Algoritmos de classifica\303\247\303\243o da p\303\241gina na InternetMichael Monagan
Departamento de Matem\303\241ticaUniversidade Simon Frasermmonagan@sfu.caNo outono de 2014, Cedric Chauve, um colega meu em matem\303\241tica na SFU me mostrou como o Google classifica as p\303\241ginas que ele apresenta quando voc\303\252 usa o google para pesquisar uma p\303\241gina na internet. Cedric est\303\241 usando este exemplo no ensino de nossa aula de \303\201lgebra Linear na SFU. Ele e outros dois que ensinaramo curso acha que este \303\251 um exemplo t\303\243o maravilhoso que decidimos inclu\303\255-lo em todos os nossos Cursos de \303\241lgebra linear. Tamb\303\251m o usei no ensino de computa\303\247\303\243o MACM 204 com c\303\241lculo, umsegundo ano para ensinar aos alunos como usar o Maple para fazer c\303\241lculos. MACM 204 \303\251 um cr\303\251dito de 2curso com uma hora de aula e uma hora de laborat\303\263rio por semana. Neste curso, diferentemente da \303\241lgebra linear curso, fa\303\247o com que os alunos simulem o "internauta" descrito abaixo. Isso requer alguma programa\303\247\303\243o por parte do aluno. O problema \303\251 bom porque introduz alguma teoria de grafos,matrizes estoc\303\241sticas e algumas id\303\251ias da computa\303\247\303\243o, usando o m\303\251todo de pot\303\252ncia para calcular umavetor de estado estacion\303\241rio.O Problema de Classifica\303\247\303\243o da P\303\241gina.Suponha que voc\303\252 digite "Elimina\303\247\303\243o Gaussiana" ou "Como fatorar um polin\303\264mio" no Google. Google vaiprimeiro identifique quais p\303\241ginas da internet s\303\243o de interesse. Vamos rotular essas p\303\241ginas 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 e denote esse conjunto de p\303\241ginas por P. Geralmente haver\303\241 muitas p\303\241ginas poss\303\255veis, milhares delas, talvezcentenas de milhares deles, ent\303\243o N \303\251 grande. Como o Google os ordena de provavelmente \303\272teis paramenos prov\303\241vel \303\272til? E se voc\303\252 clicar no Estou me sentindo com sorte bot\303\243o de pesquisa, como o Google escolhe a melhor p\303\241gina para lhe mostrar? A resposta (ignorando enfeites) \303\251 que ele usa os hiperlinks entre as p\303\241ginas 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 para classific\303\241-los. Vamosconsidere um exemplo.
Suponha que tenhamos cinco p\303\241ginas 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 e suponha que haja hiperlinks da p\303\241gina
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1ElODE5MEYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSU4MTg5RictRiM2Ji1JI21uR0YkNidRIjFGJ0Y1L0Y5USdub3JtYWxGJ0Y7Rj5GMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1Rkc= para p\303\241ginas 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 e
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1ElODE5MEYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSU4MTg5RictRiM2Ji1JI21uR0YkNidRIjJGJ0Y1L0Y5USdub3JtYWxGJ0Y7Rj5GMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1Rkc= para p\303\241ginas 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
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1ElODE5MEYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSU4MTg5RictRiM2Ji1JI21uR0YkNidRIjNGJ0Y1L0Y5USdub3JtYWxGJ0Y7Rj5GMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1Rkc= para p\303\241ginas 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 e
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1ElODE5MEYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSU4MTg5RictRiM2Ji1JI21uR0YkNidRIjRGJ0Y1L0Y5USdub3JtYWxGJ0Y7Rj5GMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1Rkc= para p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1ElODE5MEYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSU4MTg5RictRiM2Ji1JI21uR0YkNidRIjVGJ0Y1L0Y5USdub3JtYWxGJ0Y7Rj5GMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1Rkc= e da
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1ElODE5MEYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSU4MTg5RictRiM2Ji1JI21uR0YkNidRIjVGJ0Y1L0Y5USdub3JtYWxGJ0Y7Rj5GMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1Rkc= para p\303\241ginas 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 .A melhor maneira de imaginar isso \303\251 v\303\252-lo como uma rede, ou seja, um gr\303\241fico ac\303\255clico direcionado. Vou usarPacote GraphTheory do Maple para desenharrestart; with(GraphTheory):G := Graph(directed,[P1,P2,P3,P4,P5],
{[P1,P2],[P2,P4],[P2,P1],[P2,P3],[P3,P4],
