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Vertex numbers of simplicial complexes with free abelian fundamental group

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arXiv 2021年

作者： Frick, Florian Superdock, Matt Dept. Math. Sciences Carnegie Mellon University PittsburghPA15213 United States Inst. Math. Freie Universität Berlin Arnimallee 2 Berlin14195 Germany Dept. Mathematics and Computer Science Rhodes College MemphisTN38112 United States

We show that the minimum number of vertices of a simplicial complex with fundamental group (Formula Presented)is at most O(n) and at least (Formula Presented). For the upper bound, we use a result on orthogonal 1-factorizations of (Formula Presented). For the lower bound, we use a fractional Sylvester-Gallai result. We also prove that any group presentation (Formula Presented)whose relations are of the form (Formula Presented)for g, h, i ∈ S has at least (Formula Presented) *** Codes 05E45, 57M05, 20F05 © 2021, CC BY.

关键词： Group theory

VIETORIS THICKENINGS AND COMPLEXES HAVE ISOMORPHIC HOMOTOPY GROUPS

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arXiv 2022年

作者： Adams, Henry Frick, Florian Virk, Žiga Department of Mathematics Colorado State University Fort CollinsCO80523 United States Dept. Math. Sciences Carnegie Mellon University PittsburghPA15213 United States Inst. Math. Freie Universität Berlin Arnimallee 2 Berlin14195 Germany Faculty of Computer and Information Science Večna pot 113 LjubljanaSI-1000 Slovenia

We study the relationship between metric thickenings and simplicial complexes associated to coverings of metric spaces. Let U be a cover of a separable metric space X by open sets with a uniform diameter bound. The Vietoris complex V(U) contains all simplices with vertex set contained in some U ∈ U, and the Vietoris metric thickening Vm(U) is the space of probability measures with support in some U ∈ U, equipped with an optimal transport metric. We show that Vm(U) and V(U) have isomorphic homotopy groups in all dimensions. In particular, by choosing the cover U appropriately, we get isomorphisms between the homotopy groups of Vietoris-Rips metric thickenings and simplicial complexes πk(VRm(X;r)) ≅ πk(VR(X;r)) for all integers k ≥ 0, where both spaces are defined using the convention "diameter k(Čm(X;r)) ≅ πk(Č(X;r)) for all integers k ≥ 0, where both spaces are defined using open balls (instead of closed balls). Copyright © 2022, The Authors. All rights reserved.

关键词： Set theory

Texture synthesis via projection onto multiscale, multilayer statistics

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arXiv 2021年

作者： He, Jieqian Hirn, Matthew Dept. of Computational Math. Science & Engineering Michigan State University East LansingMI United States Dept. of Computational Math. Science & Engineering Department of Mathematics Center for Quantum Computing Science & Engineering Michigan State University East LansingMI United States

We provide a new model for texture synthesis based on a multiscale, multilayer feature extractor. Within the model, textures are represented by a set of statistics computed from ReLU wavelet coefficients at different layers, scales and orientations. A new image is synthesized by matching the target statistics via an iterative projection algorithm. We explain the necessity of the different types of pre-defined wavelet filters used in our model and the advantages of multilayer structures for image synthesis. We demonstrate the power of our model by generating samples of high quality textures and providing insights into deep representations for texture images. Copyright © 2021, The Authors. All rights reserved.

关键词： Multilayers

Is Gamification a Practical Solution for Increasing Repurchase Intention of Online Customers?

