{"id":4125,"date":"2023-05-15T18:02:15","date_gmt":"2023-05-15T18:02:15","guid":{"rendered":"https:\/\/isipta23.sipta.org\/?page_id=4125"},"modified":"2023-07-14T11:08:43","modified_gmt":"2023-07-14T11:08:43","slug":"long-alonso","status":"publish","type":"page","link":"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/","title":{"rendered":"Long Alonso"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"4125\" class=\"elementor elementor-4125\" data-elementor-post-type=\"page\">\n\t\t\t\t\t\t\t\t\t<section data-eae-particle=\"{\n  &quot;particles&quot;: {\n    &quot;number&quot;: {\n      &quot;value&quot;: 80,\n      &quot;density&quot;: {\n        &quot;enable&quot;: true,\n        &quot;value_area&quot;: 800\n      }\n    },\n    &quot;color&quot;: {\n      &quot;value&quot;: &quot;#ffffff&quot;\n    },\n    &quot;shape&quot;: {\n      &quot;type&quot;: &quot;circle&quot;,\n      &quot;stroke&quot;: {\n        &quot;width&quot;: 0,\n        &quot;color&quot;: &quot;#000000&quot;\n      },\n      &quot;polygon&quot;: {\n        &quot;nb_sides&quot;: 5\n      },\n      &quot;image&quot;: {\n        &quot;src&quot;: &quot;img\/github.svg&quot;,\n        &quot;width&quot;: 100,\n        &quot;height&quot;: 100\n      }\n    },\n    &quot;opacity&quot;: {\n      &quot;value&quot;: 0.5,\n      &quot;random&quot;: false,\n      &quot;anim&quot;: {\n        &quot;enable&quot;: false,\n        &quot;speed&quot;: 1,\n        &quot;opacity_min&quot;: 0.1,\n        &quot;sync&quot;: false\n      }\n    },\n    &quot;size&quot;: {\n      &quot;value&quot;: 3,\n      &quot;random&quot;: true,\n      &quot;anim&quot;: {\n        &quot;enable&quot;: false,\n        &quot;speed&quot;: 40,\n        &quot;size_min&quot;: 0.1,\n        &quot;sync&quot;: false\n      }\n    },\n    &quot;line_linked&quot;: {\n      &quot;enable&quot;: true,\n      &quot;distance&quot;: 150,\n      &quot;color&quot;: &quot;#ffffff&quot;,\n      &quot;opacity&quot;: 0.4,\n      &quot;width&quot;: 1\n    },\n    &quot;move&quot;: {\n      &quot;enable&quot;: true,\n      &quot;speed&quot;: 6,\n      &quot;direction&quot;: &quot;none&quot;,\n      &quot;random&quot;: false,\n      &quot;straight&quot;: false,\n      &quot;out_mode&quot;: &quot;out&quot;,\n      &quot;bounce&quot;: false,\n      &quot;attract&quot;: {\n        &quot;enable&quot;: false,\n        &quot;rotateX&quot;: 600,\n        &quot;rotateY&quot;: 1200\n      }\n    }\n  },\n  &quot;interactivity&quot;: {\n    &quot;detect_on&quot;: &quot;canvas&quot;,\n    &quot;events&quot;: {\n      &quot;onhover&quot;: {\n        &quot;enable&quot;: true,\n        &quot;mode&quot;: &quot;repulse&quot;\n      },\n      &quot;onclick&quot;: {\n        &quot;enable&quot;: true,\n        &quot;mode&quot;: &quot;push&quot;\n      },\n      &quot;resize&quot;: true\n    },\n    &quot;modes&quot;: {\n      &quot;grab&quot;: {\n        &quot;distance&quot;: 400,\n        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data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;shape_divider_bottom&quot;:&quot;wave-brush&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 283.5 27.8\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M283.5,9.7c0,0-7.3,4.3-14,4.6c-6.8,0.3-12.6,0-20.9-1.5c-11.3-2-33.1-10.1-44.7-5.7\ts-12.1,4.6-18,7.4c-6.6,3.2-20,9.6-36.6,9.3C131.6,23.5,99.5,7.2,86.3,8c-1.4,0.1-6.6,0.8-10.5,2c-3.8,1.2-9.4,3.8-17,4.7\tc-3.2,0.4-8.3,1.1-14.2,0.9c-1.5-0.1-6.3-0.4-12-1.6c-5.7-1.2-11-3.1-15.8-3.7C6.5,9.2,0,10.8,0,10.8V0h283.5V9.7z M260.8,11.3\tc-0.7-1-2-0.4-4.3-0.4c-2.3,0-6.1-1.2-5.8-1.1c0.3,0.1,3.1,1.5,6,1.9C259.7,12.2,261.4,12.3,260.8,11.3z 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d=\"M154.5,26.7c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC152.6,27.5,154.6,26.8,154.5,26.7z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M41.9,19.3c0,0,1.2-0.3,2.9-0.1c1.7,0.2,5.8,0.9,8.2,0.7c4.2-0.4,7.4-2.7,7-2.6\tc-0.4,0-4.3,2.2-8.6,1.9c-1.8-0.1-5.1-0.5-6.7-0.4S41.9,19.3,41.9,19.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M75.5,12.6c0.2,0.1,2-0.8,4.3-1.1c2.3-0.2,2.1-0.3,2.1-0.5c0-0.1-1.8-0.4-3.4,0\tC76.9,11.5,75.3,12.5,75.5,12.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M15.6,13.2c0-0.1,4.3,0,6.7,0.5c2.4,0.5,5,1.9,5,2c0,0.1-2.7-0.8-5.1-1.4\tC19.9,13.7,15.7,13.3,15.6,13.2z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b1b1d02\" data-id=\"b1b1d02\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cd1ef36 elementor-widget elementor-widget-image\" data-id=\"cd1ef36\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.16.0 - 20-09-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"128\" src=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-1024x128.png\" class=\"attachment-large size-large wp-image-546\" alt=\"LogoISIPTA23-long-white\" srcset=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-1024x128.png 1024w, https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-300x38.png 300w, https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-768x96.png 768w, https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white.png 1284w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-017a3c3 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"017a3c3\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.16.0 - 20-09-2023 *\/\n.elementor-widget-divider{--divider-border-style:none;--divider-border-width:1px;--divider-color:#0c0d0e;--divider-icon-size:20px;--divider-element-spacing:10px;--divider-pattern-height:24px;--divider-pattern-size:20px;--divider-pattern-url:none;--divider-pattern-repeat:repeat-x}.elementor-widget-divider .elementor-divider{display:flex}.elementor-widget-divider .elementor-divider__text{font-size:15px;line-height:1;max-width:95%}.elementor-widget-divider .elementor-divider__element{margin:0 var(--divider-element-spacing);flex-shrink:0}.elementor-widget-divider .elementor-icon{font-size:var(--divider-icon-size)}.elementor-widget-divider .elementor-divider-separator{display:flex;margin:0;direction:ltr}.elementor-widget-divider--view-line_icon .elementor-divider-separator,.elementor-widget-divider--view-line_text .elementor-divider-separator{align-items:center}.elementor-widget-divider--view-line_icon .elementor-divider-separator:after,.elementor-widget-divider--view-line_icon 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.elementor-divider__element{margin-right:0}.elementor-widget-divider:not(.elementor-widget-divider--view-line_text):not(.elementor-widget-divider--view-line_icon) .elementor-divider-separator{border-top:var(--divider-border-width) var(--divider-border-style) var(--divider-color)}.elementor-widget-divider--separator-type-pattern{--divider-border-style:none}.elementor-widget-divider--separator-type-pattern.elementor-widget-divider--view-line .elementor-divider-separator,.elementor-widget-divider--separator-type-pattern:not(.elementor-widget-divider--view-line) .elementor-divider-separator:after,.elementor-widget-divider--separator-type-pattern:not(.elementor-widget-divider--view-line) .elementor-divider-separator:before,.elementor-widget-divider--separator-type-pattern:not([class*=elementor-widget-divider--view]) .elementor-divider-separator{width:100%;min-height:var(--divider-pattern-height);-webkit-mask-size:var(--divider-pattern-size) 100%;mask-size:var(--divider-pattern-size) 100%;-webkit-mask-repeat:var(--divider-pattern-repeat);mask-repeat:var(--divider-pattern-repeat);background-color:var(--divider-color);-webkit-mask-image:var(--divider-pattern-url);mask-image:var(--divider-pattern-url)}.elementor-widget-divider--no-spacing{--divider-pattern-size:auto}.elementor-widget-divider--bg-round{--divider-pattern-repeat:round}.rtl .elementor-widget-divider .elementor-divider__text{direction:rtl}.e-con-inner>.elementor-widget-divider,.e-con>.elementor-widget-divider{width:var(--container-widget-width,100%);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9adf215 elementor-widget elementor-widget-heading\" data-id=\"9adf215\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.16.0 - 20-09-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Alonso de la Fuente and Ter\u00e1n<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-18464be elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"18464be\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1257321\" data-id=\"1257321\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e9ad79c elementor-widget elementor-widget-text-editor\" data-id=\"e9ad79c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.16.0 - 20-09-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<a class=\"boton-volver\" href=\"javascript:history.back()\">\u2aa1 Back<\/a>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-99180d5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"99180d5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1cf27c4\" data-id=\"1cf27c4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-63d4f60 elementor-widget elementor-widget-heading\" data-id=\"63d4f60\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Sets of probability measures and convex combination spaces<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-56b42ba elementor-widget elementor-widget-heading\" data-id=\"56b42ba\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<span class=\"elementor-heading-title elementor-size-default\">The Wasserstein distances between probability distributions are an important tool