Numerical and computational analysis on a dissipative dynamical system: Slow invariant manifold for complex chemical mechanism.

This article presents the notion about Slow Invariant Manifold (SIM) and their fundamental role in model reduction techniques (MRTs) for challenges encountered in mechanical engineering within dissipative systems of chemical kinetics. Focusing on the reaction routes of complex mechanisms, we construct and compare primary approximations of the SIM through MRTs, including the Spectral Quasi Equilibrium Manifold (SQEM) and Intrinsic Low Dimensional Manifold (ILDM). These methods effectively transform high-dimensional complex problems into lower dimensions, solving them without compromising crucial information about the complex systems modified for homogeneous reactive systems. Employing the sensitivity analysis by using the MATLAB's toolbox, we present the numerical findings in a tabular format obtained through MRTs. This study provides the understanding about the accessible exploration of numerical solutions, improving insights of the complex variation within the system.

Graph-based, dynamics-preserving reduction of (bio)chemical systems.

Complex dynamical systems are often governed by equations containing many unknown parameters whose precise values may or may not be important for the system's dynamics. In particular, for chemical and biochemical systems, there may be some reactions or subsystems that are inessential to understanding the bifurcation structure and consequent behavior of a model, such as oscillations, multistationarity and patterning. Due to the size, complexity and parametric uncertainties of many (bio)chemical models, a dynamics-preserving reduction scheme that is able to isolate the necessary contributors to particular dynamical behaviors would be useful. In this contribution, we describe model reduction methods for mass-action (bio)chemical models based on the preservation of instability-generating subnetworks known as critical fragments. These methods focus on structural conditions for instabilities and so are parameter-independent. We apply these results to an existing model for the control of the synthesis of the NO-detoxifying enzyme Hmp in Escherichia coli that displays bistability.

Reinforcement learning-based estimation for spatio-temporal systems.

State estimators such as Kalman filters compute an estimate of the instantaneous state of a dynamical system from sparse sensor measurements. For spatio-temporal systems, whose dynamics are governed by partial differential equations (PDEs), state estimators are typically designed based on a reduced-order model (ROM) that projects the original high-dimensional PDE onto a computationally tractable low-dimensional space. However, ROMs are prone to large errors, which negatively affects the performance of the estimator. Here, we introduce the reinforcement learning reduced-order estimator (RL-ROE), a ROM-based estimator in which the correction term that takes in the measurements is given by a nonlinear policy trained through reinforcement learning. The nonlinearity of the policy enables the RL-ROE to compensate efficiently for errors of the ROM, while still taking advantage of the imperfect knowledge of the dynamics. Using examples involving the Burgers and Navier-Stokes equations with parametric uncertainties, we show that in the limit of very few sensors, the trained RL-ROE outperforms a Kalman filter designed using the same ROM and yields accurate instantaneous estimates of high-dimensional states corresponding to unknown initial conditions and physical parameter values. The RL-ROE opens the door to lightweight real-time sensing of systems governed by parametric PDEs.

An efficient PGD solver for structural dynamics applications.

We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based on the Hamiltonian formalism. The novelty of this work lies in the implementation of a solver that is halfway between Modal Decomposition and the conventional PGD framework, so as to accelerate the fixed-point iteration algorithm. Additional procedures such that Aitken's delta-squared process and mode-orthogonalization are incorporated to ensure convergence and stability of the algorithm. Numerical results regarding the ROM accuracy, time complexity, and scalability are provided to demonstrate the performance of the new solver when applied to dynamic simulation of a three-dimensional structure.

Predicting inmate suicidal behavior with an interpretable ensemble machine learning approach in smart prisons.

The convergence of smart technologies and predictive modelling in prisons presents an exciting opportunity to revolutionize the monitoring of inmate behaviour, allowing for the early detection of signs of distress and the effective mitigation of suicide risks. While machine learning algorithms have been extensively employed in predicting suicidal behaviour, a critical aspect that has often been overlooked is the interoperability of these models. Most of the work done on model interpretations for suicide predictions often limits itself to feature reduction and highlighting important contributing features only. To address this research gap, we used Anchor explanations for creating human-readable statements based on simple rules, which, to our knowledge, have never been used before for suicide prediction models. We also overcome the limitation of anchor explanations, which create weak rules on high-dimensionality datasets, by first reducing data features with the help of SHapley Additive exPlanations (SHAP). We further reduce data features through anchor interpretations for the final ensemble model of XGBoost and random forest. Our results indicate significant improvement when compared with state-of-the-art models, having an accuracy and precision of 98.6% and 98.9%, respectively. The F1-score for the best suicide ideation model appeared to be 96.7%.

