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The effect of graph complexity and planning on graph writing performance and descriptive strategies

FOREIGN LANGUAGE ANNALS 2023年第1期56卷 117-143页

作者： Golparvar, Seyyed Ehsan Azizsahra, Mahsa Univ Bojnord Bojnurd Iran

The impact of task complexity on integrated writing performance is under-researched. This study purports to investigate the effect of graph complexity and planning time on graph writing performance as well as graph description strategies. Ninety-six EFL learners of English were assigned into three groups to examine the effect of three planning conditions, that is, pretask planning, within-task planning, and no planning. Moreover, graph complexity, operationalized as the number of visual chunks in a graph, was the within-subject variable. In general, there were some benefits of graph complexity for syntactic complexity and some planning benefits for fluency, accuracy, and lexical diversity. However, graph complexity had a negative impact on accuracy, and measures of lexical sophistication were not affected in any condition. On the graph description side, pretask planning and graph complexity had a positive impact on graph description strategies. The theoretical and pedagogical implications of these findings are discussed.

关键词： integrated writing task complexity planning time graph complexity graph description

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Monocular graph SLAM with complexity Reduction

Monocular Graph SLAM with Complexity Reduction

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IEEE/RSJ International Conference on Intelligent Robots and Systems

作者： Eade, Ethan Fong, Philip Munich, Mario E. Evolution Robotics United States

ISBN: (纸本)9781424466757

We present a graph-based SLAM approach, using monocular vision and odometry, designed to operate on computationally constrained platforms. When computation and memory are limited, visual tracking becomes difficult or impossible, and map representation and update costs must remain low. Our system constructs a map of structured views using only weak temporal assumptions, and performs recognition and relative pose estimation over the set of views. Visual observations are fused with differential sensors in an incrementally optimized graph representation. Using variable elimination and constraint pruning, the graph complexity and storage is kept linear in explored space rather than in time. We evaluate performance on sequences with ground truth, and also compare to a standard graph SLAM approach.

关键词： SLAM (robots) complexity reduction constraint pruning differential sensor distance measurement graph based SLAM graph complexity graph theory map representation monocular vision odometry pose estimation relative pose estimation robot vision variable elimination visual tracking

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On the likelihood of forests

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2016年 456卷 157-166页

作者： Shang, Yilun Tongji Univ Dept Math Shanghai 200092 Peoples R China

How complex a network is crucially impacts its function and performance. In many modern applications, the networks involved have a growth property and sparse structures, which pose challenges to physicists and applied mathematicians. In this paper, we introduce the forest likelihood as a plausible measure to gauge how difficult it is to construct a forest in a non-preferential attachment way. Based on the notions of admittable labeling and path construction, we propose algorithms for computing the forest likelihood of a given forest. Concrete examples as well as the distributions of forest likelihoods for all forests with some fixed numbers of nodes are presented. Moreover, we illustrate the ideas on real-life networks, including a benzenoid tree, a mathematical family tree, and a peer-to-peer network. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Likelihood Growing networks Forest graph complexity

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Disproving the single level conjecture

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SIAM JOURNAL ON COMPUTING 2006年第1期36卷 83-98页

作者： Jukna, S Inst Math & Informat LT-08663 Vilnius Lithuania

We consider the size of monotone circuits for quadratic Boolean functions, that is, disjunctions of length-2 monomials. Our motivation is that a good ( linear in the number of variables) lower bound on the monotone circuit size for a certain type of quadratic function would imply a good ( even exponential) lower bound on the general nonmonotone circuit size. To get more insight into the structure of monotone circuits for quadratic functions, we consider the so-called single level conjecture posed explicitly in the early 1990s. The conjecture claims that monotone single level circuits, that is, circuits which have only one level of AND gates, for quadratic functions are not much larger than arbitrary monotone circuits. In this paper we disprove the conjecture as follows: there exist quadratic functions whose monotone circuits have linear size but whose monotone single level circuits require almost quadratic size.

关键词： quadratic functions monotone circuits Boolean sums graph complexity clique covering number Kneser graph Sylvester graph

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Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2018年第3期112卷 781-792页

作者： Cristofori, Paola Fominykh, Evgeny Mulazzani, Michele Tarkaev, Vladimir Univ Modena & Reggio Emilia Dept Phys Informat & Math Modena Italy Russian Acad Sci Ural Branch Krasovskii Inst Math & Mech Ekaterinburg Russia Chelyabinsk State Univ Dept Math Chelyabinsk Russia Univ Bologna Dept Math Bologna Italy Univ Bologna ARCES Bologna Italy

The graph complexity of a compact 3-manifold is defined as the minimum order among all 4-colored graphs representing it. Exact calculations of graph complexity have been already performed, through tabulations, for closed orientable manifolds (up to graph complexity 32) and for compact orientable 3-manifolds with toric boundary (up to graph complexity 12) and for infinite families of lens spaces. In this paper we extend to graph complexity 14 the computations for orientable manifolds with toric boundary and we give two-sided bounds for the graph complexity of tetrahedral manifolds. As a consequence, we compute the exact value of this invariant for an infinite family of such manifolds.

关键词： 3-Manifolds Colored graphs graph complexity Tetrahedral manifolds

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A history of graph entropy measures

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INFORMATION SCIENCES 2011年第1期181卷 57-78页

作者： Dehmer, Matthias Mowshowitz, Abbe UMIT Inst Bioinformat & Translat Res Eduard Wallnoefer Zentrum 1 A-6060 Hall In Tirol Austria Vienna Univ Technol Inst Discrete Math & Geometry A-1040 Vienna Austria CUNY City Coll Dept Comp Sci New York NY 10031 USA

This survey seeks to describe methods for measuring the entropy of graphs and to demonstrate the wide applicability of entropy measures. Setting the scene with a review of classical measures for determining the structural information content of graphs, we discuss graph entropy measures which play an important role in a variety of problem areas, including biology, chemistry, and sociology. In addition, we examine relationships between selected entropy measures, illustrating differences quantitatively with concrete examples. (C) 2010 Elsevier Inc. All rights reserved.

