Understanding cell diversity: many types, many states for each type. Applications: cancer mutations, dynamic of adaptation, development, … Tissue Dissociation isolation RNA Amplification Sequencing … RNA: expression of the DNA. <latexit sha1_base64="v4HVUJlrkr1NIl1MUAlx55L31yI=">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</latexit> d ⇠ 104
Understanding cell diversity: many types, many states for each type. Applications: cancer mutations, dynamic of adaptation, development, … Tissue Dissociation isolation RNA Amplification Sequencing … RNA: expression of the DNA. <latexit 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d ⇠ 104 <latexit 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d ⇠ 105 <latexit 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d ⇠ 105 <latexit 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d ⇠ 102 ATAC: chromatine accessibility Methylation: presence of methyl groups Proteome: presence of proteins geometry of DNA cause of differential expression result of expression
Understanding cell diversity: many types, many states for each type. Applications: cancer mutations, dynamic of adaptation, development, … Tissue Dissociation isolation RNA Amplification Sequencing … 10X Multiome (RNA + ATAC) CITE-seq (RNA + proteines) Paired multi-omics: Un-paired multi-omics: next frontier … RNA: expression of the DNA. <latexit 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d ⇠ 104 <latexit 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d ⇠ 105 <latexit 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d ⇠ 105 <latexit 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d ⇠ 102 ATAC: chromatine accessibility Methylation: presence of methyl groups Proteome: presence of proteins geometry of DNA cause of differential expression result of expression
cells (bulk omics) ay, we can measure omics at the single cell level1. 2 2018 2Lähnemann et al. 2020 Single-cell profiling uncovers cellular heterogeneity • Until recently, samples contained many cells (bulk omics) • Today, we can measure omics at the single cell level1. 2 1Mincarelli et al. 2018 2Lähnemann et al. 2020 <latexit sha1_base64="8h9qfn6MXuBvKOcg4p0NkYUZouc=">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</latexit> Bulk <latexit sha1_base64="xfWO8cpwoNz5R1B8gV9utdLBqVI=">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</latexit> Single cell
cells (bulk omics) ay, we can measure omics at the single cell level1. 2 2018 2Lähnemann et al. 2020 Single-cell profiling uncovers cellular heterogeneity • Until recently, samples contained many cells (bulk omics) • Today, we can measure omics at the single cell level1. 2 1Mincarelli et al. 2018 2Lähnemann et al. 2020 <latexit sha1_base64="8h9qfn6MXuBvKOcg4p0NkYUZouc=">AAACx3icjVHLTsJAFD3UF+ILdemmkZi4Ii0x6pLgRneYCJIgMe0wwITSNu2USIgLf8Ct/pnxD/QvvDMOiUqMTtP2zLn3nJl7rx8HIpWO85qzFhaXllfyq4W19Y3NreL2TjONsoTxBouCKGn5XsoDEfKGFDLgrTjh3sgP+LU/PFPx6zFPUhGFV3IS887I64eiJ5gnFVXLguFtseSUHb3seeAaUIJZ9aj4ght0EYEhwwgcISThAB5Setpw4SAmroMpcQkhoeMc9yiQNqMsThkesUP69mnXNmxIe+WZajWjUwJ6E1LaOCBNRHkJYXWareOZdlbsb95T7anuNqG/b7xGxEoMiP1LN8v8r07VItHDqa5BUE2xZlR1zLhkuivq5vaXqiQ5xMQp3KV4Qphp5azPttakunbVW0/H33SmYtWemdwM7+qWNGD35zjnQbNSdo/LR5eVUrVmRp3HHvZxSPM8QRXnqKNB3gM84gnP1oUVWWPr7jPVyhnNLr4t6+EDdTmQuA==</latexit> Bulk <latexit sha1_base64="xfWO8cpwoNz5R1B8gV9utdLBqVI=">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</latexit> Single cell <latexit sha1_base64="pydPpuNuJAJzk3J9ohxA5exGGlo=">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</latexit> ? <latexit sha1_base64="QNHLtJL77Xel7kqDwcr8uqkXoFI=">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</latexit> Cluster cells from a single biopsy. <latexit sha1_base64="NAYrO+hblycchNy+rUEIB63nwtY=">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</latexit> “Distance” between cells? <latexit sha1_base64="yFN6xhMLWSFTo6y4Ic3WSee5g64=">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</latexit> OT on genes’ space. <latexit sha1_base64="pydPpuNuJAJzk3J9ohxA5exGGlo=">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</latexit> ?
