Dataset Information

Ghost hunting in the nonlinear dynamic machine.

ABSTRACT: Integrating dynamic systems modeling and machine learning generates an exploratory nonlinear solution for analyzing dynamical systems-based data. Applying dynamical systems theory to the machine learning solution further provides a pathway to interpret the results. Using random forest models as an illustrative example, these models were able to recover the temporal dynamics of time series data simulated using a modified Cusp Catastrophe Monte Carlo. By extracting the points of no change (set points) and the predicted changes surrounding the set points, it is possible to characterize the topology of the system, both for systems governed by global equation forms and complex adaptive systems. RESULTS: The model for the simulation was able to recover the cusp catastrophe (i.e. the qualitative changes in the dynamics of the system) even when applied to data that have a significant amount of error variance. To further illustrate the approach, a real-world accelerometer example was examined, where the model differentiated between movement dynamics patterns by identifying set points related to cyclic motion during walking and attraction during stair climbing. These example findings suggest that integrating machine learning with dynamical systems modeling provides a viable means for classifying distinct temporal patterns, even when there is no governing equation for the nonlinear dynamics. Results of these integrated models yield solutions with both a prediction of where the system is going next and a decomposition of the topological features implied by the temporal dynamics.

SUBMITTER: Butner JE

PROVIDER: S-EPMC6922341 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Ghost hunting in the nonlinear dynamic machine.

Butner Jonathan E JE Munion Ascher K AK Baucom Brian R W BRW Wong Alexander A

PloS one 20191219 12

Integrating dynamic systems modeling and machine learning generates an exploratory nonlinear solution for analyzing dynamical systems-based data. Applying dynamical systems theory to the machine learning solution further provides a pathway to interpret the results. Using random forest models as an illustrative example, these models were able to recover the temporal dynamics of time series data simulated using a modified Cusp Catastrophe Monte Carlo. By extracting the points of no change (set poi ...[more]

PMID: 31856235

Similar Datasets

Project description:Terahertz (THz) imaging is a rapidly emerging field, thanks to many potential applications in diagnostics, manufacturing, medicine and material characterisation. However, the relatively coarse resolution stemming from the large wavelength limits the deployment of THz imaging in micro- and nano-technologies, keeping its potential benefits out-of-reach in many practical scenarios and devices. In this context, single-pixel techniques are a promising alternative to imaging arrays, in particular when targeting subwavelength resolutions. In this work, we discuss the key advantages and practical challenges in the implementation of time-resolved nonlinear ghost imaging (TIMING), an imaging technique combining nonlinear THz generation with time-resolved time-domain spectroscopy detection. We numerically demonstrate the high-resolution reconstruction of semi-transparent samples, and we show how the Walsh-Hadamard reconstruction scheme can be optimised to significantly reduce the reconstruction time. We also discuss how, in sharp contrast with traditional intensity-based ghost imaging, the field detection at the heart of TIMING enables high-fidelity image reconstruction via low numerical-aperture detection. Even more striking-and to the best of our knowledge, an issue never tackled before-the general concept of "resolution" of the imaging system as the "smallest feature discernible" appears to be not well suited to describing the fidelity limits of nonlinear ghost-imaging systems. Our results suggest that the drop in reconstruction accuracy stemming from non-ideal detection conditions is complex and not driven by the attenuation of high-frequency spatial components (i.e., blurring) as in standard imaging. On the technological side, we further show how achieving efficient optical-to-terahertz conversion in extremely short propagation lengths is crucial regarding imaging performance, and we propose low-bandgap semiconductors as a practical framework to obtain THz emission from quasi-2D structures, i.e., structure in which the interaction occurs on a deeply subwavelength scale. Our results establish a comprehensive theoretical and experimental framework for the development of a new generation of terahertz hyperspectral imaging devices.

Project description:BACKGROUND: The reconstruction of gene regulatory networks from time series gene expression data is one of the most difficult problems in systems biology. This is due to several reasons, among them the combinatorial explosion of possible network topologies, limited information content of the experimental data with high levels of noise, and the complexity of gene regulation at the transcriptional, translational and post-translational levels. At the same time, quantitative, dynamic models, ideally with probability distributions over model topologies and parameters, are highly desirable. RESULTS: We present a novel approach to infer such models from data, based on nonlinear differential equations, which we embed into a stochastic Bayesian framework. We thus address both the stochasticity of experimental data and the need for quantitative dynamic models. Furthermore, the Bayesian framework allows it to easily integrate prior knowledge into the inference process. Using stochastic sampling from the Bayes' posterior distribution, our approach can infer different likely network topologies and model parameters along with their respective probabilities from given data. We evaluate our approach on simulated data and the challenge #3 data from the DREAM 2 initiative. On the simulated data, we study effects of different levels of noise and dataset sizes. Results on real data show that the dynamics and main regulatory interactions are correctly reconstructed. CONCLUSIONS: Our approach combines dynamic modeling using differential equations with a stochastic learning framework, thus bridging the gap between biophysical modeling and stochastic inference approaches. Results show that the method can reap the advantages of both worlds, and allows the reconstruction of biophysically accurate dynamic models from noisy data. In addition, the stochastic learning framework used permits the computation of probability distributions over models and model parameters, which holds interesting prospects for experimental design purposes.

Dataset Information

Ghost hunting in the nonlinear dynamic machine.

Publications

Ghost hunting in the nonlinear dynamic machine.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets