Atrial fibrillation (AF) is a heart condition commonly diagnosed within the clinical praxis. During an AF episode, rapid and irregular heartbeats are present and they underly a complex electrical activity. It is known that the atrial structural alterations play a role in establishing the fibrillatory propagation patterns. However, the specific mechanisms are not fully understood. Fibrosis is a hallmark of AF and it represents structural abnormalities that disturbs the atrial electrical conduction. In this work, the behavior of the cardiomyocytes resting action potential in a fibrotic tissue, under distinct textures, is studied. A computational model of atrial electrophysiology is implemented. For the fibrosis model, spatial complex-order derivatives are used. Several values for the derivative order are tested in order to generate different degrees of structural complexity. The fibrosis model also includes cellular heterogeneity through the presence of fibroblasts coupled to cardiomyocytes. Diffuse, interstitial and compact fibrosis textures are implemented in a 2D domain and the amount of fibrosis is varied. The distribution of the resting potential is assessed using the Shannon entropy and the tissue is stimulated in order to evaluate the conduction velocity. The results indicate that, the distinct fibrosis structural conditions generate a wide range of resting potential distributions: from normal to heavy-tailed. The entropy values indicate the changes in the resting potential distribution when the structural complexity varies. Such analysis evinced that the amount of fibrosis generates specific entropy curves respect the derivative order. Moreover, the conduction velocity outside the fibrotic area is affected by the fibrotic configuration, which evinces the long-range effect of the fractional derivative operator and agrees with experimental observations. These results suggest that the proposed complex-order model can be useful for modeling fibrosis during atrial fibrillation and the entropy approach allows characterizing the wide range of fibrillatory scenarios under distinct fibrosis configurations.

Recently, a generic bioprocess gray box modeling approach [1] used entropy measure to plan the feeding solution profile. Multiple industrial experiments showed that such modeling is useful in cultivations with limited substrate feeding. The feeding profile served as a scaled approximation of the cumulative biomass profile. The cumulative glucose volume served as uncertainty to find the gray box model parameters in the feedback control scenarios. The numeric convex approach passed an analysis of its sensitivity to different initial computational conditions. The validation showed that the numeric routines were independent of the selected initial conditions. Such simplicity makes it useful for practical industrial applications.
Maximization of entropy presented online estimation of biomass concentration in fed-batch cultures of four types of recombinant E.coli strains and Saccharomyces cerevisiae cells [2]. Practical experience disclosed that entropy is a relevant measure for both limited substrate feeding and dosed substrate feeding biotechnological processes. Moreover, the approach showed neither numeric nor structural model dependence on the strain type.
Research progress revealed that entropy measure by the use of fundamental knowledge could make the general model (Luedeking-Piret) more common for technological use when estimating target protein, compared to a sophisticated artificial neural network (ANN) [3]. In fact, it replaces the ANN approach without compromising estimation accuracy.

[1] Urniezius, R.; Galvanauskas, V.; Survyla, A.; Simutis, R.; Levisauskas, D. From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time. Entropy 2018, 20, 779.

[2] Urniezius, R.; Survyla, A.; Paulauskas, D.; Bumelis, V.A.; Galvanauskas, V. Generic estimator of biomass concentration for Escherichia coli and Saccharomyces cerevisiae fed-batch cultures based on cumulative oxygen consumption rate. Microb. Cell Fact. 2019, 18, 190.

[3] Urniezius, R.; Survyla, A. Identification of Functional Bioprocess Model for Recombinant E. Coli Cultivation Process. Entropy 2019, 21, 1221.

This project has received funding from European Regional Development Fund (project No 01.2.2-LMT-K-718-03-0039) under grant agreement with the Research Council of Lithuania (LMTLT).

