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Graph-theoretic approach to dimension witnessing [article]

Maharshi Ray, Naresh Goud Boddu, Kishor Bharti, Leong-Chuan Kwek, Adán Cabello
<span title="2020-11-13">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Here, we introduce a novel approach to quantum dimension witnessing for scenarios with one preparation and several measurements, which uses the graphs of mutual exclusivity between sets of measurement  ...  We present the concepts and tools needed for graph-theoretic quantum dimension witnessing and illustrate their use by identifying novel quantum dimension witnesses, including a family that can certify  ...  Acknowledgments The authors thank Zhen-Peng Xu for valuable comments on the arχiv version and suggesting the use of weighted graphs for increasing the quantum-classical gap as described in the conclusions  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.10746v2">arXiv:2007.10746v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cwjx4dvdczd2xb33l3b6uqry4y">fatcat:cwjx4dvdczd2xb33l3b6uqry4y</a> </span>
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Page 5206 of Mathematical Reviews Vol. , Issue 2002G [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The first point of view has led to developing the categorical ap- proach to graph rewriting, known as the double pushout approach.  ...  We think these results give a theoretical justification for the numer- ous heuristic approaches to cope with these problems found in the literature.”  ... 
<span class="external-identifiers"> </span>
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Fast construction of the Vietoris-Rips complex

Afra Zomorodian
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/eu2m4gixpvbj3bgkrmcfu4ezdi" style="color: black;">Computers &amp; graphics</a> </i> &nbsp;
This complex is popular in topological data analysis as its construction extends easily to higher dimensions.  ...  We formulate a two-phase approach for its construction that separates geometry from topology.  ...  ACKNOWLEDGMENTS The author would like to thank Frédéric Cazals for discussion on maximal cliques, Doug Moore for his implementation of lexicographic generation of combinations, Harlan Sexton for JPlex,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cag.2010.03.007">doi:10.1016/j.cag.2010.03.007</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mksafszti5a3vl5huw3wlxdley">fatcat:mksafszti5a3vl5huw3wlxdley</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110401061426/http://www.cs.dartmouth.edu/~afra/papers/smi10/vietoris.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e5/03/e503c24dcc7a8110a001ae653913ccd064c1044b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cag.2010.03.007"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A growing self-organizing network for reconstructing curves and surfaces

Marco Piastra
<span title="">2009</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qm5nunzmyva4tfjekdcm34uvhq" style="color: black;">2009 International Joint Conference on Neural Networks</a> </i> &nbsp;
The approach presented here takes a different perspective, namely by assuming that the input space is a manifold of known dimension.  ...  Self-organizing networks such as Neural Gas, Growing Neural Gas and many others have been adopted in actual applications for both dimensionality reduction and manifold learning.  ...  Thanks are also due to an anonymous referee and to Alessandro Bollini for their precious comments on a preliminary version of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ijcnn.2009.5178709">doi:10.1109/ijcnn.2009.5178709</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ijcnn/Piastra09.html">dblp:conf/ijcnn/Piastra09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m6qs3zjuxnb2rptwkhctxdboge">fatcat:m6qs3zjuxnb2rptwkhctxdboge</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200321093322/https://vision.unipv.it/people/bianchi/tmp/m.piastra.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/aa/4f/aa4faa5a7087076a5c53c289c5c0aa57c2cacf48.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ijcnn.2009.5178709"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema

Tobias Rupp, Stefan Funke
<span title="2021-05-25">2021</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/63zsvf7vxzfznojpqgfvpyk2lu" style="color: black;">Algorithms</a> </i> &nbsp;
For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds.  ...  Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by  ...  Acknowledgments: We like to thank the OpenStreetMap community for making free geodata available for our experiments. Conflicts of Interest: The authors declare no conflict of interest.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/a14060164">doi:10.3390/a14060164</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cwzbxc7twfdxxh2m22zxihj64q">fatcat:cwzbxc7twfdxxh2m22zxihj64q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210603012941/https://res.mdpi.com/d_attachment/algorithms/algorithms-14-00164/article_deploy/algorithms-14-00164-v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/61/77/61774d82527dd675bb663b5ebcde0804aea7ba8d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/a14060164"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

A note on the 1-prevalence of continuous images with full Hausdorff dimension [article]

