Time-dependent propagators for stochastic models of gene expression: an analytical method

The inherent stochasticity of gene expression in the context of regulatory networks profoundly influences the dynamics of the involved species. Mathematically speaking, the propagators which describe the evolution of such networks in time are typically defined as solutions of the corresponding chemical master equation (CME). However, it is not possible in general to obtain exact solutions to the CME in closed form, which is due largely to its high dimensionality. In the present article, we propose an analytical method for the efficient approximation of these propagators. We illustrate our method on the basis of two categories of stochastic models for gene expression that have been discussed in the literature. The requisite procedure consists of three steps: a probability-generating function is introduced which transforms the CME into (a system of) partial differential equations (PDEs); application of the method of characteristics then yields (a system of) ordinary differential equations (ODEs) which can be solved using dynamical systems techniques, giving closed-form expressions for the generating function; finally, propagator probabilities can be reconstructed numerically from these expressions via the Cauchy integral formula. The resulting ‘library’ of propagators lends itself naturally to implementation in a Bayesian parameter inference scheme, and can be generalised systematically to related categories of stochastic models beyond the ones considered here.

Interpersonal coordination analysis of tennis players from different levels during official matches

The purpose of this study was to assess the interpersonal coordination during official male tennis matches in players of different skill levels. Players' trajectories of three levels (Juvenile, ATP-Future, ATP-250) were obtained using video-based tracking system. A vector coding technique was applied to obtain players' interpersonal coordination in four coordination patterns: "anti-phase", "in-phase", "serving player phase" and "returning player phase". These patterns allowed identification of the nature of the coupling and lead/lag relations between players. In all categories, players presented higher degree of "anti-phase" and "serving player phase" (when only the serving player is moving on the court or his opponent is moving with a time lag) coordination. Young players spent more time in "serving player phase" during lateral displacements than professional players. On the other hand, professional players spent more time in "returning player phase" (when only the returning player is moving on the court or his opponent is moving with a time lag) during antero posterior displacements, than young players. Interpersonal coordination did not change from the first to the second set of the match, showing that tennis players maintain their displacement characteristics and strategy, independently of proficiency level. The vector coding technique allowed to identify new coordination patterns in tennis, providing additional information about tennis dynamics and how players from different categories and proficiency levels behave during the matches.

Stable Control of Firing Rate Mean and Variance by Dual Homeostatic Mechanisms

Homeostatic processes that provide negative feedback to regulate neuronal firing rates are essential for normal brain function. Indeed, multiple parameters of individual neurons, including the scale of afferent synapse strengths and the densities of specific ion channels, have been observed to change on homeostatic time scales to oppose the effects of chronic changes in synaptic input. This raises the question of whether these processes are controlled by a single slow feedback variable or multiple slow variables. A single homeostatic process providing negative feedback to a neuron's firing rate naturally maintains a stable homeostatic equilibrium with a characteristic mean firing rate; but the conditions under which multiple slow feedbacks produce a stable homeostatic equilibrium have not yet been explored. Here we study a highly general model of homeostatic firing rate control in which two slow variables provide negative feedback to drive a firing rate toward two different target rates. Using dynamical systems techniques, we show that such a control system can be used to stably maintain a neuron's characteristic firing rate mean and variance in the face of perturbations, and we derive conditions under which this happens. We also derive expressions that clarify the relationship between the homeostatic firing rate targets and the resulting stable firing rate mean and variance. We provide specific examples of neuronal systems that can be effectively regulated by dual homeostasis. One of these examples is a recurrent excitatory network, which a dual feedback system can robustly tune to serve as an integrator.

Design of an optimum Poincaré plane for extracting meaningful samples from EEG signals

Biosignals are considered as important sources of data for diagnosing and detecting abnormalities, and modeling dynamics in the body. These signals are usually analyzed using features taken from time and frequency domain. In theory' these dynamics can also be analyzed utilizing Poincaré plane that intersects system's trajectory. However' selecting an appropriate Poincaré plane is a crucial part of extracting best Poincaré samples. There is no unique way to choose a Poincaré plane' because it is highly dependent to the system dynamics. In this study, a new algorithm is introduced that automatically selects an optimum Poincaré plane able to transfer maximum information from EEG time series to a set of Poincaré samples. In this algorithm' EEG time series are first embedded; then a parametric Poincaré plane is designed and finally the parameters of the plane are optimized using genetic algorithm. The presented algorithm is tested on EEG signals and the optimum Poincaré plane is obtained with more than 99% data information transferred. Results are compared with some typical method of creating Poinare samples and showed that the transferred information using with this method is higher. The generated samples can be used for feature extraction and further analysis.