Entropy calculation is an important step in the postprocessing of molecular
dynamics trajectories or predictive models. In recent years the nearest
neighbor method proposed by Demchuk and coworkers [1] has emerged as a powerful
method to deal in a flexible way with the dimensionality of the problem.
Applications to most important biomolecular processes have been presented [2,3]
and a specific development has concerned the computation of
rotational-translational entropy which required in turn the definition of a
metric in rotation-translation space [4].
Two programs have been developed to compute conformational and
rotational-translational entropies from biomolecular ensembles [5].
Possible estensions of the method will be presented.

[1] Nearest neighbor estimates of entropy
H Singh, N Misra, V Hnizdo, A Fedorowicz, E Demchuk
American Journal of Mathematical and Management Sciences, 23 (3-4), 301-321,
2003

[2] Free energy, enthalpy and entropy from implicit solvent end-point
simulations
F Fogolari, A Corazza, G Esposito
Frontiers in Molecular Biosciences 5, 11, 2018

[3] Distance-based configurational entropy of proteins from molecular dynamics
simulations
F Fogolari, A Corazza, S Fortuna, MA Soler, B VanSchouwen, G Brancolini, S
Corni, G Melacini, G Esposito
PLoS One 10 (7), 2015

[4] Accurate Estimation of the Entropy of Rotation-Translation Probability
Distributions
F Fogolari, CJ Dongmo Foumthuim, S Fortuna, MA Soler, A Corazza, G Esposito
Journal of chemical theory and computation 12 (1), 1-8, 2016

[5] PDB2ENTROPY and PDB2TRENT: Conformational and Translational-Rotational
Entropy from Molecular Ensembles
F Fogolari, O Maloku, CJ Dongmo Foumthuim, A Corazza, G Esposito
Journal of chemical information and modeling 58 (7), 1319-1324, 2018

Frailty in older adults is characterised by dysregulation in multiple physiological systems. The frailty phenotype is defined on the basis of exhaustion, unexplained weight loss, weakness, slowness and low physical activity (one or two: pre-frail; 3 or more: frail). Our aim was to explore if increasing frailty is associated with the complexity of resting state physiological signals in a large cohort of community-dwelling older adults, enrolled as part of The Irish Longitudinal Study on Ageing (TILDA).

Systolic/diastolic blood pressure (SBP/DBP), mean arterial pressure (MAP), and heart rate (HR) were measured in 3,154 participants (66.2% non-frail; 31.3% pre-frail; 2.5% frail) using a Finometer® device at 200Hz; and frontal lobe oxygenation (tissue saturation index (TSI)) in 2,749 individuals (66.3% non-frail; 31.3% pre-frail; 2.4% frail) at 50Hz using an Artinis Portalite® near infrared spectroscopy system. Data were acquired continuously during five minutes of supine rest and the last minute (downsampled to 5Hz) was utilised in these analyses. The complexity of signals was quantified using approximate entropy (ApEn) with m=2 and an optimal r derived via multiple iterations, implemented in Matlab (R2019a). Statistical analysis was performed using multivariate linear regression models in STATA (v14.1), controlling for age, sex, education, antihypertensive medication, diabetes, number of cardiovascular conditions, smoking, alcohol, and depression.

Mean age for both groups was 64.3±8.1 years and 53% were female. The pre-frail group was associated with significantly increased ApEn for all measures investigated (sBP: β=0.014, P≤0.001; dBP: β=0.009, P=0.002; MAP: β=0.012, P≤0.001; HR: β=0.011, P=0.003; TSI: β=0.009, P=0.002). Likewise, the frail group was associated with further increased ApEn for all measures investigated (sBP: β=0.031, P=0.002; dBP: β=0.028, P=0.003; MAP: β=0.038, P≤0.001; HR: β=0.034, P=0.001; TSI: β=0.018, P=0.029).

Approximate entropy seems to be a sensitive method to capture increasing signal complexity in multiple physiological systems associated with the frailty phenotype during resting state.

