Eigenvalue analysis of SARS-CoV-2 viral load data: illustration for eight COVID-19 patients.

Eigenvalue analysis is an important tool in economics and nonlinear physics to analyze industrial processes and instability phenomena, respectively. A model-based eigenvalue analysis of viral load data from eight symptomatic COVID-19 patients was conducted. The eigenvalues and eigenvectors of the instabilities were determined that give rise to COVID-19. For all eight patients, it was found that the virus dynamics followed the unstable eigenvectors until the viral load reached the respective peak values. At the peak virus values, the virus dynamics branched off from the directions specified by the eigenvectors. The temporal course of the unstable eigenvalues was determined as well. For all patients, it was found that the eigenvalues switched from positive to negative values just when the virus load reached peak values. These findings suggest that the fixed, instability-related eigenvalues and eigenvectors determine initial stages of SARS-CoV-2 infections during which virus load increases. In contrast, the time-dependent eigenvalues show a sign-switching phenomenon that indicates when the virus dynamics switches from the growth stage (increasing virus load) to the decay stage (decreasing virus load). The virus dynamics model was a standard three-variable virus dynamics model frequently used in the literature.

Association between out-patient visits and air pollution in Chiang Mai, Thailand: Lessons from a unique situation involving a large data set showing high seasonal levels of air pollution.

Chiang Mai is one of the most known cities of Northern Thailand, representative for various cities in the East and South-East Asian region exhibiting seasonal smog crises. While a few studies have attempted to address smog crises effects on human health in that geographic region, research in this regard is still in its infancy. We exploited a unique situation based on two factors: large pollutant concentration variations due to the Chiang Mai smog crises and a relatively large sample of out-patient visits. About 216,000 out-patient visits in the area of Chiang Mai during the period of 2011 to 2014 for upper (J30-J39) and lower (J44) respiratory tract diseases were evaluated with respect to associations with particulate matter (PM10), ozone (O3), and nitrogen dioxide (NO2) concentrations using single-pollutant and multiple-pollutants Poisson regression models. All three pollutants were found to be associated with visits due to upper respiratory tract diseases (with relative risks RR = 1.023 at cumulative lag 05, 95% CI: 1.021-1.025, per 10 µg/m3 PM10 increase, RR = 1.123 at lag 05, 95% CI: 1.118-1.129, per 10 ppb O3 increase, and RR = 1.110 at lag 05, 95% CI: 1.102-1.119, per 10 ppb NO2 increase). Likewise, all three pollutants were found to be associated with visits due to lower respiratory tract diseases (with RR = 1.016 at lag 06, 95% CI: 1.015-1.017, per 10 µg/m3 PM10 increase, RR = 1.073 at lag 06, 95% CI: 1.070-1.076, per 10 ppb O3 increase, and RR = 1.046 at lag 06, 95% CI: 1.040-1.051, per 10 ppb NO2 increase). Multi-pollutants modeling analysis identified O3 as a relatively independent risk factor and PM10-NO2 pollutants models as promising two-pollutants models. Overall, these results demonstrate the adverse effects of all three air pollutants on respiratory morbidity and call for air pollution reduction and control.

Rise and Decay of the COVID-19 Epidemics in the USA and the State of New York in the First Half of 2020: A Nonlinear Physics Perspective Yielding Novel Insights.

As of December 2020, since the beginning of the year 2020, the COVID-19 pandemic has claimed worldwide more than 1 million lives and has changed human life in unprecedented ways. Despite the fact that the pandemic is far from over, several countries managed at least temporarily to make their first-wave COVID-19 epidemics to subside to relatively low levels. Combining an epidemiological compartment model and a stability analysis as used in nonlinear physics and synergetics, it is shown how the first-wave epidemics in the state of New York and nationwide in the USA developed through three stages during the first half of the year 2020. These three stages are the outbreak stage, the linear stage, and the subsiding stage. Evidence is given that the COVID-19 outbreaks in these two regions were due to instabilities of the COVID-19 free states of the corresponding infection dynamical systems. It is shown that from stage 1 to stage 3, these instabilities were removed, presumably due to intervention measures, in the sense that the COVID-19 free states were stabilized in the months of May and June in both regions. In this context, stability parameters and key directions are identified that characterize the infection dynamics in the outbreak and subsiding stages. Importantly, it is shown that the directions in combination with the sign-switching of the stability parameters can explain the observed rise and decay of the epidemics in the state of New York and the USA. The nonlinear physics perspective provides a framework to obtain insights into the nature of the COVID-19 dynamics during outbreak and subsiding stages and allows to discuss possible impacts of intervention measures. For example, the directions can be used to determine how different populations (e.g., exposed versus symptomatic individuals) vary in size relative to each other during the course of an epidemic. Moreover, the timeline of the computationally obtained stages can be compared with the history of the implementation of intervention measures to discuss the effectivity of such measures.

