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Networks of splicing processors: path graph topology simulation

NATURAL COMPUTING 2025年 1-12页

作者： Martin, Jose Angel Sanchez Mitrana, Victor Paun, Mihaela Univ Rey Juan Carlos Dept Comp Sci & Stat Calle Tulipan S-N Mostoles 28933 Madrid Spain Univ Politecn Madrid Dept Informat Syst Calle Alan Turing S-N Madrid 28031 Spain Natl Inst R&D Biol Sci Bioinformat Dept Splaiul Independentei 296 Bucharest 060031 Romania Univ Bucharest Fac Adm & Business B Dul Regina Elisabeta 4-12 Bucharest 030015 Romania

We propose a direct simulation of an arbitrary network of splicing processors by a network of splicing processors having an underlying path graph. This is in line with similar simulations where the target network has other widely used graph topologies: complete graph, lattice graph, star graph, wheel graph, etc. Along with the effective construction, we provide an analysis of the size and time complexity of the obtained network. Our construction may not be the most economic conversion in terms of number of nodes, hence further investigation to find more succinct networks are of (at least) theoretical interest.

关键词： Splicing Splicing processor Network of splicing processors path graph Time and size complexity

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Design of Matrix Filter Using Discrete Cosine Transform and path graph

Design of Matrix Filter Using Discrete Cosine Transform and ...

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IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)

作者： Tseng, Chien-Cheng Lee, Su-Ling Natl Kaohsiung Univ Sci & Technol Dept Comp & Commun Engn Kaohsiung Taiwan Chang Jung Christian Univ Dept Comp Sci & Informat Engn Tainan Taiwan

ISBN: (纸本)9781665450737

In this paper, the design of matrix filter using discrete cosine transform (DCT) and path graph is presented. First, the DCT is used to design matrix filter without considering the prior information of transform basis of DCT. Then, the graph spectral theory is employed to show that the DCT is the graph Fourier transform (GFT) of path graph such that graph filter method can be used to design and implement the matrix filter. Next, the weighted least squares (WLS) method is applied to design the graph filters which can be used to implement the matrix filter with low computational complexity because graph shift matrix is very sparse. Finally, the design examples of matrix Butterworth filter and matrix Riesz fractional order differentiator (FOD) are illustrated to demonstrate the effectiveness of the proposed matrix filter design method.

关键词： matrix filter discrete cosine transform graph Fourier transform graph filter path graph

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Identification of rail cracks based on path graph features and SVM

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ADVANCES IN MECHANICAL ENGINEERING 2024年第5期16卷

作者： Ye, Yunfei Ji, Kailun Wang, Ping Nanjing Inst Railway Technol Sch Intelligent Engn Nanjing Peoples R China CETC Deqing Huaying Elect Co Ltd Deqing Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Jiangjun Ave Nanjing Jiangsu Peoples R China

In order to improve the accuracy of rail crack identification, a new method based on path graph feature and support vector machine is proposed. This method uses graph signal processing and graph theory to transform the magnetic flux leakage signal of rail crack, calculates the "time domain" and "frequency domain" statistics of the path graph signal, and effectively identifies rail cracks with different defect parameters by SVM classifier. The measured data verify the effectiveness of this method, which shows that the method of identifying rail cracks by using path graph features has higher accuracy and stability. The innovation of this method is that it draws on the idea of transform domain features to extract the graph domain features that can best represent the MFL signal. Compared with the 31 features used by the traditional method, this method only needs 22 features to achieve better recognition results and has shorter training time. For the recognition rate of 18 kinds of cracks, the average recognition rate of this method is more than 83.51%, and the highest recognition rate is 95.34%. Therefore, this study provides a new way for magnetic leakage analysis and treatment of rail crack detection, has important practical value, and provides beneficial enlightenment for further research in related fields.

