scholarly journals Uncertainty quantification for quantum chemical models of complex reaction networks

2016 ◽  
Vol 195 ◽  
pp. 497-520 ◽  
Author(s):  
Jonny Proppe ◽  
Tamara Husch ◽  
Gregor N. Simm ◽  
Markus Reiher
Keyword(s):  
Free Energy ◽  
Electronic Structure ◽  
State Space ◽  
Time Scales ◽  
Reaction Network ◽  
Reaction Networks ◽  
Multiple Time Scales ◽  
Complex Reaction ◽  
Discrete State ◽  
Continuous State

For the quantitative understanding of complex chemical reaction mechanisms, it is, in general, necessary to accurately determine the corresponding free energy surface and to solve the resulting continuous-time reaction rate equations for a continuous state space. For a general (complex) reaction network, it is computationally hard to fulfill these two requirements. However, it is possible to approximately address these challenges in a physically consistent way. On the one hand, it may be sufficient to consider approximate free energies if a reliable uncertainty measure can be provided. On the other hand, a highly resolved time evolution may not be necessary to still determine quantitative fluxes in a reaction network if one is interested in specific time scales. In this paper, we present discrete-time kinetic simulations in discrete state space taking free energy uncertainties into account. The method builds upon thermo-chemical data obtained from electronic structure calculations in a condensed-phase model. Our kinetic approach supports the analysis of general reaction networks spanning multiple time scales, which is here demonstrated for the example of the formose reaction. An important application of our approach is the detection of regions in a reaction network which require further investigation, given the uncertainties introduced by both approximate electronic structure methods and kinetic models. Such cases can then be studied in greater detail with more sophisticated first-principles calculations and kinetic simulations.

scholarly journals Multiscale Free Energy Analysis of Human Ecosystem Engineering

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 396
Author(s):  
Stephen Fox
Keyword(s):  
Free Energy ◽  
State Space ◽  
Human Life ◽  
Limited Range ◽  
Ecosystem Engineering ◽  
Discrete State ◽  
Living Things ◽  
Continuous State ◽  
Human Ecosystem ◽  
Free Energy Analysis

Unlike ecosystem engineering by other living things, which brings a relatively limited range of sensations that are connected to a few enduring survival preferences, human ecosystem engineering brings an increasing variety and frequency of novel sensations. Many of these novel sensations can quickly become preferences as they indicate that human life will be less strenuous and more stimulating. Furthermore, they can soon become addictive. By contrast, unwanted surprise from these novel sensations may become apparent decades later. This recognition can come after the survival of millions of humans and other species has been undermined. In this paper, it is explained that, while multiscale free energy provides a useful hypothesis for framing human ecosystem engineering, disconnects between preferences and survival from human ecosystem engineering limit the application of current assumptions that underlie continuous state-space and discrete state-space modelling of active inference.

scholarly journals Improved estimations of stochastic chemical kinetics by finite-state expansion

2021 ◽  
Vol 477 (2251) ◽  
pp. 20200964
Author(s):  
Tabea Waizmann ◽  
Luca Bortolussi ◽  
Andrea Vandin ◽  
Mirco Tribastone
Keyword(s):  
Master Equation ◽  
State Space ◽  
Stochastic Dynamics ◽  
Reaction Network ◽  
Discrete State ◽  
State Expansion ◽  
Analytical Approximations ◽  
Finite State ◽  
Stochastic Reaction ◽  
Discrete State Space

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations and multi-stability.

Asymptotic behaviour of continuous time, continuous state-space branching processes

1974 ◽  
Vol 11 (04) ◽  
pp. 669-677 ◽  
Author(s):  
D. R. Grey
Keyword(s):  
Asymptotic Behaviour ◽  
State Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Discrete State ◽  
Space And Time ◽  
Continuous State Space ◽  
Continuous State ◽  
Discrete State Space

Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.

A STATISTICAL METHOD FOR DETECTING CYCLES IN DISCRETE DYNAMICAL SYSTEMS

1996 ◽  
Vol 06 (12a) ◽  
pp. 2375-2388 ◽  
Author(s):  
MARKUS LOHMANN ◽  
JAN WENZELBURGER
Keyword(s):  
Dynamical Systems ◽  
State Space ◽  
Statistical Method ◽  
Basins Of Attraction ◽  
Discrete State ◽  
Continuous State Space ◽  
Continuous State ◽  
Long Term Behavior ◽  
Discrete Time Dynamical Systems

This paper introduces a statistical method for detecting cycles in discrete time dynamical systems. The continuous state space is replaced by a discrete one consisting of cells. Hashing is used to represent the cells in the computer’s memory. An algorithm for a two-parameter bifurcation analysis is presented which uses the statistical method to detect cycles in the discrete state space. The output of this analysis is a colored cartogram where parameter regions are marked according to the long-term behavior of the system. Moreover, the algorithm allows the computation of basins of attraction of cycles.

scholarly journals Stochastic analysis of biochemical reaction networks with absolute concentration robustness

2014 ◽  
Vol 11 (93) ◽  
pp. 20130943 ◽  
Author(s):  
David F. Anderson ◽  
Germán A. Enciso ◽  
Matthew D. Johnston
Keyword(s):  
State Space ◽  
Stationary Distribution ◽  
Stochastic Dynamics ◽  
Reaction Network ◽  
Fine Tuning ◽  
Mass Action ◽  
Absolute Concentration ◽  
Biochemical Reaction Networks ◽  
Discrete State ◽  
Quasi Stationary Distribution

It has recently been shown that structural conditions on the reaction network, rather than a ‘fine-tuning’ of system parameters, often suffice to impart ‘absolute concentration robustness’ (ACR) on a wide class of biologically relevant, deterministically modelled mass-action systems. We show here that fundamentally different conclusions about the long-term behaviour of such systems are reached if the systems are instead modelled with stochastic dynamics and a discrete state space. Specifically, we characterize a large class of models that exhibit convergence to a positive robust equilibrium in the deterministic setting, whereas trajectories of the corresponding stochastic models are necessarily absorbed by a set of states that reside on the boundary of the state space, i.e. the system undergoes an extinction event. If the time to extinction is large relative to the relevant timescales of the system, the process will appear to settle down to a stationary distribution long before the inevitable extinction will occur. This quasi-stationary distribution is considered for two systems taken from the literature, and results consistent with ACR are recovered by showing that the quasi-stationary distribution of the robust species approaches a Poisson distribution.

