scholarly journals Fractional Dynamics Identification via Intelligent Unpacking of the Sample Autocovariance Function by Neural Networks

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1322
Author(s):  
Dawid Szarek ◽  
Grzegorz Sikora ◽  
Michał Balcerek ◽  
Ireneusz Jabłoński ◽  
Agnieszka Wyłomańska
Keyword(s):  
Gaussian Process ◽  
Theoretical Models ◽  
Single Particle Tracking ◽  
Fractional Dynamics ◽  
Complex Data ◽  
Diffusion Behavior ◽  
Autocovariance Function ◽  
Dynamics Identification ◽  
Crowded Environments ◽  
Anomalous Dynamics

Many single-particle tracking data related to the motion in crowded environments exhibit anomalous diffusion behavior. This phenomenon can be described by different theoretical models. In this paper, fractional Brownian motion (FBM) was examined as the exemplary Gaussian process with fractional dynamics. The autocovariance function (ACVF) is a function that determines completely the Gaussian process. In the case of experimental data with anomalous dynamics, the main problem is first to recognize the type of anomaly and then to reconstruct properly the physical rules governing such a phenomenon. The challenge is to identify the process from short trajectory inputs. Various approaches to address this problem can be found in the literature, e.g., theoretical properties of the sample ACVF for a given process. This method is effective; however, it does not utilize all of the information contained in the sample ACVF for a given trajectory, i.e., only values of statistics for selected lags are used for identification. An evolution of this approach is proposed in this paper, where the process is determined based on the knowledge extracted from the ACVF. The designed method is intuitive and it uses information directly available in a new fashion. Moreover, the knowledge retrieval from the sample ACVF vector is enhanced with a learning-based scheme operating on the most informative subset of available lags, which is proven to be an effective encoder of the properties inherited in complex data. Finally, the robustness of the proposed algorithm for FBM is demonstrated with the use of Monte Carlo simulations.

scholarly journals Single-molecule diffusometry reveals no catalysis-induced diffusion enhancement of alkaline phosphatase as proposed by FCS experiments

2020 ◽  
Author(s):  
Zhijie Chen ◽  
Alan Shaw ◽  
Hugh Wilson ◽  
Maxime Woringer ◽  
Xavier Darzacq ◽  
...  
Keyword(s):  
Alkaline Phosphatase ◽  
Single Molecule ◽  
Fluorescence Correlation Spectroscopy ◽  
Theoretical Models ◽  
Single Particle Tracking ◽  
Correlation Spectroscopy ◽  
Diffusion Behavior ◽  
Fluorescence Correlation ◽  
Apparent Diffusion ◽  
Diffusion Enhancement

ABSTRACTTheoretical and experimental observations that catalysis enhances the diffusion of enzymes have generated exciting implications about nanoscale energy flow, molecular chemotaxis and self-powered nanomachines. However, contradictory claims on the origin, magnitude, and consequence of this phenomenon continue to arise. Experimental observations of catalysis-enhanced enzyme diffusion, to date, have relied almost exclusively on fluorescence correlation spectroscopy (FCS), a technique that provides only indirect, ensemble-averaged measurements of diffusion behavior. Here, using an Anti-Brownian ELectrokinetic (ABEL) trap and in-solution spectroscopy (FCS), a technique that provides only indirect, ensemble-averaged measurements of diffusion behavior. Here, using an Anti-Brownian ELectrokinetic (ABEL) trap and in-solution single-particle tracking (SPT), we show that catalysis does not increase the diffusion of alkaline phosphatase (ALP) at the single-molecule level, in sharp contrast to the ~20% enhancement seen in parallel FCS experiments using p-nitrophenyl phosphate (pNPP) as substrate. Combining comprehensive FCS controls, ABEL trap, surface-based single-molecule fluorescence, and Monte-Carlo simulations, we establish that pNPP-induced dye blinking at the ~10 ms timescale is responsible for the apparent diffusion enhancement seen in FCS. Our observations urge a crucial revisit of various experimental findings and theoretical models––including those of our own––in the field, and indicate that in-solution SPT and ABEL trap are more reliable means to investigate diffusion phenomena at the nanoscale.SIGNIFICANCE STATEMENTRecent experiments have suggested that the energy released by a chemical reaction can propel its enzyme catalyst (for example, alkaline phosphatase, ALP). However, this topic remains controversial, partially due to the indirect and ensemble nature of existing measurements. Here, we used recently developed single-molecule approaches to monitor directly the motions of individual proteins in aqueous solution and find that single ALP enzymes do not diffuse faster under catalysis. Instead, we demonstrate that interactions between the fluorescent dye and the enzyme’s substrate can produce the signature of apparent diffusion enhancement in fluorescence correlation spectroscopy (FCS), the standard ensemble assay currently used to study enzyme diffusion and indicate that single-molecule approaches provide a more robust means to investigate diffusion at the nanoscale.

