An iterative action minimizing method for computing optimal paths in stochastic dynamical systems

Lindley, Brandon; Schwartz, Ira B.

doi:10.1016/j.physd.2013.04.001

Cited by 48 publications

(53 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…q st0 m and q st 1 m are the two steady-state solutions of interest. Many numerical schemes have been proposed to solve such two-sided first-order equations (21,29,30), and here we use the geometric minimum action method (gMAM) (29) because of its robustness and computational efficiency. From the most probable transition path, we can estimate the transition rate k ∝ exp½−S (31), with the transition action S defined as…”

Section: Theoretical Approaches For Gene Networkmentioning

confidence: 99%

Stem cell differentiation as a many-body problem

Zhang

Wolynes

2014

Proc. Natl. Acad. Sci. U.S.A.

108

129

View full text Add to dashboard Cite

Stem cell differentiation has been viewed as coming from transitions between attractors on an epigenetic landscape that governs the dynamics of a regulatory network involving many genes. Rigorous definition of such a landscape is made possible by the realization that gene regulation is stochastic, owing to the small copy number of the transcription factors that regulate gene expression and because of the single-molecule nature of the gene itself. We develop an approximation that allows the quantitative construction of the epigenetic landscape for large realistic model networks. Applying this approach to the network for embryonic stem cell development explains many experimental observations, including the heterogeneous distribution of the transcription factor Nanog and its role in safeguarding the stem cell pluripotency, which can be understood by finding stable steady-state attractors and the most probable transition paths between those attractors. We also demonstrate that the switching rate between attractors can be significantly influenced by the gene expression noise arising from the fluctuations of DNA occupancy when binding to a specific DNA site is slow.gene network | most probable path | master equation

show abstract

Section: Theoretical Approaches For Gene Networkmentioning

confidence: 99%

Stem cell differentiation as a many-body problem

Zhang

Wolynes

2014

Proc. Natl. Acad. Sci. U.S.A.

108

129

View full text Add to dashboard Cite

show abstract

“…the numerical solutions of the Hamilton equations, which yield the optimal paths to extinction/switching and the corresponding actions along these paths, were found by using the Iterative Action Minimization Method, see Ref. [26] for further details. Matlab code is available upon request.…”

Section: Sis Hamiltonian For Arbitrary Degree Distributionsmentioning

confidence: 99%

“…Plugging Eqs. (26) and (27) into the action [Eq. (11) in the main text] yields the final result for the mean switching time Here we generalize our results for the spin model in the absence of detailed balance.…”

Section: Finding the Optimal Path And Action In The Spin Modelmentioning

confidence: 99%

Degree Dispersion Increases the Rate of Rare Events in Population Networks

Hindes

Assaf

2019

Phys. Rev. Lett.

View full text Add to dashboard Cite

There is great interest in predicting rare and extreme events in complex systems, and in particular, understanding the role of network topology in facilitating such events. In this work, we show that degree dispersion -the fact that the number of local connections in networks varies broadlyincreases the probability of large, rare fluctuations in population networks generically. We perform explicit calculations for two canonical and distinct classes of rare events: network extinction and switching. When the distance to threshold is held constant, and hence stochastic effects are fairly compared among networks, we show that there is a universal, exponential increase in the rate of rare events proportional to the variance of a network's degree distribution over its mean squared.

show abstract

“…Although tracking an optimal path as a parameter slowly varies is easier than finding a path without prior information, this remains a complicated, high dimensional problem. Recent work by Lindley and Schwartz has led to improved numerical methods for finding optimal paths [7], and we are working with these researchers to combine our approaches. These ideas will be extended to extinction in adaptive networks, including extinction in the presence of vaccine control strategies [15].…”

Section: Epidemic Extinctionmentioning

confidence: 99%

Adaptive Networks Foundations: Modeling, Dynamics, and Applications

Shaw¹

2013

View full text Add to dashboard Cite

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. We are studying adaptive social networks, focusing on spread of infectious disease as our primary example and including terrorist recruitment as an additional example. In an adaptive network, individuals change their social connections in response to their neighbors' characteristics, and these changes in network topology affect subsequent properties of the individuals. The network adaptation can be disease avoidance or connecting to potential recruits. Major goals of the project included extending previous models to incorporate more realistic network structure, ABSTRACTWe are studying adaptive social networks, focusing on spread of infectious disease as our primary example and including terrorist recruitment as an additional example. In an adaptive network, individuals change their social connections in response to their neighbors' characteristics, and these changes in network topology affect subsequent properties of the individuals. The network adaptation can be disease avoidance or connecting to potential recruits. Major goals of the project included extending previous models to incorporate more realistic network structure, adding spread of information that affects human behavior, studying the extinction of diseases, developing control strategies for epidemics on adaptive networks, and developing tools to analyze and monitor adaptive network properties. We have extended models to include network community structure, information spread, and more realistic social adaptation. We developed the first adaptive network model for terrorist recruitment. Our analytic work includes new techniques for predicting extinction rates of epidemics and the trajectory to extinction, methods to apply this to extinction on a network, and new moment closure approximation techniques that lead to more accurate predictions. For monitoring and control, we developed a method to quantify network adaptation and studied vaccine control for epidemics in adaptive networks.(a) Papers published in peer-reviewed journals (N/A for none)Enter List of papers submitted or published that acknowledge ARO support from the start of the project to the date of this printing. List the papers, including journal references, in the following categories:

show abstract

An iterative action minimizing method for computing optimal paths in stochastic dynamical systems

Cited by 48 publications

References 44 publications

Stem cell differentiation as a many-body problem

Stem cell differentiation as a many-body problem

Degree Dispersion Increases the Rate of Rare Events in Population Networks

Adaptive Networks Foundations: Modeling, Dynamics, and Applications

Contact Info

Product

Resources

About