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Following a conjecture of P. Erdos, we show that if 9 is a family of k-subsets of an n-set no two of which intersect in exactly I elements then for k 2 21+ 2 and n sufficiently large IF:/ < (;:‘,I:) with equality holding if and only if 9 consists of all the k-sets containing a fixed (I+ I)-set. In general we show 19) <dknmax(‘.k-‘-l), where dk is a constant depending only on k. These results ar...
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The term brain activity refers to a wide range of mental faculties that can be assessed either on anatomical/functional micro-, mesoand macrospatiotemporal scales of observation, or on intertwined levels with mutual interactions. Here we show, based on novel topological findings, how every brain activity encompassed in a given anatomical or functional level necessarily displays a counterpart in...
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ژورنال
عنوان ژورنال: Science
سال: 2014
ISSN: 0036-8075,1095-9203
DOI: 10.1126/science.346.6211.795