5,986 research outputs found
Topics in inference and decision-making with partial knowledge
Two essential elements needed in the process of inference and decision-making are prior probabilities and likelihood functions. When both of these components are known accurately and precisely, the Bayesian approach provides a consistent and coherent solution to the problems of inference and decision-making. In many situations, however, either one or both of the above components may not be known, or at least may not be known precisely. This problem of partial knowledge about prior probabilities and likelihood functions is addressed. There are at least two ways to cope with this lack of precise knowledge: robust methods, and interval-valued methods. First, ways of modeling imprecision and indeterminacies in prior probabilities and likelihood functions are examined; then how imprecision in the above components carries over to the posterior probabilities is examined. Finally, the problem of decision making with imprecise posterior probabilities and the consequences of such actions are addressed. Application areas where the above problems may occur are in statistical pattern recognition problems, for example, the problem of classification of high-dimensional multispectral remote sensing image data
A Bayesian Framework for Collaborative Multi-Source Signal Detection
This paper introduces a Bayesian framework to detect multiple signals
embedded in noisy observations from a sensor array. For various states of
knowledge on the communication channel and the noise at the receiving sensors,
a marginalization procedure based on recent tools of finite random matrix
theory, in conjunction with the maximum entropy principle, is used to compute
the hypothesis selection criterion. Quite remarkably, explicit expressions for
the Bayesian detector are derived which enable to decide on the presence of
signal sources in a noisy wireless environment. The proposed Bayesian detector
is shown to outperform the classical power detector when the noise power is
known and provides very good performance for limited knowledge on the noise
power. Simulations corroborate the theoretical results and quantify the gain
achieved using the proposed Bayesian framework.Comment: 15 pages, 9 pictures, Submitted to IEEE Trans. on Signal Processin
Efficiency of a thermodynamic motor at maximum power
Several recent theories address the efficiency of a macroscopic thermodynamic
motor at maximum power and question the so-called "Curzon-Ahlborn (CA)
efficiency." Considering the entropy exchanges and productions in an n-sources
motor, we study the maximization of its power and show that the controversies
are partly due to some imprecision in the maximization variables. When power is
maximized with respect to the system temperatures, these temperatures are
proportional to the square root of the corresponding source temperatures, which
leads to the CA formula for a bi-thermal motor. On the other hand, when power
is maximized with respect to the transitions durations, the Carnot efficiency
of a bi-thermal motor admits the CA efficiency as a lower bound, which is
attained if the duration of the adiabatic transitions can be neglected.
Additionally, we compute the energetic efficiency, or "sustainable efficiency,"
which can be defined for n sources, and we show that it has no other universal
upper bound than 1, but that in certain situations, favorable for power
production, it does not exceed 1/2
An introduction to DSmT
The management and combination of uncertain, imprecise, fuzzy and even
paradoxical or high conflicting sources of information has always been, and
still remains today, of primal importance for the development of reliable
modern information systems involving artificial reasoning. In this
introduction, we present a survey of our recent theory of plausible and
paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for
dealing with imprecise, uncertain and conflicting sources of information. We
focus our presentation on the foundations of DSmT and on its most important
rules of combination, rather than on browsing specific applications of DSmT
available in literature. Several simple examples are given throughout this
presentation to show the efficiency and the generality of this new approach
Carnot cycle for an oscillator
Carnot established in 1824 that the efficiency of cyclic engines operating
between a hot bath at absolute temperature and a bath at a lower
temperature cannot exceed . We show that linear
oscillators alternately in contact with hot and cold baths obey this principle
in the quantum as well as in the classical regime. The expression of the work
performed is derived from a simple prescription. Reversible and non-reversible
cycles are illustrated. The paper begins with historical considerations and is
essentially self-contained.Comment: 19 pages, 3 figures, sumitted to European Journal of Physics Changed
content: Fluctuations are considere
Hydrogen-Helium Mixtures in the Interiors of Giant Planets
Equilibrium properties of hydrogen-helium mixtures under conditions similar
to the interior of giant gas planets are studied by means of first principle
density functional molecular dynamics simulations. We investigate the molecular
and atomic fluid phase of hydrogen with and without the presence of helium for
densities between gcm and gcm and
temperatures from K to . Helium has a crucial influence on
the ionic and electronic structure of the liquid. Hydrogen molecule bonds are
shortened as well as strengthened which leads to more stable hydrogen molecules
compared to pure hydrogen for the same thermodynamic conditions. The {\it ab
initio} treatment of the mixture enables us to investigate the validity of the
widely used linear mixing approximation. We find deviations of up to 8% in
energy and volume from linear mixing at constant pressure in the region of
molecular dissociation.Comment: 13 pages, 18 figures, submitted to PR
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