Grasp Affordances in Bistable Perception of the Necker Cube.

Stimulus-response compatibility effects illustrate the mutual depen-dence of perception and action processes. Ellis and Tucker (2000) showed that object identification was facilitated when the response required a grip that was compatible with the stimulus. In the current study, we extend grip-compatibility effects to perception of the Necker cube. Participants reported the perceived orientation of a Necker cube by orienting a hand-held cube into a compatible or an incompatible position. Participants in the incompatible condition were quickly attracted to the FRB (front-side right bottom) percept, consistent with previous work. However, participants in the compatible condition showed an extended period of metastability, switching between the two perceptual states about equally. A second experiment replicated these results and showed that a control condition in which responses were made with a key press produced intermediate levels of metastability. These results are interpreted in terms of the dynamics of bistable perception.

Embodied gestalts: Unstable visual phenomena become stable when they are stimuli for competitive action selection.

An animal's environment is rich with affordances. Different possible actions are specified by visual information while competing for dominance over neural dynamics. Affordance competition models account for this in terms of winner-takes-all cross-inhibition dynamics. Multistable phenomena also reveal how the visual system deals with ambiguity. Their key property is spontaneous instability, in forms such as alternating dominance in binocular rivalry. Theoretical models of self-inhibition or self-organized instability posit that the instability is tied to some kind of neural adaptation and that its functional significance is to enable flexible perceptual transitions. We hypothesized that the two perspectives are interlinked. Spontaneous instability is an intrinsic property of perceptual systems, but it is revealed when they are stripped from the constraints of possibilities for action. To test this, we compared a multistable gestalt phenomenon against its embodied version and estimated the neural adaptation and competition parameters of an affordance transition dynamic model. Wertheimer's (Zeitschrift fur Psychologie 61, 161-265, 1912) optimal (ß) and pure (φ) forms of apparent motion from a stroboscopic point-light display were endowed with action relevance by embedding the display in a visual object-tracking task. Thus, each mode was complemented by its action, because each perceptual mode uniquely enabled different ways of tracking the target. Perceptual judgment of the traditional apparent motion exhibited spontaneous instabilities, in the form of earlier switching when the frame rate was changed stepwise. In contrast, the embodied version exhibited hysteresis, consistent with affordance transition studies. Consistent with our predictions, the parameter for competition between modes in the affordance transition model increased, and the parameter for self-inhibition vanished.

A cluster phase analysis for collective behavior in team sports.

Collective behavior can be defined as the ability of humans to coordinate with others through a complex environment. Sports offer exquisite examples of this dynamic interplay, requiring decision making and other perceptual-cognitive skills to adjust individual decisions to the team self-organization and vice versa. Considering players of a team as periodic phase oscillators, synchrony analyses can be used to model the coordination of a team. Nonetheless, a main limitation of current models is that collective behavior is context independent. In other words, players on a team can be highly synchronized without this corresponding to a meaningful coordination dynamics relevant to the context of the game. Considering these issues, the aim of this study was to develop a method of analysis sensitive to the context for evidence-based measures of collective behavior.

Three-factor models versus time series models: quantifying time-dependencies of interactions between stimuli in cell biology and psychobiology for short longitudinal data.

