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Recently, this notion of distance has found several applications in Data Science and in Machine Learning. With the goal of aiding both the interpretability of dissimilarity measures computed through the Gromov\u2013Wasserstein distance and the assessment of the approximation quality of computational techniques designed to estimate the Gromov\u2013Wasserstein distance, we determine the precise value of a certain variant of the Gromov\u2013Wasserstein distance between unit spheres of different dimensions. Indeed, we consider a two-parameter family\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\{d_{{{\\text {GW}}}p,q}\\}_{p,q=1}^{\\infty }$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msubsup>\n                            <mml:mrow>\n                              <mml:mo>{<\/mml:mo>\n                              <mml:msub>\n                                <mml:mi>d<\/mml:mi>\n                                <mml:mrow>\n                                  <mml:mtext>GW<\/mml:mtext>\n                                  <mml:mi>p<\/mml:mi>\n                                  <mml:mo>,<\/mml:mo>\n                                  <mml:mi>q<\/mml:mi>\n                                <\/mml:mrow>\n                              <\/mml:msub>\n                              <mml:mo>}<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mrow>\n                              <mml:mi>p<\/mml:mi>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mi>q<\/mml:mi>\n                              <mml:mo>=<\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:mrow>\n                            <mml:mi>\u221e<\/mml:mi>\n                          <\/mml:msubsup>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    of Gromov\u2013Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific values of the parameters\n                    <jats:italic>p<\/jats:italic>\n                    and\n                    <jats:italic>q<\/jats:italic>\n                    and the metric of the underlying spaces, we are able to determine the exact value of the distance\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$d_{{{\\text {GW}}}4,2}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mi>d<\/mml:mi>\n                            <mml:mrow>\n                              <mml:mtext>GW<\/mml:mtext>\n                              <mml:mn>4<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    between all pairs of unit spheres of different dimensions endowed with their Euclidean distance and their uniform measure.\n                  <\/jats:p>","DOI":"10.1007\/s10208-024-09678-3","type":"journal-article","created":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T14:06:41Z","timestamp":1726495601000},"page":"75-130","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The Gromov\u2013Wasserstein Distance Between Spheres"],"prefix":"10.1007","volume":"26","author":[{"given":"Shreya","family":"Arya","sequence":"first","affiliation":[]},{"given":"Arnab","family":"Auddy","sequence":"additional","affiliation":[]},{"given":"Ranthony A.","family":"Clark","sequence":"additional","affiliation":[]},{"given":"Sunhyuk","family":"Lim","sequence":"additional","affiliation":[]},{"given":"Facundo","family":"M\u00e9moli","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"Packer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,9,16]]},"reference":[{"key":"9678_CR1","unstructured":"Henry Adams, Johnathan Bush, Nate Clause, Florian Frick, Mario G\u00f3mez, Michael Harrison, R\u00a0Amzi Jeffs, Evgeniya Lagoda, Sunhyuk Lim, and Facundo M\u00e9moli. 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