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Origins of Randomness in Physical Systems

Physical Review Letters, 1985
Randomness and chaos in physical systems are usually ultimately attributed to external noise. But it is argued here that even without such random input, the intrinsic behavior of many nonlinear systems can be computationally so complicated as to seem random in all practical experiments.
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Random-field mechanism in random-bond multicritical systems

Physical Review Letters, 1989
It is argued on general grounds that bond randomness drastically alters multicritical phase diagrams via a random-field mechanism. For example, tricritical points and critical end points are entirely eliminated (d\ensuremath{\le}2) or depressed in temperature (dg2). These predictions are confirmed by a renormalization-group calculation.
, Hui, , Berker
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RECURRENCE IN SYSTEMS WITH RANDOM PERTURBATIONS

International Journal of Bifurcation and Chaos, 2013
We introduce the notion of (f, δ)-recurrence for the so-called (f, δ)-processes. We show that if a function of type 2∞ has no attractive periodic points of periods greater than 2N for some positive integer N and has an infinite ω-limit set, then each point belonging to its infinite ω-limit set is (f, δ)-recurrent provided that δ is small enough.
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Wigner distribution for random systems

Journal of Modern Optics, 2002
We use the Wigner distribution to study systems subjected to random forces. We define the instantaneous spectrum as the ensemble average of the Wigner distribution, and we write the differential equation whose solution gives us the time-varying spectrum of the state variable. We consider the cases of both constant and time-varying coefficients.
GALLEANI, Lorenzo, COHEN L.
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Random set system identification

IEEE Transactions on Fuzzy Systems, 2002
The paper gives a brief review of the basic mathematical aspects of random set theory. Concepts such as a random set mapping and its coverage function are introduced in a comprehensive way, avoiding too much detail. We adapt this theory to system identification and forecasting of time series. This is achieved by using the one-point coverage function of
Javier Nunez-Garcia, Olaf Wolkenhauer
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On Randomization in MTD Systems

Proceedings of the 9th ACM Workshop on Moving Target Defense, 2022
Ghaderi, Majid   +3 more
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Random processes and random systems: An introduction

1983
We introduce and review a number of topics drawn from the theories of random processes and random systems. In particular we address the following subjects: random walks in continuous spaces and on lattices; continuum limits of random walks and stable distributions; master equations, generalized master equations and continuous-time random walks; self ...
Barry D. Hughes, Stephen Prager
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Random Signals and Systems with Random Inputs

1999
In the problem of estimating a signal s(n) from the measurements z(n) = g(s(n), v(n), n), the noise term v(n) usually varies “randomly,” and thus modeling v(n) requires that we use a random signal formulation. The signal s(n) may also include some random variation, and thus it too must be modeled in general as a random signal.
E. W. Kamen, J. K. Su
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Stability of Systems with Random Parameters

Proceedings of the 45th IEEE Conference on Decision and Control, 2006
This paper addresses the problem of stability of a system with uncertainty modelled as a random matrix. The mean of the matrix is assumed to be stable while the variations around the mean model the effect of uncertainty in the parameters. Using some recent advances in random matrix theory, we provide sufficient conditions under which stability is ...
Vasanthan Raghavan, B. Ross Barmish
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