Mathematical and sensitivity analysis for chemical species in multistep dynamical system: A computational study.

This study presents a significant contribution to the field of chemical kinetics by providing a detailed analysis of a multi-step chemical kinetic process using ordinary differential equations (ODEs). The aim is to describe complex chemical processes' kinetics and the steady-state behavior of chemical species. The research employs reduction techniques to simplify the model by separating fast and slow processes based on their time scales, with a focus on a two-step reversible reaction mechanism. Special consideration is given to the phase flow of solution trajectories near equilibrium points, providing a clear depiction of system behavior. MATLAB simulations demonstrate the physical properties of observed data, while sensitivity analysis reveals parameters' impact on species behavior. Overall, this study enhances our understanding of chemical kinetics and offers insights into modeling complex reaction processes, with implications for various applications in chemistry and related fields.

Reconstructing rodent brain signals during euthanasia with eigensystem realization algorithm (ERA).

We accurately reconstruct the Local Field Potential time series obtained from anesthetized and awake rats, both before and during CO 2 euthanasia. We apply the Eigensystem Realization Algorithm to identify an underlying linear dynamical system capable of generating the observed data. Time series exhibiting more intricate dynamics typically lead to systems of higher dimensions, offering a means to assess the complexity of the brain throughout various phases of the experiment. Our results indicate that anesthetized brains possess complexity levels similar to awake brains before CO 2 administration. This resemblance undergoes significant changes following euthanization, as signals from the awake brain display a more resilient complexity profile, implying a state of heightened neuronal activity or a last fight response during the euthanasia process. In contrast, anesthetized brains seem to enter a more subdued state early on. Our data-driven techniques can likely be applied to a broader range of electrophysiological recording modalities.

Analysis of a detailed multi-stage model of stochastic gene expression using queueing theory and model reduction.

We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA into protein. The processes in sub-cellular compartments are described by an arbitrary number of processing stages, thus accounting for a significantly finer molecular description of gene expression than conventional models such as the telegraph, two-stage and three-stage models of gene expression. We use two distinct tools, queueing theory and model reduction using the slow-scale linear-noise approximation, to derive exact or approximate analytic expressions for the moments or distributions of nuclear mRNA, cytoplasmic mRNA and protein fluctuations, as well as lower bounds for their Fano factors in steady-state conditions. We use these to study the phase diagram of the stochastic model; in particular we derive parametric conditions determining three types of transitions in the properties of mRNA fluctuations: from sub-Poissonian to super-Poissonian noise, from high noise in the nucleus to high noise in the cytoplasm, and from a monotonic increase to a monotonic decrease of the Fano factor with the number of processing stages. In contrast, protein fluctuations are always super-Poissonian and show weak dependence on the number of mRNA processing stages. Our results delineate the region of parameter space where conventional models give qualitatively incorrect results and provide insight into how the number of processing stages, e.g. the number of rate-limiting steps in initiation, splicing and mRNA degradation, shape stochastic gene expression by modulation of molecular memory.

Adaptive Machine Learning Approach for Importance Evaluation of Multimodal Breast Cancer Radiomic Features.

