Quantifying simulator discrepancy in discrete-time dynamical simulators

When making predictions with complex simulators it can be important to quantify the various sources of uncertainty. Errors in the structural specification of the simulator, for example due to missing processes or incorrect mathematical specification, can be a major source of uncertainty, but are often ignored. We introduce a methodology for inferring the discrepancy between the simulator and the system in discrete-time dynamical simulators. We assume a structural form for the discrepancy function, and show how to infer the maximum-likelihood parameter estimates using a particle filter embedded within a Monte Carlo expectation maximization (MCEM) algorithm. We illustrate the method on a conceptual rainfall-runoff simulator (logSPM) used to model the Abercrombie catchment in Australia. We assess the simulator and discrepancy model on the basis of their predictive performance using proper scoring rules. This article has supplementary material online. © 2011 International Biometric Society.

One-Parameter Bifurcation Analysis of Dynamical Systems using Maple

This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.

An agro-ecological simulation model system

In this paper five different models, as five modules of a complex agro-ecosystem are investigated. The water and nutrient flow in soil is simulated by the nutrient-in-soil model while the biomass change according to the seasonal weather aspects, the nutrient content of soil and the biotic interactions amongst the other terms of the food web are simulated by the food web population dynamical model that is constructed for a piece of homogeneous field. The food web model is based on the nutrient-in-soil model and on the activity function evaluator model that expresses the effect of temperature. The numbers of individuals in all phenological phases of the different populations are given by the phenology model. The food web model is extended to an inhomogeneous piece of field by the spatial extension model. Finally, as an additional module, an application of the above models for multivariate state-planes, is given. The modules built into the system are closely connected to each other as they utilize each other’s outputs, nevertheless, they work separately, too. Some case studies are analysed and a summarized outlook is given.

A C80 DSP-based active vision system for real-time tracking

[EN]Active Vision Systems can be considered as dynamical systems which close the loop around artificial visual perception, controlling camera parameters, motion and also controlling processing to simplify, accelerate and do more robust visual perception. Research and Development in Active Vision Systems [Aloi87], [Bajc88] is a main area of interest in Computer Vision, mainly by its potential application in different scenarios where real-time performance is needed such as robot navigation, surveillance, visual inspection, among many others. Several systems have been developed during last years using robotic-heads for this purpose...

Dimensionality hyper-reduction and machine learning for dynamical systems with varying parameters

Thesis (Ph.D.)--University of Washington, 2016-08

Quantification of the human postural control system to perturbations

Human standing posture is inherently unstable. The postural control system (PCS), which maintains standing posture, is composed of the sensory, musculoskeletal, and central nervous systems. Together these systems integrate sensory afferents and generate appropriate motor efferents to adjust posture. The PCS maintains the body center of mass (COM) with respect to the base of support while constantly resisting destabilizing forces from internal and external perturbations. To assess the human PCS, postural sway during quiet standing or in response to external perturbation have frequently been examined descriptively. Minimal work has been done to understand and quantify the robustness of the PCS to perturbations. Further, there have been some previous attempts to assess the dynamical systems aspects of the PCS or time evolutionary properties of postural sway. However those techniques can only provide summary information about the PCS characteristics; they cannot provide specific information about or recreate the actual sway behavior. This dissertation consists of two parts: part I, the development of two novel methods to assess the human PCS and, part II, the application of these methods. In study 1, a systematic method for analyzing the human PCS during perturbed stance was developed. A mild impulsive perturbation that subjects can easily experience in their daily lives was used. A measure of robustness of the PCS, 1/MaxSens that was based on the inverse of the sensitivity of the system, was introduced. 1/MaxSens successfully quantified the reduced robustness to external perturbations due to age-related degradation of the PCS. In study 2, a stochastic model was used to better understand the human PCS in terms of dynamical systems aspect. This methodology also has the advantage over previous methods in that the sway behavior is captured in a model that can be used to recreate the random oscillatory properties of the PCS. The invariant density which describes the long-term stationary behavior of the center of pressure (COP) was computed from a Markov chain model that was applied to postural sway data during quiet stance. In order to validate the Invariant Density Analysis (IDA), we applied the technique to COP data from different age groups. We found that older adults swayed farther from the centroid and in more stochastic and random manner than young adults. In part II, the tools developed in part I were applied to both occupational and clinical situations. In study 3, 1/MaxSens and IDA were applied to a population of firefighters to investigate the effects of air bottle configuration (weight and size) and vision on the postural stability of firefighters. We found that both air bottle weight and loss of vision, but not size of air bottle, significantly decreased balance performance and increased fall risk. In study 4, IDA was applied to data collected on 444 community-dwelling elderly adults from the MOBILIZE Boston Study. Four out of five IDA parameters were able to successfully differentiate recurrent fallers from non-fallers, while only five out of 30 more common descriptive and stochastic COP measures could distinguish the two groups. Fall history and the IDA parameter of entropy were found to be significant risk factors for falls. This research proposed a new measure for the PCS robustness (1/MaxSens) and a new technique for quantifying the dynamical systems aspect of the PCS (IDA). These new PCS analysis techniques provide easy and effective ways to assess the PCS in occupational and clinical environments.

An extreme planetary system around HD 219828: one long-period super Jupiter to a hot-Neptune host star

Context. With about 2000 extrasolar planets confirmed, the results show that planetary systems have a whole range of unexpected properties. This wide diversity provides fundamental clues to the processes of planet formation and evolution. Aims: We present a full investigation of the HD 219828 system, a bright metal-rich star for which a hot Neptune has previously been detected. Methods: We used a set of HARPS, SOPHIE, and ELODIE radial velocities to search for the existence of orbiting companions to HD 219828. The spectra were used to characterise the star and its chemical abundances, as well as to check for spurious, activity induced signals. A dynamical analysis is also performed to study the stability of the system and to constrain the orbital parameters and planet masses. Results: We announce the discovery of a long period (P = 13.1 yr) massive (m sini = 15.1 MJup) companion (HD 219828 c) in a very eccentric orbit (e = 0.81). The same data confirms the existence of a hot Neptune, HD 219828 b, with a minimum mass of 21 M⊕ and a period of 3.83 days. The dynamical analysis shows that the system is stable, and that the equilibrium eccentricity of planet b is close to zero. Conclusions: The HD 219828 system is extreme and unique in several aspects. First, ammong all known exoplanet systems it presents an unusually high mass ratio. We also show that systems like HD 219828, with a hot Neptune and a long-period massive companion are more frequent than similar systems with a hot Jupiter instead. This suggests that the formation of hot Neptunes follows a different path than the formation of their hot jovian counterparts. The high mass, long period, and eccentricity of HD 219828 c also make it a good target for Gaia astrometry as well as a potential target for atmospheric characterisation, using direct imaging or high-resolution spectroscopy. Astrometric observations will allow us to derive its real mass and orbital configuration. If a transit of HD 219828 b is detected, we will be able to fully characterise the system, including the relative orbital inclinations. With a clearly known mass, HD 219828 c may become a benchmark object for the range in between giant planets and brown dwarfs.