Canard phenomenon in a slow-fast modified Leslie-Gower model

Geometrical Singular Perturbation Theory has been successful to investigate a broad range of biological problems with different time scales. The aim of this paper is to apply this theory to a predator-prey model of modified Leslie-Gower type for which we consider that prey reproduces mush faster than predator. This naturally leads to introduce a small parameter ϵ which gives rise to a slow-fast system. This system has a special folded singularity which has not been analyzed in the classical work [15]. We use the blow-up technique to visualize the behavior near this fold point P. Outside of this region the dynamics are given by classical regular and singular perturbation theory. This allows to quantify geometrically the attractive limit-cycle with an error of O(ϵ) and shows that it exhibits the canard phenomenon while crossing P.

Phonetic drift in Spanish-English bilinguals: Experiment and a self-organizing model

Studies of speech accommodation provide evidence for change in use of language structures beyond the critical/sensitive period. For example, Sancier and Fowler (1997) found changes in the voice-onset-times (VOTs) of both languages of a Portuguese-English bilingual as a function of her language context. Though accommodation has been studied widely within a monolingual context, it has received less attention in and between the languages of bilinguals. We tested whether these findings of phonetic accommodation, speech accommodation at the phonetic level, would generalize to a sample of Spanish-English bilinguals. We recorded participants reading Spanish and English sentences after 3-4 months in the US and after 2-4 weeks in a Spanish speaking country and measured the VOTs of their voiceless plosives. Our statistical analyses show that participants' English VOTs drifted towards those of the ambient language, but their Spanish VOTs did not. We found considerable variation in the extent of individual participants' drift in English. Further analysis of our results suggested that native-likeness of L2 VOTs and extent of active language use predict the extent of drift. We provide a model based on principles of self-organizing dynamical systems to account for our Spanish-English phonetic drift findings and the Portuguese-English findings.

CA1 pyramidal cells have diverse biophysical properties, affected by development, experience, and aging

Neuron types (e.g., pyramidal cells) within one area of the brain are often considered homogeneous, despite variability in their biophysical properties. Here we review literature demonstrating variability in the electrical activity of CA1 hippocampal pyramidal cells (PCs), including responses to somatic current injection, synaptic stimulation, and spontaneous network-related activity. In addition, we describe how responses of CA1 PCs vary with development, experience, and aging, and some of the underlying ionic currents responsible. Finally, we suggest directions that may be the most impactful in expanding this knowledge, including the use of text and data mining to systematically study cellular heterogeneity in more depth; dynamical systems theory to understand and potentially classify neuron firing patterns; and mathematical modeling to study the interaction between cellular properties and network output. Our goals are to provide a synthesis of the literature for experimentalists studying CA1 PCs, to give theorists an idea of the rich diversity of behaviors models may need to reproduce to accurately represent these cells, and to provide suggestions for future research.

Generalised approach to modelling a three-tiered microbial food-web

The complexity of the anaerobic digestion process has motivated the development of complex models, such as the widely used Anaerobic Digestion Model No. 1. However, this complexity makes it intractable to identify the stability profile coupled to the asymptotic behaviour of existing steady-states as a function of conventional chemostat operating parameters (substrate inflow concentration and dilution rate). In a previous study this model was simplified and reduced to its very backbone to describe a three-tiered chlorophenol mineralising food-web, with its stability analysed numerically using consensus values for the various biological parameters of the Monod growth functions. Steady-states where all organisms exist were always stable and non-oscillatory. Here we investigate a generalised form of this three-tiered food-web, whose kinetics do not rely on the specific kinetics of Monod form. The results are valid for a large class of growth kinetics as long as they keep the signs of their derivatives. We examine the existence and stability of the identified steady-states and find that, without a maintenance term, the stability of the system may be characterised analytically. These findings permit a better understanding of the operating region of the bifurcation diagram where all organisms exist, and its dependence on the biological parameters of the model. For the previously studied Monod kinetics, we identify four interesting cases that show this dependence of the operating diagram with respect to the biological parameters. When maintenance is included, it is necessary to perform numerical analysis. In both cases we verify the discovery of two important phenomena; i) the washout steady-state is always stable, and ii) a switch in dominance between two organisms competing for hydrogen results in the system becoming unstable and a loss in viability. We show that our approach results in the discovery of an unstable operating region in its positive steady-state, where all three organisms exist, a fact that has not been reported in a previous numerical study. This type of analysis can be used to determine critical behaviour in microbial communities in response to changing operating conditions.

