22 research outputs found
Crossings of smooth shot noise processes
In this paper, we consider smooth shot noise processes and their expected
number of level crossings. When the kernel response function is sufficiently
smooth, the mean number of crossings function is obtained through an integral
formula. Moreover, as the intensity increases, or equivalently, as the number
of shots becomes larger, a normal convergence to the classical Rice's formula
for Gaussian processes is obtained. The Gaussian kernel function, that
corresponds to many applications in physics, is studied in detail and two
different regimes are exhibited.Comment: Published in at http://dx.doi.org/10.1214/11-AAP807 the Annals of
Applied Probability ( http://www.imstat.org/aap/ ) by the Institute of
Mathematical Statistics (http://www.imstat.org
On level crossings for a general class of piecewise-deterministic Markov processes
We consider a piecewise-deterministic Markov process governed by a jump
intensity function, a rate function that determines the behaviour between
jumps, and a stochastic kernel describing the conditional distribution of jump
sizes. We study the point process of upcrossings of a level by the Markov
process. Our main result shows that, under a suitable scaling , the
point process converges, as tends to infinity, weakly to a geometrically
compound Poisson process. We also prove a version of Rice's formula relating
the stationary density of the process to level crossing intensities. This
formula provides an interpretation of the scaling factor . While our
proof of the limit theorem requires additional assumptions, Rice's formula
holds whenever the (stationary) overall intensity of jumps is finite.Comment: 25 page
Level crossings and other level functionals of stationary Gaussian processes
This paper presents a synthesis on the mathematical work done on level
crossings of stationary Gaussian processes, with some extensions. The main
results [(factorial) moments, representation into the Wiener Chaos, asymptotic
results, rate of convergence, local time and number of crossings] are
described, as well as the different approaches [normal comparison method, Rice
method, Stein-Chen method, a general -dependent method] used to obtain them;
these methods are also very useful in the general context of Gaussian fields.
Finally some extensions [time occupation functionals, number of maxima in an
interval, process indexed by a bidimensional set] are proposed, illustrating
the generality of the methods. A large inventory of papers and books on the
subject ends the survey.Comment: Published at http://dx.doi.org/10.1214/154957806000000087 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Theory, Software and Testing Examples in Decision Support Systems
This volume summarizes the results of a four-year cooperative contracted study "Theory, Software and Testing Examples for Decision Support Systems" conducted in Poland by four institutions: the Institute of Automatic Control, Warsaw University of Technology, the System Research Institute of the Polish Academy of Sciences, the Institute of Control and Systems Engineering, Academy of Mining and Metallurgy in Cracow, and the Institute of Informatics, University of Warsaw in cooperation with the Methodology of the Decision Analysis Project of the System and Decision Sciences Program at IIASA. This research was supported mostly by IIASA funds in Polish national currency, but also by other sources and research grants in Poland, such as the grant RP.1.02 of the Ministry of Education for research in optimization and automatic control; totally, it represents the results of a part-time work of about 30 researchers from these institutions. This volume concentrates on the theoretical and methodological advances of this cooperative study, although it describes also experiences of applications in the area of programming the development of chemical industry together with a decision support system for such purposes as well as presents short descriptions of eight software packages (prototype decision support systems, multiobjective mathematical programming packages and a pilot negotiation support system) that are available together with more detailed documentation as scientific software constituting a part of results of this study.
The research on the Polish side was coordinated by Professor Andrzej P. Wierzbicki and on IIASA's side by Dr. Andrzej Lewandowski, the project leader of the Methodology of Decision Analysis; they served also as the editors of this volume
Aspiration Based Decision Support Systems
This book focuses the methodology of decision analysis and support related to the principle of reference point optimization (developed by the editors of this volume and called also variously: aspiration-led decision support, quasi-satisfying framework of rationality, DIDAS methodology etc.).
The selection principle applied for this volume was to concentrate on advances of theory and methodology, related to the focusing theme, to supplement them by experiences and methodological advances gained through wide applications and tests in one particular application area - the programming of development of industrial structures in chemical industry, and finally to give a very short description of various software products developed in the contracted study agreement
Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance
Issued as Progress report, and Final report, Project no. E-21-67
Quantum-enhanced measurements without entanglement
Quantum-enhanced measurements exploit quantum mechanical effects for increasing the sensitivity of measurements of certain physical parameters and have great potential for both fundamental science and concrete applications. Most of the research has so far focused on using highly entangled states, which are, however, difficult to produce and to stabilize for a large number of constituents. In the following we review alternative mechanisms, notably the use of more general quantum correlations such as quantum discord, identical particles, or non-trivial Hamiltonians; the estimation of thermodynamical parameters or parameters characterizing non-equilibrium states; and the use of quantum phase transitions. We describe both theoretically achievable enhancements and enhanced sensitivities, not primarily based on entanglement, that have already been demonstrated experimentally, and indicate some possible future research directions
Nonclassical correlations in the motion of dissociated Feshbach molecules
This thesis proposes two complementary scenarios to observe Bell correlations in the motion of two macroscopically separated material particles. Both are based on the gradual dissociation of ultracold Feshbach molecules and result in macroscopic delocalizations of the single-atom states. By giving a full account of these scenarios, including the coupled-channel description of the Feshbach dissociation, the optically guided dispersive propagation, interferometric processing and the final position measurements, I demonstrate for both cases their potential to violate a Bell inequality under experimentally viable conditions that correspond to delocalizations and interatomic separations on the order of centimeters