关键词： graphs Information theory Information measures Information inequalities Entropy graph entropy graph complexity Structural complexity

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The H₀ function, a new index for detecting structural/topological complexity information in undirected graphs

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2016年 447卷 355-378页

作者： Buscema, Massimo Asadi-Zeydabadi, Masoud Lodwick, Weldon Breda, Marco Seme Res Ctr Sci Commun Via Sersale 117 I-00128 Rome Italy Univ Colorado CCMB Dept Math & Stat Sci POB 173364 Denver CO 80217 USA Univ Colorado Dept Phys POB 173364 Denver CO 80217 USA

Significant applications such as the analysis of Alzheimer's disease differentiated from dementia, or in data mining of social media, or in extracting information of drug cartel structural composition, are often modeled as graphs. The structural or topological complexity or lack of it in a graph is quite often useful in understanding and more importantly, resolving the problem. We are proposing a new index we call the Ho function to measure the structural/topological complexity of a graph. To do this, we introduce the concept of graph pruning and its associated algorithm that is used in the development of our measure. We illustrate the behavior of our measure, the Ho function, through different examples found in the appendix. These examples indicate that the Ho function contains information that is useful and important characteristics of a graph. Here, we restrict ourselves to undirected. (C) 2015 Elsevier B.V. All rights reserved.

关键词： graph complexity graph index graph pruning

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Reliable graphs for SLAM

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INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2019年第2-3期38卷 260-298页

作者： Khosoussi, Kasra Giamou, Matthew Sukhatme, Gaurav S. Huang, Shoudong Dissanayake, Gamini How, Jonathan P. MIT LIDS 77 Massachusetts Ave Cambridge MA 02139 USA Univ Southern Calif Dept Comp Sci Viterbi Sch Engn Los Angeles CA USA Univ Technol Sydney CAS Sydney NSW Australia

Estimation-over-graphs (EoG) is a class of estimation problems that admit a natural graphical representation. Several key problems in robotics and sensor networks, including sensor network localization, synchronization over a group, and simultaneous localization and mapping (SLAM) fall into this category. We pursue two main goals in this work. First, we aim to characterize the impact of the graphical structure of SLAM and related problems on estimation reliability. We draw connections between several notions of graph connectivity and various properties of the underlying estimation problem. In particular, we establish results on the impact of the weighted number of spanning trees on the D-optimality criterion in 2D SLAM. These results enable agents to evaluate estimation reliability based only on the graphical representation of the EoG problem. We then use our findings and study the problem of designing sparse SLAM problems that lead to reliable maximum likelihood estimates through the synthesis of sparse graphs with the maximum weighted tree connectivity. Characterizing graphs with the maximum number of spanning trees is an open problem in general. To tackle this problem, we establish several new theoretical results, including the monotone log-submodularity of the weighted number of spanning trees. We exploit these structures and design a complementary greedy-convex pair of efficient approximation algorithms with provable guarantees. The proposed synthesis framework is applied to various forms of the measurement selection problem in resource-constrained SLAM. Our algorithms and theoretical findings are validated using random graphs, existing and new synthetic SLAM benchmarks, and publicly available real pose-graph SLAM datasets.

关键词： SLAM measurement selection resource-constrained SLAM estimation over graphs pose-graph pruning number of spanning trees graph complexity

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On the CNF-complexity of bipartite graphs containing no squares

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LITHUANIAN MATHEMATICAL JOURNAL 2012年第4期52卷 385-389页

作者： Katz, Nets Hawk Indiana Univ Dept Math Bloomington IN 47405 USA

By a probabilistic construction, we find a bipartite graph having average degree d which can be expressed as a conjunctive normal form using C log d clauses. This negatively resolves Research Problem 1.33 of Jukna [S. Jukna, Boolean Function complexity: Advances and Frontiers, Algorithms Comb., Vol. 27, Springer, Berlin, Heidelberg, 2012].

关键词： squares graph complexity probabilistic construction

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The Entropy of graph Embeddings: A Proxy of Potential Mobility in Covid19 Outbreaks

The Entropy of Graph Embeddings: A Proxy of Potential Mobili...

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Joint IAPR International Workshop on Structural and Syntactic Pattern Recognition (SSPR) / International Workshop on Statistical Techniques in Pattern Recognition (SPR)

作者： Escolano, Francisco Angel Lozano, Miguel Hancock, Edwin R. Univ Alicante Alicante Spain COVID 19 Data Sci Task Force Alicante Spain Univ York York N Yorkshire England

ISBN: (纸本)9783030739720;9783030739737

In this paper, we propose a proxy of the R-0 (reproductive number) of COVID-19 by computing the entropy of the mobility graph during the first peak of the pandemic. The study was performed by the COVID-19 Data Science Task Force at the Comunidad Valenciana (Spain) during 70 days. Since mobility graphs are naturally attributed, directed and become more and more disconnected as more and more non-pharmaceutical measures are implemented, we discarded spectral complexity measures and classical ones such as network efficiency. Alternatively, we turned our attention to embeddings resulting from random walks and their links with stochastic matrices. In our experiments, we show that this leads to a powerful tool for predicting the spread of the virus and to assess the effectiveness of the political interventions.

关键词： graph embeddings graph complexity COVID-19

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