scholarly journals Mathematical Models for Dynamics of Molecular Processes in Living Biological Cells. A Single Particle Tracking Approach

2018 ◽  
Vol 32 (1) ◽  
pp. 5-41
Author(s):  
Aleksander Weron
Keyword(s):  
Particle Tracking ◽  
Single Particle ◽  
Moving Average ◽  
Single Particle Tracking ◽  
Fractional Dynamics ◽  
Data Sets ◽  
Molecular Processes ◽  
Survey Paper ◽  
Systematic Methodology ◽  
Dynamics Identification

Abstract In this survey paper we present a systematic methodology of how to identify origins of fractional dynamics. We consider three models leading to it, namely fractional Brownian motion (FBM), fractional Lévy stable motion (FLSM) and autoregressive fractionally integrated moving average (ARFIMA) process. The discrete-time ARFIMA process is stationary, and when aggregated, in the limit, it converges to either FBM or FLSM. In this sense it generalizes both models. We discuss three experimental data sets related to some molecular biology problems described by single particle tracking. They are successfully resolved by means of the universal ARFIMA time series model with various noises. Even if the finer details of the estimation procedures are case specific, we hope that the suggested checklist will still have been of great use as a practical guide. In Appendices A-F we describe useful fractional dynamics identification and validation methods.

scholarly journals Single-molecule diffusometry reveals no catalysis-induced diffusion enhancement of alkaline phosphatase as proposed by FCS experiments

2020 ◽  
Vol 117 (35) ◽  
pp. 21328-21335
Author(s):  
Zhijie Chen ◽  
Alan Shaw ◽  
Hugh Wilson ◽  
Maxime Woringer ◽  
Xavier Darzacq ◽  
...  
Keyword(s):  
Alkaline Phosphatase ◽  
Single Molecule ◽  
Particle Tracking ◽  
Single Particle ◽  
Theoretical Models ◽  
Single Particle Tracking ◽  
Correlation Spectroscopy ◽  
Single Molecule Level ◽  
Diffusion Phenomena ◽  
Diffusion Enhancement

Theoretical and experimental observations that catalysis enhances the diffusion of enzymes have generated exciting implications about nanoscale energy flow, molecular chemotaxis, and self-powered nanomachines. However, contradictory claims on the origin, magnitude, and consequence of this phenomenon continue to arise. To date, experimental observations of catalysis-enhanced enzyme diffusion have relied almost exclusively on fluorescence correlation spectroscopy (FCS), a technique that provides only indirect, ensemble-averaged measurements of diffusion behavior. Here, using an anti-Brownian electrokinetic (ABEL) trap and in-solution single-particle tracking, we show that catalysis does not increase the diffusion of alkaline phosphatase (ALP) at the single-molecule level, in sharp contrast to the ∼20% enhancement seen in parallel FCS experiments usingp-nitrophenyl phosphate (pNPP) as substrate. Combining comprehensive FCS controls, ABEL trap, surface-based single-molecule fluorescence, and Monte Carlo simulations, we establish thatpNPP-induced dye blinking at the ∼10-ms timescale is responsible for the apparent diffusion enhancement seen in FCS. Our observations urge a crucial revisit of various experimental findings and theoretical models––including those of our own––in the field, and indicate that in-solution single-particle tracking and ABEL trap are more reliable means to investigate diffusion phenomena at the nanoscale.

A weak convergence theorem for the empirical characteristic function

1975 ◽  
Vol 12 (3) ◽  
pp. 515-523 ◽  
Author(s):  
John T. Kent
Keyword(s):  
Weak Convergence ◽  
Characteristic Function ◽  
Gaussian Process ◽  
Convergence Theorem ◽  
Stationary Gaussian Process ◽  
Empirical Characteristic Function ◽  
Autocovariance Function ◽  
Weak Convergence Theorem

The purpose of this paper is to show that the empirical characteristic function, when suitably normalised, converges weakly to a stationary Gaussian process whose autocovariance function is the theoretical characteristic function.

The challenges of developing and evaluating complex care scenarios using simulation in nursing education

2012 ◽  
Vol 17 (4) ◽  
pp. 329-345 ◽  
Author(s):  
Mary Gobbi ◽  
Eloise Monger ◽  
Mark J. Weal ◽  
John W. McDonald ◽  
Danius Michaelides ◽  
...  
Keyword(s):  
Nursing Education ◽  
Patient Outcomes ◽  
Theoretical Models ◽  
Educational Interventions ◽  
High Fidelity ◽  
Complex Data ◽  
Complex Care ◽  
High Fidelity Simulation ◽  
High Current ◽  
The Impact

Demonstrating the impact and effectiveness of educational interventions, including medium and high-fidelity simulation, has long been fraught with methodological challenges and ambiguities. This is particularly the case when there are several confounding factors and variables operating in situations where control trials are inappropriate, and investigative costs can be high. Current theoretical and empirical evidence, while emerging, is parsimonious and fails to take account of the characteristics of different modes of simulation, their contested theoretical models of learning and the opportunities presented by cutting edge computer science. Medium and high-fidelity simulations, situated within technology-rich environments, generate new forms of complex data that have the potential to provide insights into ‘real-world’ practices. Drawing on a range of locally based studies, we argue that until the methodological questions and data management systems can be addressed, the evidence to determine the judicious and optimal use of simulation to improve student and practitioner performance and patient outcomes will remain primarily reliant on proxy measures of self-efficacy and competence.

A weak convergence theorem for the empirical characteristic function

1975 ◽  
Vol 12 (03) ◽  
pp. 515-523 ◽  
Author(s):  
John T. Kent
Keyword(s):  
Weak Convergence ◽  
Characteristic Function ◽  
Gaussian Process ◽  
Convergence Theorem ◽  
Stationary Gaussian Process ◽  
Empirical Characteristic Function ◽  
Autocovariance Function ◽  
Weak Convergence Theorem

The purpose of this paper is to show that the empirical characteristic function, when suitably normalised, converges weakly to a stationary Gaussian process whose autocovariance function is the theoretical characteristic function.

scholarly journals Automated discovery of relationships, models and principles in ecology

2015 ◽  
Author(s):  
Pedro Cardoso ◽  
Paulo A. V. Borges ◽  
José C. Carvalho ◽  
François Rigal ◽  
Rosalina Gabriel ◽  
...  
Keyword(s):  
Species Richness ◽  
Statistical Modelling ◽  
Theoretical Models ◽  
Ecological Systems ◽  
Formal Structure ◽  
Free Form ◽  
List Type ◽  
Complex Data ◽  
Linear Relationships ◽  
Patterns And Processes