[P3,P5],[P4,P5],[P5,P1],[P5,P4]});DrawGraph(G);Observando o gr\303\241fico, podemos ver que a p\303\241gina P4 possui links para as p\303\241ginas P2, P3 e P5. \303\211 o\303\272nica p\303\241gina com tr\303\252s hiperlinks apontando para ela. Dizemos que a p\303\241gina P4 \303\251 uma autoridade, o que significa que, porquemuitas outras p\303\241ginas da web fazem refer\303\252ncia a ele, deve ser \303\272til. Portanto, uma maneira poss\303\255vel de classificar as p\303\241ginas seriasimplesmente para solicit\303\241-los pelo n\303\272mero de hiperlinks apontando para eles. Vamos definir para cada p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KVErQXV0b3JpZGFkZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKlsyNTUsMCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1ElODE5MEYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSU4MTg5RictSShtZmVuY2VkR0YkNictRiM2JS1JJW1zdWJHRiQ2JS1GLDYoUSJQRidGL0Y1RjhGO0Y+LUYjNiYtRiw2KFEiaUYnRi9GNUY4RjtGPkYvRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjUvRjlRJ25vcm1hbEYnRjVGVEY7Rj5GNUZU \303\251 o n\303\272mero de hiperlinks para a p\303\241gina 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. No Maple, o comando Arrivals fornece, para cada v\303\251rtice 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 uma lista de v\303\251rtices com arestas direcionadas para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1ElODE5MEYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSU4MTg5RidGMi9GNlEnbm9ybWFsRic=.Arrivals(G);Authority := map(numelems,Arrivals(G));Ent\303\243o n\303\263s os classificamos 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 . Existem dois problemas com esse ranking brutoalgoritmo. Primeiro, provavelmente haver\303\241 muitas p\303\241ginas com o mesmo n\303\272mero de hiperlinks apontando paraeles para que isso n\303\243o os classifique o suficiente. Segundo, embora a p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1ElODE5MEYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSU4MTg5RictRiM2Ji1JI21uR0YkNidRIjVGJ0Y1L0Y5USdub3JtYWxGJ0Y7Rj5GMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1Rkc= tenha autoridade 2, j\303\241 que o \303\272nico hiperlink na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjRGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= est\303\241 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjVGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= podemos argumentar que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjVGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= tamb\303\251m tem alta autoridade, implicitamente, por causa de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjRGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw=. De alguma forma, precisamos transferir a autoridade de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjRGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjVGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw=.A maneira como o Google faz isso e classifica as p\303\241ginas \303\251 a seguinte. Imagine que voc\303\252 est\303\241 navegando na web e restringem a vegar nas p\303\241ginas em P ;. A cada passo, voc\303\252 est\303\241 em uma p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSUmbGU7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZNLUYsNiVRImlGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrLyUrZXhlY3V0YWJsZUdGPkY1 e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJpRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJmxlO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRIk5GJ0Y0RjdGPkYrLyUrZXhlY3V0YWJsZUdGQkY+ voc\303\252 escolha aleatoriamente um hiperlink para uma das outras p\303\241ginas em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== e vamos para essa p\303\241gina. Vamos supor que escolhemos ohiperlinks com igual probabilidade. Se voc\303\252 navegar dessa maneira indefinidamente, chegar\303\241 a determinadas p\303\241ginasmais frequentemente do que outros. Podemos nos associar a cada p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= a probabilidade LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= que estamos nessap\303\241gina. Agora encomende as p\303\241ginas diminuindo a probabilidade. Esse \303\251 o ranking.Uma maneira de calcular as probabilidades LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= seria come\303\247ar na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjFGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= e simular o aleat\303\263rioweb surfista percorrendo as p\303\241ginas em P , calcule o n\303\272mero de vezes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= estamos na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= . E sefazemos isso para um n\303\272mero suficientemente grande de etapas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== ent\303\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 . Esta simula\303\247\303\243o \303\251 um exerc\303\255cio maravilhoso para os alunos empreenderem. Vou mostrar como fazer isso mais tarde. Por enquanto eu querodesenvolver uma abordagem para calcular o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= usando \303\241lgebra linear.Uma abordagem de \303\241lgebra linear
