SARS-coronavirus-2 infections: biological instabilities characterized by order parameters.

A four-variable virus dynamics TIIV model was considered that involves infected cells in an eclipse phase. The state space description of the model was transferred into an amplitude space description which is the appropriate general, nonlinear physics framework to describe instabilities. In this context, the unstable eigenvector or order parameter of the model was determined. Subsequently, a model-based analysis of viral load data from eight symptomatic COVID-19 patients was conducted. For all patients, it was found that the initial SARS-CoV-2 infection evolved along the respective patient-specific order parameter, as expected by theoretical considerations. The order parameter amplitude that described the initial virus multiplication showed doubling times between 30 min and 3 h. Peak viral loads of patients were linearly related to the amplitudes of the patient order parameters. Finally, it was found that the patient order parameters determined qualitatively and quantitatively the relationships between the increases in virus-producing infected cells and infected cells in the eclipse phase. Overall, the study echoes the 40 years old suggestion by Mackey and Glass to consider diseases as instabilities.

SEIR order parameters and eigenvectors of the three stages of completed COVID-19 epidemics: with an illustration for Thailand January to May 2020.

By end of October 2020, the COVID-19 pandemic has taken a tragic toll of 1150 000 lives and this number is expected to increase. Despite the pandemic is raging in most parts of the world, in a few countries COVID-19 epidemics subsided due to successful implementations of intervention measures. A unifying perspective of the beginnings, middle stages, and endings of such completed COVID-19 epidemics is developed based on the order parameter and eigenvalue concepts of nonlinear physics, in general, and synergetics, in particular. To this end, a standard susceptible-exposed-infected-recovered (SEIR) epidemiological model is used. It is shown that COVID-19 epidemic outbreaks follow a suitably defined SEIR order parameter. Intervention measures switch the eigenvalue of the order parameter from a positive to a negative value, and in doing so, stabilize the COVID-19 disease-free state. The subsiding of COVID-19 epidemics eventually follows the remnant of the order parameter of the infection dynamical system. These considerations are illustrated for the COVID-19 epidemic in Thailand from January to May 2020. The decay of effective contact rates throughout the three epidemic stages is demonstrated. Evidence for the sign-switching of the dominant eigenvalue is given and the order parameter and its stage-3 remnant are identified. The presumed impacts of interventions measures implemented in Thailand are discussed in this context.

COVID-19 interventions in some European countries induced bifurcations stabilizing low death states against high death states: An eigenvalue analysis based on the order parameter concept of synergetics.

Taking a dynamical systems perspective, COVID-19 infections are assumed to spread out in a human population via an instability. Conversely, government interventions to reduce the spread of the disease and the number of fatalities may induce a bifurcation that stabilizes a desirable state with low numbers of COVID-19 cases and associated deaths. The key characteristic feature of an infection dynamical system in this context is the eigenvalue that determines the stability of the states under consideration and is known in synergetics as the order parameter eigenvalue. Using a SEIR-like infection disease model, the relevant order parameter and its eigenvalue are determined. A three stage methodology is proposed to track and estimate the eigenvalue through time. The method is applied to COVID-19 infection data reported from 20 European countries during the period of January 1, 2020 to June 15. It is shown that in 15 out of the 20 countries the eigenvalue switched its sign suggesting that during the reporting period an intervention bifurcation took place that stabilized the desirable low death state. It is shown that the eigenvalue analysis also allows for a ranking of countries by the degree of the stability of the infection-free state. For the investigated countries, Ireland was found to exhibit the most stable infection-free state. Finally, a six point classification scheme is suggested with groups 5 and 6 including countries that failed to stabilize the desirable infection-free low death state. In doing so, tools for assessing the effectiveness of government interventions are provided that are at the heart of bifurcation theory, in general, and synergetics, in particular.

Correlations Between Hysteretic Categorical and Continuous Judgments of Perceptual Stimuli Supporting a Unified Dynamical Systems Approach to Perception.