A Discrete Dynamical System Approach to Pathway Activation Profiles of Signaling Cascades

In living organisms, cascades of covalent modification cycles are one of the major intracellular signaling mechanisms, allowing to transduce physical or chemical stimuli of the external world into variations of activated biochemical species within the cell. In this paper, we develop a novel method to study the stimulus-response of signaling cascades and overall the concept of pathway activation profile which is, for a given stimulus, the sequence of activated proteins at each tier of the cascade. Our approach is based on a correspondence that we establish between the stationary states of a cascade and pieces of orbits of a 2D discrete dynamical system. The study of its possible phase portraits in function of the biochemical parameters, and in particular of the contraction/expansion properties around the fixed points of this discrete map, as well as their bifurcations, yields a classification of the cascade tiers into three main types, whose biological impact within a signaling network is examined. In particular, our approach enables to discuss quantitatively the notion of cascade amplification/attenuation from this new perspective. The method allows also to study the interplay between forward and "retroactive" signaling, i.e., the upstream influence of an inhibiting drug bound to the last tier of the cascade.

Embedding the psychosocial biographies of Olympic medalists in a (meta-)theoretical model of dynamic networks

Based on in-depth interviews, Hardy et al. focused on the role of psychosocial factors in the development of elite and super-elite athletes. They reveal interesting differences and commonalities in the frequencies at which certain aspects related to life events, personality, contextual factors, etc. were reported. Here, we argue that insights in the development of (super-)elite athletes will advance if we go beyond explanations in the frequency-domain, and search for process explanations in the time-domain. This means that we should investigate how athletes develop from one time point to the next, and the next, etc., thereby examining how (psychosocial) factors change and combine across time, as well as how the timing of events can shape an athlete's further developmental trajectory. We therefore present a process-oriented dynamic network model of talent development, assuming that (super-)elite performance develops out of structures of dynamically interacting (psychosocial) factors, which we illustrate using the outcomes of Hardy et al.

Dynamical study of Νaν channel excitability under mechanical stress

Alteration of [Formula: see text] channel functions (channelopathies) has been encountered in various hereditary muscle diseases. [Formula: see text] channel mutations lead to aberrant excitability in skeletal muscle myotonia and paralysis. In general, these mutations disable inactivation of the [Formula: see text] channel, producing either repetitive action potential firing (myotonia) or electrical dormancy (flaccid paralysis) in skeletal muscles. These "sick-excitable" cell conditions were shown to correlate with a mechanical stretch-driven left shift of the conductance factors of the two gating mechanisms of a fraction of [Formula: see text] channels, which make them firing at inappropriate hyperpolarised (left-shifted) voltages. Here we elaborate on a variant of the Hodgkin-Huxley model that includes a stretch elasticity energy component in the activation and inactivation gate kinetic rates. We show that this model reproduces fairly well sick-excitable cell behaviour and can be used to predict the parameter domains where aberrant excitability or paralysis may occur. By allowing us to separate the incidences of activation and inactivation gate impairments in [Formula: see text] channel excitability, this model could be a strong asset for diagnosing the origin of excitable cell disorders.

Longitudinal quasi-static stability predicts changes in dog gait on rough terrain

Legged animals utilize gait selection to move effectively and must recover from environmental perturbations. We show that on rough terrain, domestic dogs, Canis lupus familiaris, spend more time in longitudinal quasi-statically stable patterns of movement. Here, longitudinal refers to the rostro-caudal axis. We used an existing model in the literature to quantify the longitudinal quasi-static stability of gaits neighbouring the walk, and found that trot-like gaits are more stable. We thus hypothesized that when perturbed, the rate of return to a stable gait would depend on the direction of perturbation, such that perturbations towards less quasi-statically stable patterns of movement would be more rapid than those towards more stable patterns of movement. The net result of this would be greater time spent in longitudinally quasi-statically stable patterns of movement. Limb movement patterns in which diagonal limbs were more synchronized (those more like a trot) have higher longitudinal quasi-static stability. We therefore predicted that as dogs explored possible limb configurations on rough terrain at walking speeds, the walk would shift towards trot. We gathered experimental data quantifying dog gait when perturbed by rough terrain and confirmed this prediction using GPS and inertial sensors (n=6, P<0.05). By formulating gaits as trajectories on the n-torus we are able to make tractable the analysis of gait similarity. These methods can be applied in a comparative study of gait control which will inform the ultimate role of the constraints and costs impacting locomotion, and have applications in diagnostic procedures for gait abnormalities, and in the development of agile legged robots.

