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Information theoretic cutting of a cake
, Article 2012 IEEE Information Theory Workshop, ITW 2012 ; 2012 , Pages 517-521 ; 9781467302234 (ISBN) ; Gohari, A. A ; Sharif University of Technology
Abstract
Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e. one agent may like chocolate while the other may like cream). A fair division of the cake is one that takes into account the individual valuations of agents and partitions the cake based on some fairness criterion. Fair division may be accomplished in a distributed or centralized way. Due to its natural and practical appeal, it has been a subject of study in economics under the topic of 'Fair Division'. To best of our knowledge the role of partial information in fair division has not...
On hypercontractivity and the mutual information between Boolean functions
, Article 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013, Monticello, IL ; Oct , 2013 , Pages 13-19 ; 9781479934096 (ISBN) ; Gohari, A. A ; Kamath, S ; Nair, C ; Sharif University of Technology
IEEE Computer Society
2013
Abstract
Hypercontractivity has had many successful applications in mathematics, physics, and theoretical computer science. In this work we use recently established properties of the hypercontractivity ribbon of a pair of random variables to study a recent conjecture regarding the mutual information between binary functions of the individual marginal sequences of a sequence of pairs of random variables drawn from a doubly symmetric binary source