Signal integration determines cell fate on the cellular level, affects cognitive processes and affective responses on the behavioural level, and is likely to be involved in psychoneurobiological processes underlying mood disorders. Interactions between stimuli may subjected to time effects. Time-dependencies of interactions between stimuli typically lead to complex cell responses and complex responses on the behavioural level. We show that both three-factor models and time series models can be used to uncover such time-dependencies. However, we argue that for short longitudinal data the three factor modelling approach is more suitable. In order to illustrate both approaches, we re-analysed previously published short longitudinal data sets. We found that in human embryonic kidney 293 cells cells the interaction effect in the regulation of extracellular signal-regulated kinase (ERK) 1 signalling activation by insulin and epidermal growth factor is subjected to a time effect and dramatically decays at peak values of ERK activation. In contrast, we found that the interaction effect induced by hypoxia and tumour necrosis factor-alpha for the transcriptional activity of the human cyclo-oxygenase-2 promoter in HEK293 cells is time invariant at least in the first 12-h time window after stimulation. Furthermore, we applied the three-factor model to previously reported animal studies. In these studies, memory storage was found to be subjected to an interaction effect of the beta-adrenoceptor agonist clenbuterol and certain antagonists acting on the alpha-1-adrenoceptor / glucocorticoid-receptor system. Our model-based analysis suggests that only if the antagonist drug is administer in a critical time window, then the interaction effect is relevant.

Body-scaled perception is subjected to adaptation when repetitively judging opportunities for grasping.

Experimental evidence is given that the perceptual system adapts to repetitive task execution in a perceptual two-choice judgment task. Participants were tested with respect to their perception of opportunities for plank grasping. Participants had to report whether planks were perceived as objects being graspable with either one hand or two hands. When the plank size was gradually increased and subsequently decreased, transitions from one hand judgments to two hands judgments and vice versa were observed. Analysis of the transition scores revealed that the perceptual judgments were body-scaled, as it is known in the literature. However, judgments were also found to be context dependent. Judgment transition scores were affected in a systematic way by the kind of and the number of previously made judgments. The latter quantitative impact was observed in three related experiments and suggests that perceptual judgments about opportunities for action adapt to task repetition. Overall, the experimental findings are consistent with the predictions of a dynamical systems model, which assumes that perceptual judgments are emergent properties of a self-organizing process that involves inhibitory top-down feedback.

Affordance-based perception-action dynamics: A model of visually guided braking.

Behavioral dynamics is a framework for understanding adaptive behavior as arising from the self-organizing interaction between animal and environment. The methods of nonlinear dynamics provide a language for describing behavior that is both stable and flexible. Behavioral dynamics has been criticized for ignoring the animal's sensitivity to its own capabilities, leading to the development of an alternative framework: affordance-based control. Although it is theoretically sound and empirically motivated, affordance-based control has resisted characterization in terms of nonlinear dynamics. Here, we provide a dynamical description of affordance-based control, extending behavioral dynamics to meet its criticisms. We propose a general modeling strategy consistent with both theories. We use visually guided braking as a representative behavior and construct a novel dynamical model. This model demonstrates the possibility of understanding visually guided action as respecting the limits of the actor's capabilities, while still being guided by informational variables associated with desired states of affairs. In addition to such "hard" constraints on behavior, our framework allows for the influence of "soft" constraints such as preference and comfort, opening a new area of inquiry in perception-action dynamics.

Species differential regulation of COX2 can be described by an NFκB-dependent logic AND gate.

Cyclooxygenase 2 (COX2), a key regulatory enzyme of the prostaglandin/eicosanoid pathway, is an important target for anti-inflammatory therapy. It is highly induced by pro-inflammatory cytokines in a Nuclear factor kappa B (NFκB)-dependent manner. However, the mechanisms determining the amplitude and dynamics of this important pro-inflammatory event are poorly understood. Furthermore, there is significant difference between human and mouse COX2 expression in response to the inflammatory stimulus tumor necrosis factor alpha (TNFα). Here, we report the presence of a molecular logic AND gate composed of two NFκB response elements (NREs) which controls the expression of human COX2 in a switch-like manner. Combining quantitative kinetic modeling and thermostatistical analysis followed by experimental validation in iterative cycles, we show that the human COX2 expression machinery regulated by NFκB displays features of a logic AND gate. We propose that this provides a digital, noise-filtering mechanism for a tighter control of expression in response to TNFα, such that a threshold level of NFκB activation is required before the promoter becomes active and initiates transcription. This NFκB-regulated AND gate is absent in the mouse COX2 promoter, most likely contributing to its differential graded response in promoter activity and protein expression to TNFα. Our data suggest that the NFκB-regulated AND gate acts as a novel mechanism for controlling the expression of human COX2 to TNFα, and its absence in the mouse COX2 provides the foundation for further studies on understanding species-specific differential gene regulation.

Symmetry and order parameter dynamics of the human odometer.