关键词： Rail inspection MFL testing path graph SVM rail crack identification

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Dominator chromatic number of m-Splitting graph and m-Shadow graph of path graph

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INTERNATIONAL JOURNAL OF BIOMEDICAL ENGINEERING AND TECHNOLOGY 2018年第1-2期27卷 100-113页

作者： Manjula, T. Rajeswari, R. Deemed Be Univ Sathyabama Inst Sci & Technol Dept Math Madras Tamil Nadu India

graph theory techniques are applied to several biological domains. The application of graph colouring and domination in the field of biology and medicine includes identifying drug targets, determining the role of proteins, genes of unknown function. The area obtained by combining graph colouring and domination is called the dominator colouring of a graph. This is defined as proper colouring of vertices in which every vertex of the graph dominates all vertices of at least one colour class. The least number of colours required for a dominator colouring of a graph is called the dominator chromatic number. The dominator chromatic number and domination number are obtained for m-Splitting graph and m-Shadow graph of path graph and a relationship between them is expressed in this paper.

关键词： domination colouring dominator colouring m-Splitting graph m-Shadow graph path graph

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A travelling wave approach to a multi-agent system with a path-graph topology

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SYSTEMS & CONTROL LETTERS 2017年 99卷 90-98页

作者： Martinec, Dan Herman, Ivo Sebek, Michael Czech Tech Univ Fac Elect Engn Prague Czech Republic

The paper presents a novel approach for the analysis and control of a multi-agent system with nonidentical agents and a path-graph topology. With the help of irrational wave transfer functions, the approach describes the interaction among the agents from the 'local' perspective and identifies travelling waves in the system. It is shown that different dynamics of the agents create a virtual boundary that causes a partial reflection of the travelling waves. Undesired effects due to the reflection of the waves, such as amplification/attenuation, long transients or string instability, can be compensated by the feedback controllers introduced in this paper. We show that the controllers achieve asymptotic and even string stability of the system. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Multi-agent system Travelling waves Wave transfer function path graph Irrational transfer function

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Generating k-Hop-Constrained s-t path graphs

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2025年第5期37卷 2584-2599页

作者： Cai, Yuzheng Liu, Siyuan Zheng, Weiguo Lin, Xuemin Zhang, Chengbo Zhang, Xuecang Fudan Univ Sch Data Sci Shanghai 200433 Peoples R China Carnegie Mellon Univ Heinz Coll Pittsburgh PA 15213 USA Shanghai Jiao Tong Univ Antai Coll Econ & Management Shanghai 200240 Peoples R China Huawei Technol Shenzhen 518129 Peoples R China

In this paper, we study two different problems that investigate relations between given vertices s and t. The first problem is to generate the k-hop-constrained s-t path graph, i.e., the subgraph consisting of all paths from s to t, where each path is not longer than k s.t. s and t appear only once. To solve the first problem, we propose the A-BiBFS++ method enhanced with the reduced neighbor index and an approximate vertex grouping strategy. The second problem is to generate the k-hop-constrained s-t simple path graph, i.e., the subgraph consisting of all k-hop-constrained simple paths from s to t, which is proved to be NP-hard on directed graphs. Based on A-BiBFS++, we propose the EVE method to tackle the second problem, which exploits the paradigm of edge-wise examination rather than exhaustively enumerating all simple paths. Extensive experiments show that both A-BiBFS++ and EVE significantly outperform all baselines. Moreover, by taking EVE as a built-in block, state-of-the-art for hop-constrained simple path enumeration can be accelerated by up to an order of magnitude.

关键词： Directed graphs Bidirectional control Quality of service Image edge detection Fraud Topology Routing Reviews Polynomials Organizations Hop-constrained path hop-constrained simple path path graph simple path graph essential vertices

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Powers of generalized binomial edge ideals of path graphs

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INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION 2024年第5期34卷 779-806页

作者： Shen, Yi-Huang Zhu, Guangjun Univ Sci & Technol China Sch Math Sci CAS Wu Wen Tsun Key Lab Math Hefei 230026 Anhui Peoples R China Soochow Univ Sch Math Sci Suzhou 215006 Jiangsu Peoples R China

In this paper, we study the powers of the generalized binomial edge ideal J(Km), P-n of a path graph P-n. We explicitly compute their regularities and determine the limit of their depths. We also show that these ordinary powers coincide with their symbolic powers. Additionally, we study the Rees algebra and the special fiber ring of J(Km), P-n utilizing Sagbi basis theory. In particular, we obtain precise formulas for the regularity of these blowup algebras.