Seja G; seja o gr\303\241fico que representa os hiperlinks entre as p\303\241ginas. Seja 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 ser a probabilidade desaindo da p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJqRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= assumindo que pegamos cada hiperlink na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= com igual probabilidade. Paraexemplo, em nosso gr\303\241fico 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 porque podemos ir da p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= para p\303\241ginas 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 ou LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjRGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= cada um com probabilidade LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82JFEiM0YnRjIvJS5saW5ldGhpY2tuZXNzR0YxLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRjwvJSliZXZlbGxlZEdRJmZhbHNlRicvJStleGVjdXRhYmxlR0ZBRjI= . Vou construir a matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== do nosso gr\303\241fico LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== come\303\247ando com omatriz de adjac\303\252ncia para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== .A := AdjacencyMatrix(G);DP := Departures(G);n := 5:
for i to n do
s := numelems(DP[i]);
for j to n do A[i,j] := A[i,j]/s od;
od:A;Agora a matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJURidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRIl5GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw== \303\251 uma matriz estoc\303\241stica ou matriz de Markov porque os valores s\303\243o probabilidades e oscolunas de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJURidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRIl5GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw== soma a 1. A propriedade key \303\251 que, se tivermos um vetor de probabilidade LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= \303\251 oprobabilidade atual de estar na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= , ent\303\243o o vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiV0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==, dado por 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 , \303\251 uma probabilidadevetor onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiV0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= \303\251 a probabilidade de estar na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= depois de pegar um hiperlink aleatoriamente. Desde aisso n\303\243o \303\251 \303\263bvio, o leitor pode verificar isso. Vamos verificar isso por um valor. Vamos come\303\247ar como vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Ji1JJW1zdWJHRiQ2JS1GLDYlUSJRRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiMEYnL0Y7USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R0ZALUkjbW9HRiQ2LVEpJmVxdWFscztGJ0ZBLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlotSSVtc3VwR0YkNiYtSShtZmVuY2VkR0YkNiYtRiM2Ky1JJm1mcmFjR0YkNigtRj42JFEiMUYnRkEtRiw2JVEiTkYnRjdGOi8lLmxpbmV0aGlja25lc3NHRmRvLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlxwLyUpYmV2ZWxsZWRHRkstRkY2LVEiLEYnRkFGSS9GTUY5Rk5GUEZSRlRGVi9GWVEmMC4wZW1GJy9GZm5RLDAuMzMzMzMzM2VtRidGX29GYXAtRkY2LVExJnBlcmlvZDsmcGVyaW9kO0YnRkFGSUZMRk5GUEZSRlRGVi9GWVEsMC4yMjIyMjIyZW1GJy9GZm5GZnBGYXBGX28vJStleGVjdXRhYmxlR0ZLRkFGQS8lJW9wZW5HUScmbHNxYjtGJy8lJmNsb3NlR1EnJnJzcWI7RictRiw2JVEiVEYnRjdGOi8lMXN1cGVyc2NyaXB0c2hpZnRHRkAvSSttc2VtYW50aWNzR0YkUSJeRidGQUYrRl9xRkE= , que assume que estamos inicialmente em cada p\303\241gina com igual probabilidade.with(LinearAlgebra):Q[0] := <1/5,1/5,1/5,1/5,1/5>:Q[1] := Transpose(A).Q[0];A probabilidade de estar na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjFGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= ap\303\263s uma etapa de tempo \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82JFEiNkYnRjIvJS5saW5ldGhpY2tuZXNzR0YxLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRjwvJSliZXZlbGxlZEdRJmZhbHNlRicvJStleGVjdXRhYmxlR0ZBRjI=. Isso