Asymptotic behaviour of continuous time, continuous state-space branching processes

1974 ◽  
Vol 11 (4) ◽  
pp. 669-677 ◽  
Author(s):  
D. R. Grey
Keyword(s):  
Asymptotic Behaviour ◽  
State Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Discrete State ◽  
Space And Time ◽  
Continuous State Space ◽  
Continuous State ◽  
Discrete State Space

Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.

scholarly journals Ergodicity analysis and antithetic integral control of a class of stochastic reaction networks with delays

2018 ◽  
Author(s):  
Corentin Briat ◽  
Mustafa Khammash
Keyword(s):  
State Space ◽  
Reaction Network ◽  
Reaction Networks ◽  
Delayed Reaction ◽  
Finite Dimensional ◽  
Phase Type ◽  
Free Network ◽  
Stochastic Reaction ◽  
Stochastic Reaction Networks ◽  
Stochastic Reaction Network

AbstractDelays are important phenomena arising in a wide variety of real world systems, including biological ones, because of diffusion/propagation effects or as simplifying modeling elements. We propose here to consider delayed stochastic reaction networks, a class of networks that has been relatively few studied until now. The difficulty in analyzing them resides in the fact that their state-space is infinite-dimensional. We demonstrate here that by restricting the delays to be phase-type distributed, one can represent the associated delayed reaction network as a reaction network with finite-dimensional state-space. This can be achieved by suitably adding chemical species and reactions to the delay-free network following a simple algorithm which is fully characterized. Since phase-type distributions are dense in the set of probability distributions, they can approximate any distribution arbitrarily closely and this makes their consideration only a bit restrictive. As the state-space remains finite-dimensional, usual tools developed for non-delayed reaction network directly apply. In particular, we prove, for unimolecular mass-action reaction networks, that the delayed stochastic reaction network is ergodic if and only if the delay-free network is ergodic as well. Bimolecular reactions are more difficult to consider but slightly stronger analogous results are nevertheless obtained. These results demonstrate that delays have little to no harm to the ergodicity property of reaction networks as long as the delays are phase-type distributed, and this holds regardless the complexity of their distribution. We also prove that the presence of those delays adds convolution terms in the moment equation but does not change the value of the stationary means compared to the delay-free case. The covariance, however, is influenced by the presence of the delays. Finally, the control of a certain class of delayed stochastic reaction network using a delayed antithetic integral controller is considered. It is proven that this controller achieves its goal provided that the delay-free network satisfy the conditions of ergodicity and output-controllability.

scholarly journals Activated Self-Resolution and Error-Correction in Catalytic Reaction Networks

2021 ◽  
Author(s):  
Fredrik Schaufelberger ◽  
Olof Ramstrom
Keyword(s):  
Dynamic System ◽  
Error Correction ◽  
Small Molecule ◽  
Catalytic Reaction ◽  
Reaction Network ◽  
Reaction Networks ◽  
Complex Reaction ◽  
Catalytic Systems ◽  
Systems Chemistry ◽  
Mbh Reaction

<p>To understand the emergence of function in complex reaction networks is a primary goal of systems chemistry and origin-of-life studies. Especially challenging is the establishment of systems that simultaneously exhibit several functionality parameters that can be independently tuned. In this work, a multifunctional complex reaction network of nucleophilic small molecule catalysts for the Morita-Baylis-Hillman (MBH) reaction is demonstrated. The dynamic system exhibited triggered self-resolution, preferentially amplifying a specific catalyst/product set out of a many potential alternatives. By utilizing selective reversibility of the products of the reaction set, systemic thermodynamically driven error-correction could also be introduced. To achieve this, a dynamic covalent MBH reaction based on adducts with internal H-transfer capabilities was developed, displaying rate accelerations of retro-MBH reactions up to 104 times. This study demonstrates how efficient self-sorting of catalytic systems can be achieved through an interplay of several complex emergent functionalities.</p>

scholarly journals Multi-Agent Reinforcement Learning Using Linear Fuzzy Model Applied to Cooperative Mobile Robots

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 461 ◽  
Author(s):  
David Luviano-Cruz ◽  
Francesco Garcia-Luna ◽  
Luis Pérez-Domínguez ◽  
S. Gadi
Keyword(s):  
Reinforcement Learning ◽  
Mobile Robots ◽  
State Space ◽  
Fuzzy Model ◽  
Discrete State ◽  
Continuous State Space ◽  
Continuous State ◽  
Multi Agent ◽  
Successful Approach ◽  
Q Function

A multi-agent system (MAS) is suitable for addressing tasks in a variety of domains without any programmed behaviors, which makes it ideal for the problems associated with the mobile robots. Reinforcement learning (RL) is a successful approach used in the MASs to acquire new behaviors; most of these select exact Q-values in small discrete state space and action space. This article presents a joint Q-function linearly fuzzified for a MAS’ continuous state space, which overcomes the dimensionality problem. Also, this article gives a proof for the convergence and existence of the solution proposed by the algorithm presented. This article also discusses the numerical simulations and experimental results that were carried out to validate the proposed algorithm.

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