[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-216820-en":3,"doc-seo-216820-105":30,"detail-sidebar-cat-0-en-105":84},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},216820,2336474466712,"Quinn Holloway","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Enabling Multi-scale Science - Mathematical and Computational Modeling","Enabling Multi-scale Science frames how “scale” can be understood across spatial, temporal, and conceptual dimensions, linking biological central dogma and systems biology to data-intensive knowledge discovery. It outlines conceptual scales from replication and transcription through translation, progressing from molecular levels such as DNA, mRNA, proteins, and metabolites to organism-level analysis. A practical multi-scale HOWTO presents mathematical options (continuous, discrete, multidimensional) including wavelets, pyramids and resolution, and graphs, alongside computational methods and structures.","Enabling Multi-scale Science: Mathematical and Computational Modeling  \nRoberto M. Cesar-Jr  \nIME – USP  \n[http://www.ime.usp.br/~cesar/](http://www.ime.usp.br/~cesar/)  \neScience-USP  \nFAPESP – CNPq-Capes  \n© [Roberto.Cesar@vision.ime.usp.br](Roberto.Cesar@vision.ime.usp.br)  \nSummary  \n• Which “scale”?  \n• Multi-scale HOWTO  \n• Concluding remarks?  \n© [Roberto.Cesar@vision.ime.usp.br](Roberto.Cesar@vision.ime.usp.br)  \nWhich “scale”?  \n© [Roberto.Cesar@vision.ime.usp.br](Roberto.Cesar@vision.ime.usp.br)  \nWhich “scale”   \n…are we talking about?  \n•Spatial  \n•Temporal  \n•Conceptual •?  \n© [Roberto.Cesar@vision.ime.usp.br](Roberto.Cesar@vision.ime.usp.br)  \n© [Roberto.Cesar@vision.ime.usp.br](Roberto.Cesar@vision.ime.usp.br)  \n“scale”   \nWhich  \nSpatial scales  \nWhich “scale”   \nTemporal scales  \n© [Roberto.Cesar@vision.ime.usp.br](Roberto.Cesar@vision.ime.usp.br)  \nData-intensive knowledge discovery  \nCentral dogma of biology and  \nsystems biology: Conceptual scales  \nReplication Transcription Translation  \nDNA  \nGenomics  \nmRNA  \nTranscriptmics  \nProteins  \nProteomics  \nMetabolites  \nMetabolomics  \nOrganisms  \nVarious analysis  \nHeterogeneous, complex, distributed databases  \n© [Roberto.Cesar@vision.ime.usp.br](Roberto.Cesar@vision.ime.usp.br)  \nData-intensive knowledge discovery  \n Central dogma of biology and Replication Transcription Translation systems biology  \nDNA mRNA Proteins Metabolites Organisms  \nGenomics Transcriptmics Proteomics Metabolomics  \nSecond order conceptual scales  \n© [Roberto.Cesar@vision.ime.usp.br](Roberto.Cesar@vision.ime.usp.br)  \nMulti-scale HOWTO  \n© [Roberto.Cesar@vision.ime.usp.br](Roberto.Cesar@vision.ime.usp.br)  \nHOWTO  \n• Problems with or without inherent scales  \n• Mathematical approaches available (continuous, discrete, multidimensional):  \n–Wavelets  \n– Pyramids and Resolution  \n–Graphs  \n–  \n….  \n• Computational methods and structures  \n© [Roberto.Cesar@vision.ime.usp.br](Roberto.Cesar@vision.ime.usp.br)","cbCaiatMsodxPJE5","https://ap.wps.com/l/cbCaiatMsodxPJE5","pdf",1454560,1,19,"English","en",105,"# Which \"scale\"?\n## Spatial scales\n## Temporal scales\n## Conceptual scales\n# Multi-scale HOWTO\n## Mathematical approaches\n## Computational methods and structures","[{\"question\":\"What mathematical approaches are suggested for multi-scale problems?\",\"answer\":\"The document mentions mathematical approaches such as wavelets, pyramids and resolution, and graphs for problems with or without inherent scales.\"}]","Enabling Multi-scale Science - Mathematical and Computational Modeling | PDF",1788827864,48,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":79,"head_meta":81,"extra_data":83,"updated_unix":28},"enabling-multi-scale-science-mathematical-and-computational-modeling","",{"@graph":36,"@context":78},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/enabling-multi-scale-science-mathematical-and-computational-modeling/216820/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-09-11","2026-09-08",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72],{"name":73,"@type":74,"acceptedAnswer":75},"What mathematical approaches are suggested for multi-scale problems?","Question",{"text":76,"@type":77},"The document mentions mathematical approaches such as wavelets, pyramids and resolution, and graphs for problems with or without inherent scales.","Answer","https://schema.org",{"og:url":52,"og:type":80,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":82,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":85},[86,90,94,98,103,108,113,116,121,124,128],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":87,"show_sort_weight":88,"slug":89},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":91,"show_sort_weight":92,"slug":93},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Exam",70,"exam",{"id":99,"doc_module":4,"doc_module_name":46,"category_name":100,"show_sort_weight":101,"slug":102},5,"Comic",60,"comic",{"id":104,"doc_module":4,"doc_module_name":46,"category_name":105,"show_sort_weight":106,"slug":107},6,"Technology",50,"technology",{"id":109,"doc_module":4,"doc_module_name":46,"category_name":110,"show_sort_weight":111,"slug":112},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":114,"slug":115},30,"research-report",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},9,"Religion & Spirituality",20,"religion-spirituality",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":122,"show_sort_weight":119,"slug":123},"World Cup","world-cup",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":125,"slug":127},10,"Lifestyle","lifestyle",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":99,"slug":130},"General","general"]