Jonathan M. Fraser, James T. Hyde
<span title="2014-01-27">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We extend this result by showing that 'prevalent' can be replaced by '1-prevalent', i.e. it is possible to witness this prevalence using a measure supported on a one dimensional subspace.  ...  has to be used.  ...  They also thank Márton Elekes for drawing their attention to the paper [D].  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1203.0548v2">arXiv:1203.0548v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tqrjhcboo5fubptw3mwfgktbka">fatcat:tqrjhcboo5fubptw3mwfgktbka</a> </span>
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ϵ-net Induced Lazy Witness Complexes on Graphs [article]

Naheed Anjum Arafat, Debabrota Basu, Stéphane Bressan
<span title="2020-09-25">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a lazy witness complex approach leveraging the notion of ϵ-net that we adapt to weighted graphs and their geodesic distance to select landmarks.  ...  This metric space of a graph is amenable to topological data analysis. We discuss the computation of persistent homologies on a weighted graph.  ...  The empirical performance analysis instantiates Iterative--Net as the practical and efficient choice to construct -net induced lazy witness complex for graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2009.13071v1">arXiv:2009.13071v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ticmllamr5bqdmcqgofvvw473m">fatcat:ticmllamr5bqdmcqgofvvw473m</a> </span>
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Page 5116 of Mathematical Reviews Vol. , Issue 2000g [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Rytter, Theoret. Comput. Sci. 88 (1991), no. 1, 59-82; MR 92k:68105] in the computation of the three-dimensional witness table is demonstrated.  ...  The advantage of our approach is that it is essentially two-dimensional.  ... 
<span class="external-identifiers"> </span>
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A Short Survey of Topological Data Analysis in Time Series and Systems Analysis [article]

Shafie Gholizadeh, Wlodek Zadrozny
<span title="2018-10-20">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In some recent contributions, TDA has been utilized as an alternative to the conventional signal processing methods. Specifically, TDA is been considered to deal with noisy signals and time series.  ...  In these applications, TDA is used to find the shapes in data as the main properties, while the other properties are assumed much less informative.  ...  For the application section, we reviewed the approaches that utilize the introduced theoretical concepts in real applications.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1809.10745v2">arXiv:1809.10745v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cqr5asnhxrdc7lc5g4jcaswdku">fatcat:cqr5asnhxrdc7lc5g4jcaswdku</a> </span>
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Role action embeddings: scalable representation of network positions [article]

George Berry
<span title="2018-12-03">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It combines a within-node loss function and a graph neural network (GNN) architecture to place nodes with similar local neighborhoods close in embedding space.  ...  We find that the model architecture proposed here provides strong performance on both graph and node classification tasks, in some cases competitive with semi-supervised methods.  ...  ACKNOWLEDGEMENTS Thanks to Nima Noorshams, Katerina Marazopoulou, Lada Adamic, Saurabh Verma, Alex Dow, Shaili Jain, and Alex Pesyakhovich for discussions and suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.08019v2">arXiv:1811.08019v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r6ttyp6ws5bjjmbu43scnoxhpe">fatcat:r6ttyp6ws5bjjmbu43scnoxhpe</a> </span>
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Quantum theory allows for absolute maximal contextuality

Barbara Amaral, Marcelo Terra Cunha, Adán Cabello
<span title="2015-12-16">2015</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/iedolmzeofgc3ezyedga7h4eba" style="color: black;">Physical Review A. Atomic, Molecular, and Optical Physics</a> </i> &nbsp;
Linear contextuality witnesses can be expressed as a sum S of n probabilities, and the independence number α and the Tsirelson-like number ϑ of the corresponding exclusivity graph are, respectively, the  ...  It is therefore important to investigate how large contextuality can be in quantum theory.  ...  ACKNOWLEDGMENTS The authors thank Israel Vainsencher for his help with the graph of Theorem 2 and Gustavo Cañas for his help with Fig. 1 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.92.062125">doi:10.1103/physreva.92.062125</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ng76mdr4l5cirjzini7z2keete">fatcat:ng76mdr4l5cirjzini7z2keete</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190306212557/http://pdfs.semanticscholar.org/ed4a/9ef784fbca4575d8fc821145a1b55a90f233.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ed/4a/ed4a9ef784fbca4575d8fc821145a1b55a90f233.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.92.062125"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Is there a diagram invariant?

