556 research outputs found
State space formulas for a suboptimal rational Leech problem I: Maximum entropy solution
For the strictly positive case (the suboptimal case) the maximum entropy
solution to the Leech problem and
, with and stable rational
matrix functions, is proved to be a stable rational matrix function. An
explicit state space realization for is given, and turns out
to be strictly less than one. The matrices involved in this realization are
computed from the matrices appearing in a state space realization of the data
functions and . A formula for the entropy of is also given.Comment: 19 page
State space formulas for stable rational matrix solutions of a Leech problem
Given stable rational matrix functions and , a procedure is presented
to compute a stable rational matrix solution to the Leech problem
associated with and , that is, and . The solution is given in the form of a state space
realization, where the matrices involved in this realization are computed from
state space realizations of the data functions and .Comment: 25 page
State space formulas for a suboptimal rational Leech problem II: Parametrization of all solutions
For the strictly positive case (the suboptimal case), given stable rational
matrix functions and , the set of all solutions to the
Leech problem associated with and , that is, and
, is presented as the range of a linear
fractional representation of which the coefficients are presented in state
space form. The matrices involved in the realizations are computed from state
space realizations of the data functions and . On the one hand the
results are based on the commutant lifting theorem and on the other hand on
stabilizing solutions of algebraic Riccati equations related to spectral
factorizations.Comment: 28 page
All solutions to the relaxed commutant lifting problem
A new description is given of all solutions to the relaxed commutant lifting
problem. The method of proof is also different from earlier ones, and uses only
an operator-valued version of a classical lemma on harmonic majorants.Comment: 15 page
Krein systems
In the present paper we extend results of M.G. Krein associated to the
spectral problem for Krein systems to systems with matrix valued accelerants
with a possible jump discontinuity at the origin. Explicit formulas for the
accelerant are given in terms of the matrizant of the system in question.
Recent developments in the theory of continuous analogs of the resultant
operator play an essential role
Whanaungatanga: Sybil-proof routing with social networks
Decentralized systems, such as distributed hash tables, are subject to the Sybil attack, in which an adversary creates many false identities to increase its influence. This paper proposes a routing protocol for a distributed hash table that is strongly resistant to the Sybil attack. This is the first solution to this problem with sublinear run time and space usage. The protocol uses the social connections between users to build routing tables that enable Sybil-resistant distributed hash table lookups. With a social network of N well-connected honest nodes, the protocol can tolerate up to O(N/log N) "attack edges" (social links from honest users to phony identities). This means that an adversary has to fool a large fraction of the honest users before any lookups will fail. The protocol builds routing tables that contain O(N log^(3/2) N) entries per node. Lookups take O(1) time. Simulation results, using social network graphs from LiveJournal, Flickr, and YouTube, confirm the analytical results
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