cells (bulk omics) ay, we can measure omics at the single cell level1. 2 2018 2Lähnemann et al. 2020 Single-cell profiling uncovers cellular heterogeneity • Until recently, samples contained many cells (bulk omics) • Today, we can measure omics at the single cell level1. 2 1Mincarelli et al. 2018 2Lähnemann et al. 2020 <latexit sha1_base64="8h9qfn6MXuBvKOcg4p0NkYUZouc=">AAACx3icjVHLTsJAFD3UF+ILdemmkZi4Ii0x6pLgRneYCJIgMe0wwITSNu2USIgLf8Ct/pnxD/QvvDMOiUqMTtP2zLn3nJl7rx8HIpWO85qzFhaXllfyq4W19Y3NreL2TjONsoTxBouCKGn5XsoDEfKGFDLgrTjh3sgP+LU/PFPx6zFPUhGFV3IS887I64eiJ5gnFVXLguFtseSUHb3seeAaUIJZ9aj4ght0EYEhwwgcISThAB5Setpw4SAmroMpcQkhoeMc9yiQNqMsThkesUP69mnXNmxIe+WZajWjUwJ6E1LaOCBNRHkJYXWareOZdlbsb95T7anuNqG/b7xGxEoMiP1LN8v8r07VItHDqa5BUE2xZlR1zLhkuivq5vaXqiQ5xMQp3KV4Qphp5azPttakunbVW0/H33SmYtWemdwM7+qWNGD35zjnQbNSdo/LR5eVUrVmRp3HHvZxSPM8QRXnqKNB3gM84gnP1oUVWWPr7jPVyhnNLr4t6+EDdTmQuA==</latexit> Bulk <latexit sha1_base64="xfWO8cpwoNz5R1B8gV9utdLBqVI=">AAACznicjVHLSsNAFD2Nr1pfVZdugkVwVZIi6rLoxmVF+4BaJJlO69BpEpJJoZTi1h9wq58l/oH+hXfGFNQiOiHJmXPPuTP3Xj+SIlGO85qzFhaXllfyq4W19Y3NreL2TiMJ05jxOgtlGLd8L+FSBLyuhJK8FcXcG/qSN/3BuY43RzxORBhcq3HEO0OvH4ieYJ4iqn0lgr7kNuNS3hZLTtkxy54HbgZKyFYtLL7gBl2EYEgxBEcARVjCQ0JPGy4cRMR1MCEuJiRMnGOKAnlTUnFSeMQO6NunXTtjA9rrnIlxMzpF0huT08YBeULSxYT1abaJpyazZn/LPTE59d3G9PezXENiFe6I/cs3U/7Xp2tR6OHU1CCopsgwujqWZUlNV/TN7S9VKcoQEadxl+IxYWacsz7bxpOY2nVvPRN/M0rN6j3LtCne9S1pwO7Pcc6DRqXsHpePLiul6lk26jz2sI9DmucJqrhADXXT8Uc84dmqWSNrat1/Sq1c5tnFt2U9fACwKpOS</latexit> Single cell <latexit sha1_base64="pydPpuNuJAJzk3J9ohxA5exGGlo=">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</latexit> ? <latexit sha1_base64="QNHLtJL77Xel7kqDwcr8uqkXoFI=">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</latexit> Cluster cells from a single biopsy. <latexit sha1_base64="NAYrO+hblycchNy+rUEIB63nwtY=">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</latexit> “Distance” between cells? <latexit sha1_base64="yFN6xhMLWSFTo6y4Ic3WSee5g64=">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</latexit> OT on genes’ space. <latexit sha1_base64="c8Nzu7i/2HdZbRFNoq24LWiMXCg=">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</latexit> Match cells between two biopsies. <latexit sha1_base64="smAhPpTgHUrzBKRMXffs73pgv0w=">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</latexit> OT on cells’ space. <latexit sha1_base64="pydPpuNuJAJzk3J9ohxA5exGGlo=">AAACyHicjVHLSsNAFD2Nr1pfVZdugkVwVZIi6s6iG3FVwbSFtkgyndaheZFMlFLc+ANu9cvEP9C/8M6YglpEJyQ5c+49Z+be68W+SKVlvRaMufmFxaXicmlldW19o7y51UyjLGHcYZEfJW3PTbkvQu5IIX3ejhPuBp7PW97oTMVbtzxJRRReyXHMe4E7DMVAMFcS5XS9gXlyXa5YVUsvcxbYOaggX42o/IIu+ojAkCEARwhJ2IeLlJ4ObFiIiethQlxCSOg4xz1KpM0oi1OGS+yIvkPadXI2pL3yTLWa0Sk+vQkpTeyRJqK8hLA6zdTxTDsr9jfvifZUdxvT38u9AmIlboj9SzfN/K9O1SIxwLGuQVBNsWZUdSx3yXRX1M3NL1VJcoiJU7hP8YQw08ppn02tSXXtqreujr/pTMWqPctzM7yrW9KA7Z/jnAXNWtU+rB5c1ir103zURexgF/s0zyPUcY4GHPIWeMQTno0LIzbujPFnqlHINdv4toyHD4JFkLc=</latexit> ?
(ATAC) <latexit 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wk <latexit 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⇡ <latexit 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⇥ <latexit 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a(ATAC) k <latexit 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a(RNA) k <latexit 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⇡ <latexit 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H (RNA) <latexit 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(wk)k > 0 <latexit 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min (H( )) >0 X X k W d (H ( ) wk, a ( ) k )