Summary: Dogs co-ordinate their limbs on rough terrain in a manner consistent with optimization for quasi-static longitudinal stability.

Problem-Solving Phase Transitions During Team Collaboration

Multiple theories of problem-solving hypothesize that there are distinct qualitative phases exhibited during effective problem-solving. However, limited research has attempted to identify when transitions between phases occur. We integrate theory on collaborative problem-solving (CPS) with dynamical systems theory suggesting that when a system is undergoing a phase transition it should exhibit a peak in entropy and that entropy levels should also relate to team performance. Communications from 40 teams that collaborated on a complex problem were coded for occurrence of problem-solving processes. We applied a sliding window entropy technique to each team's communications and specified criteria for (a) identifying data points that qualify as peaks and (b) determining which peaks were robust. We used multilevel modeling, and provide a qualitative example, to evaluate whether phases exhibit distinct distributions of communication processes. We also tested whether there was a relationship between entropy values at transition points and CPS performance. We found that a proportion of entropy peaks was robust and that the relative occurrence of communication codes varied significantly across phases. Peaks in entropy thus corresponded to qualitative shifts in teams' CPS communications, providing empirical evidence that teams exhibit phase transitions during CPS. Also, lower average levels of entropy at the phase transition points predicted better CPS performance. We specify future directions to improve understanding of phase transitions during CPS, and collaborative cognition, more broadly.

Multivariate dynamical modelling of structural change during development

Here we introduce a multivariate framework for characterising longitudinal changes in structural MRI using dynamical systems. The general approach enables modelling changes of states in multiple imaging biomarkers typically observed during brain development, plasticity, ageing and degeneration, e.g. regional gray matter volume of multiple regions of interest (ROIs). Structural brain states follow intrinsic dynamics according to a linear system with additional inputs accounting for potential driving forces of brain development. In particular, the inputs to the system are specified to account for known or latent developmental growth/decline factors, e.g. due to effects of growth hormones, puberty, or sudden behavioural changes etc. Because effects of developmental factors might be region-specific, the sensitivity of each ROI to contributions of each factor is explicitly modelled. In addition to the external effects of developmental factors on regional change, the framework enables modelling and inference about directed (potentially reciprocal) interactions between brain regions, due to competition for space, or structural connectivity, and suchlike. This approach accounts for repeated measures in typical MRI studies of development and aging. Model inversion and posterior distributions are obtained using earlier established variational methods enabling Bayesian evidence-based comparisons between various models of structural change. Using this approach we demonstrate dynamic cortical changes during brain maturation between 6 and 22 years of age using a large openly available longitudinal paediatric dataset with 637 scans from 289 individuals. In particular, we model volumetric changes in 26 bilateral ROIs, which cover large portions of cortical and subcortical gray matter. We account for (1) puberty-related effects on gray matter regions; (2) effects of an early transient growth process with additional time-lag parameter; (3) sexual dimorphism by modelling parameter differences between boys and girls. There is evidence that the regional pattern of sensitivity to dynamic hidden growth factors in late childhood is similar across genders and shows a consistent anterior-posterior gradient with strongest impact to prefrontal cortex (PFC) brain changes. Finally, we demonstrate the potential of the framework to explore the coupling of structural changes across a priori defined subnetworks using an example of previously established resting state functional connectivity.

Methods for Modeling Brassinosteroid-Mediated Signaling in Plant Development

Mathematical modeling of biological processes is a useful tool to draw conclusions that are contained in the data, but not directly reachable, as well as to make predictions and select the most efficient follow-up experiments. Here we outline a method to model systems of a few proteins that interact transcriptionally and/or posttranscriptionally, by representing the system as Ordinary Differential Equations and to study the model dynamics and stationary states. We exemplify this method by focusing on the regulation by the brassinosteroid (BR) signaling component BRASSINOSTEROID INSENSITIVE1 ETHYL METHYL SULFONATE SUPPRESSOR1 (BES1) of BRAVO, a quiescence-regulating transcription factor expressed in the quiescent cells of Arabidopsis thaliana roots. The method to extract the stationary states and the dynamics is provided as a Mathematica code and requires basic knowledge of the Mathematica software to be executed.

