in the target group. We propose an algorithm named Reinforcement Learning for Target Group (RLTG) based on the analysis of the influence of nodes on the target group. The algorithm uses the reinforcement learning approach to learn the optimal path from each target node to some candidate influencers. The experimental results indicate that the recommended approach outperforms known methods.

关键词： Q-learning Social networking (online) Network analyzers Benchmark testing Task analysis

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