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309-4314, 2009, J Exp Psychol Hum Percept Perform 38:1014-1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.

Balance affects prism adaptation: evidence from the latent aftereffect.

In prism adaptation experiments, the effect on throwing to a target is reduced (primary aftereffect is smaller) when the throwing condition with prisms removed (first test phase) is different from the throwing condition with prisms (the training phase). The missing adaptation, however, can be revealed through further testing (second test phase) in which the throwing condition during training is fully reinstated. We studied throwing underhand to a target flush with the floor. During training, participants wore left-shifting prism glasses while standing on the floor (Group 1) or on a balance board (Groups 2 and 3). Tests 1 and 2 following training involved the same underhand throwing. For Group 2, Test 1 was on the balance board and Test 2 on the ground; for Group 3, the order was reversed; and for Group 1, both tests were on the ground. The Group 3 Test 1 aftereffect was smaller, and the Test 2 aftereffect was larger than the respective tests for Groups 1 and 2, with the aftereffect sum the same for all three groups. A parallel was noted between prism adaptation and implicit memory: whether given training (study) conditions lead to better or poorer persistence of adaptation (memory performance) at test depends on the fit between the conditions at test relative to the conditions at training (study). In the general memory case, those conditions will involve nonobvious contributors to memory performance, analogous to the support for upright standing in the adaptation of the visual system to prismatic distortion investigated in the present research.

Negative hysteresis in the behavioral dynamics of the affordance "graspable".

One commonly perceives whether a visible object will afford grasping with one hand or with both hands. In experiments in which differently sized objects of a fixed type are presented, the transition from using one of these manual modes to the other depends on the ratio of object size to hand span and on the presentation sequence, with size increasing versus decreasing. Conventional positive hysteresis (i.e., a larger transition ratio for the increasing sequence) can be accommodated by the order parameter dynamics that typify self-organizing systems (Lopresti-Goodman, Turvey, and Frank, Attention, Perception, & Psychophysics 73:1948-1965, 2011). Here we identified and addressed conditions of unconventional negative hysteresis (i.e., a larger transition ratio for the decreasing sequence). They suggest a second control parameter in the self-organization of affordance perception, one that is seemingly regulated by inhibitory dynamics occurring in the agent-task-environment system. Our experimental results and modeling extend the investigation of affordance perception within dynamical systems theory.

Measuring group synchrony: a cluster-phase method for analyzing multivariate movement time-series.

A new method for assessing group synchrony is introduced as being potentially useful for objectively determining degree of group cohesiveness or entitativity. The cluster-phase method of Frank and Richardson (2010) was used to analyze movement data from the rocking chair movements of six-member groups who rocked their chairs while seated in a circle facing the center. In some trials group members had no information about others' movements (their eyes were shut) or they had their eyes open and gazed at a marker in the center of the group. As predicted, the group level synchrony measure was able to distinguish between situations where synchrony would have been possible and situations where it would be impossible. Moreover, other aspects of the analysis illustrated how the cluster phase measures can be used to determine the type of patterning of group synchrony, and, when integrated with multi-level modeling, can be used to examine individual-level differences in synchrony and dyadic level synchrony as well.

Catching transcriptional regulation by thermostatistical modeling.

Gene expression is frequently regulated by multiple transcription factors (TFs). Thermostatistical methods allow for a quantitative description of interactions between TFs, RNA polymerase and DNA, and their impact on the transcription rates. We illustrate three different scales of the thermostatistical approach: the microscale of TF molecules, the mesoscale of promoter energy levels and the macroscale of transcriptionally active and inactive cells in a cell population. We demonstrate versatility of combinatorial transcriptional activation by exemplifying logic functions, such as AND and OR gates. We discuss a metric for cell-to-cell transcriptional activation variability known as Fermi entropy. Suitability of thermostatistical modeling is illustrated by describing the experimental data on transcriptional induction of NFκB and the c-Fos protein.

Versatility of cooperative transcriptional activation: a thermodynamical modeling analysis for greater-than-additive and less-than-additive effects.