An integrated model for motor control of song in Serinus canaria

Birdsong is a learned motor behavior controlled by an interconnected structure of neural nuclei. This pathway is bilaterally organized, with anatomically indistinguishable structures in each brain hemisphere. In this work, we present a computational model whose variables are the average activities of different neural nuclei of the song system of oscine birds. Two of the variables are linked to the air sac pressure and the tension of the labia during canary song production. We show that these time dependent gestures are capable of driving a model of the vocal organ to synthesize realistic canary like songs.

Nonlinear statistical data assimilation for HVC[Formula: see text] neurons in the avian song system

With the goal of building a model of the HVC nucleus in the avian song system, we discuss in detail a model of HVC[Formula: see text] projection neurons comprised of a somatic compartment with fast Na[Formula: see text] and K[Formula: see text] currents and a dendritic compartment with slower Ca[Formula: see text] dynamics. We show this model qualitatively exhibits many observed electrophysiological behaviors. We then show in numerical procedures how one can design and analyze feasible laboratory experiments that allow the estimation of all of the many parameters and unmeasured dynamical variables, given observations of the somatic voltage [Formula: see text] alone. A key to this procedure is to initially estimate the slow dynamics associated with Ca, blocking the fast Na and K variations, and then with the Ca parameters fixed estimate the fast Na and K dynamics. This separation of time scales provides a numerically robust method for completing the full neuron model, and the efficacy of the method is tested by prediction when observations are complete. The simulation provides a framework for the slice preparation experiments and illustrates the use of data assimilation methods for the design of those experiments.

Developmental coordination disorder and its cause: The road less travelled

We critically review the research literature that seeks to focus on the possible cause of children diagnosed with developmental coordination disorder (DCD). In so doing we contrast the traditional information processing (IP) approach as a model to explain the causal factors that account for the motor deficits present in children with DCD, with a dynamical systems (DS) account which argues that coordination deficits in children with DCD is less to do with problems of poor internal models (a cornerstone of IP theory) and more with a degrading of perception-action coupling. We review and comment on the extant empirical data and conclusions of both approaches. We conclude that the data for an IP explanation is weak and a reconsideration of DCD is in order with respect to the underlying cause of this issue.

Abrupt transitions to tumor extinction: a phenotypic quasispecies model

The dynamics of heterogeneous tumor cell populations competing with healthy cells is an important topic in cancer research with deep implications in biomedicine. Multitude of theoretical and computational models have addressed this issue, especially focusing on the nature of the transitions governing tumor clearance as some relevant model parameters are tuned. In this contribution, we analyze a mathematical model of unstable tumor progression using the quasispecies framework. Our aim is to define a minimal model incorporating the dynamics of competition between healthy cells and a heterogeneous population of cancer cell phenotypes involving changes in replication-related genes (i.e., proto-oncogenes and tumor suppressor genes), in genes responsible for genomic stability, and in house-keeping genes. Such mutations or loss of genes result into different phenotypes with increased proliferation rates and/or increased genomic instabilities. Despite bifurcations in the classical deterministic quasispecies model are typically given by smooth, continuous shifts (i.e., transcritical bifurcations), we here identify a novel type of bifurcation causing an abrupt transition to tumor extinction. Such a bifurcation, named as trans-heteroclinic, is characterized by the exchange of stability between two distant fixed points (that do not collide) involving tumor persistence and tumor clearance. The increase of mutation and/or the decrease of the replication rate of tumor cells involves this catastrophic shift of tumor cell populations. The transient times near bifurcation thresholds are also characterized, showing a power law dependence of exponent [Formula: see text] of the transients as mutation is changed near the bifurcation value. These results are discussed in the context of targeted cancer therapy as a possible therapeutic strategy to force a catastrophic shift by simultaneously delivering mutagenic and cytotoxic drugs inside tumor cells.

A dynamical systems model of progesterone receptor interactions with inflammation in human parturition

BACKGROUND

Progesterone promotes uterine relaxation and is essential for the maintenance of pregnancy. Withdrawal of progesterone activity and increased inflammation within the uterine tissues are key triggers for parturition. Progesterone actions in myometrial cells are mediated by two progesterone receptor (PR) isoforms, PR-A and PR-B, that function as ligand-activated transcription factors. PR-B mediates relaxatory actions of progesterone, in part, by decreasing myometrial cell responsiveness to pro-inflammatory stimuli. These same pro-inflammatory stimuli promote the expression of PR-A which inhibits the anti-inflammatory activity of PR-B. Competitive interaction between the progesterone receptors then augments myometrial responsiveness to pro-inflammatory stimuli. The interaction between PR-B transcriptional activity and inflammation in the pregnancy myometrium is examined using a dynamical systems model in which quiescence and labor are represented as phase-space equilibrium points. Our model shows that PR-B transcriptional activity and the inflammatory load determine the stability of the quiescent and laboring phenotypes. The model is tested using published transcriptome datasets describing the mRNA abundances in the myometrium before and after the onset of labor at term. Surrogate transcripts were selected to reflect PR-B transcriptional activity and inflammation status.