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Is Gamification a Practical Solution for Increasing Repurcha...

computer science, computer Engineering, & Applied Computing (CSCE), Congress in

作者： Khalil Safari Zohreh Safari Fatemeh Keshavarzi Dept. of Business Management and Information Technology Payam Noor University Tehran Iran Dept. Computer Science Math Engineering Technology Elizabeth City State University Elizabeth City USA Dept.Information Technology Engineering Qazvin Islamic Azad University Qazvin Iran

With the growth of online shopping, organizations should update their portals and websites in response to changing conditions and competitors' actions. To attract and retain online customers, various tools such as reputation building, trust en-hancement, and gamification are utilized and reinforced. This study has investigated 243 users of DigiKala company through paper and electronic questionnaires. Due to the non-normality of the data, non-parametric statistical methods using SPSS and Smart-PLS3.0 software were employed to analyze structural relationships. Additionally, machine learning tools were utilized to optimize the analysis of customer behavior and identify patterns for effective customer retention strategies. The results show that contrary to the research background, the use of gamification on DigiKala's website has not had a positive and significant impact on customers using this company's website and their repurchase intention. Thus, it seems that DigiKala should focus on context and infrastructures, while simultaneously strengthening and revamping gamification dimensions.

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Key Exchange in the Quantum Era: Evaluating a Hybrid System of Public-Key Cryptography and Physical-Layer Security

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arXiv 2024年

作者： Staat, Paul Dörpinghaus, Meik Sheikholeslami, Azadeh Paar, Christof Fettweis, Gerhard Goeckel, Dennis Max Planck Institute for Security and Privacy Bochum Germany Vodafone Chair Mobile Communications Systems Technische Universität Dresden Dresden Germany Math and Computer Science Department Suffolk University Boston United States Dept. Electrical and Computer Engineering University of Massachusetts Amherst United States

Today’s information society relies on cryptography to achieve security goals such as confidentiality, integrity, authentication, and non-repudiation for digital communications. Here, public-key cryptosystems play a pivotal role to share encryption keys and create digital signatures. However, quantum computers threaten the security of traditional public-key cryptosystems as they can tame computational problems underlying the schemes, i.e., discrete logarithm and integer factorization. The prospective arrival of capable-enough quantum computers already threatens today’s secret communication in terms of their long-term secrecy when stored to be later decrypted. Therefore, researchers strive to develop and deploy alternative schemes. In this work, evaluate a key exchange protocol based on combining public-key schemes with physical-layer security, anticipating the prospect of quantum attacks. If powerful quantum attackers cannot immediately obtain private keys, legitimate parties have a window of short-term secrecy to perform a physical-layer jamming key exchange (JKE) to establish a long-term shared secret. Thereby, the protocol constraints the computation time available to the attacker to break the employed public-key cryptography. In this paper, we outline the protocol, discuss its security, and point out challenges to be resolved. © 2024, CC BY-NC-SA.

关键词： Quantum computers

On the Evaluation of the Eigendecomposition of the Airy Integral Operator

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arXiv 2021年

作者： Shen, Zewen Serkh, Kirill Dept. of Computer Science University of Toronto TorontoONM5S 2E4 Canada Dept. of Math. and Computer Science University of Toronto TorontoONM5S 2E4 Canada

The distributions of the k-th largest level at the soft edge scaling limit of Gaussian ensembles are some of the most important distributions in random matrix theory, and their numerical evaluation is a subject of great practical importance. One numerical method for evaluating the distributions uses the fact that they can be represented as Fredholm determinants involving the so-called Airy integral operator. When the spectrum of the integral operator is computed by discretizing it directly, the eigenvalues are known to at most absolute precision. Remarkably, the Airy integral operator is an example of a so-called bispectral operator, which admits a commuting differential operator that shares the same eigenfunctions. In this paper, we develop an efficient numerical algorithm for evaluating the eigendecomposition of the Airy integral operator to full relative precision, using the eigendecomposition of the commuting differential operator. This allows us to rapidly evaluate the distributions of the k-th largest level to full relative precision rapidly everywhere, except in the left tail, where they are computed to absolute precision. In addition, we characterize the eigenfunctions of the Airy integral operator, and describe their extremal properties in relation to an uncertainty principle involving the Airy transform. We observe that the Airy integral operator is fairly universal, and we describe a separate application to Airy beams in optics. © 2021, CC BY.