Many physical and biological dynamical systems operate away from thermodynamic equilibrium, driven by their own activity as well as their interaction with the environment. The kinetic Ising model is a prototypical model for studying such non-equilibrium dynamics. Since its behaviour is generally intractable for large sizes due to combinatorial explosion, mean field theories are often employed to approximate network dynamics. However, mean field methods are often unable to capture systems displaying long-range correlations such as those operating near critical phase transitions. To tackle this problem, different variants of mean field approximations have been proposed for kinetic Ising models, each making unique assumptions about the correlation structure of the system. This disparity complicates the challenge of systematically advancing beyond previous contributions. Here, using information geometry, we propose that existing methods can be described and extended in a unified framework. Our method is defined as a family of expansions (called Plefka expansions) of an intractable marginal probability distribution around a specific point of a simplified model, defined in an information geometric space. These points are obtained by an orthogonal projection to a sub-manifold of probability distributions displaying a simplified correlation structure. This approach not only unifies previous methods but allows us to define novel methods that make unusual assumptions for mean field methods, like models preserving specific correlations of the system. By comparing analytic approximations and exact numerical simulations in a kinetic Sherrington Kirkpatrick model, we show that the new approximations found by our method provide more accurate estimates of the dynamics of the systems than classical equations, even near critical phase transitions presenting large fluctuations. In sum, our framework unifies and extends existing mean field methods in the kinetic Ising model from an information theoretic view, constituting a powerful tool for studying the dynamics of complex systems.

Background

The Multiscale Permutation Entropy (MPE) is a powerful tool in the differentiation of physiological electrical activity. In particular, the literature has found a clear link between the presence of faults in rotatory machines signals (Zheng 2018), and a reduction in Entropy within them. Therefore, any improvement in the precision of the MPE estimation enhances the chances of detecting increasingly nuanced changes in fault detection.

Objectives

In the present work, we first provide an alternative Permutation Entropy approach: the Refined Composite Downsampling Multiscale Permutation Entropy (rcDPE), which further reduces the variance over Refined Composite Multiscale Permutation Entropy (rcMPE) [Humeau-Heutier, 2015], by applying an alternative to the widely used coarse-graining procedure for multiscaling.

Methodology

Using the Bechhoffer bearing fault dataset (2013), we performed a 3-way ANOVA test with the following factors: Type of signal (presence of faults), Method, and Dimension. We also found the optimal parameters in this dataset in order to increase the entropy difference between faulty and non-faulty components.

Results

From the ANOVA test, we found all factors and interactions to be statistically significant (p<0.001). Furthermore we found that, albeit rcDPE greatly reduces the variance in PE measurements, the difference between Type of signal is reduced due to aliasing effects. The best performance is achieved with the use of an anti-aliasing filter in conjunction with rcDPE. For this particular dataset, classification between Types is reduced with increased Dimension, where only the filtered rcDPE remains significant. Therefore, rcDPE presents an important alternative in the exploration of Complexity-based classification techniques, capable of discerning more subtle changes between fatigued and non-fatigued muscle contractions.

Relations between the non-linear structure of neuronal activity and the way that neurons are involved in the behaviour were studied. To describe the non-linear structure of neuronal activity, the complexity of inter-spike intervals sequences was assessed calculating the sample entropy (SampEn). The experimental data used in analyses consisted of recordings of singular neuronal activity in the cingulate cortex of rabbits performing cyclic appetitive operant behaviour. All neurons were divided into two groups: specialized cells (N=29) and cells with nonspecific activity (N=84). The specialization of a neuron in relation to a defined behaviour is assessed via the probability of activation in behavioral acts. Neuronal activity and behaviour were recorded during the first and the second week after rabbits reach the learning criterion (10 right behaviour cycles performance one after another).

