{"id":1067,"date":"2023-01-15T18:37:43","date_gmt":"2023-01-15T18:37:43","guid":{"rendered":"http:\/\/scandinavianbusiness.dk\/?p=1067"},"modified":"2023-01-15T19:18:43","modified_gmt":"2023-01-15T19:18:43","slug":"covid-beregning-foerte-til-loesning-paa-gammelt-datalogisk-problem","status":"publish","type":"post","link":"https:\/\/scandinavianbusiness.dk\/index.php\/2023\/01\/15\/covid-beregning-foerte-til-loesning-paa-gammelt-datalogisk-problem\/","title":{"rendered":"COVID-beregning f\u00f8rte til l\u00f8sning p\u00e5 gammelt datalogisk problem"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Matematiker fra K\u00f8benhavns Universitet ville regne p\u00e5 COVID-epidemien, men endte med at l\u00f8se et problem, som har drillet dataloger i \u00e5rtier.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"500\" height=\"25\" src=\"http:\/\/scandinavianbusiness.dk\/wp-content\/uploads\/2023\/01\/0.png\" alt=\"overs\u00e6ttelse svensk\" class=\"wp-image-999\" srcset=\"https:\/\/scandinavianbusiness.dk\/wp-content\/uploads\/2023\/01\/0.png 500w, https:\/\/scandinavianbusiness.dk\/wp-content\/uploads\/2023\/01\/0-300x15.png 300w, https:\/\/scandinavianbusiness.dk\/wp-content\/uploads\/2023\/01\/0-495x25.png 495w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/via.ritzau.dk\/data\/images\/00980\/21360e3b-ec7f-4c29-817a-2fa72ea8dda9-w_720.JPG\" alt=\"Joachim Kock\nLektor\nMatematisk Institut\nK\u00f8benhavns Universitet\"\/><figcaption class=\"wp-element-caption\">Joachim Kock Lektor Matematisk Institut K\u00f8benhavns Universitet<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Corona gjorde mange af os til hobby-matematikere. Hvor hurtigt ville antallet af indlagte p\u00e5 hospitalerne stige, og hvorn\u00e5r ville der indtr\u00e6de flok-immunitet? Ogs\u00e5 de professionelle matematikere blev udfordret. Endda s\u00e5 meget, at det har inspireret en forsker ved K\u00f8benhavns Universitet til at l\u00f8se et 30 \u00e5r gammelt datalogisk problem.&nbsp;<a href=\"https:\/\/dl.acm.org\/doi\/10.1145\/3559103\">Gennembruddet er netop udgivet&nbsp;i det prestigefyldte tidsskrift Journal of the ACM (Association for Computing Machinery).<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201dEgentlig ville jeg bare regne p\u00e5 COVID-epidemien lige som s\u00e5 mange andre. Jeg ville eksperimentere med nogle ideer fra teoretisk datalogi, men her viste det sig, at det gamle problem var en stopklods,\u201d siger Joachim Kock, lektor ved Matematisk Institut, K\u00f8benhavns Universitet.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">L\u00f8sningen p\u00e5 problemet kan f\u00e5 anvendelse inden for epidemiologien og datalogien, men potentielt ogs\u00e5 en lang r\u00e6kke andre fagomr\u00e5der. F\u00e6lles for disse omr\u00e5der er, at der optr\u00e6der systemer med mange forskellige komponenter, som indbyrdes har indflydelse p\u00e5 hinanden. For eksempel kan m\u00f8det mellem en rask person og en COVID-smittet f\u00f8re til, at der nu er to COVID-smittede.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Tysk teenager opfandt smart metode<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For at forst\u00e5 gennembruddet m\u00e5 man vide, at denne type komplekse systemer kan beskrives matematisk med s\u00e5kaldte Petri-net. Metoden blev opfundet i 1939 af tyske Carl Adam Petri (i \u00f8vrigt i en alder af blot 13 \u00e5r) til brug for kemi. Lige som m\u00f8det mellem en rask og en COVID-smittet kan f\u00f8re til en forandring, kan det samme ske, n\u00e5r to kemiske stoffer m\u00f8des og reagerer.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I et Petri-net tegnes de indg\u00e5ende komponenter som cirkler, mens begivenheder tegnes som firkanter. Cirkler og firkanter forbindes derefter med pile, der viser de indbyrdes sammenh\u00e6nge.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Dataloger ans\u00e5 problemet for ul\u00f8seligt<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I kemi anvendes Petri-net til at beskrive, hvordan koncentrationerne af forskellige kemiske stoffer udvikler sig i en blanding. Den tankegang har pr\u00e6get brugen af Petri-net i epidemiologi: man forestiller sig, at der i udgangspunktet er en h\u00f8j \u201dkoncentration\u201d af raske, hvorefter \u201dkoncentrationen\u201d af smittede begynder at stige. I datalogi bruges Petri-net p\u00e5 en lidt anden m\u00e5de: her drejer det sig om individer snarere end koncentrationer, og udviklingen er snarere trinvis end kontinuerlig.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Joachim Kocks id\u00e9 var at anvende de mere individ-baserede datalogiske Petri-net ogs\u00e5 til COVID-beregninger. Her l\u00f8b han imidlertid ind i det gamle datalogiske problem:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201dGrundl\u00e6ggende er der to forskellige tilgange til at beskrive processerne i et Petri-net. I den f\u00f8rste tilgang betragtes en proces som en lang serie af begivenheder. I den anden tilgang betragter man nettet som en grafisk fremstilling af sammenh\u00e6ngene mellem de forskellige komponenter og begivenheder,\u201d forklarer Joachim Kock og uddyber:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201dDen serielle tilgang er velegnet til udregninger. Men ulempen er, at den ikke beskriver \u00e5rsagssammenh\u00e6nge lige s\u00e5 godt som den grafiske tilgang. Den serielle tilgang har ogs\u00e5 sv\u00e6rt ved at beskrive begivenheder, der finder sted samtidig.