We report from two variants of a figure-ground experiment that is known in the literature to involve a bistable perceptual domain. The first variant was conducted as a two-alternative forced-choice experiment and in doing so tested participants on a categorical measurement scale. The second variant involved a Likert scale measure that was considered to represent a continuous measurement scale. The two variants were conducted as a single within-subjects experiment. Measures of bistability operationalized in terms of hysteresis size scores showed significant positive correlations across the two response conditions. The experimental findings are consistent with a dualistic interpretation of self-organizing perceptual systems when they are described on a macrolevel by means of so-called amplitude equations. This is explicitly demonstrated for a Lotka-Volterra-Haken amplitude equation model of task-related brain activity. As a by-product, the proposed dynamical systems perspective also sheds new light on the anchoring problem of producing numerical, continuous judgments.

Front waves in the early RNA world: The Schlögl model and the logistic growth model.

Front wave solutions of nonlinear reaction-diffusion models describing the spatio-temporal growth of RNA populations in the early RNA world are discussed. A two-variable model for RNA enzymes and enzyme complex molecules as well as single-variable models obtained via adiabatic elimination of the complex molecules are considered. In both models, the focus is on enzyme diffusion in one spatial dimension, assuming that the diffusion of complex molecules can be neglected. It is shown that one of the single-variable models corresponds to a Schlögl model of front propagation. In general, for the single-variable models it is found that front speed corresponds to the minimal speed of traveling fronts. In contrast, the two-variable model exhibits even slower front propagation. Front propagation might be an important factor in competitive evolutionary processes in the early RNA world.

Perception adapts via top-down regulation to task repetition: A Lotka-Volterra-Haken modeling analysis of experimental data.

Two experiments are reported in which participants perceived different physical quantities: size and speed. The perceptual tasks were performed in the context of motor performance problems. Participants perceived the size of objects in order to grasp the objects single handed or with both hands. Likewise, participants perceived the speed of a moving treadmill in order to control walking or running at that speed. In both experiments, the perceptual tasks were repeatedly performed by the participants while the to-be-perceived quantity was gradually varied from small to large objects (Experiment 1) and from low to high speeds (Experiment 2). Hysteresis with negative sign was found when participants were not allowed to execute the motor component, that is, when the execution stage was decoupled from the planning stage. No such effect was found in the control condition, when participants were allowed to execute the motor action. Using a Lotka-Volterra-Haken model for two competing neural populations, it is argued that the observations are consistent with the notion that the repetitions induce an adaptation effect of the perceptual system via top-down regulation. Moreover, the amount of synaptic modulation involved in the adaptation is estimated from participant data.

Interplay between order-parameter and system parameter dynamics: considerations on perceptual-cognitive-behavioral mode-mode transitions exhibiting positive and negative hysteresis and on response times.

A mathematical model is presented for the emergence of perceptual-cognitive-behavioral modes in psychophysical experiments in which participants are confronted with two alternatives. The model is based on the theory of self-organization and, in particular, the order parameter concept such that the emergence of a mode is conceptualized as an instability leading to the emergence of an appropriately defined order parameter. The order parameter model is merged with a second model that describes adaptation in terms of a system parameter dynamics. It is shown that the two-component model predicts hysteretic mode-mode transitions when control parameters are increased or decreased beyond critical values. The two-component model can account for both positive and negative hysteresis effects due to the interaction between order parameter and system parameter dynamics. Moreover, the model-based analysis reveals that response time curves look rather flat when response times are relatively decoupled from the mode-mode transition phenomenon. In general, response time curves exhibit a peaked close to the mode-mode transition point. In this context, the possibility is discussed that such peaked response time curves belong to the class of critical phenomena of self-organizing systems. In order to illustrate the relevance of peaked response time curves for future research and research reported in the past, results from a perceptual judgment experiment are reported, in which participants judged their ability to stand on a tilted slope for various angles of inclination. Response time curves were found that exhibited a peak around the mode-mode-transition points between "yes" and "no" responses.

On the Interplay between Order Parameter Dynamics and System Parameter Dynamics in Human Perceptual-Cognitive-Behavioral Systems.