SampEn of inter-spike intervals was significantly lower in the group of specialized cells than in the group of cells with nonspecific activity (Mann–Whitney test; p=0.01). Concurrently, the average frequency of spikes didn’t differentiate between groups (p=0.33). In the whole set of cells, SampEn didn’t differ significantly between the first and the second weeks of training sessions p=0.34). Yet the group of specialized cells performed lower SampEn during the second week of training than the first week (p=0.03). The group of cells with nonspecific activity showed higher SampEn during the second week of training than the first week (p=0.02).

The results can reflect the difference in the constancy of relations between neurons in the group. Specialized cells have a more constant set and links between each other than cells that have unidentified specialization in the experiment. Their activity is less constant in the observed behaviour and they are more changeable in the set and the structure of links.

Supported by RSF Grant №18-78-10114.

The analysis of ordinal pattern distributions provides a relatively new and interesting approach to nonlinear time series analysis leading, for example, to the concept of permutation entropy. Data analysis methods based on ordinal patterns have been applied in different fields of research such as biomedicine, econophysics and engineering. Main reasons for the increasing success of these analysis methods are that ordinal patterns contain intrinsic information on the dynamical structure of a system and that ordinal pattern-based methods are robust and simple from a computational viewpoint.

Whereas some nice asymptotic results have been found for pattern length going to infinity, in practical data analysis short patterns describing certain features of data and models behind them are of some special interest. We demonstrate this point by discussing some statistics based on counting monotone changes and on considering asymmetries in ordinal pattern distributions. The data analysis methods obtained on this base are illustrated by considering some real world data.

The study of the dynamics of the nanoelectromechanical sensor (NEMS) is currently relevant since they are the next step in the evolution and miniaturization of sensors. Due to the nanosized of sense elements and other components of NEMS, they need in non-classical approaches for the study of their dynamics. Furthermore, the development of these non-classical approaches is a fundamental problem, and many scientists are working on its resolving. One more significant problem is the application of these non-classical approaches to components of the different kinds of NEMS and the obtainment the mathematical models are ready to use for a practical purpose.

In the paper, the mathematical model of the sensing element of pressure nanosensors was constructed based on the new modified couple-stress theory and the third-order plate theory. The sensing element was considered as a simply supported rectangular nanoplate under the distributed force at the bottom of the plate. The dynamic version of the principle of virtual displacements was used for obtaining the differential equations of motion and natural boundary conditions.

A series of computational experiments were carried out for an orthotropic nanoplate. Some combinations of parameters of the mathematical model are found for which chaotic motion is possible.

An exponential family is a manifold of generalized Gibbs state of the form exp(H)/Tr(exp(H)), where H belongs to a vector space of (possibly non-commutative) hermitian matrices. Generalized Gibbs states are important in small-scale thermodynamics, they represent equilibrium states regarding several conserved quantities that admit novel operations without heat dissipation [1]. Quantum information theory and condensed matter physics consider a space of local Hamiltonians acting on spins. The entropy distance from this exponential family is a measure of many-body complexity [2,3,4].

This talk is concerned with the geometry and topology of an exponential family and its entropy distance [5]. The maximum-entropy inference map parametrizes the exponential family. This map is continuous in the interior of its domain, the joint numerical range [6]. We describe the points of discontinuity in terms of open mapping theorems and eigenvalue crossings. Because of the discontinuity, the inference map and the entropy distance cannot be approximated through interior points. Instead, it is necessary to study faces (flat portions on the boundary) of the joint numerical range. With local Hamiltonians, this requires studying the faces of the set of quantum marginals.

References.

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[2] N. Ay, E. Olbrich, N. Bertschinger, and J. Jost,
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[4] B. Zeng, X. Chen, D.-L. Zhou, and X.-G. Wen,
Quantum Information Meets Quantum Matter,
New York: Springer, 2019.

[5] S. Weis, Journal of Convex Analysis 21, 339-399 (2014).

[6] L. Rodman, I. M. Spitkovsky, A. Szkoła, and S. Weis,
Journal of Mathematical Physics 57, 015204 (2016).