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Page 802 of Mathematical Reviews Vol. , Issue 90B [page]

<span title="">1990</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 order complexes on the 2-sphere.  ...  Theorem: The order complex of a poset P is a triangulation of the 2-sphere if and only if P is the face poset of a 2-connected plane graph.  ... 
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Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations

Hector Zenil, Narsis Kiani, Jesper Tegnér
<span title="2018-07-18">2018</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4d3elkqvznfzho6ki7a35bt47u" style="color: black;">Entropy</a> </i> &nbsp;
We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov–Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP  ...  We introduce a definition of algorithmic symmetry in the context of geometric and spatial complexity able to capture mathematical aspects of different objects using as a case study polyominoes and polyhedral  ...  Every convex polyhedron can be represented in the plane or on the surface of a sphere by a three-connected planar graph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e20070534">doi:10.3390/e20070534</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/33265623">pmid:33265623</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pmg65kxoabaqbadiarbiwzpr3m">fatcat:pmg65kxoabaqbadiarbiwzpr3m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190302074847/http://pdfs.semanticscholar.org/988b/d85ec386e1379a03d9d67cabd131292b23b1.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/98/8b/988bd85ec386e1379a03d9d67cabd131292b23b1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e20070534"> <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>

Page 5484 of Mathematical Reviews Vol. , Issue 98I [page]

<span title="">1998</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 authors show that this intuition is correct for |-sphere orders and false for k-sphere orders if k > 2.  ...  Furthermore it has the structure of a CW-complex.  ... 
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Characterization of Isospectral Graphs Using Graph Invariants and Derived Orthogonal Parameters

Krishnan Balasubramanian, Subhash C. Basak
<span title="">1998</span> <i title="American Chemical Society (ACS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/w5xmmnnx3ffvnj7c6ggs54ppje" style="color: black;">Journal of chemical information and computer sciences</a> </i> &nbsp;
Results show that lower order connectivity and information theoretic TIs suffer from a high degree of redundancy, whereas higher order indices can characterize the graphs reasonably well.  ...  On the other hand, PCs derived from the TIs had no redundancy for the set of isospectral graphs studied.  ...  This is contribution number 222 from the Center of Water and the Environment of the Natural Resources Research Institute.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1021/ci970052g">doi:10.1021/ci970052g</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/57kdpzss5rfgvb3qsih53gynxi">fatcat:57kdpzss5rfgvb3qsih53gynxi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812090033/http://www-eio.upc.edu/~nasini/Blog/Blog_MathematicalSociologyPapers/Characterization%20of%20Isospectral%20Graphs.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/8f/ed/8fed8643bcdac96706204a8d0642e384aa6d5abe.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1021/ci970052g"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acs.org </button> </a>

Boolean complexes and boolean numbers

Bridget Eileen Tenner
<span title="2010-01-01">2010</span> <i title="Centre pour la Communication Scientifique Directe (CCSD)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/aagtqr2vajamvduhte7kigeygi" style="color: black;">Discrete Mathematics &amp; Theoretical Computer Science</a> </i> &nbsp;
This simplicial poset defines the boolean complex for the group. In a Coxeter system of rank n, we show that the boolean complex is homotopy equivalent to a wedge of (n-1)-dimensional spheres.  ...  The Bruhat order gives a poset structure to any Coxeter group. The ideal of elements in this poset having boolean principal order ideals forms a simplicial poset.  ...  The boolean Complex arises from the (strong) Bruhat order on W .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.46298/dmtcs.2833">doi:10.46298/dmtcs.2833</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vmmrhedfb5dt3ixahvper4vb6y">fatcat:vmmrhedfb5dt3ixahvper4vb6y</a> </span>
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INFORMATION-THEORETIC CONCEPTS FOR THE ANALYSIS OF COMPLEX NETWORKS

