Electronic Notes in Discrete Mathematics最新文献

{"title":"On characterizing the extreme points of the generalized transitive tournament polytope","authors":"Konstantinos Papalamprou","doi":"10.1016/j.endm.2018.06.047","DOIUrl":"10.1016/j.endm.2018.06.047","url":null,"abstract":"<div><p>A non-negative <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrix [<span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span>] is called generalized tournament, denoted GTT(n), if: <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>i</mi></mrow></msub><mo>=</mo><mn>0</mn></math></span> (for all i), <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi><mi>i</mi></mrow></msub><mo>=</mo><mn>1</mn></math></span> (for all(i,j) with <span><math><mi>i</mi><mo>≠</mo><mi>j</mi></math></span>) and <span><math><mn>1</mn><mo>≤</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi><mi>k</mi></mrow></msub><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>k</mi><mi>i</mi></mrow></msub><mo>≤</mo><mn>2</mn></math></span> (for all (i,j,k) with <span><math><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></math></span> pairwise distinct). In [9], using hypergraphs associated with GTT matrices, it has been shown that for <span><math><mi>n</mi><mo>≤</mo><mn>6</mn></math></span> all the vertices of the GTT(n) polytope are half-integral. In this work, we show that these matrices belong to the class of 2-regular matrices and highlight the related optimization implications. Finally, based on our approach and known partial results, conjectures on characterizing the extreme points of the GTT(n) polytope for <span><math><mi>n</mi><mo>≥</mo><mn>7</mn></math></span> are provided.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.047","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121136628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Autoparatopism stabilized colouring games on rook's graphs","authors":"Stephan Dominique Andres,&nbsp;Helena Bergold,&nbsp;Raúl M. Falcón","doi":"10.1016/j.endm.2018.06.040","DOIUrl":"10.1016/j.endm.2018.06.040","url":null,"abstract":"<div><p>We introduce the autoparatopism variant of the autotopism stabilized colouring game on the <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> rook's graph as a natural generalization of the latter so that each board configuration is uniquely related to a partial Latin square of order <em>n</em> that respects a given autoparatopism (<em>θ</em>; <em>π</em>). To this end, we distinguish between <span><math><mi>π</mi><mo>∈</mo><mo>{</mo><mrow><mi>Id</mi></mrow><mo>,</mo><mo>(</mo><mn>12</mn><mo>)</mo><mo>}</mo></math></span> and <span><math><mi>π</mi><mo>∈</mo><mo>{</mo><mo>(</mo><mn>13</mn><mo>)</mo><mo>,</mo><mo>(</mo><mn>23</mn><mo>)</mo><mo>,</mo><mo>(</mo><mn>123</mn><mo>)</mo><mo>,</mo><mo>(</mo><mn>132</mn><mo>)</mo><mo>}</mo></math></span>. The complexity of this variant is examined by means of the autoparatopism stabilized game chromatic number. Some illustrative examples and results are shown.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.040","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133425286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two-line graphs of partial Latin rectangles","authors":"Eiran Danan,&nbsp;Raúl M. Falcón,&nbsp;Dani Kotlar,&nbsp;Trent G. Marbach,&nbsp;Rebecca J. Stones","doi":"10.1016/j.endm.2018.06.010","DOIUrl":"10.1016/j.endm.2018.06.010","url":null,"abstract":"<div><p>Two-line graphs of a given partial Latin rectangle are introduced as vertex-and-edge-coloured bipartite graphs that give rise to new autotopism invariants. They reduce the complexity of any currently known method for computing autotopism groups of partial Latin rectangles.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133145514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The complete classification of empty lattice 4-simplices","authors":"Óscar Iglesias Valiño ,&nbsp;Francisco Santos","doi":"10.1016/j.endm.2018.06.027","DOIUrl":"https://doi.org/10.1016/j.endm.2018.06.027","url":null,"abstract":"<div><p>In previous work we classified all empty 4-simplices of width at least three. We here classify those of width two. There are 2 two-parameter families that project to the second dilation of a unimodular triangle, <span><math><mn>29</mn><mo>+</mo><mn>23</mn></math></span> one-parameter families of them that project to hollow 3-polytopes, and 2282 individual ones that do not.