veio do produto escalar dos dois vetoresA[1..5,1], Q[0];Portanto, o produto escalar desses dois vetores representa a probabilidade de estar na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjFGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= depois de umO hiperlink de cada p\303\241gina \303\251 obtido aleatoriamente. Agora s\303\263 podemos obter a p\303\241gina 1 da p\303\241gina 2 e 5 comprobabilidade LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82JFEiM0YnRjIvJS5saW5ldGhpY2tuZXNzR0YxLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRjwvJSliZXZlbGxlZEdRJmZhbHNlRicvJStleGVjdXRhYmxlR0ZBRjI= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82JFEiMkYnRjIvJS5saW5ldGhpY2tuZXNzR0YxLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRjwvJSliZXZlbGxlZEdRJmZhbHNlRicvJStleGVjdXRhYmxlR0ZBRjI= respectivamente. Portanto, depois de pegar um hiperlink, estamos na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjFGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= comprobabilidade 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. Deixando 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 por conveni\303\252ncia, agora podemos determinar oprobabilidades de estar em cada p\303\241gina depois de tomar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== hiperlinks aleat\303\263rios multiplicando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjBGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdGOy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYmLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJrRidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRIl5GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw==. Aqui est\303\241 o que acontece para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJrRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJmVxdWFscztGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1JI21uR0YkNiRRIjVGJ0Y+Rj5GKy8lK2V4ZWN1dGFibGVHRkJGPg==.B := Transpose(A);for k to 5 do Q[k] := B.Q[k-1] od:
evalf(Q[5]);Agora, porque nosso gr\303\241fico em particular est\303\241 fortemente conectado, ou seja, voc\303\252 pode obter de todas as p\303\241ginas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= paratodas as outras p\303\241ginas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJqRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= , isso significa a matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJURidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRIl5GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw== \303\251 uma matriz regular. Segue-se do Per\303\263n-Teorema de Frobenius que a sequ\303\252ncia 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 ir\303\241 convergir para um vetor de estado estacion\303\241rio 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 que satisfa\303\247a 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. A partir desta \303\272ltima identidade, temos 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 o que nos fornece uma maneira direta de resolver o vetor de estado estacion\303\241rio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==. O vetor V est\303\241 no espa\303\247o nulo de 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 . A equa\303\247\303\243o 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 tamb\303\251m significa que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== \303\251 um vetor pr\303\263prio de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJURidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRIl5GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw== com autovalor 1. Vamos tentar resolver para V; usando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNiYtSShtZmVuY2VkR0YkNiQtRiM2Ji1JJW1zdXBHRiQ2Ji1GLDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiVRIlRGJ0Y+RkEvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEiXkYnLUkjbW9HRiQ2LVEoJm1pbnVzO0YnL0ZCUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGVS8lKXN0cmV0Y2h5R0ZVLyUqc3ltbWV0cmljR0ZVLyUobGFyZ2VvcEdGVS8lLm1vdmFibGVsaW1pdHNHRlUvJSdhY2NlbnRHRlUvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zeby1JI21uR0YkNiRRLSZJbWFnaW5hcnlJO0YnRlFGUUZRLUZONjBRMSZJbnZpc2libGVUaW1lcztGJy8lK2V4ZWN1dGFibGVHRlVGUS8lKnJlZmVyZW5jZUdRJTQ2ODNGJy8lMmRpc3BsYXlfcmVmZXJlbmNlR1ElNDY4MkYnRlNGVkZYRlpGZm5GaG5Gam4vRl1vUSYwLjBlbUYnL0Zgb0ZhcC1GLDYlUSJWRidGPkZBRlEtRk42LVEpJmVxdWFscztGJ0ZRRlNGVkZYRlpGZm5GaG5Gam4vRl1vUSwwLjI3Nzc3NzhlbUYnL0Zgb0ZqcC1GYm82JEZJRlFGUUYrRmhvRlE=.Agora, uma coisa que eu gostaria de fazer \303\251 usar a letra I para a matriz de