Decomposition Theorem for Perverse sheaves on Artin stacks over finite fields

We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.Comment: 10 pages; submitted. The part on foundations of topological theory is removed for no

Does observational equivalence always hold in hyperbolic discounting models?

Observation equivalence holds in the hyperbolic discounting models such as Laibson (1996), Barro (1999), and Krusell et al (2002). We study a hyperbolic discounting model where the policy function cannot be replicated by a geometric discounting model. Under the logarithmic utility and Cobb-Douglas production, we obtain the explicit solution for consumer's consumption-saving decision. Different from the literatures of exponential discounting, our model shows that the habit persistence affects consumer''s consumption-saving decision. Therefore, observational equivalence does not hold in our hyperbolic discounting model.Consumption function

Beyond the Cut-Set Bound: Uncertainty Computations in Network Coding with Correlated Sources

Cut-set bounds on achievable rates for network communication protocols are not in general tight. In this paper we introduce a new technique for proving converses for the problem of transmission of correlated sources in networks, that results in bounds that are tighter than the corresponding cut-set bounds. We also define the concept of "uncertainty region" which might be of independent interest. We provide a full characterization of this region for the case of two correlated random variables. The bounding technique works as follows: on one hand we show that if the communication problem is solvable, the uncertainty of certain random variables in the network with respect to imaginary parties that have partial knowledge of the sources must satisfy some constraints that depend on the network architecture. On the other hand, the same uncertainties have to satisfy constraints that only depend on the joint distribution of the sources. Matching these two leads to restrictions on the statistical joint distribution of the sources in communication problems that are solvable over a given network architecture.Comment: 12 pages, A short version appears in ISIT 201