Random Fields in Physics, Biology and Data Science

Hernández‐Lemus, Enrique

doi:10.3389/fphy.2021.641859

Cited by 17 publications

(6 citation statements)

References 175 publications

(181 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…individual paths in a PGM do not in general have a simple meaning. For example, our choice of analyzing separator sets was motivated by the definition of the Global Markov Property of Markov Fields; analyzing collections of cliques may also be useful, motivated by the factorizations defined by the Hammersley-Clifford Theorem 10 . Intermediates are obviously vital to understanding cascades in a network, and so applications of PGMs to biological big data would benefit from future developments on interpreting and computing global features of PGMs.…”

Section: Discussionmentioning

confidence: 99%

Markov Field network model of multi-modal data predicts effects of immune system perturbations on intravenous BCG vaccination in macaques

Wang,

Myers,

Irvine

et al. 2024

Preprint

View full text Add to dashboard Cite

Multi-modal biological datasets provide rich information from diverse scales or facets of complex biological systems that can be analyzed to highlight the critical multi-scale interactions underlying specific biological phenomena. However, identifying the most vital associations among features and outputs can be beset by a high degree of spurious connections due to indirect effects of various immune features propagating through an unmapped biological network. Here, we applied a probabilistic graphical modeling approach, Markov Fields, to empirically dissect the most direct associations correlations between features from a public multi-modal dataset (antibody titers, antibody-dependent functions, cytokines, cytometry) from macaques undergoing intravenous BCG vaccination—a promising vaccine strategy against the major public health threat tuberculosis. This yielded a network influence model that interprets the assemblage of multi-scale paths by which vaccine effects propagate through the immune network to eventually protect against tuberculosis infection. Importantly, our modeling shows that the vast majority of apparent correlations between features arise from indirect effects relating distant immune features. For a test of predictive capability, we conducted experimental depletion of B cells during BCG IV vaccination in macaques--which did not reduce BCG IV-mediated protection against tuberculosis— and validated that our Markov Field model can predict systems-wide modulation of numerous features across the immune system in response to this perturbation. Finally, we applied our model to discern perturbations in the network that could have strong effects on IV-BCG efficacy. All together, we have demonstrated that probabilistic graphical modeling can increase interpretability and predictive value of multi-modal datasets for identifying new disease treatment targets.SummaryMulti-modal datasets provide rich information that can help identify critical multi-scale interactions underlying biological systems. However, identifying associations between features and outputs can be beset by spurious connections due to indirect impacts propagating through an unmapped biological network. We applied a probabilistic graphical modeling approach, Markov Fields, to dissect correlations between immune features in a public multi-modal dataset (systems serology, cytokines, cytometry) of macaques undergoing intravenous BCG vaccination against tuberculosis. This yielded an interaction network that interprets network paths underlying vaccine efficacy, and shows how correlations between features often arise indirectly. We next conducted experimental depletion of B cells during vaccination in macaques—which did not reduce protection against tuberculosis—to validate our Markov Field model’s predictions of network-wide shifts post-depletion. Finally, we highlight immune changes predicted to strongly affect intravenous BCG vaccine efficacy, showing that probabilistic graphical models increase the interpretability of multi-modal datasets for identifying new disease targets.

show abstract

Section: Discussionmentioning

confidence: 99%

Markov Field network model of multi-modal data predicts effects of immune system perturbations on intravenous BCG vaccination in macaques

Wang,

Myers,

Irvine

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Random fields are mathematical models used in the study of stochastic and non-linear complex systems [27]. Among all the random field models categorized in the literature, Gaussian random fields are remarkably important [28].…”

Section: Gaussian Random Fieldsmentioning

confidence: 99%

The curvature effect in Gaussian random fields

Levada¹

2022

J. Phys. Complex.

View full text Add to dashboard Cite

Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher information matrices). Using Markov chain Monte Carlo techniques, we simulate the dynamics of these random fields and compute the Gaussian, mean and principal curvatures of the parametric space, analyzing how these quantities change along dynamics exhibiting phase transitions. During the simulations, we have observed an unexpected phenomenon that we called the curvature effect, which indicates that a highly asymmetric geometric deformation happens in the underlying parametric space when there are significant increase/decrease in the system’s entropy. When the system undergoes a phase transition from randomness to clustered behavior the curvature is smaller than that observed in the reverse phase transition. This asymmetric pattern relates to the emergence of hysteresis phenomenon, leading to an intrinsic arrow of time along the random field dynamics.

show abstract

“…In addition to this, many random systems like prewetting transition on a disordered substrate [3], binary fluid mixtures in random porous media [4], phase transitions and interfaces in random media [5], structural phase transitions in random alloys [6], binary fluids in gels [7], collective effects induced by imitation and social pressure on society via network models [8] etc are modelled by ferromagnets in the presence of random field. Geophysical models of marine climate pattern [9], identification of subsurface soil patterns [10], analysis of molecular structures [11], biomedical imaging [12,13], population genetics [14], data science [15] and many more problems in other disciplines [16] have also been modelled using random fields.…”

Section: Introductionmentioning

confidence: 99%

Phase transitions in the Blume-Capel model with trimodal and Gaussian random fields

Mukherjee

2022

Preprint

View full text Add to dashboard Cite

We obtain the phase diagram for the infinite range random field Blume capel (RFBC) model for the symmetric trimodal distribution of the random field (h) in the temperature (T )-crystal field (∆) and T − h planes. We find 4 ordered and 2 disordered phases in the model at T = 0. Depending on the disorder strength, there are 5 different ground state phase diagrams in the ∆ − h plane. The T − ∆ and T − h phase diagrams also can be classified into 5 different categories as a function of the strength of the disorder, consistent with the 5 different ground state phase diagrams. The phase diagrams at finite temperature consist of lines of first order and second order transitions, multicritical points like tricritical point, bicritical points, critical end point, and also many multiphase coexistence points. We find re-entrance in the T −h phase diagram for the symmetric trimodal distribution for some values of ∆. We also studied the Gaussian distribution of the random field. In contrast, the ground state for the Gaussian distribution consists of only one ordered and one disordered phase. At low disorder strength (σ) the T − ∆ phase diagram has a line of first order and a line of second order transitions, separated by a TCP. However at higher σ the phase diagram only has a line of second order transition. In general the phase diagram of the random field problems is expected to be similar for symmetric distributions as has been observed for the random field O(n) models. In the case of RFBC we find that while for Gaussian distribution, the phase diagram is similar to the phase diagram of the infinite range random field Ising model (RFIM) with the bimodal random field distribution, for the symmetric trimodal distribution there are many different T − ∆ and T − h phase diagrams with multiple multicritical and multi-phase coexistence points.

show abstract

Random Fields in Physics, Biology and Data Science

Cited by 17 publications

References 175 publications

Markov Field network model of multi-modal data predicts effects of immune system perturbations on intravenous BCG vaccination in macaques

Markov Field network model of multi-modal data predicts effects of immune system perturbations on intravenous BCG vaccination in macaques

The curvature effect in Gaussian random fields

Phase transitions in the Blume-Capel model with trimodal and Gaussian random fields

Contact Info

Product

Resources

About