Previous research has demonstrated that perceiving, thinking, and acting are human activities that correspond to self-organized patterns. The emergence of such patterns can be completely described in terms of the dynamics of the pattern amplitudes, which are referred to as order parameters. The patterns emerge at bifurcations points when certain system parameters internal and external to a human agent exceed critical values. At issue is how one might study the order parameter dynamics for sequences of consecutive, emergent perceptual, cognitive, or behavioral activities. In particular, these activities may in turn impact the system parameters that have led to the emergence of the activities in the first place. This interplay between order parameter dynamics and system parameter dynamics is discussed in general and formulated in mathematical terms. Previous work that has made use of this two-tiered framework of order parameter and system parameter dynamics are briefly addressed. As an application, a model for perception under functional fixedness is presented. Finally, it is argued that the phenomena that emerge in this framework and can be observed when human agents perceive, think, and act are just as likely to occur in pattern formation systems of the inanimate world. Consequently, these phenomena do not necessarily have a neurophysiological basis but should instead be understood from the perspective of the theory of self-organization.

Capturing and quantifying the dynamics of valenced emotions and valenced events of the organism-environment system.

The events we encounter and the emotions we experience are valenced-they are positively or negatively charged. Although these occurrences seem to be distributed irregularly throughout the day, the two experiments presented here reveal systematicity in the temporal dynamics of affective experience using a variety of time-series analyses. In Experiment 1, participants used a portable button to respond to event valence (the positive or negative charge of an event in the environment) or affective valence (one's positive or negative feeling at the time of responding). This methodology yields signed response durations, indexing the valence and intensity of an occurrence, and inter-response intervals, indexing their distribution. These measures revealed that valenced occurrences are correlated with both temporally proximal and remote occurrences. Experiment 2 validated the methodology employed in Experiment 1 using artificial, laboratory-created event structures. Implications of dynamical approaches to understanding emotion are discussed.

Unstable eigenvectors and reduced amplitude spaces specifying limit cycles of coupled oscillators with simultaneously diagonalizable matrices: with applications from electric circuits to gene regulation.

Abstract: A fascinating phenomenon is the self-organization of coupled systems to a whole. This phenomenon is studied for a particular class of coupled oscillatory systems exhibiting so-called simultaneously diagonalizable matrices. For three exemplary systems, namely, an electric circuit, a coupled system of oscillatory neurons, and a system of coupled oscillatory gene regulatory pathways, eigenvectors and amplitude equations are derived. It is shown that for all three systems, only the unstable eigenvectors and their amplitudes matter for the dynamics of the systems on their respective limit cycle attractors. A general class of coupled second-order dynamical oscillators is presented in which stable limit cycles emerging via Hopf bifurcations are solely specified by appropriately defined unstable eigenvectors and their amplitudes. While the eigenvectors determine the orientation of limit cycles in state spaces, the amplitudes determine the evolution of states along those limit cycles. In doing so, it is shown that the unstable eigenvectors define reduced amplitude spaces in which the relevant long-term dynamics of the systems under consideration takes place. Several generalizations are discussed. First, if stable and unstable system parts exhibit a slow-fast dynamics, the fast variables may be eliminated and approximative descriptions of the emerging limit cycle dynamics in reduced amplitude spaces may be again obtained. Second, the principle of reduced amplitude spaces holds not only for coupled second-order oscillators, but can be applied to coupled third-order and higher order oscillators. Third, the possibility to apply the approach to multifrequency limit cycle attractors and other types of attractors is discussed.

Characterizing stages of COVID-19 epidemics: a nonlinear physics perspective based on amplitude equations.