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.027","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138362561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extended Lagrange's four-square theorem","authors":"J. Lacalle,&nbsp;L.N. Gatti","doi":"10.1016/j.endm.2018.06.036","DOIUrl":"10.1016/j.endm.2018.06.036","url":null,"abstract":"<div><p>We prove the following extension of Lagrange's theorem: given a prime number <em>p</em> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>,</mo><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>3</mn></math></span>, such that <span><math><msup><mrow><mo>∥</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∥</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mi>p</mi></math></span> for all <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>k</mi></math></span> and <span><math><mo>〈</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>〉</mo><mo>=</mo><mn>0</mn></math></span> for all <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>&lt;</mo><mi>j</mi><mo>≤</mo><mi>k</mi></math></span>, then there exists <span><math><mi>v</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>)</mo><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> such that <span><math><mo>〈</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mi>v</mi><mo>〉</mo><mo>=</mo><mn>0</mn></math></span> for all <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>k</mi></math></span> and<span><span><span><math><mo>∥</mo><mi>v</mi><mo>∥</mo><mo>=</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mi>p</mi></math></span></span></span> This means that, in <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>, any system of orthogonal vectors of norm <em>p</em> can be completed to a base. We conjecture that the result holds for every norm <span><math><mi>p</mi><mo>≥</mo><mn>1</mn></math></span>.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134166636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An improvement of the lower bound on the maximum number of halving lines in planar sets with 32 points","authors":"Javier Rodrigo,&nbsp;Ma Dolores López","doi":"10.1016/j.endm.2018.06.052","DOIUrl":"10.1016/j.endm.2018.06.052","url":null,"abstract":"<div><p>In this paper we give a recursive lower bound on the maximum number of halving lines for sets in the plane and as a consequence we improve the current best lower bound on the maximum number of halving lines for sets in the plane with 32 points.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.052","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116093958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sums of finite subsets in Rd","authors":"Mario Huicochea","doi":"10.1016/j.endm.2018.06.012","DOIUrl":"10.1016/j.endm.2018.06.012","url":null,"abstract":"<div><p>Let <span><math><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> be nonempty finite subsets of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> with <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> not contained in an affine hyperplane for each <span><math><mi>i</mi><mo>∈</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>m</mi><mo>}</mo></math></span>. First we get a sharp lower bound on <span><math><mo>|</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>|</mo></math></span> when <span><math><mo>|</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>|</mo><mo>=</mo><mi>d</mi><mo>+</mo><mn>1</mn></math></span>. Using this result and other ideas, we find a nontrivial lower bound on <span><math><mo>|</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><mo>…</mo><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>|</mo></math></span> which generalizes a result of M. Matolcsi and I. Z. Ruzsa [7].</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113938794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Iterated Sumsets and Olson's Generalization of the Erdős-Ginzburg-Ziv Theorem","authors":"David J. Grynkiewicz","doi":"10.1016/j.endm.2018.06.006","DOIUrl":"10.1016/j.endm.2018.06.006","url":null,"abstract":"<div><p>Let <span><math><mi>G</mi><mo>≅</mo><mi>Z</mi><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>Z</mi><mo>×</mo><mo>…</mo><mo>×</mo><mi>Z</mi><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>r</mi></mrow></msub><mi>Z</mi></math></span> be a finite abelian group with <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>|</mo><mo>…</mo><mo>|</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>=</mo><mi>exp</mi><mo>⁡</mo><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. The Kemperman Structure Theorem characterizes all subsets <span><math><mi>A</mi><mo>,</mo><mi>B</mi><mo>⊆</mo><mi>G</mi></math></span> satisfying <span><math><mo>|</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>|</mo><mo>&lt;</mo><mo>|</mo><mi>A</mi><mo>|</mo><mo>+</mo><mo>|</mo><mi>B</mi><mo>|</mo></math></span> and has been extended to cover the case when <span><math><mo>|</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>|</mo><mo>≤</mo><mo>|</mo><mi>A</mi><mo>|</mo><mo>+</mo><mo>|</mo><mi>B</mi><mo>|</mo></math></span>. Utilizing these results, we provide a precise structural description of all finite subsets <span><math><mi>A</mi><mo>⊆</mo><mi>G</mi></math></span> with <span><math><mo>|</mo><mi>n</mi><mi>A</mi><mo>|</mo><mo>≤</mo><mo>(</mo><mo>|</mo><mi>A</mi><mo>|</mo><mo>+</mo><mn>1</mn><mo>)</mo><mi>n</mi><mo>−</mo><mn>3</mn></math></span> when <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span> (also when <em>G</em> is infinite), in which case many of the pathological possibilities from the case <span><math><mi>n</mi><mo>=</mo><mn>2</mn></math></span> vanish, particularly for large <span><math><mi>n</mi><mo>≥</mo><mi>exp</mi><mo>⁡</mo><mo>(</mo><mi>G</mi><mo>)</mo><mo>−</mo><mn>1</mn></math></span>. The structural description is combined with other arguments to generalize a subsequence sum result of Olson asserting that a sequence <em>S</em> of terms from <em>G</em> having length <span><math><mo>|</mo><mi>S</mi><mo>|</mo><mo>≥</mo><mn>2</mn><mo>|</mo><mi>G</mi><mo>|</mo><mo>−</mo><mn>1</mn></math></span> must either have every element of <em>G</em> representable as a sum of <span><math><mo>|</mo><mi>G</mi><mo>|</mo></math></span>-terms from <em>S</em> or else have all but <span><math><mo>|</mo><mi>G</mi><mo>/</mo><mi>H</mi><mo>|</mo><mo>−</mo><mn>2</mn></math></span> of its terms lying in a common <em>H</em>-coset for some <span><math><mi>H</mi><mo>≤</mo><mi>G</mi></math></span>. We show that the much weaker hypothesis <span><math><mo>|</mo><mi>S</mi><mo>|</mo><mo>≥</mo><mo>|</mo><mi>G</mi><mo>|</mo><mo>+</mo><mi>exp</mi><mo>⁡</mo><mo>(</mo><mi>G</mi><mo>)</mo></math></span> suffices to obtain a nearly identical conclusion, where for the case <em>H</em> is trivial we must allow all but <span><math><mo>|</mo><mi>G</mi><mo>/</mo><mi>H</mi><mo>|</mo><mo>−</mo><mn>1</mn></math></span> terms of <em>S</em> to be from the same <em>H</em>-coset. The bound on <span><math><mo>|</mo><mi>S</mi><mo>|</mo></math></span> is improved for sever","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123742548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Structure and Enumeration of K4-minor-free links and link diagrams","authors":"Juanjo Rué ,&nbsp;Dimitrios M. Thilikos ,&nbsp;Vasiliki Velona","doi":"10.1016/j.endm.2018.06.021","DOIUrl":"10.1016/j.endm.2018.06.021","url":null,"abstract":"<div><p>We study the class <span><math><mi>L</mi></math></span> of link types that admit a K₄-minor-free diagram, i.e., they can be projected on the plane so that the resulting graph does not contain any subdivision of K₄. We prove that <span><math><mi>L</mi></math></span> is the closure of a subclass of torus links under the operation of connected sum. Using this structural result, we enumerate <span><math><mi>L</mi></math></span> and subclasses of it, with respect to the minimal number of crossings or edges in a projection of <span><math><mi>L</mi><mo>∈</mo><mi>L</mi></math></span>. Further, we enumerate (both exactly and asymptotically) all connected K₄-minor-free link diagrams, all minimal connected K₄-minor-free link diagrams, and all K₄-minor-free diagrams of the unknot.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128307561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kirchhoff index of the connections of two networks by an edge","authors":"Silvia Gago","doi":"10.1016/j.endm.2018.06.049","DOIUrl":"10.1016/j.endm.2018.06.049","url":null,"abstract":"<div><p>In this work we compute the group inverse of the Laplacian of the connections of two networks by and edge in terms of the Laplacians of the original networks. Thus the effective resistances and Kirchhoff index of the new network can be derived from the Kirchhoff indexes of the original networks.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115070816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}