identidade. No Maple, por padr\303\243o, eu sou ounidade complexa, isto \303\251 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. I^2;Para desativar isso, podemos fazer o seguinte, o que torna LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjX2lGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRic= a unidade complexa e libera a letra LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JFEtJkltYWdpbmFyeUk7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGLw== para uso geral.interface(imaginaryunit=_i);with(LinearAlgebra):I := IdentityMatrix(5);V := NullSpace(B-I);Esta \303\251 uma base para o espa\303\247o nulo (um conjunto de vetores), portanto, precisamos escolher o vetor de probabilidade em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFElU3BhbkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUqcmVmZXJlbmNlR1ElODE5MEYnLyUyZGlzcGxheV9yZWZlcmVuY2VHUSU4MTg5RictSShtZmVuY2VkR0YkNictRiM2JC1GLDYoUSJWRidGL0YyRjVGOEY7L0Y2USdub3JtYWxGJ0YyRkZGOEY7RkY= e impomos que as entradas s\303\243o probabilidades que somam 1.V := V[1]:
s := add(V[i],i=1..5);
V := V/s;Ent\303\243o, essas s\303\243o as probabilidades o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic=. Podemos ver o qu\303\243o perto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjVGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= \303\251 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==.evalf( V-Q[5] );Agora a matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJURidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRIl5GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw== \303\251 muito grande, mas muito escasso. A maioria das entradas \303\251 zero. Isto \303\251 simplesmenteporque cada p\303\241gina da web normalmente possui apenas alguns hiperlinks para p\303\241ginas em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==. Esse m\303\251todo direto deresolu\303\247\303\243o para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== usando elimina\303\247\303\243o gaussiana na matriz 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 leva ao preenchimento, o que torna oabordagem direta muito lenta para N grande. Por esse motivo, o google n\303\243o resolve o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== diretamente, mas em vez dissogera a sequ\303\252ncia LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KC1JJW1zdWJHRiQ2JS1GLDYlUSJRRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiMUYnL0Y7USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEoJmNvbW1hO0YnRkEvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGTC8lKnN5bW1ldHJpY0dGTC8lKGxhcmdlb3BHRkwvJS5tb3ZhYmxlbGltaXRzR0ZMLyUnYWNjZW50R0ZMLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjI2JUY0LUY+NiRRIjJGJ0ZBRkNGRi1GRzYtUTEmcGVyaW9kOyZwZXJpb2Q7RidGQUZKL0ZORkxGT0ZRRlNGVUZXL0ZaUSwwLjIyMjIyMjJlbUYnL0ZnbkZlbkZBRisvJStleGVjdXRhYmxlR0ZMRkE= usando a multiplica\303\247\303\243o de vetores matriciais 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que, como a matriz \303\251 esparsa, essa multiplica\303\247\303\243o de vetor de matriz \303\251 eficiente. Normalmente osequ\303\252ncia ter\303\241 convergido em 100 etapas. Vamos tentarfor k from 6 to 100 do Q[k] := B.Q[k-1] od:
evalf(Q[100]),evalf(V);Podemos ver que a sequ\303\252ncia convergiu para 6 casas decimais. Assim, classificamos as p\303\241ginas 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. Ent\303\243o, p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjVGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= \303\251 a primeira p\303\241gina.Correntes n\303\243o regulares de MarkovAssumimos que a matriz de Markov LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJURidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRIl5GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw== \303\251 regular, esse \303\251 o gr\303\241fico LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== est\303\241 fortemente conectado.N\303\243o h\303\241 raz\303\243o para que isso ocorra na pr\303\241tica. De fato, podemos ver facilmente que haver\303\241muitas p\303\241ginas da web sem links para eles - talvez a maioria. A exist\303\252ncia do estado estacion\303\241rioO vetor depende dessa propriedade de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJURidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRIl5GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw==. Uma solu\303\247\303\243o simples \303\251 conectar todos os v\303\251rtices em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== com todos os outros v\303\251rtices e pegam esses hiperlinks com