The relevant dynamics underlying COVID-19 waves is described from an amplitude space perspective. To this end, the amplitude dynamics of infected populations is considered in different stages of epidemic waves. Eigenvectors and their corresponding amplitudes are derived analytically for low-dimensional models and by means of computational methods for high-dimensional models. It is shown that the amplitudes of all eigenvectors as functions of time can be tracked through the diverse stages of COVID-19 waves featuring jumps at the stage boundaries. In particular, it is shown that under certain circumstances the initial, outbreak stage and the final, subsiding stage of an epidemic wave are primarily determined by the unstable eigenvector of the initial stage and its corresponding remnant vector of the final stage. The corresponding amplitude captures most of the dynamics of the emerging and subsiding epidemics such that the problem at hand effectively becomes one dimensional leading to a dramatic reduction of the complexity of the problem at hand. Explicitly demonstrated for the first-wave COVID-19 epidemics of the year 2020 in the state of New York and Pakistan are given.

Unifying mass-action kinetics and Newtonian mechanics by means of Nambu brackets.

We demonstrate that elementary biochemical reactions defined by mass-action kinetics satisfy a particular Nambu structure. To this end, we express biochemical reaction equations in terms of Nambu brackets and certain ω-factors. The ω-factors account for the fact that mass-action kinetics exhibits in general flow fields with finite divergence. The proposed approach by means of Nambu brackets and ω-factors unifies divergence freeflow fields of Newtonian mechanics and flow fields with finite divergence of mass-action kinetics.

On a multistable dynamic model of behavioral and perceptual infant development.

In this theoretical work, we treat behavioral and perceptual issues on an equal footing and examine the emergence of mutually exclusive behavioral patterns and perceptual variables during infant development from the perspective of multistable competitive dynamic systems. Accordingly, behavioral modes and modes of perception compete with each other for activation. One and only one mode survives the mode-mode competition, which accounts for the incompatibility of modes being considered. However, the winning behavioral or perceptual state is not predefined. Rather, we argue that during particular stages of maturation multiple modes coexist for the same set of developmental, body-scaled, and environmental parameters or constraints. The winning behavioral or perceptual state depends on these parameters as well as on initial conditions as operationalized in terms of previously performed behaviors or utilized perceptual stimuli. We give explicit examples of our approach and address the emergence of two-handed grasping and catching movements and the emergence of monocular and binocular vision during infant development. In particular, we propose that the emergence of midline crossing movements in 3- to 6-month-old infants involves two independent but interaction control parameters: a body-scaled and a developmental one. Likewise, we argue that the onset of binocularity in infants involves two independent but interaction control parameters: a developmental and an environmental one.

A quantitative dynamical systems approach to differential learning: self-organization principle and order parameter equations.

Differential learning is a learning concept that assists subjects to find individual optimal performance patterns for given complex motor skills. To this end, training is provided in terms of noisy training sessions that feature a large variety of between-exercises differences. In several previous experimental studies it has been shown that performance improvement due to differential learning is higher than due to traditional learning and performance improvement due to differential learning occurs even during post-training periods. In this study we develop a quantitative dynamical systems approach to differential learning. Accordingly, differential learning is regarded as a self-organized process that results in the emergence of subject- and context-dependent attractors. These attractors emerge due to noise-induced bifurcations involving order parameters in terms of learning rates. In contrast, traditional learning is regarded as an externally driven process that results in the emergence of environmentally specified attractors. Performance improvement during post-training periods is explained as an hysteresis effect. An order parameter equation for differential learning involving a fourth-order polynomial potential is discussed explicitly. New predictions concerning the relationship between traditional and differential learning are derived.

Increasing isoniazid preventive therapy uptake in an HIV program in rural Papua New Guinea.

Setting: Tuberculosis (TB) is the leading cause of death among people living with the human immunodeficiency virus (PLHIV) in Papua New Guinea. Despite a policy for isoniazid preventive therapy (IPT) among PLHIV, implementation has been slow. Objective: We prospectively evaluated a standardized guided screening process, including TB diagnostic support, to increase IPT initiation in adult PLHIV on antiretro-viral treatment. Design: The guided process included a paper-based IPT screening tool that prompted review of patient history and TB symptoms and sputum analysis by smear microscopy and Xpert® MTB/RIF. Chest X-ray was performed at the provider's discretion. We quantified the yield of this guided process on IPT initiation and detection of TB and rifampicin resistance, and examined the contributions of each diagnostic modality. Results: Among 532 patients, TB was ruled out and IPT initiated in 450 (84%). TB was diagnosed and treatment was started in 82 (15%) patients. Xpert detected rifampicin resistance in one of 21 patients (5%, 95%CI 0.24-21.3) with a positive Xpert result. All TB cases were diagnosed by chest X-ray and/or Xpert. No cases were diagnosed by sputum smear alone. Conclusion: A standardized guided process, including TB diagnostic support, successfully enabled IPT initiation and identified a large burden of undetected TB.