We derive a statistical model of transcriptional activation using equilibrium thermodynamics of chemical reactions. We examine to what extent this statistical model predicts synergy effects of cooperative activation of gene expression. We determine parameter domains in which greater-than-additive and less-than-additive effects are predicted for cooperative regulation by two activators. We show that the statistical approach can be used to identify different causes of synergistic greater-than-additive effects: nonlinearities of the thermostatistical transcriptional machinery and three-body interactions between RNA polymerase and two activators. In particular, our model-based analysis suggests that at low transcription factor concentrations cooperative activation cannot yield synergistic greater-than-additive effects, i.e., DNA transcription can only exhibit less-than-additive effects. Accordingly, transcriptional activity turns from synergistic greater-than-additive responses at relatively high transcription factor concentrations into less-than-additive responses at relatively low concentrations. In addition, two types of re-entrant phenomena are predicted. First, our analysis predicts that under particular circumstances transcriptional activity will feature a sequence of less-than-additive, greater-than-additive, and eventually less-than-additive effects when for fixed activator concentrations the regulatory impact of activators on the binding of RNA polymerase to the promoter increases from weak, to moderate, to strong. Second, for appropriate promoter conditions when activator concentrations are increased then the aforementioned re-entrant sequence of less-than-additive, greater-than-additive, and less-than-additive effects is predicted as well. Finally, our model-based analysis suggests that even for weak activators that individually induce only negligible increases in promoter activity, promoter activity can exhibit greater-than-additive responses when transcription factors and RNA polymerase interact by means of three-body interactions. Overall, we show that versatility of transcriptional activation is brought about by nonlinearities of transcriptional response functions and interactions between transcription factors, RNA polymerase and DNA.

Human odometry verifies the symmetry perspective on bipedal gaits.

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary gaits are characterized by dihedral symmetry, whereas secondary gaits are characterized by a lower, cyclic symmetry. This fact was used in a test of human odometry. Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. Lessons are drawn from modeling the dynamics of behaviors executed in parallel (e.g., interlimb coordination) to model the dynamics of human odometry, in which the behaviors are executed sequentially. The major observations are characterized in terms of a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of that dynamic.

Symmetry breaking analysis of prism adaptation's latent aftereffect.

The effect of prism adaptation on movement is typically reduced when the movement at test (prisms off) differs on some dimension from the movement at training (prisms on). Some adaptation is latent, however, and only revealed through further testing in which the movement at training is fully reinstated. Applying a nonlinear attractor dynamic model (Frank, Blau, & Turvey, 2009) to available data (Blau, Stephen, Carello, & Turvey, 2009), we provide evidence for a causal link between the latent (or secondary) aftereffect and an additive force term that is known to account for symmetry breaking. The evidence is discussed in respect to the hypothesis that recalibration aftereffects reflect memory principles (encoding specificity, transfer-appropriate processing) oriented to time-translation invariance-when later testing conserves the conditions of earlier training. Forgetting or reduced adaptation effects follow from the loss of this invariance and are reversed by its reinstatement.

Equivalence of human odometry by walk and run is indifferent to self-selected speed.

Humans and other animals can measure distances nonvisually by legged locomotion. Experiments typically employ an outbound measure (M) and an inbound report (R) phase. Previous research has found distance reproduction to be maximally accurate, when gait symmetry and speed of M and R are of like kind: Successful human odometry manifests at the level of the M-R system. In the present work, M was an experimenter-set distance produced by a blindfolded participant using a primary gait (walk, run). R was always by walk. Fast and slow versions of walk and run were adopted by participants, such that when M was fast R was slow, and vice versa. Distance was underestimated when M was slower than R and overestimated when M was faster than R. However, the pattern of participant-adopted velocities indicated that it was the instructions, not the speed as such, that yielded the pattern of results. The results are interpretable through a dynamical perspective and indicate speed is an imperfection parameter acting on the attractors of the M-R system.

From the W-method to the canonical-dissipative method for studying uni-manual rhythmic behavior.

A novel method for the analysis of repetitive limb behavior oscillation is presented. It is based on a model used to account for self-sustained limit cycles that involve energy pumping compensating for dissipative processes. The experiment involved a uni-manual pendulum swinging task paced at five frequencies. The median frequency corresponded to the resonant one for the chosen pendulum and hand parameters. We applied the model-based analysis to explore the relationship between behavioral observables and model parameters not available from previous methods. Oscillation amplitude and energy, and motor variability were the behavioral observables we focused on while energy pumping, attractor strength, and noise amplitude were the model parameters. As expected, energy pumping was found to increase with pacing frequency. Noise amplitude did not change and stability decreased.