ABSTRACTEcological systems are the quintessential complex systems, involving numerous high-order interactions and non-linear relationships. The most commonly used statistical modelling techniques can hardly reflect the complexity of ecological patterns and processes. Finding hidden relationships in complex data is now possible through the use of massive computational power, particularly by means of Artificial Intelligence methods, such as evolutionary computation.Here we use symbolic regression (SR), which searches for both the formal structure of equations and the fitting parameters simultaneously, hence providing the required flexibility to characterize complex ecological systems.First, we demonstrate how SR can deal with complex datasets for: 1) modelling species richness; and 2) modelling species spatial distributions. Second, we illustrate how SR can be used to find general models in ecology, by using it to: 3) develop species richness estimators; and 4) develop the species-area relationship and the general dynamic model of oceanic island biogeography.All the examples suggest that evolving free-form equations purely from data, often without prior human inference or hypotheses, may represent a very powerful tool for ecologists and biogeographers to become aware of hidden relationships and suggest general theoretical models and principles.

scholarly journals Automated Discovery of Relationships, Models, and Principles in Ecology

2020 ◽  
Vol 8 ◽  
Author(s):  
Pedro Cardoso ◽  
Vasco V. Branco ◽  
Paulo A. V. Borges ◽  
José C. Carvalho ◽  
François Rigal ◽  
...  
Keyword(s):  
Species Richness ◽  
Theoretical Models ◽  
Symbolic Regression ◽  
Ecological Systems ◽  
Formal Structure ◽  
Free Form ◽  
Complex Data ◽  
Linear Relationships ◽  
Automated Discovery ◽  
Patterns And Processes

Ecological systems are the quintessential complex systems, involving numerous high-order interactions and non-linear relationships. The most used statistical modeling techniques can hardly accommodate the complexity of ecological patterns and processes. Finding hidden relationships in complex data is now possible using massive computational power, particularly by means of artificial intelligence and machine learning methods. Here we explored the potential of symbolic regression (SR), commonly used in other areas, in the field of ecology. Symbolic regression searches for both the formal structure of equations and the fitting parameters simultaneously, hence providing the required flexibility to characterize complex ecological systems. Although the method here presented is automated, it is part of a collaborative human–machine effort and we demonstrate ways to do it. First, we test the robustness of SR to extreme levels of noise when searching for the species-area relationship. Second, we demonstrate how SR can model species richness and spatial distributions. Third, we illustrate how SR can be used to find general models in ecology, namely new formulas for species richness estimators and the general dynamic model of oceanic island biogeography. We propose that evolving free-form equations purely from data, often without prior human inference or hypotheses, may represent a very powerful tool for ecologists and biogeographers to become aware of hidden relationships and suggest general theoretical models and principles.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Analytical Electron Microscopy of Surface-Modified Ceramics

1985 ◽  
Vol 43 ◽  
pp. 276-279
Author(s):  
P. S. Sklad
Keyword(s):  
Electron Microscopy ◽  
Analytical Electron Microscopy ◽  
Theoretical Models ◽  
Ceramic Materials ◽  
Solute Concentration ◽  
Second Phase ◽  
Analytical Electron ◽  
Implantation Techniques ◽  
Lattice Damage ◽  
Surface Modified

Over the past several years, it has become increasingly evident that materials for proposed advanced energy systems will be required to operate at high temperatures and in aggressive environments. These constraints make structural ceramics attractive materials for these systems. However it is well known that the condition of the specimen surface of ceramic materials is often critical in controlling properties such as fracture toughness, oxidation resistance, and wear resistance. Ion implantation techniques offer the potential of overcoming some of the surface related limitations.While the effects of implantation on surface sensitive properties may be measured indpendently, it is important to understand the microstructural evolution leading to these changes. Analytical electron microscopy provides a useful tool for characterizing the microstructures produced in terms of solute concentration profiles, second phase formation, lattice damage, crystallinity of the implanted layer, and annealing behavior. Such analyses allow correlations to be made with theoretical models, property measurements, and results of complimentary techniques.

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