Contexte : La tuberculose (TB) est la première cause de décès parmi les personnes vivant avec le VIH (PVVIH) en Papouasie Nouvelle Guinée. En dépit d'une politique en faveur du traitement préventif par isoniazide (TPI) parmi les PVVIH, la mise en oeuvre a été lente.Objectif : Nous avons prospectivement évalué un processus de dépistage standardisé guidé, incluant le soutien au diagnostic de la TB, pour augmenter la mise en route du TPI chez les adultes PVVIH sous traitement antirétroviral.Schéma : Le processus guidé a inclus un outil de dépistage sur support papier du TPI qui a suscité la revue des antécédents des patients, les symptômes de TB et l'analyse des crachats par microscopie de frottis et Xpert® MTB/RIF. Une radiographie pulmonaire a été réalisée à la discrétion du prestataire de soins. Nous avons quantifié le rendement de ce processus guidé relatif à la mise en route du TPI et à la détection de la TB et de la résistance à la rifampicine et examiné les contributions de chaque modalité de diagnostic.Résultats : Parmi 532 patients, la TB a été éliminée et le TPI a été initié chez 450 (84%) patients. Une TB a été diagnostiquée et le traitement a été mis en œuvre chez 82 (15%) patients. L'Xpert a détecté la résistance à la rifampicine chez un des 21 patients (5% ; IC95% 0,24­21,3) avec un résultat d'Xpert positif. Tous les cas de TB ont été diagnostiqués par radiographie pulmonaire et/ou Xpert. Aucun cas n'a été diagnostiqué par frottis de crachats seul.Conclusion : Un processus guidé standardisé, incluant la soutien au diagnostic de la TB, a permis la mise en route du TPI et identifié une large charge de TB non détectée.

Marco de referencia: La tuberculosis (TB) es la principal causa de muerte en las personas infectadas por el virus de la inmunodeficiencia humana (VIH) en Papua Nueva Guinea. Pese a las políticas vigentes en materia de tratamiento preventivo con isoniazida (TPI) en las personas afectadas por el VIH, su aplicación ha sido lenta.Objetivo: Se evaluó de manera prospectiva un procedimiento normalizado dirigido de detección sistemática, que comprendía el apoyo al diagnóstico de la TB, con el objeto de aumentar la tasa de iniciación del TPI en los adultos aquejados de infección por el VIH que recibían tratamiento antirretrovírico.Método: El procedimiento dirigido comportaba un instrumento impreso de detección para el TPI, que incitaba la evaluación de los antecedentes del paciente, los síntomas de TB y un análisis del esputo mediante la baciloscopia y la prueba Xpert® MTB/RIF. La radiografía de tórax se practicó según el criterio del profesional de salud. Se cuantificó el efecto de este método dirigido sobre la iniciación del TPI, la detección de la TB y la resistencia a rifampicina y se examinaron además las contribuciones de cada modalidad diagnóstica.Resultados: De los 532 pacientes, en 450 se descartó el diagnóstico de TB y se inició el TPI (84%). Se diagnosticó la TB y se inició el tratamiento a 82 personas (15%). Mediante la prueba Xpert se detectó la resistencia a rifampicina en uno de los 21 pacientes con resultado positivo a esta prueba (5%; intervalo de confianza del 95% de 0,24 a 21,3). Todos los casos de TB se diagnosticaron mediante la radiografía de tórax, la prueba Xpert o ambas. La baciloscopia por sí sola no permitió el diagnostico de ningún caso.Conclusión: Un procedimiento normalizado dirigido, que comportaba apoyo al diagnóstico de la TB, hizo posible la iniciación del TPI y favoreció el reconocimiento de una gran carga de morbilidad por TB no detectada.