Maurice Pouzet, Ivan Rival
<span title="">1988</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Neve comparability graph is really not much used in the theory of irony of our subject that thz diagram, whose usage is univers illustrate, to find counterexamples, to prompt discovery-is To draw an ordered  ...  Are there any nontrivial, order-theoretical properties shared among all of the reorientations of the diagram of an ordered set? We know of no such property.  ...  Let G be its covering graph. Then, according to Theorem C, there is a subdivision S of G, a lattice wit covering graph L, and a graph retraction g of L to S.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(88)90146-x">doi:10.1016/0012-365x(88)90146-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rv3oivxbzbhnfp2jzwzesicg3u">fatcat:rv3oivxbzbhnfp2jzwzesicg3u</a> </span>
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Algebraic Theoretic Properties of the Non-associative Class of (132)-Avoiding Patterns of AUNU Permutations: Applications in the Generation and Analysis of a General Cyclic Code

Chun P. B, Ibrahim A.A, Garba A.I
<span title="">2016</span> <i title="Horizon Research Publishing Co., Ltd."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/i2eweabxwvgdbar4wvuqytursu" style="color: black;">Computer Science and Information Technology</a> </i> &nbsp;
To achieve this, the generator matrix G as in [1] that generated C is further developed to give a matrix say 1 G which now spans a larger linear code 1 C of length 5 n = , dimension 4 k = and size 32 M  ...  The author had in [1] and based on the report as in [2] , established interplay between the adjacency matrices due to Eulerian graphs constructed by the application of AUNU numbers and the generation and  ...  To achieve this, the generator matrix G as in [1] that generated C is further developed to give a matrix say 1 G which now spans a larger linear code 1 C of length 5 n = , dimension 4 k = and size  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.13189/csit.2016.040201">doi:10.13189/csit.2016.040201</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zgvda4s7nnckjnh6pfjdcxqg2e">fatcat:zgvda4s7nnckjnh6pfjdcxqg2e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200801010906/http://www.hrpub.org/download/20160430/CSIT1-13505467.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/58/2b/582b04ffe824a7d116d7fe3bee98cf885f0d2c22.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.13189/csit.2016.040201"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

The Hausdorff dimension of graphs of prevalent continuous functions [article]

Jonathan M. Fraser, James T. Hyde
<span title="2011-04-12">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove that the Hausdorff dimension of the graph of a prevalent continuous function is 2.  ...  We also indicate how our results can be extended to the space of continuous functions on [0,1]^d for d ∈N and use this to obtain results on the 'horizon problem' for fractal surfaces.  ...  witness the prevalence of functions whose graph has Hausdorff dimension 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1104.2206v1">arXiv:1104.2206v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iz7no6cmgrchro23plsixdd5ky">fatcat:iz7no6cmgrchro23plsixdd5ky</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1104.2206/1104.2206.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d7/bf/d7bfe09e3b0ad66475fcf76abf7c368eefe6eb70.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1104.2206v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Connectivity-Based Localization of Large Scale Sensor Networks with Complex Shape

S. Lederer, Y. Wang, J. Gao
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2n2fyi4qgfa53mwrtarkk6ysnm" style="color: black;">IEEE INFOCOM 2008 - The 27th Conference on Computer Communications</a> </i> &nbsp;
A major challenge with respect to such networks is to figure out the correct network layout, i.e., avoid global flips where a part of the network folds on top of another.  ...  In comparison, previous connectivity-based localization algorithms such as multi-dimensional scaling and rubberband representation generate globally flipped or distorted localization results.  ...  In our case, when there is degeneracy theoretically we will have to embed in a space with dimension higher than 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/infocom.2008.130">doi:10.1109/infocom.2008.130</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/infocom/LedererWG08.html">dblp:conf/infocom/LedererWG08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sc2sso5gsrdabo5zo6mwzsem4q">fatcat:sc2sso5gsrdabo5zo6mwzsem4q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150620083633/http://www3.cs.stonybrook.edu/%7Ejgao/paper/layout-infocom08.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cb/96/cb96f0b1af6715e7bde0c1653860ad1a94e128f6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/infocom.2008.130"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
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