Random Perturbation Model Research Articles

Stability of topological purity under random local unitaries

In this work, we provide an analytical proof of the robustness of a form of topological entanglement under a model of random local perturbations. We define the notion of topological purity and show that, in the context of quantum double models, this quantity does detect topological order and is robust under the action of a random shallow quantum circuit.

Role of random thermal perturbations in the magmatic segmentation of mid-oceanic ridges: Insights from numerical simulations

Using a random thermal perturbation (RTP) model this study investigates the process of magmatic segmentation along mid-oceanic ridge (MOR) axes as a function of the upwelling dynamics, controlled by coupled solidification–melting processes. The RTP model suggests that the variation in along-axis velocity (VL) fields constitutes the underlying mechanism of segmentation in natural MORs, showing temperature variations within a steady-state range, irrespective of large initial thermal perturbations imposed at the model base. The VL patterns are initially transient, characterized by multi-order segments, but attain a stable configuration with dominantly large segments (average size ~100km) within a time scale of 2.3Ma. Buoyant-melt driven thermal convection explains this transient segmentation. Small scale convection cells are found to be progressively consumed by larger cells, resulting in a stable convection structure over a similar time scale. Slow- and fast-spreading ridges (SSR and FSR) undergo upwelling with contrasting melt flow patterns. SSRs involve melt feeding into the ridge axis by horizontal flows from segment centers, trailing into large-scale conduits at an early stage. With time, vertical upwelling occurs throughout the segment. In the case of FSRs, both melt supply avenues prevail throughout their development. We also evaluate the variation of the across-axis flow velocity (VT) to investigate the mode of geometric evolution of MORs. Time series VT maps suggest that a ridge structure develops through localization of discrete axes (VT=0) with offsets varying up to 15km, which coalesce with one another to form a single axis. The matured ridge, however, retains higher-order offsets (up to 9km).

Bounded noises as a natural tool to model extrinsic fluctuations in biomolecular networks

In the first part of this invited paper we review the role of both extrinsic and intrinsic stochasticity in shaping the dynamics of biomolecular networks. In particular, we stress the use of bounded stochastic processes as a model of extrinsic random perturbations. In the second part, we propose three examples of molecular circuits under the influence of external fluctuations modeled by means of bounded noises. The first two examples involve the linear decay of a protein with, respectively, large or low number of molecules, so to stress different modeling approaches. The third example concerns the spatio-temporal dynamics of proteins determining the chemotaxis-driven polarization of a cell. In these examples one can observe phenomena that are dependent on the specific class of employed bounded noise.

Fire-growth modelling using meteorological data with random and systematic perturbations

The focus of this investigation is to quantify the effects of perturbations in the meteorological data used in a fire-growth model. Observed variations of temperature, humidity, wind speed, and wind direction are applied as perturbations to hourly values within a simulated weather forecast to produce several forecasts. In turn, these are used by a deterministic eight-point fire-growth model to produce an ensemble of possible final fire perimeters. Two studies were conducted to assess the value of applying perturbations. In the first study, fire growth using detailed, one-minute data was compared to growth based on the more commonly used hourly data. Results showed that the detailed weather produced fire growth larger and wider than the hourly based data. By applying perturbations, variations in the flank and back-fire spread were captured by the random-perturbation model while the forward spread fell within the 20 to 30% probability prediction. A sensitivity analysis based on the observed variations showed that wind speed accounted for a 44% difference in area burned, while temperature accounted for only a 16% difference. In the second study, case studies were conducted on four observed forest fires in Wood Buffalo National Park. Results showed that daily fire-growth predictions using simulated weather forecasts over-predicted fire growth using actual hourly weather observations by 27%. Systematic-perturbation models best compensated for this with most fire growth falling within the predicted range of the models (52 out of 63 days).

Random perturbation models for boundary extraction sequence

Computer vision algorithms are composed of different sub-algorithms often applied in sequence. Determination of the performance of a total computer vision algorithm is possible if the performance of each of the sub-algorithm constituents is given. The performance characterization of an algorithm has to do with establishing the correspondence between the random variations and imperfections in the output data and the random variations and imperfections in the input data. In this paper we illustrate how random perturbation models can be set up for a vision algorithm sequence involving edge finding, edge linking, and gap filling. By starting with an appropriate noise model for the input data we derive random perturbation models for the output data at each stage of our example sequence. By utilizing the perturbation model for edge detector output derived, we illustrate how pixel noise can be successively propagated to derive an error model for the boundary extraction output. It is shown that the fragmentation of an ideal boundary can be described by an alternating renewal process and that the parameters of the renewal process are related to the probability of correct detection and grouping at the edge linking step. It is also shown that the characteristics of random segments generated due to gray-level noise are functions of the probability of false alarm of the edge detector. Theoretical results are validated through systematic experiments.

PROPAGATING COVARIANCE IN COMPUTER VISION

This paper describes how to propagate approximately additive random perturbations through any kind of vision algorithm step in which the appropriate random perturbation model for the estimated quantity produced by the vision step is also an additive random perturbation. We assume that the vision algorithm step can be modeled as a calculation (linear or non-linear) that produces an estimate that minimizes an implicit scaler function of the input quantity and the calculated estimate. The only assumption is that the scaler function has finite second partial derivatives and that the random perturbations are small enough so that the relationship between the scaler function evaluated at the ideal but unknown input and output quantities and the observed input quantity and perturbed output quantity can be approximated sufficiently well by a first order Taylor series expansion. The paper finally discusses the issues of verifying that the derived statistical behavior agrees with the experimentally observed statistical behavior.

A perturbation scheme for nonlinear models

In nonlinear regression, we measure the interaction between observations in a random perturbation model for assessing the local influence. Our perturbation model perturbs all cases separately, and our measures combine all sides together. Approximations are given for these measures. An example of a nonlinear model shows the effectiveness of these measures when masking exists. This perturbation scheme has proved useful in applications beyond the scope of this paper.

Transient resonant light scattering under random perturbations

Abstract A theory of light scattering for transient phenomena is formulated; a general scattering formula is obtained for pulse excitations. For a general stochastic model of random perturbations on a matter system, the formula is exactly expressed in terms of continued fractions. A detailed analysis is given for time-resolved spectra. It is explicitly shown that a change from “scattering” to luminescence can be observed separately as a function of time.

Temperature-dependent fermi resonance studies and lineshape simulation by random perturbation model

The lineshapes of Fermi diads of thioacetamide and methyl thiourea have been measured at different temperatures in the 120–300 K range. For computation of the lineshape, the dynamic part of the Fermi resonance interaction has been considered as a random perturbation by Redfield's theory. The optical Bloch equations are set up including the Redfield relaxation terms. The steady state solution of these equations lead to the absorption spectrum. The computed lineshape of a Fermi diad is shown to be a superposition of two Lorentzians and an interaction term. The linewidth of the Lorentzians are controlled by the Redfield and 1/ T 2 relaxation terms. The comparison of the computed curves with the observed spectra demonstrates the importance of the dynamic part of the interaction on the lineshape.

Random Wave-Front Perturbations and Telescopic Star Images

A computational model of random perturbations induced in wavefronts in the entry pupil of telescopes of moderate aperture has been constructed and used to predict the instantaneous distribution of intensity in the perturbed stellar images formed by such telescopes. Parameters of the model have been chosen to give a reasonably life-like imitation of perturbations due to imperfect ‘seeing’; and in order to gain some idea of the adequacy of the model, instantaneous intensity distributions in images of α-Aur have been obtained by computer reduction of observations made at the Cambridge 36-inch telescope using a spectracon electrono-graphic image tube. The model and its predictions are described and compared with the observations.