Breast cancer holds the highest diagnosis rate among female tumors and is the leading cause of death among women. Quantitative analysis of radiological images shows the potential to address several medical challenges, including the early detection and classification of breast tumors. In the P.I.N.K study, 66 women were enrolled. Their paired Automated Breast Volume Scanner (ABVS) and Digital Breast Tomosynthesis (DBT) images, annotated with cancerous lesions, populated the first ABVS+DBT dataset. This enabled not only a radiomic analysis for the malignant vs. benign breast cancer classification, but also the comparison of the two modalities. For this purpose, the models were trained using a leave-one-out nested cross-validation strategy combined with a proper threshold selection approach. This approach provides statistically significant results even with medium-sized data sets. Additionally it provides distributional variables of importance, thus identifying the most informative radiomic features. The analysis proved the predictive capacity of radiomic models even using a reduced number of features. Indeed, from tomography we achieved AUC-ROC 89.9 % using 19 features and 92.1 % using 7 of them; while from ABVS we attained an AUC-ROC of 72.3 % using 22 features and 85.8 % using only 3 features. Although the predictive power of DBT outperforms ABVS, when comparing the predictions at the patient level, only 8.7% of lesions are misclassified by both methods, suggesting a partial complementarity. Notably, promising results (AUC-ROC ABVS-DBT 71.8 % - 74.1 % ) were achieved using non-geometric features, thus opening the way to the integration of virtual biopsy in medical routine.

Application and reduction of a nonlinear hyperelastic wall model capturing ex vivo relationships between fluid pressure, area, and wall thickness in normal and hypertensive murine left pulmonary arteries.

Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.

A new causal centrality measure reveals the prominent role of subcortical structures in the causal architecture of the extended default mode network.

Network representation has been an incredibly useful concept for understanding the behavior of complex systems in social sciences, biology, neuroscience, and beyond. Network science is mathematically founded on graph theory, where nodal importance is gauged using measures of centrality. Notably, recent work suggests that the topological centrality of a node should not be over-interpreted as its dynamical or causal importance in the network. Hence, identifying the influential nodes in dynamic causal models (DCM) remains an open question. This paper introduces causal centrality for DCM, a dynamics-sensitive and causally-founded centrality measure based on the notion of intervention in graphical models. Operationally, this measure simplifies to an identifiable expression using Bayesian model reduction. As a proof of concept, the average DCM of the extended default mode network (eDMN) was computed in 74 healthy subjects. Next, causal centralities of different regions were computed for this causal graph, and compared against several graph-theoretical centralities. The results showed that the subcortical structures of the eDMN were more causally central than the cortical regions, even though the graph-theoretical centralities unanimously favored the latter. Importantly, model comparison revealed that only the pattern of causal centrality was causally relevant. These results are consistent with the crucial role of the subcortical structures in the neuromodulatory systems of the brain, and highlight their contribution to the organization of large-scale networks. Potential applications of causal centrality-to study causal models of other neurotypical and pathological functional networks-are discussed, and some future lines of research are outlined.

Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species' Concentrations.

The current manuscript addresses the problem of parameter estimation for kinetic models of chemical reaction networks from observed time series partial experimental data of species concentrations. It is demonstrated how the Kron reduction method of kinetic models, in conjunction with the (weighted) least squares optimization technique, can be used as a tool to solve the above-mentioned ill-posed parameter estimation problem. First, a new trajectory-independent measure is introduced to quantify the dynamical difference between the original mathematical model and the corresponding Kron-reduced model. This measure is then crucially used to estimate the parameters contained in the kinetic model so that the corresponding values of the species' concentrations predicted by the model fit the available experimental data. The new parameter estimation method is tested on two real-life examples of chemical reaction networks: nicotinic acetylcholine receptors and Trypanosoma brucei trypanothione synthetase. Both weighted and unweighted least squares techniques, combined with Kron reduction, are used to find the best-fitting parameter values. The method of leave-one-out cross-validation is utilized to determine the preferred technique. For nicotinic receptors, the training errors due to the application of unweighted and weighted least squares are 3.22 and 3.61 respectively, while for Trypanosoma synthetase, the application of unweighted and weighted least squares result in training errors of 0.82 and 0.70 respectively. Furthermore, the problem of identifiability of dynamical systems, i.e., the possibility of uniquely determining the parameters from certain types of output, has also been addressed.

Rate-dependent effects of state-specific sodium channel blockers in cardiac tissue: Insights from idealized models.

