{"product_id":"9783540427179","title":"Lecture Notes in Computer Science","description":"\u003ch1\u003eLecture Notes in Computer Science\u003c\/h1\u003e \u003ch2\u003eLeyton, Michael\u003c\/h2\u003e \u003cp\u003eThe purpose of this book is to develop a generative theory of shape that has two properties we regard as fundamental to intelligence –(1) maximization of transfer: whenever possible, new structure should be described as the transfer of existing structure; and (2) maximization of recoverability: the generative operations in the theory must allow maximal inferentiability from data sets. We shall show that, if generativity satis?es these two basic criteria of - telligence, then it has a powerful mathematical structure and considerable applicability to the computational disciplines. The requirement of intelligence is particularly important in the gene- tion of complex shape. There are plenty of theories of shape that make the generation of complex shape unintelligible. However, our theory takes the opposite direction: we are concerned with the conversion of complexity into understandability. In this, we will develop a mathematical theory of und- standability. The issue of understandability comes down to the two basic principles of intelligence - maximization of transfer and maximization of recoverability. We shall show how to formulate these conditions group-theoretically. (1) Ma- mization of transfer will be formulated in terms of wreath products. Wreath products are groups in which there is an upper subgroup (which we will call a control group) that transfers a lower subgroup (which we will call a ?ber group) onto copies of itself. (2) maximization of recoverability is insured when the control group is symmetry-breaking with respect to the ?ber group.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2001-10-26\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540427179\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/3-540-45488-8\u003c\/p\u003e \u003cp\u003eDimensions: 233cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 549\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":45369859506316,"sku":"9783540427179","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540427179.jpg?v=1773965934","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783540427179","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}