3,899 research outputs found
Concavity of Mutual Information Rate for Input-Restricted Finite-State Memoryless Channels at High SNR
We consider a finite-state memoryless channel with i.i.d. channel state and
the input Markov process supported on a mixing finite-type constraint. We
discuss the asymptotic behavior of entropy rate of the output hidden Markov
chain and deduce that the mutual information rate of such a channel is concave
with respect to the parameters of the input Markov processes at high
signal-to-noise ratio. In principle, the concavity result enables good
numerical approximation of the maximum mutual information rate and capacity of
such a channel.Comment: 26 page
Analyticity of Entropy Rate of Hidden Markov Chains
We prove that under mild positivity assumptions the entropy rate of a hidden
Markov chain varies analytically as a function of the underlying Markov chain
parameters. A general principle to determine the domain of analyticity is
stated. An example is given to estimate the radius of convergence for the
entropy rate. We then show that the positivity assumptions can be relaxed, and
examples are given for the relaxed conditions. We study a special class of
hidden Markov chains in more detail: binary hidden Markov chains with an
unambiguous symbol, and we give necessary and sufficient conditions for
analyticity of the entropy rate for this case. Finally, we show that under the
positivity assumptions the hidden Markov chain {\em itself} varies
analytically, in a strong sense, as a function of the underlying Markov chain
parameters.Comment: The title has been changed. The new main theorem now combines the old
main theorem and the remark following the old main theorem. A new section is
added as an introduction to complex analysis. General principle and an
example to determine the domain of analyticity of entropy rate have been
added. Relaxed conditions for analyticity of entropy rate and the
corresponding examples are added. The section about binary markov chain
corrupted by binary symmetric noise is taken out (to be part of another
paper
Derivatives of Entropy Rate in Special Families of Hidden Markov Chains
Consider a hidden Markov chain obtained as the observation process of an
ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how,
in principle, one can explicitly compute the derivatives of the entropy rate of
at extreme values of the noise. Namely, they showed that the derivatives of
standard upper approximations to the entropy rate actually stabilize at an
explicit finite time. We generalize this result to a natural class of hidden
Markov chains called ``Black Holes.'' We also discuss in depth special cases of
binary Markov chains observed in binary symmetric noise, and give an abstract
formula for the first derivative in terms of a measure on the simplex due to
Blackwell.Comment: The relaxed condtions for entropy rate and examples are taken out (to
be part of another paper). The section about general principle and an example
to determine the domain of analyticity is taken out (to be part of another
paper). A section about binary Markov chains corrupted by binary symmetric
noise is adde
Mean sensitive, mean equicontinuous and almost periodic functions for dynamical systems
We show that an -topological dynamical system equipped with an invariant
ergodic measure has discrete spectrum if and only it is -mean
equicontinuous (proven for before). In order to do this we introduce mean
equicontinuity and mean sensitivity with respect to a function. We study this
notion in the topological and measure theoretic setting. In the measure
theoretic case we characterize almost periodic functions and in the topological
case we show that weakly almost periodic functions are mean equicontinuous (the
converse does not hold)
COMPETENCE ACQUISITION IN RETAIL FOOD: EFFICIENT CONSUMER RESPONSE AND ENVIRONMENTAL MANAGEMENT
Based on interviews with retail food store managers and a subsequent survey, this paper traces the pathways that spawn competence acquisition in the retail food industry. It finds that having an essential capability for learning, that is, obtaining new ideas, concepts, methods, tends to breed competencies in a number of areas which are of both business and social significance. In this study, the capacity of this essential capability to generate competencies in efficient consumer response (ECR) and environmental management (EM) are examined. These competencies have attracted the attention of the retail food industry in its efforts to become more competitive with alternative retail food channels. The results show that firms possessing the essential capability of generating new ideas are more likely to have higher sales per square foot. Ties with suppliers lead to higher sales per square foot through improved environmental practices and more consumer education. Technical assistance helps retail grocers acquire a social competence in environmental management.Agribusiness, Environmental Economics and Policy, Industrial Organization, Marketing,
- …