A common side effect of pharmaceutical drugs is an increased propensity for cardiac arrhythmias. Many drugs bind to cardiac ion-channels in a state-specific manner, which alters the ionic conductances in complicated ways, making it difficult to identify the mechanisms underlying pro-arrhythmic drug effects. To better understand the fundamental mechanisms underlying the diverse effects of state-dependent sodium (Na+) channel blockers on cellular excitability, we consider two canonical motifs of drug-ion-channel interactions and compare the effects of Na+ channel blockers on the rate-dependence of peak upstroke velocity, conduction velocity, and vulnerable window size. In the literature, both motifs are referred to as "guarded receptor," but here we distinguish between state-specific binding that does not alter channel gating (referred to here as "guarded receptor") and state-specific binding that blocks certain gating transitions ("gate immobilization"). For each drug binding motif, we consider drugs that bind to the inactivated state and drugs that bind to the non-inactivated state of the Na+ channel. Exploiting the idealized nature of the canonical binding motifs, we identify the fundamental mechanisms underlying the effects on excitability of the various binding interactions. Specifically, we derive the voltage-dependence of the drug binding time constants and the equilibrium fractions of channels bound to drug, and we then derive a formula that incorporates these time constants and equilibrium fractions to elucidate the fundamental mechanisms. In the case of charged drug, we find that drugs that bind to inactivated channels exhibit greater rate-dependence than drugs that bind to non-inactivated channels. For neutral drugs, the effects of guarded receptor interactions are rate-independent, and we describe a novel mechanism for reverse rate-dependence resulting from neutral drug binding to non-inactivated channels via the gate immobilization motif.

The development of deep-ocean anoxia in a comprehensive ocean phosphorus model.

We analyse a model of the phosphorus cycle in the ocean given by Slomp and Van Cappellen (Biogeosciences 4:155-171, 2007. 10.5194/bg-4-155-2007). This model contains four distinct oceanic boxes and includes relevant parts of the water, carbon and oxygen cycles. We show that the model can essentially be solved analytically, and its behaviour completely understood without recourse to numerical methods. In particular, we show that, in the model, the carbon and phosphorus concentrations in the different ocean reservoirs are all slaved to the concentration of soluble reactive phosphorus in the deep ocean, which relaxes to an equilibrium on a time scale of 180,000 y, and we show that the deep ocean is either oxic or anoxic, depending on a critical parameter which we can determine explicitly. Finally, we examine how the value of this critical parameter depends on the physical parameters contained in the model. The presented methodology is based on tools from applied mathematics and can be used to reduce the complexity of other large, biogeochemical models. Supplementary Information: The online version contains supplementary material available at 10.1007/s13137-023-00221-0.

Optimized cell type signatures revealed from single-cell data by combining principal feature analysis, mutual information, and machine learning.

Machine learning techniques are excellent to analyze expression data from single cells. These techniques impact all fields ranging from cell annotation and clustering to signature identification. The presented framework evaluates gene selection sets how far they optimally separate defined phenotypes or cell groups. This innovation overcomes the present limitation to objectively and correctly identify a small gene set of high information content regarding separating phenotypes for which corresponding code scripts are provided. The small but meaningful subset of the original genes (or feature space) facilitates human interpretability of the differences of the phenotypes including those found by machine learning results and may even turn correlations between genes and phenotypes into a causal explanation. For the feature selection task, the principal feature analysis is utilized which reduces redundant information while selecting genes that carry the information for separating the phenotypes. In this context, the presented framework shows explainability of unsupervised learning as it reveals cell-type specific signatures. Apart from a Seurat preprocessing tool and the PFA script, the pipeline uses mutual information to balance accuracy and size of the gene set if desired. A validation part to evaluate the gene selection for their information content regarding the separation of the phenotypes is provided as well, binary and multiclass classification of 3 or 4 groups are studied. Results from different single-cell data are presented. In each, only about ten out of more than 30000 genes are identified as carrying the relevant information. The code is provided in a GitHub repository at https://github.com/AC-PHD/Seurat_PFA_pipeline.

Neurochemistry-enriched dynamic causal models of magnetoencephalography, using magnetic resonance spectroscopy.

