1,887,699 research outputs found
The output distribution of important LULU-operators
Two procedures to compute the output distribution phi_S of certain stack
filters S (so called erosion-dilation cascades) are given. One rests on the
disjunctive normal form of S and also yields the rank selection probabilities.
The other is based on inclusion-exclusion and e.g. yields phi_S for some
important LULU-operators S. Properties of phi_S can be used to characterize
smoothing properties of S. One of the methods discussed also allows for the
calculation of the reliability polynomial of any positive Boolean function
(e.g. one derived from a connected graph).Comment: 20 pages, up to trivial differences this is the final version to be
published in Quaestiones Mathematicae 201
Randomized Quantization and Source Coding with Constrained Output Distribution
This paper studies fixed-rate randomized vector quantization under the
constraint that the quantizer's output has a given fixed probability
distribution. A general representation of randomized quantizers that includes
the common models in the literature is introduced via appropriate mixtures of
joint probability measures on the product of the source and reproduction
alphabets. Using this representation and results from optimal transport theory,
the existence of an optimal (minimum distortion) randomized quantizer having a
given output distribution is shown under various conditions. For sources with
densities and the mean square distortion measure, it is shown that this optimum
can be attained by randomizing quantizers having convex codecells. For
stationary and memoryless source and output distributions a rate-distortion
theorem is proved, providing a single-letter expression for the optimum
distortion in the limit of large block-lengths.Comment: To appear in the IEEE Transactions on Information Theor
Output Statistics of MIMO Channels with General Input Distribution
The information that can be conveyed through a wireless channel, with multiple-antenna equipped transmitter and receiver, crucially depends on the channel behavior as well as on the input structure. In this paper, we derive analytical results, concerning the probability density function (pdf) of the output of a single-user, multiple-antenna communication. The analysis is carried out under the assumption of an optimized input structure, and assuming Gaussian noise and a Rayleigh block-fading channel. Our analysis therefore provides a quite general and compact expression for the conditional output pdf. We also highlight the relation between such an expression and the results already available in the literature for some specific input structure
What can quantum optics say about computational complexity theory?
Considering the problem of sampling from the output photon-counting
probability distribution of a linear-optical network for input Gaussian states,
we obtain results that are of interest from both quantum theory and the
computational complexity theory point of view. We derive a general formula for
calculating the output probabilities, and by considering input thermal states,
we show that the output probabilities are proportional to permanents of
positive-semidefinite Hermitian matrices. It is believed that approximating
permanents of complex matrices in general is a #P-hard problem. However, we
show that these permanents can be approximated with an algorithm in BPP^NP
complexity class, as there exists an efficient classical algorithm for sampling
from the output probability distribution. We further consider input
squeezed-vacuum states and discuss the complexity of sampling from the
probability distribution at the output.Comment: 5 pages, 1 figur
Modelling and control of the flame temperature distribution using probability density function shaping
This paper presents three control algorithms for the output probability density function (PDF) control of the 2D and 3D flame distribution systems. For the 2D flame distribution systems, control methods for both static and dynamic flame systems are presented, where at first the temperature distribution of the gas jet flames along the cross-section is approximated. Then the flame energy distribution (FED) is obtained as the output to be controlled by using a B-spline expansion technique. The general static output PDF control algorithm is used in the 2D static flame system, where the dynamic system consists of a static temperature model of gas jet flames and a second-order actuator. This leads to a second-order closed-loop system, where a singular state space model is used to describe the dynamics with the weights of the B-spline functions as the state variables. Finally, a predictive control algorithm is designed for such an output PDF system. For the 3D flame distribution systems, all the temperature values of the flames are firstly mapped into one temperature plane, and the shape of the temperature distribution on this plane can then be controlled by the 3D flame control method proposed in this paper. Three cases are studied for the proposed control methods and desired simulation results have been obtained
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