关键词： Regularity depth generalized binomial edge ideal path graph Rees algebra special fiber ring

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Succinct Data Structures for path graphs and Chordal graphs Revisited

Succinct Data Structures for Path Graphs and Chordal Graphs ...

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Data Compression Conference (DCC)

作者： He, Meng Munro, J. Ian Wu, Kaiyu Dalhousie Univ Fac Comp Sci Halifax NS Canada Univ Waterloo Cheriton Sch Comp Sci Waterloo ON Canada

ISBN: (纸本)9798350385885;9798350385878

We enhance space efficient representations of two types of intersection graphs. We refine the data structure for path graphs of Balakrishnan et al. to give a succinct data structure of n log n + o(n log n) bits that supports adjacency test, degree and neighbourhood queries in O(log n/log log n) time (for neighbourhood queries, this is the amount of time for each neighbour reported). To achieve O(1) query times, we give a data structure using (3 + epsilon)n log n + o(n log n) bits for any constant epsilon > 0. Furthermore, we are able to support both the distance and shortest path queries on unweighted path graphs using (2 + epsilon)n log n+ o(n log n) bits in O(log n/log log n) time (shortest path uses an additional O(1) time per vertex on the path). This is the first compact distance oracles for path graphs. Turning to chordal graphs, we enhance the succinct data structure of Munro and Wu to reduce all query times including performing adjacency test in O(1) time.

关键词： Chordal graph path graph Succinct Data Structure

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Quadratic embedding constants of path graphs

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LINEAR ALGEBRA AND ITS APPLICATIONS 2022年 644卷 95-107页

作者： Mlotkowski, Wojciech Uniwersytet Wroclawski Inst Matemat Plac Grunwaldzki 2-4 PL-50384 Wroclaw Poland

We characterize positive definiteness for some family of matrices. As an application, we derive the explicit value of the quadratic embedding constants of the path graphs.(c) 2022 The Author(s). Published by Elsevier ... 详细信息

关键词： Positive definite matrix Conditionally negative definite matrix Distance matrix of a graph path graph Quadratic embedding constant

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path graphs: Iterative path Space Filtering

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ACM TRANSACTIONS ON graphICS 2021年第6期40卷 1-15页

作者： Deng, Xi Hasan, Milos Carr, Nathan Xu, Zexiang Marschner, Steve Cornell Univ 345 Gates Hall Ithaca NY 14850 USA Adobe Res 345 Pk Ave San Jose CA 95110 USA Cornell Univ 313 Gates Hall Ithaca NY USA

To render higher quality images from the samples generated by path tracing with a low sample count, we propose a novel path reuse approach that processes a fixed collection of paths to iteratively refine and improve radiance estimates throughout the scene. Our method operates on a path graph consisting of the union of the traced paths with additional neighbor edges inserted among clustered nearby vertices. Our approach refines the initial noisy radiance estimates via an aggregation operator, treating vertices within clusters as independent sampling techniques that can be combined using MIS. In a novel step, we also introduce a propagation operator to forward the refined estimates along the paths to successive bounces. We apply the aggregation and propagation operations to the graph iteratively, progressively refining the radiance values, converging to fixed-point radiance estimates with lower variance than the original ones. We also introduce a decorrelation (final gather) step, which uses information already in the graph and is cheap to compute, allowing us to combine the method with standard denoisers. Our approach is lightweight, in the sense that it can be easily plugged into any standard path tracer and neural final image denoiser. Furthermore, it is independent of scene complexity, as the graph size only depends on image resolution and average path depth. We demonstrate that our technique leads to realistic rendering results starting from as low as 1 path per pixel, even in complex indoor scenes dominated by multi-bounce indirect illumination.

关键词： ray tracing global illumination Monte Carlo path graph path space filtering

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