Matthias Dehmer
<span title="2008-08-26">2008</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pcyo5wihbzcwxb7m76lyrd4tvu" style="color: black;">Applied Artificial Intelligence</a> </i> &nbsp;
In order to give a short overview on such methods, we now briefly outline the most important information-theoretic and statistical methods to characterize or compare network structures: Analysis of Complex  ...  The main contribution of this article is a method for determining the structural information content of graphs that is based on a tree decomposition.  ...  As an example, Figure 2 shows the j-spheres ðj ¼ 1; 2; 3Þ for a graph G 2 G UC .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/08839510802164101">doi:10.1080/08839510802164101</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h6e2vwy2bbbqdc7ls3fqp2t2ka">fatcat:h6e2vwy2bbbqdc7ls3fqp2t2ka</a> </span>
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On the Ehrenfeucht-Fraïssé game in theoretical computer science [chapter]

Wolfgang Thomas
<span title="">1993</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
These are concerned with the expressive power of first-order logic over graphs, formal languages definable in first-order logic, and modal logic over labelled transition systems.  ...  An introduction to (first-order) Ehrenfeucht-Fra~ss~ games is presented, al~.d three applications in theoretical computer science are discussed.  ...  By the Sphere Lemma and the Distributive Normal Form, any first-order formula is equivalent (over graphs of degree < d) to a boolean combination of statements "there are > k occurrences of spheres of type  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-56610-4_89">doi:10.1007/3-540-56610-4_89</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mjlu34stm5ewpktubjowlkn5jy">fatcat:mjlu34stm5ewpktubjowlkn5jy</a> </span>
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Page 3587 of Mathematical Reviews Vol. , Issue 2003e [page]

<span title="">2003</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;
Gora) Geometrical aspects of a relation ordering the field of complex numbers.  ...  The author considers a linear ordering < on the field of complex numbers, namely a ~ b if and only if either there is Re(a) < Re(d) or there holds Re(a) = Re(b) and Im(a) < Im(/).  ... 
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The Structural Information Content of Chemical Networks

Matthias Dehmer, Frank Emmert-Streib
<span title="2008-01-01">2008</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s64b2sxnwvhhfhtkiimyzjknxa" style="color: black;">Zeitschrift fur Naturforschung A-A Journal of Physical Sciences</a> </i> &nbsp;
We present an information-theoretic method to measure the structural information content of networks and apply it to chemical graphs.  ...  Further, we demonstrate that our measure reflects the essence of molecular branching meaningfully by determining the structural information content of some chemical graphs numerically.  ...  Acknowledgements We would like to thank the referees of this paper and Danail Bonchev for fruitful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/zna-2008-3-407">doi:10.1515/zna-2008-3-407</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/igzz3cdzvjdfrh4hcu2iovjhry">fatcat:igzz3cdzvjdfrh4hcu2iovjhry</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809152812/http://www.znaturforsch.com/s63a/s63a0155.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/c3/e6/c3e6a26ec1ac220a82c8468be486a17ee8868192.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/zna-2008-3-407"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> degruyter.com </button> </a>

Graph based topological analysis of tessellated surfaces

Tula Ram Ban, Dibakar Sen
<span title="">2003</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sl7g43a53farbgnszuvagjd5jm" style="color: black;">Proceedings of the eighth ACM symposium on Solid modeling and applications - SM &#39;03</a> </i> &nbsp;
In this paper a graph-based method is presented which not only characterizes topological classification of the tessellated surfaces but also simultaneously generates the substantial circles or generators  ...  The graph is then decomposed into its constituent loops and paths. Based on the type of edges present, the loops are classified into three types.  ...  In [9, 30] it is theoretically proved that the problem of topological equivalence could be reduced to a problem of graph isomorphism for general (nonmanifold) 2-complexes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/781606.781651">doi:10.1145/781606.781651</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/sma/BanS03.html">dblp:conf/sma/BanS03</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mxa2dzbzeffbpcbbuhjolza7cy">fatcat:mxa2dzbzeffbpcbbuhjolza7cy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705070921/http://eprints.iisc.ernet.in/278/1/p274-ban.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/63/01/63016f6cff78e32a0d529267137bcc26017d8f93.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/781606.781651"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