(ATAC) <latexit sha1_base64="MZfrebrKqsnYft3Y6+M09BPaIdo=">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</latexit> wk <latexit 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⇡ <latexit 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⇥ <latexit 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a(ATAC) k <latexit 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a(RNA) k <latexit 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⇡ <latexit 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H (RNA) <latexit 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clustering <latexit 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(wk)k > 0 <latexit 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min (H( )) >0 X X k W d (H ( ) wk, a ( ) k )
(ATAC) <latexit sha1_base64="MZfrebrKqsnYft3Y6+M09BPaIdo=">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</latexit> wk <latexit 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⇡ <latexit 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⇥ <latexit 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a(ATAC) k <latexit 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a(RNA) k <latexit 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⇡ <latexit 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H (RNA) <latexit 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clustering <latexit 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Gene set <latexit 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enrichment <latexit 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(wk)k > 0 <latexit 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min (H( )) >0 X X k W d (H ( ) wk, a ( ) k )
1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring of cor- ds that metric ransfer mind, at opti- ective. rtation, able to ix. We rgence tasks. frame- stance on, and Source Targets Figure 1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring <latexit 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Y <latexit 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Y <latexit 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?
1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring of cor- ds that metric ransfer mind, at opti- ective. rtation, able to ix. We rgence tasks. frame- stance on, and Source Targets Figure 1: Entropic GW can find correspondences between a source surface (left) and a surface with similar structure, a surface with shared semantic structure, a noisy 3D point cloud, an icon, and a hand drawing. Each fuzzy map was computed using the same code. In this paper, we propose a new correspondence algorithm that minimizes distortion of long- and short-range distances alike. We study an entropically-regularized version of the Gromov-Wasserstein (GW) mapping objective function from [M´ emoli 2011] measuring <latexit 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Y <latexit 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Y <latexit 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Y <latexit 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? <latexit 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[Demetci et al 2020] <latexit 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Single-cell <latexit 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multi-omics: <latexit 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ATAC-seq <latexit 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RNA-seq <latexit 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X <latexit 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Y <latexit sha1_base64="8H4xN4xGPG5ztU4N+maxzHTbjXo=">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</latexit> dim ⇠ 103(genes) <latexit sha1_base64="NRLid9ocOcEHNQq7hjUXkZi7pNg=">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</latexit> dim ⇠ 102(peaks)