Choice resolutions

AbstractWe describe a process to compose and decompose choice behavior, called resolution. In the forward direction, resolutions amalgamate simple choices to create a complex one. In the backward direction, resolutions detect when and how a primitive choice can be deconstructed into smaller choices. A choice is resolvable if it is the resolution of smaller choices. Rationalizability, rationalizability by a preorder, and path independence are all preserved (backward and forward) by resolutions, whereas rationalizability by a weak order (equivalently, ) is not. We characterize resolvable choices, and show that resolvability generalizes

Attribute network models, stochastic approximation, and network sampling and ranking algorithms

We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation techniques we show that, in the large network limit, such networks converge in the local weak sense to randomly stopped multitype branching processes whose explicit description allows for the derivation of asymptotics for a wide class of network functionals. These asymptotics imply that while degree distribution tail exponents depend on the attribute type (already derived by Jordan (2013)), Page-rank centrality scores have the \emph{same} tail exponent across attributes. Moreover, the mean behavior of the limiting Page-rank score distribution can be explicitly described and shown to depend on the attribute type. The limit results also give explicit formulae for the performance of various network sampling mechanisms. One surprising consequence is the efficacy of Page-rank and walk based network sampling schemes for directed networks in the setting of rare minorities. The results also allow one to evaluate the impact of various proposed mechanisms to increase degree centrality of minority attributes in the network, and to quantify the bias in inferring about the network from an observed sample. Further, we formalize the notion of resolvability of such models where, owing to propagation of chaos type phenomenon in the evolution dynamics for such models, one can set up a correspondence to models driven by continuous time branching process dynamics.Comment: 48 page

Information-theoretic Physical Layer Security for Satellite Channels

Shannon introduced the classic model of a cryptosystem in 1949, where Eve has access to an identical copy of the cyphertext that Alice sends to Bob. Shannon defined perfect secrecy to be the case when the mutual information between the plaintext and the cyphertext is zero. Perfect secrecy is motivated by error-free transmission and requires that Bob and Alice share a secret key. Wyner in 1975 and later I.~Csisz\'ar and J.~K\"orner in 1978 modified the Shannon model assuming that the channels are noisy and proved that secrecy can be achieved without sharing a secret key. This model is called wiretap channel model and secrecy capacity is known when Eve's channel is noisier than Bob's channel. In this paper we review the concept of wiretap coding from the satellite channel viewpoint. We also review subsequently introduced stronger secrecy levels which can be numerically quantified and are keyless unconditionally secure under certain assumptions. We introduce the general construction of wiretap coding and analyse its applicability for a typical satellite channel. From our analysis we discuss the potential of keyless information theoretic physical layer security for satellite channels based on wiretap coding. We also identify system design implications for enabling simultaneous operation with additional information theoretic security protocols