We present a hierarchical empirical Bayesian framework for testing hypotheses about neurotransmitters' concertation as empirical prior for synaptic physiology using ultra-high field magnetic resonance spectroscopy (7T-MRS) and magnetoencephalography data (MEG). A first level dynamic causal modelling of cortical microcircuits is used to infer the connectivity parameters of a generative model of individuals' neurophysiological observations. At the second level, individuals' 7T-MRS estimates of regional neurotransmitter concentration supply empirical priors on synaptic connectivity. We compare the group-wise evidence for alternative empirical priors, defined by monotonic functions of spectroscopic estimates, on subsets of synaptic connections. For efficiency and reproducibility, we used Bayesian model reduction (BMR), parametric empirical Bayes and variational Bayesian inversion. In particular, we used Bayesian model reduction to compare alternative model evidence of how spectroscopic neurotransmitter measures inform estimates of synaptic connectivity. This identifies the subset of synaptic connections that are influenced by individual differences in neurotransmitter levels, as measured by 7T-MRS. We demonstrate the method using resting-state MEG (i.e., task-free recording) and 7T-MRS data from healthy adults. Our results confirm the hypotheses that GABA concentration influences local recurrent inhibitory intrinsic connectivity in deep and superficial cortical layers, while glutamate influences the excitatory connections between superficial and deep layers and connections from superficial to inhibitory interneurons. Using within-subject split-sampling of the MEG dataset (i.e., validation by means of a held-out dataset), we show that model comparison for hypothesis testing can be highly reliable. The method is suitable for applications with magnetoencephalography or electroencephalography, and is well-suited to reveal the mechanisms of neurological and psychiatric disorders, including responses to psychopharmacological interventions.

Reducing Boolean networks with backward equivalence.

BACKGROUND: Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis. RESULTS: We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance. CONCLUSIONS: BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs.

Determination of significant immunological timescales from mRNA-LNP-based vaccines in humans.

A compartment model for an in-host liquid nanoparticle delivered mRNA vaccine is presented. Through non-dimensionalisation, five timescales are identified that dictate the lifetime of the vaccine in-host: decay of interferon gamma, antibody priming, autocatalytic growth, antibody peak and decay, and interleukin cessation. Through asymptotic analysis we are able to obtain semi-analytical solutions in each of the time regimes which allows us to predict maximal concentrations and better understand parameter dependence in the model. We compare our model to 22 data sets for the BNT162b2 and mRNA-1273 mRNA vaccines demonstrating good agreement. Using our analysis, we estimate the values for each of the five timescales in each data set and predict maximal concentrations of plasma B-cells, antibody, and interleukin. Through our comparison, we do not observe any discernible differences between vaccine candidates and sex. However, we do identify an age dependence, specifically that vaccine activation takes longer and that peak antibody occurs sooner in patients aged 55 and greater.

Low-dimensional models of single neurons: a review.

The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as subthreshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type.

Modeling and tracking control of dielectric elastomer actuators based on fractional calculus.

Dielectric elastomer actuators (DEAs) show broad application prospects in the area of soft robots since they offer merits of fast response, large deformation, light weight and high energy conversion efficiency. Practical soft robot applications would usually require the study on the modeling and control of the DEA. However, the DEA has a memory property, which results in a highly nonlinear characteristics, bringing difficulties to the subject. To address this issue, an effective strategy is the utilization of the fractional order model, which is a type of modeling approach that can accurately characterize the memory property of a material with a small amount of parameters. Meanwhile, the fractional order controller can better handler the memory property, and it owns a better flexibility than traditional integer order controllers. With the above considerations, this paper proposes a modeling strategy and a tracking control strategy for the DEA on the basis of the fractional calculus. In the proposed strategy, a fractional order model is established to characterize the complicated nonlinear characteristics of the DEA. Then, to facilitate the computer simulation, the Oustaloup filter is used to construct an integer order approximation model (IOAM) of the fractional order model. Since the IOAM is difficult to be employed in the system controller design due to its high order, the IOAM is further simplified into a reduced order model based on the square root balance truncation algorithm. To realize the high accuracy control of the DEA, a feedforward-feedback combined controller is devised, which is composed of a feedforward controller and a fractional order proportional integral feedback controller (FOPIFC). Among which, the feedforward controller is devised based on the analytical inverse of the reduced order model to compensate the complicated nonlinear characteristics of the DEA, and the FOPIFC is devised to handle the bad influence from the modeling error and uncertainties on the control performance. Based on the proposed strategy, control experiment was conducted, and the root-mean-square errors in experiment are all below 0.7%, indicating the superiority of the presented modeling and tracking control strategies.