5,031 research outputs found
The Separation Principle in Stochastic Control, Redux
Over the last 50 years a steady stream of accounts have been written on the
separation principle of stochastic control. Even in the context of the
linear-quadratic regulator in continuous time with Gaussian white noise, subtle
difficulties arise, unexpected by many, that are often overlooked. In this
paper we propose a new framework for establishing the separation principle.
This approach takes the viewpoint that stochastic systems are well-defined maps
between sample paths rather than stochastic processes per se and allows us to
extend the separation principle to systems driven by martingales with possible
jumps. While the approach is more in line with "real-life" engineering thinking
where signals travel around the feedback loop, it is unconventional from a
probabilistic point of view in that control laws for which the feedback
equations are satisfied almost surely, and not deterministically for every
sample path, are excluded.Comment: 23 pages, 6 figures, 2nd revision: added references, correction
Likelihood Analysis of Power Spectra and Generalized Moment Problems
We develop an approach to spectral estimation that has been advocated by
Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance
extension problem, by Enqvist and Karlsson. The aim is to determine the power
spectrum that is consistent with given moments and minimizes the relative
entropy between the probability law of the underlying Gaussian stochastic
process to that of a prior. The approach is analogous to the framework of
earlier work by Byrnes, Georgiou and Lindquist and can also be viewed as a
generalization of the classical work by Burg and Jaynes on the maximum entropy
method. In the present paper we present a new fast algorithm in the general
case (i.e., for general Gaussian priors) and show that for priors with a
specific structure the solution can be given in closed form.Comment: 17 pages, 4 figure
On time-reversibility of linear stochastic models
Reversal of the time direction in stochastic systems driven by white noise
has been central throughout the development of stochastic realization theory,
filtering and smoothing. Similar ideas were developed in connection with
certain problems in the theory of moments, where a duality induced by time
reversal was introduced to parametrize solutions. In this latter work it was
shown that stochastic systems driven by arbitrary second-order stationary
processes can be similarly time-reversed. By combining these two sets of ideas
we present herein a generalization of time-reversal in stochastic realization
theory.Comment: 10 pages, 4 figure
Debugging tasked Ada programs
The applications for which Ada was developed require distributed implementations of the language and extensive use of tasking facilities. Debugging and testing technology as it applies to parallel features of languages currently falls short of needs. Thus, the development of embedded systems using Ada pose special challenges to the software engineer. Techniques for distributing Ada programs, support for simulating distributed target machines, testing facilities for tasked programs, and debugging support applicable to simulated and to real targets all need to be addressed. A technique is presented for debugging Ada programs that use tasking and it describes a debugger, called AdaTAD, to support the technique. The debugging technique is presented together with the use interface to AdaTAD. The component of AdaTAD that monitors and controls communication among tasks was designed in Ada and is presented through an example with a simple tasked program
Unsupervised machine learning for detection of phase transitions in off-lattice systems I. Foundations
We demonstrate the utility of an unsupervised machine learning tool for the
detection of phase transitions in off-lattice systems. We focus on the
application of principal component analysis (PCA) to detect the freezing
transitions of two-dimensional hard-disk and three-dimensional hard-sphere
systems as well as liquid-gas phase separation in a patchy colloid model. As we
demonstrate, PCA autonomously discovers order-parameter-like quantities that
report on phase transitions, mitigating the need for a priori construction or
identification of a suitable order parameter--thus streamlining the routine
analysis of phase behavior. In a companion paper, we further develop the method
established here to explore the detection of phase transitions in various model
systems controlled by compositional demixing, liquid crystalline ordering, and
non-equilibrium active forces
A focusing X-ray telescope for high altitude observations of cosmic X-rays in the energy range 20-140 keV
Focusing X ray telescope for high altitude observations of cosmic rays in 20-140 keV energy rang
Unsupervised machine learning for detection of phase transitions in off-lattice systems II. Applications
We outline how principal component analysis (PCA) can be applied to particle
configuration data to detect a variety of phase transitions in off-lattice
systems, both in and out of equilibrium. Specifically, we discuss its
application to study 1) the nonequilibrium random organization (RandOrg) model
that exhibits a phase transition from quiescent to steady-state behavior as a
function of density, 2) orientationally and positionally driven equilibrium
phase transitions for hard ellipses, and 3) compositionally driven demixing
transitions in the non-additive binary Widom-Rowlinson mixture
Dynamic relations in sampled processes
Linear dynamical relations that may exist in continuous-time, or at some
natural sampling rate, are not directly discernable at reduced observational
sampling rates. Indeed, at reduced rates, matricial spectral densities of
vectorial time series have maximal rank and thereby cannot be used to ascertain
potential dynamic relations between their entries. This hitherto undeclared
source of inaccuracies appears to plague off-the-shelf identification
techniques seeking remedy in hypothetical observational noise. In this paper we
explain the exact relation between stochastic models at different sampling
rates and show how to construct stochastic models at the finest time scale that
data allows. We then point out that the correct number of dynamical dependences
can only be ascertained by considering stochastic models at this finest time
scale, which in general is faster than the observational sampling rate.Comment: 13 pages, 4 figure
On a Fejer-Riesz factorization of generalized trigonometric polynomials
Function theory on the unit disc proved key to a range of problems in
statistics, probability theory, signal processing literature, and applications,
and in this, a special place is occupied by trigonometric functions and the
Fejer-Riesz theorem that non-negative trigonometric polynomials can be
expressed as the modulus of a polynomial of the same degree evaluated on the
unit circle. In the present note we consider a natural generalization of
non-negative trigonometric polynomials that are matrix-valued with specified
non-trivial poles (i.e., other than at the origin or at infinity). We are
interested in the corresponding spectral factors and, specifically, we show
that the factorization of trigonometric polynomials can be carried out in
complete analogy with the Fejer-Riesz theorem. The affinity of the
factorization with the Fejer-Riesz theorem and the contrast to classical
spectral factorization lies in the fact that the spectral factors have degree
smaller than what standard construction in factorization theory would suggest.
We provide two juxtaposed proofs of this fundamental theorem, albeit for the
case of strict positivity, one that relies on analytic interpolation theory and
another that utilizes classical factorization theory based on the
Yacubovich-Popov-Kalman (YPK) positive-real lemma.Comment: 11 page
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