关键词： Eigenvalues and eigenfunctions

Degree 2 Boolean Functions on Grassmann Graphs

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arXiv 2022年

作者： De Beule, Jan D'haeseleer, Jozefien Ihringer, Ferdinand Mannaert, Jonathan Department of Mathematics and Data Science Research Group Digital Mathematics Vrije Universiteit Brussel BrusselsB-1050 Belgium Dept. of Mathematics: Analysis Logic and Discrete Math. Ghent University Belgium

We investigate the existence of Boolean degree d functions on the Grassmann graph of k-spaces in the vector space Fnq. For d = 1 several non-existence and classification results are known, and no non-trivial examples are known for n ≥ 5. This paper focusses on providing a list of examples on the case d = 2 in general dimension and in particular for (n, k) = (6, 3) and (n, k) = (8, 4). We also discuss connections to the analysis of Boolean functions, regular sets/equitable bipartitions/perfect 2-colorings in graphs, q-analogs of designs, and permutation groups. In particular, this represents a natural generalization of Cameron-Liebler line classes. © 2022, CC BY-SA.

关键词： Boolean functions

Neuro-heuristic Pallet Detection for Automated Guided Vehicle Navigation

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Neuro-heuristic Pallet Detection for Automated Guided Vehicl...

IEEE International Conference on Big Data

作者： Katarzyna Prokop Dawid Połap Gautam Srivastava Faculty of Applied Mathematics Silesian University of Technology Gliwice Poland Dept. of Math and Computer Science Brandon University Brandon MB Canada

ISBN: (纸本)9781665480468

Automated guided vehicles (AGV) allow for the automation of operations in warehouse environments. From an application point of view, vehicles can use sensors to move and perform a variety of tasks, including moving objects. In this paper, we focus on the analysis of the environment and the preparation of data for vehicle navigation. The proposed solution is based on two paths of action. In the first, the image of the room is processed by heuristics to locate the robot’s target - the palette. The found pattern allows one to locate the destination as well as create a mask. The mask can be used to train the U-Net network. When a network is trained, the use of heuristics for pallet location can be omitted. Locating the target allows the image to be processed to obtain an AGV navigation map. The proposed solution based on heuristics and U-Net networks has been described and tested in simulations to indicate the potential of the proposed approach.

关键词： Remotely guided vehicles Navigation Heuristic algorithms Stars Big Data Time measurement Sensors

Identification and Categorization of Unusual Internet of Vehicles Events in Noisy Audio

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Identification and Categorization of Unusual Internet of Veh...

IEEE Conference on Vehicular Technology (VTC)

作者： Farkhund Iqbal Ahmad Abbasi Abdul Rehman Javed Gautam Srivastava Zunera Jalil Thippa Reddy Gadekallu Department of Cyber Security Zayed University UAE Department of Cyber Security Air University Islamabad Pakistan Dept. of Math and Computer Science Brandon University Brandon Canada Department of Electrical and Computer Engineering Lebanese American University Byblos Lebanon

The volume of multimedia data produced by various smart devices has increased dramatically with the advent of new digital technologies, including in the Internet of Vehicles (IoV). It has become more difficult to extract valuable insights from multimedia data due to several challenges during data analysis. The main problem is the need to quickly and precisely identify abnormalities in multimedia data. This research presents an unusual occurrence of the audio forensics database named UOAFDB and a practical method for identifying and categorizing unusual occurrences in audio files. To study the detection of abnormal audio and the classification of rare sound (e.g., car crash—machine gun, explosion) events for audio forensics, we construct a large audio dataset containing ten rare special events (anomalies) with 15 different background environmental settings (e.g., beach, restaurant, and train). The suggested method determines the optimal amount of features using the best feature extraction methodology available by extracting Mel-frequency cepstral coefficients (MFCCs) features from the audio signals of the newly formed dataset. Modern deep learning algorithms use these features as input to assess performance. Additionally, we apply deep learning methods to the most recent and best available dataset and obtain promising outcomes. The experimental findings demonstrate promising results on the UOAFDB dataset.

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