in modern probability theory which has been generalized to sets of probability distributions. We will show that the (generalized) <span class=\"katex-eq\" data-katex-display=\"false\">L^1<\/span>-Wasserstein metric, with the operations of convolution and rescaling, fits in the abstract framework of convex combination spaces: nonlinear metric spaces preserving some of the nice properties of a normed space but accomodating other unusual behaviours. For instance, unlike in a linear space, a singleton <span class=\"katex-eq\" data-katex-display=\"false\">\\{P\\}<\/span> is typically not convex (it is so only if <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> is degenerate). Also, some theorems for convex combination spaces are applied to this setting.<\/span>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-813bbd0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"813bbd0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-960fdb8\" data-id=\"960fdb8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-df07f7d oew-align-center elementor-widget elementor-widget-oew-button-effects\" data-id=\"df07f7d\" data-element_type=\"widget\" data-widget_type=\"oew-button-effects.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\r\n\r\n\t\t<div class=\"oew-button oew-btn-effect-30\">\r\n\t\t\t<a href=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2023\/06\/alonsodelafuente23a.pdf\" class=\"oew-link\">\r\n\t\t\t\t\r\n\t\t\t\t<span>PAPER<\/span>\r\n\r\n\t\t\t\t\t\t\t<\/a>\r\n\t\t<\/div>\r\n\r\n\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5b5f4e9\" data-id=\"5b5f4e9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b0fb290 oew-align-center elementor-widget elementor-widget-oew-button-effects\" data-id=\"b0fb290\" data-element_type=\"widget\" data-widget_type=\"oew-button-effects.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\r\n\r\n\t\t<div class=\"oew-button oew-btn-effect-30\">\r\n\t\t\t<a href=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2023\/07\/2Alonso.pdf\" class=\"oew-link\">\r\n\t\t\t\t\r\n\t\t\t\t<span>PRESENTATION<\/span>\r\n\r\n\t\t\t\t\t\t\t<\/a>\r\n\t\t<\/div>\r\n\r\n\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c617d82\" data-id=\"c617d82\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0aeed9c oew-align-center elementor-widget elementor-widget-oew-button-effects\" data-id=\"0aeed9c\" data-element_type=\"widget\" data-widget_type=\"oew-button-effects.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\r\n\r\n\t\t<div class=\"oew-button oew-btn-effect-30\">\r\n\t\t\t<a href=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2023\/07\/alonso-poster.pdf\" class=\"oew-link\">\r\n\t\t\t\t\r\n\t\t\t\t<span>POSTER<\/span>\r\n\r\n\t\t\t\t\t\t\t<\/a>\r\n\t\t<\/div>\r\n\r\n\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-dd2b88d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"dd2b88d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e2b8390\" data-id=\"e2b8390\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e9aa4b4 elementor-widget elementor-widget-text-editor\" data-id=\"e9aa4b4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<a class=\"boton-volver\" href=\"javascript:history.back()\">\u2aa1 Back<\/a>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Alonso de la Fuente and Ter\u00e1n \u2aa1 Back Sets of probability measures and convex combination spaces The Wasserstein distances between probability distributions are an important tool in modern probability theory which has been generalized to sets of probability distributions. We will show that the (generalized) -Wasserstein metric, with the operations of convolution and rescaling, fits [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3821,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"footnotes":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Long Alonso - ISIPTA 2023<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Long Alonso - ISIPTA 2023\" \/>\n<meta property=\"og:description\" content=\"Alonso de la Fuente and Ter\u00e1n \u2aa1 Back Sets of probability measures and convex combination spaces The Wasserstein distances between probability distributions are an important tool in modern probability theory which has been generalized to sets of probability distributions. We will show that the (generalized) -Wasserstein metric, with the operations of convolution and rescaling, fits [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/\" \/>\n<meta property=\"og:site_name\" content=\"ISIPTA 2023\" \/>\n<meta property=\"article:modified_time\" content=\"2023-07-14T11:08:43+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-1024x128.