A Systematic Framework and Characterization of Influence-Based Network Centrality [article]

Wei Chen, Shang-Hua Teng, Hanrui Zhang
<span title="2018-10-23">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our framework systematically extends a family of classical graph-theoretical centrality formulations, including degree centrality, harmonic centrality, and their "sphere-of-influence" generalizations,  ...  Moreover, the uniqueness is fully determined by the centrality formulation on the class of layered graphs, which is derived from a beautiful algebraic structure of influence instances modeled by cascading  ...  The Shapley value of a player v measures the expected marginal contribution of v on the set of players ordered before v in a random order.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1810.09981v1">arXiv:1810.09981v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/254nvelngzajthjxgusulyufxi">fatcat:254nvelngzajthjxgusulyufxi</a> </span>
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Graph based topological analysis of tessellated surfaces

Tula Ram Ban, Dibakar Sen
<span title="">2003</span> <i title="ACM Press"> Proceedings of the eighth ACM symposium on Solid modeling and applications - SM &#39;03 </i> &nbsp;
In this paper a graph-based method is presented which not only characterizes topological classification of the tessellated surfaces but also simultaneously generates the substantial circles or generators  ...  The graph is then decomposed into its constituent loops and paths. Based on the type of edges present, the loops are classified into three types.  ...  In [9, 30] it is theoretically proved that the problem of topological equivalence could be reduced to a problem of graph isomorphism for general (nonmanifold) 2-complexes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/781650.781651">doi:10.1145/781650.781651</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uwwjrahewvdhlctwo6t64pcj5i">fatcat:uwwjrahewvdhlctwo6t64pcj5i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705070921/http://eprints.iisc.ernet.in/278/1/p274-ban.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/63/01/63016f6cff78e32a0d529267137bcc26017d8f93.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/781650.781651"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Let Δ be a Cohen-Macaulay complex [article]

Anders Björner
<span title="2014-11-08">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The characterization of Gorenstein* and homotopy Gorenstein* complexes and the relevance in that connection of the Poincar\'e conjecture is discussed.  ...  Another topic is combinatorial aspects of a recent result on the homotopy Cohen-Macaulayness of certain subsets of geometric lattices, motivated by questions in tropical geometry.  ...  Acknowledgment: The pen sketch on the title page is due to artist Berta Hansson.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1411.2165v1">arXiv:1411.2165v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yyxwk3bqnfdkxoprfph7uyf4gm">fatcat:yyxwk3bqnfdkxoprfph7uyf4gm</a> </span>
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High-Dimensional Spectral Feature Selection for 3D Object Recognition Based on Reeb Graphs [chapter]

Boyan Bonev, Francisco Escolano, Daniela Giorgi, Silvia Biasotti
<span title="">2010</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We show experimentally that a small change in the order of selection has a significant impact on the classification performance and we study the impact of the precision of the selection criterion.  ...  We extract spectral features from different Reeb graph representations and successfully deal with a multi-class problem. We use an information-theoretic filter for feature selection.  ...  Histograms are used in order to characterize the graph without dependence on the number and order of nodes. Only the complexity flow curve is not histogrammed, for the sake of order preservation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-14980-1_11">doi:10.1007/978-3-642-14980-1_11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zbjstcv2kzajxj7pntiy5zscpu">fatcat:zbjstcv2kzajxj7pntiy5zscpu</a> </span>
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Quantifying Free-volume Topology in Atomistic Structures Through a Combination of Voxelization and Graph Theory [article]

James Chapman, Nir Goldman
<span title="2021-11-11">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This scheme employs a three-stage workflow, by which spheres are iteratively grown inside of voxels, and ultimately converted to planar graphs, which are then characterized via a graph-based order parameter  ...  Validation of our methodology is performed on several sets of materials problems: (1) classification of unique free volumes in various crystal phases, (2) characterization of free volume defects in metals  ...  Acknowledgements This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract No. DE-AC52-07NA27344.  ... 
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