9,402 research outputs found
Improving non-linear fits
In this notes we describe an algorithm for non-linear fitting which
incorporates some of the features of linear least squares into a general
minimum fit and provide a pure Python implementation of the algorithm.
It consists of the variable projection method (varpro), combined with a Newton
optimizer and stabilized using the steepest descent with an adaptative step.
The algorithm includes a term to account for Bayesian priors. We performed
tests of the algorithm using simulated data. This method is suitable, for
example, for fitting with sums of exponentials as often needed in Lattice
Quantum Chromodynamics
Sequential nonideal measurements of quantum oscillators: Statistical characterization with and without environmental coupling
A one-dimensional quantum oscillator is monitored by taking repeated position
measurements. As a first con- tribution, it is shown that, under a quantum
nondemolition measurement scheme applied to a system initially at the ground
state, (i) the observed sequence of measurements (quantum tracks) corresponding
to a single experiment converges to a limit point, and that (ii) the limit
point is random over the ensemble of the experiments, being distributed as a
zero-mean Gaussian random variable with a variance at most equal to the
ground-state variance. As a second contribution, the richer scenario where the
oscillator is coupled with a frozen (i.e., at the ground state) ensemble of
independent quantum oscillators is considered. A sharply different behavior
emerges: under the same measurement scheme, here we observe that the
measurement sequences are essentially divergent. Such a rigorous statistical
analysis of the sequential measurement process might be useful for
characterizing the main quantities that are currently used for inference,
manipulation, and monitoring of many quantum systems. Several interesting
properties of the quantum tracks evolution, as well as of the associated
(quantum) threshold crossing times, are discussed and the dependence upon the
main system parameters (e.g., the choice of the measurement sampling time, the
degree of interaction with the environment, the measurement device accuracy) is
elucidated. At a more fundamental level, it is seen that, as an application of
basic quantum mechanics principles, a sharp difference exists between the
intrinsic randomness unavoidably present in any quantum system, and the
extrinsic randomness arising from the environmental coupling, i.e., the
randomness induced by an external source of disturbance.Comment: pages 16 Figures
Probabilistic data flow analysis: a linear equational approach
Speculative optimisation relies on the estimation of the probabilities that
certain properties of the control flow are fulfilled. Concrete or estimated
branch probabilities can be used for searching and constructing advantageous
speculative and bookkeeping transformations.
We present a probabilistic extension of the classical equational approach to
data-flow analysis that can be used to this purpose. More precisely, we show
how the probabilistic information introduced in a control flow graph by branch
prediction can be used to extract a system of linear equations from a program
and present a method for calculating correct (numerical) solutions.Comment: In Proceedings GandALF 2013, arXiv:1307.416
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