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/\",\"url\":\"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/\",\"name\":\"Long Alonso - ISIPTA 2023\",\"isPartOf\":{\"@id\":\"https:\/\/isipta23.sipta.org\/#website\"},\"datePublished\":\"2023-05-15T18:02:15+00:00\",\"dateModified\":\"2023-07-14T11:08:43+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/#breadcrumb\"},\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/isipta23.sipta.org\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Accepted Papers\",\"item\":\"https:\/\/isipta23.sipta.org\/accepted-papers\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Long Alonso\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/isipta23.sipta.org\/#website\",\"url\":\"https:\/\/isipta23.sipta.org\/\",\"name\":\"ISIPTA 2023\",\"description\":\"The International Symposium on Imprecise Probabilities\",\"publisher\":{\"@id\":\"https:\/\/isipta23.sipta.org\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/isipta23.sipta.org\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-GB\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/isipta23.sipta.org\/#organization\",\"name\":\"ISIPTA 2023\",\"url\":\"https:\/\/isipta23.sipta.org\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\/\/isipta23.sipta.org\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/cropped-LogoISIPTA23-white.png\",\"contentUrl\":\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/cropped-LogoISIPTA23-white.png\",\"width\":500,\"height\":500,\"caption\":\"ISIPTA 2023\"},\"image\":{\"@id\":\"https:\/\/isipta23.sipta.org\/#\/schema\/logo\/image\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Long Alonso - ISIPTA 2023","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/","og_locale":"en_GB","og_type":"article","og_title":"Long Alonso - ISIPTA 2023","og_description":"Alonso de la Fuente and Ter\u00e1n \u2aa1 Back Sets of probability measures and convex combination spaces The Wasserstein distances between probability distributions are an important tool in modern probability theory which has been generalized to sets of probability distributions. We will show that the (generalized) -Wasserstein metric, with the operations of convolution and rescaling, fits [&hellip;]","og_url":"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/","og_site_name":"ISIPTA 2023","article_modified_time":"2023-07-14T11:08:43+00:00","og_image":[{"url":"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-1024x128.png"}],"twitter_card":"summary_large_image","twitter_misc":{"Estimated reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/","url":"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/","name":"Long Alonso - ISIPTA 2023","isPartOf":{"@id":"https:\/\/isipta23.sipta.org\/#website"},"datePublished":"2023-05-15T18:02:15+00:00","dateModified":"2023-07-14T11:08:43+00:00","breadcrumb":{"@id":"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/isipta23.sipta.org\/accepted-papers\/long-alonso\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/isipta23.sipta.org\/"},{"@type":"ListItem","position":2,"name":"Accepted Papers","item":"https:\/\/isipta23.sipta.org\/accepted-papers\/"},{"@type":"ListItem","position":3,"name":"Long Alonso"}]},{"@type":"WebSite","@id":"https:\/\/isipta23.sipta.org\/#website","url":"https:\/\/isipta23.sipta.org\/","name":"ISIPTA 2023","description":"The International Symposium on Imprecise Probabilities","publisher":{"@id":"https:\/\/isipta23.sipta.org\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/isipta23.sipta.org\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-GB"},{"@type":"Organization","@id":"https:\/\/isipta23.sipta.org\/#organization","name":"ISIPTA 2023","url":"https:\/\/isipta23.sipta.org\/","logo":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/isipta23.sipta.org\/#\/schema\/logo\/image\/","url":"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/cropped-LogoISIPTA23-white.png","contentUrl":"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/cropped-LogoISIPTA23-white.png","width":500,"height":500,"caption":"ISIPTA 2023"},"image":{"@id":"https:\/\/isipta23.sipta.org\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/pages\/4125"}],"collection":[{"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/comments?post=4125"}],"version-history":[{"count":30,"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/pages\/4125\/revisions"}],"predecessor-version":[{"id":6991,"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/pages\/4125\/revisions\/6991"}],"up":[{"embeddable":true,"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/pages\/3821"}],"wp:attachment":[{"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/media?parent=4125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}