Stochastic order parameter equation of isometric force production revealed by drift-diffusion estimates.

We address two questions that are central to understanding human motor control variability: what kind of dynamical components contribute to motor control variability (i.e., deterministic and/or random ones), and how are those components structured? To this end, we derive a stochastic order parameter equation for isometric force production from experimental data using drift-diffusion estimates. We show that the force variability increases with the required force output because of a decrease of deterministic stability and an accompanying increase of noise intensity. A structural analysis reveals that the deterministic component consists of a linear control loop, while the random component involves a noise source that scales with force output. In addition, we present evidence for the existence of a subject-independent overall noise level of human isometric force production.

Theoretical analysis of destabilization resonances in time-delayed stochastic second-order dynamical systems and some implications for human motor control.

A linear stochastic delay differential equation of second order is studied that can be regarded as a Kramers model with time delay. An analytical expression for the stationary probability density is derived in terms of a Gaussian distribution. In particular, the variance as a function of the time delay is computed analytically for several parameter regimes. Strikingly, in the parameter regime close to the parameter regime in which the deterministic system exhibits Hopf bifurcations, we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks. These peaks are interpreted as delay-induced destabilization resonances arising from oscillatory ghost instabilities. On the basis of the obtained theoretical findings, reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided.

On a Fitzhugh-Nagumo type model for the pulse-like jasmonate defense response in plants.

A mechanistic model of the Fitzhugh-Nagumo type is proposed for the pulse-like jasmonate response in plants. The model is composed of a bistable signaling pathway coupled to a negative feedback loop. The bistable signaling pathway describes a recently discovered positive feedback loop involving jasmonate and the MYC2 transcription factor regulating promoter activity during plant defense. The negative feedback loop is assumed to reflect a second jasmonate-dependent signaling pathway that is also used for ethylene signaling. The impact of the negative feedback loop is to destroy the high-level jasmonate fixed-point of the bistable jasmonate/MYC2 module. As a result, the high-level state becomes a ghost attractor and the jasmonate defense response becomes pulse-like.

Reaction kinetics of the jasmonate-isoleucine complex formation during wound-induced plant defense responses: A model-based re-analysis of published data.

Three studies were considered in which jasmonate-isoleucine levels were observed for several hours after plant wounding. The data from these studies were fitted to a first order kinetical model describing jasmonate-isoleucine complex formation and dissociation. It was found that the model could explain up to 97 percent of the variations in the data sets. In general, the data re-analysis confirmed that the protein-protein interactions involved in the biosynthesis and dissociation of the jasmonate-isoleucine complex are fast relative to the dynamics of the jasmonate levels themselves. Moreover, the data re-analysis supported the notion that transgenic plant manipulations affecting the defense-responses in plants not only affect the jasmonate-isoleucine levels indirectly by affecting jasmonate levels during plant responses. Rather, it seems that transgenic plant manipulations affect kinetic rate parameters of the jasmonate-isoleucine complex formation and dissociation reactions. In addition to these general findings, several specific conclusions for the three experimental studies were obtained.

Maier-Saupe model of liquid crystals: isotropic-nematic phase transitions and second-order statistics studied by Shiino's perturbation theory and strongly nonlinear Smoluchowski equations.

We study the first- and second-order statistical properties of a dynamical Maier-Saupe model for liquid crystals that is given in terms of a nonlinear Smoluchowski equation. Using Shiino's perturbation theory, we analyze the first-order statistics and give a rigorous proof of the emergence of a phase transition from a uniform distribution to a nonuniform distribution, reflecting phase transitions from isotropic to nematic phases, as observed in nematic liquid crystals. Using the concept of strongly nonlinear Fokker-Planck equations, the second-order statistics of the dynamical Maier-Saupe model is studied and an analytical expression for the short-time autocorrelation function of the orientation of the crystal molecules is derived.