57,776 research outputs found
Polytopal realizations of finite type -vector fans
This paper shows the polytopality of any finite type -vector fan,
acyclic or not. In fact, for any finite Dynkin type , we construct a
universal associahedron with the property
that any -vector fan of type is the normal fan of a
suitable projection of .Comment: 27 pages, 9 figures; Version 2: Minor changes in the introductio
New Results on Multiple-Input Multiple-Output Broadcast Channels with Confidential Messages
This paper presents two new results on multiple-input multiple-output (MIMO)
Gaussian broadcast channels with confidential messages. First, the problem of
the MIMO Gaussian wiretap channel is revisited. A matrix characterization of
the capacity-equivocation region is provided, which extends the previous result
on the secrecy capacity of the MIMO Gaussian wiretap channel to the general,
possibly imperfect secrecy setting. Next, the problem of MIMO Gaussian
broadcast channels with two receivers and three independent messages: a common
message intended for both receivers, and two confidential messages each
intended for one of the receivers but needing to be kept asymptotically
perfectly secret from the other, is considered. A precise characterization of
the capacity region is provided, generalizing the previous results which
considered only two out of three possible messages.Comment: Submitted to the IEEE Transactions on Information Theory, 11 pages, 5
figure
A Random Matrix Approach to Dynamic Factors in macroeconomic data
We show how random matrix theory can be applied to develop new algorithms to
extract dynamic factors from macroeconomic time series. In particular, we
consider a limit where the number of random variables N and the number of
consecutive time measurements T are large but the ratio N / T is fixed. In this
regime the underlying random matrices are asymptotically equivalent to Free
Random Variables (FRV).Application of these methods for macroeconomic
indicators for Poland economy is also presented.Comment: arXiv admin note: text overlap with arXiv:physics/0512090 by other
author
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