baixa probabilidade LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==. Let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== ser a matriz com 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 por algum pequeno valor de 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. Agora ajuste as colunas da matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJURidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRIl5GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y2USdub3JtYWxGJw== de modo que 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 \303\251 uma matriz de Markov (estoc\303\241stica). Esta \303\251 uma solu\303\247\303\243o pr\303\241tica.Simulando o internauta.Pe\303\247o aos meus alunos que fa\303\247am o seguinte. Come\303\247ando na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjFGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= simule um internauta que tome 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 hiperlinks aleatoriamente. Calcule as frequ\303\252ncias LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= de estar na p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= e use-os para estimar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic=. Agora, para ver a converg\303\252ncia, periodicamente, ap\303\263s cada 100 hiperlinks obtidos, calcule as estimativaspara as probabilidades, fa\303\247a um gr\303\241fico delas para que possamos ver com que rapidez isso converge. O gr\303\241fico abaixo esclarecer\303\241o que eu quero que os alunos mostrem. Aqui est\303\241 a minha solu\303\247\303\243o. DP := Departures(G);Para obter hiperlinks aleat\303\263rios, para a p\303\241gina LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjUDJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRic= aqui precisamos gerar um de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUSNQMUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZjb21tYTtGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEjUDNGJ0Y0RjdGOi1GLDYlUSNQNEYnRjRGN0Y+RisvJStleGVjdXRhYmxlR0ZCRj4= aleatoriamente. eu vouuse um gerador de n\303\272meros aleat\303\263rios LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjNGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= para gerar 1, 2 ou 3 aleatoriamente (uniformemente) e, em seguida, selecione um dosessas p\303\241ginas. Tamb\303\251m precisarei de geradores de n\303\272meros aleat\303\263rios para 1 e 2 p\303\241ginas. Conseq\303\274entementeR[1] := rand(1..1):
R[2] := rand(1..2):
R[3] := rand(1..3):DP[2][R[3]()];DP[2][R[3]()];Agora eu rotulei as p\303\241ginas 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 e no meu c\303\263digo Maple, preciso determinar a partir de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJpRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic=,o \303\255ndice LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==.P\303\241gina := table():
for i to 5 do P\303\241gina[P||i] := i od:
P\303\241gina[P3];x := P1; # x \303\251 a p\303\241gina atual
N := 10000; # n\303\272mero de etapas
F := Array(1..5); # frequ\303\252ncias
V := Array(1..iquo(N,100)): # instant\303\242neos de probabilidades
for i to N do
Nx := DP[P\303\241gina[x]];
r := R[nops(Nx)]();
x := Nx[r]; # ir para pr\303\263xima p\303\241gina
F[P\303\241gina[x]] := F[P\303\241gina[x]] + 1;
if i mod 100 = 0 then
V[i/100] := evalf( [seq( F[j]/i, j=1..5 )] );
fi;
od: data := [seq( [seq([100*i,V[i][j]],i=1..i/100)],j=1..5 )]:cols := [red,green,blue,black,yellow];
plot( data, style=line, color=cols, view=[0..N,0..0.4], labels=["#steps","Prob"],
legend=["P\303\241gina 1", "P\303\241gina 2", "P\303\241gina 3", "P\303\241gina 4", "P\303\241gina 5"] );Portanto, o eixo vertical \303\251 a probabilidade de estar em uma das p\303\241ginas. Voc\303\252 pode ver que ele converge bastantelentamente, mais lento que a sequ\303\252ncia 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. O valor de gerar esse gr\303\241fico \303\251 que oo aluno aprende como fazer uma simula\303\247\303\243o, reunir dados e exibi-los de maneira significativa. Ali\303\241s, sevoc\303\252 clicar com o bot\303\243o direito do mouse na trama, obter\303\241 um menu de op\303\247\303\265es. Uma delas \303\251 a op\303\247\303\243o de sonda, que seselecionado, faz com que o Maple exiba (quando voc\303\252 move o cursor sobre o gr\303\241fico) o 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) coordenadas daposi\303\247\303\243o do cursor. Este \303\251 um recurso muito \303\272til. Aqui, posso ver qual a probabilidade de cada uma das curvas acimaest\303\241 convergindo para.