914 research outputs found
Sequences of binary irreducible polynomials
In this paper we construct an infinite sequence of binary irreducible
polynomials starting from any irreducible polynomial f_0 \in \F_2 [x]. If
is of degree , where is odd and is a
non-negative integer, after an initial finite sequence of polynomials with , the degree of is twice the degree
of for any .Comment: 7 pages, minor adjustment
Non-Existence of Stabilizing Policies for the Critical Push-Pull Network and Generalizations
The push-pull queueing network is a simple example in which servers either
serve jobs or generate new arrivals. It was previously conjectured that there
is no policy that makes the network positive recurrent (stable) in the critical
case. We settle this conjecture and devise a general sufficient condition for
non-stabilizability of queueing networks which is based on a linear martingale
and further applies to generalizations of the push-pull network.Comment: 14 pages, 3 figure
Risk-sensitive optimal control for Markov decision processes with monotone cost
The existence of an optimal feedback law is established for the risk-sensitive optimal control problem with denumerable state space. The main assumptions imposed are irreducibility and anear monotonicity condition on the one-step cost function. A solution can be found constructively using either value iteration or policy iteration under suitable conditions on initial feedback law
Asymptotic entanglement in 1D quantum walks with a time-dependent coined
Discrete-time quantum walk evolve by a unitary operator which involves two
operators a conditional shift in position space and a coin operator. This
operator entangles the coin and position degrees of freedom of the walker. In
this paper, we investigate the asymptotic behavior of the coin position
entanglement (CPE) for an inhomogeneous quantum walk which determined by two
orthogonal matrices in one-dimensional lattice. Free parameters of coin
operator together provide many conditions under which a measurement perform on
the coin state yield the value of entanglement on the resulting position
quantum state. We study the problem analytically for all values that two free
parameters of coin operator can take and the conditions under which
entanglement becomes maximal are sought.Comment: 23 pages, 4 figures, accepted for publication in IJMPB. arXiv admin
note: text overlap with arXiv:1001.5326 by other author
Geometric ergodicity in a weighted sobolev space
For a discrete-time Markov chain evolving on with
transition kernel , natural, general conditions are developed under which
the following are established:
1. The transition kernel has a purely discrete spectrum, when viewed as a
linear operator on a weighted Sobolev space of functions with
norm, where is a Lyapunov function and .
2. The Markov chain is geometrically ergodic in : There is a
unique invariant probability measure and constants and
such that, for each , any initial condition
, and all : where .
3. For any function there is a function solving Poisson's equation: Part of the
analysis is based on an operator-theoretic treatment of the sensitivity process
that appears in the theory of Lyapunov exponents
A Random Search Framework for Convergence Analysis of Distributed Beamforming with Feedback
The focus of this work is on the analysis of transmit beamforming schemes
with a low-rate feedback link in wireless sensor/relay networks, where nodes in
the network need to implement beamforming in a distributed manner.
Specifically, the problem of distributed phase alignment is considered, where
neither the transmitters nor the receiver has perfect channel state
information, but there is a low-rate feedback link from the receiver to the
transmitters. In this setting, a framework is proposed for systematically
analyzing the performance of distributed beamforming schemes. To illustrate the
advantage of this framework, a simple adaptive distributed beamforming scheme
that was recently proposed by Mudambai et al. is studied. Two important
properties for the received signal magnitude function are derived. Using these
properties and the systematic framework, it is shown that the adaptive
distributed beamforming scheme converges both in probability and in mean.
Furthermore, it is established that the time required for the adaptive scheme
to converge in mean scales linearly with respect to the number of sensor/relay
nodes.Comment: 8 pages, 3 figures, presented partially at ITA '08 and PSU School of
Info. Theory '0
Markov Chain Monte Carlo Method without Detailed Balance
We present a specific algorithm that generally satisfies the balance
condition without imposing the detailed balance in the Markov chain Monte
Carlo. In our algorithm, the average rejection rate is minimized, and even
reduced to zero in many relevant cases. The absence of the detailed balance
also introduces a net stochastic flow in a configuration space, which further
boosts up the convergence. We demonstrate that the autocorrelation time of the
Potts model becomes more than 6 times shorter than that by the conventional
Metropolis algorithm. Based on the same concept, a bounce-free worm algorithm
for generic quantum spin models is formulated as well.Comment: 5 pages, 5 figure
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