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201dProblemet best\u00e5r i, at ingen har kunnet forene de to synspunkter. Datalogerne havde vel egentlig givet op, og betragtede n\u00e6rmest problemet som ul\u00f8seligt. Det skyldes, at ingen t\u00e6nkte p\u00e5, at man var n\u00f8dt til at g\u00e5 helt tilbage og revidere selve definitionen af Petri-net,\u201d siger Joachim Kock.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Lille justering med stor effekt<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Den danske matematikers opdagelse var, at en lille \u00e6ndring i definitionen af Petri-net faktisk muligg\u00f8r en l\u00f8sning af problemet:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201dVed at tillade parallelle pile i stedet for bare at t\u00e6lle dem og skrive et tal, er der pludselig en smule mere information tilg\u00e6ngelig. Tingene g\u00e5r op, og de to tilgange til at beskrive processerne kan forenes.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Den matematiske begrundelse for, at den ekstra information er vigtig, er indviklet, men kan anskueligg\u00f8res ved en analogi:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201dGennem menneskehedens historie har vi haft stor gavn af at s\u00e6tte tal p\u00e5 fysiske st\u00f8rrelser. For eksempel er det jo praktisk, at jeg p\u00e5 forh\u00e5nd kan finde det rigtige antal stole frem, n\u00e5r jeg venter g\u00e6ster til middag, i stedet for, at jeg skal pr\u00f8ve mig frem, n\u00e5r de har indfundet sig. Men antallet af stole og g\u00e6ster siger ikke noget om, hvem som skal sidde hvor. Information g\u00e5r tabt, n\u00e5r vi betragter tal i stedet for objekter.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P\u00e5 samme m\u00e5de g\u00e5r der information tabt, n\u00e5r de individuelle pile i Petri-nettet kun angives ved deres antal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201dTingene bliver en anelse mere besv\u00e6rlige, n\u00e5r man skal holde styr p\u00e5 de individuelle pile. Til geng\u00e6ld kan de to tilgange nu forenes, og deres fordele kan opn\u00e5s samtidigt.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ringen til COVID er sluttet<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">L\u00f8sningen af problemet g\u00f8r det muligt at beskrive komplekse systemer med mange indbyrdes sammenh\u00e6nge mere pr\u00e6cist. Joachim Kock forventer dog ikke, at opdagelsen vil f\u00e5 stor praktisk betydning for dataloger, som anvender Petri-net:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201dDet skyldes, at det er muligt at foretage den n\u00f8dvendige tilpasning uden at revidere hele teorien om Petri-net.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201dLidt overraskende er der nu nogle epidemiologer, som er begyndt at anvende de reviderede Petri-net. S\u00e5 man kan sige, at ringen er sluttet!\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Samtidig er der en morale i historien om den nye opdagelse, mener Joachim Kock:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201dMit \u00e6rinde var jo slet ikke at l\u00f8se et gammelt datalogisk problem, men at regne p\u00e5 COVID. Det svarer lidt til, at man leder efter sin kuglepen, men indser, at man nok skal starte med at finde sine briller. P\u00e5 den m\u00e5de vil jeg gerne sl\u00e5 et slag for vigtigheden af forskning, hvor man ikke har defineret p\u00e5 forh\u00e5nd, hvad man skal finde ud af. Det er nogle gange forskning, som er drevet af nysgerrighed, der giver banebrydende resultater.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Kilde: K\u00f8benhavns Universitet &#8211; Det Natur- og Biovidenskabelige Fakultet<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><\/h2>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Overs\u00e6ttelse til svensk<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Tag Scandinavian Office Solutions med ombord p\u00e5 din salgsrejse. Vi har leveret kvalitetsovers\u00e6ttelser siden 2011, og vi overs\u00e6tter gerne din webside, webshop, produktnyhed, opdatering til SoMe etc.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"mailto:scandinavianoffice@gmail.com\" target=\"_blank\" rel=\"noreferrer noopener\">Kontakt os<\/a> for et tilbud, du bliver glad for!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><a href=\"https:\/\/scandinavianoffice.net\/\" target=\"_blank\" rel=\"noreferrer noopener\">Scandinavian Office Solutions<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/scandinavianoffice.net\/oversaettelse-til-svensk\/\" target=\"_blank\" rel=\"noreferrer noopener\">Overs\u00e6ttelse til svensk<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>Matematiker fra K\u00f8benhavns Universitet ville regne p\u00e5 COVID-epidemien, men endte med at l\u00f8se et problem, som har drillet dataloger i \u00e5rtier. Corona gjorde mange af [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1067","post","type-post","status-publish","format-standard","hentry","category-generelle-nyheder"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>COVID-beregning f\u00f8rte til l\u00f8sning p\u00e5 gammelt datalogisk problem -<\/title>\n<meta name=\"description\" content=\"Matematiker fra K\u00f8benhavns Universitet ville regne p\u00e5 COVID-epidemien, men endte med at l\u00f8se et problem, som har drillet dataloger i \u00e5rtier.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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