RESULTS

The model coupling PR-B activity and inflammation predicts contractile status (i.e., laboring or quiescent) with high precision and recall and outperforms uncoupled single and two-gene classifiers. Linear stability analysis shows that phase space bifurcations exist in our model that may reflect the phenotypic states of the pregnancy uterus. The model describes a possible tipping point for the transition of the quiescent to the contractile laboring phenotype.

CONCLUSIONS

Our model describes the functional interaction between the PR-A:PR-B hypothesis and tissue level inflammation in the pregnancy uterus and is a first step in more sophisticated dynamical systems modeling of human partition. The model explains observed biochemical dynamics and as such will be useful for the development of a range of systems-based models using emerging data to predict preterm birth and identify strategies for its prevention.

Structure and dynamics of European sports science textual contents: Analysis of ECSS abstracts (1996-2014)

The article discusses general structure and dynamics of the sports science research content as obtained from the analysis of 21998 European College of Sport Science abstracts belonging to 12 science topics. The structural analysis showed intertwined multidisciplinary and unifying tendencies structured along horizontal (scope) and vertical (level) axes. Methodological (instrumental and mode of inquiry) integrative tendencies are dominant. Theoretical integrative tendencies are much less detectable along both horizontal and vertical axes. The dynamic analysis of written abstracts text content over the 19 years reveals the contextualizing and guiding role of thematic skeletons of each sports science topic in forming more detailed contingent research ideas and the role of the latter in stabilizing and procreating the former. This circular causality between both hierarchical levels and functioning on separate characteristic time scales is crucial for understanding how stable research traditions self-maintain and self-procreate through innovative contingencies. The structure of sports science continuously rebuilds itself through use and re-use of contingent research ideas. The thematic skeleton ensures its identity and the contingent conceptual sets its flexibility and adaptability to different research or applicative problems.

The Episodic Nature of Experience: A Dynamical Systems Analysis

Context is an important construct in many domains of cognition, including learning, memory, and emotion. We used dynamical systems methods to demonstrate the episodic nature of experience by showing a natural separation between the scales over which within-context and between-context relationships operate. To do this, we represented an individual's emails extending over about 5 years in a high-dimensional semantic space and computed the dimensionalities of the subspaces occupied by these emails. Personal discourse has a two-scaled geometry with smaller within-context dimensionalities than between-context dimensionalities. Prior studies have shown that reading experience (Doxas, Dennis, & Oliver, 2010) and visual experience (Sreekumar, Dennis, Doxas, Zhuang, & Belkin, 2014) have a similar two-scaled structure. Furthermore, the recurrence plot of the emails revealed that experience is predictable and hierarchical, supporting the constructs of some influential theories of memory. The results demonstrate that experience is not scale-free and provide an important target for accounts of how experience shapes cognition.

Kinds versus continua: a review of psychometric approaches to uncover the structure of psychiatric constructs

The question of whether psychopathology constructs are discrete kinds or continuous dimensions represents an important issue in clinical psychology and psychiatry. The present paper reviews psychometric modelling approaches that can be used to investigate this question through the application of statistical models. The relation between constructs and indicator variables in models with categorical and continuous latent variables is discussed, as are techniques specifically designed to address the distinction between latent categories as opposed to continua (taxometrics). In addition, we examine latent variable models that allow latent structures to have both continuous and categorical characteristics, such as factor mixture models and grade-of-membership models. Finally, we discuss recent alternative approaches based on network analysis and dynamical systems theory, which entail that the structure of constructs may be continuous for some individuals but categorical for others. Our evaluation of the psychometric literature shows that the kinds-continua distinction is considerably more subtle than is often presupposed in research; in particular, the hypotheses of kinds and continua are not mutually exclusive or exhaustive. We discuss opportunities to go beyond current research on the issue by using dynamical systems models, intra-individual time series and experimental manipulations.

Feedback mechanisms control coexistence in a stem cell model of acute myeloid leukaemia

Haematopoietic stem cell dynamics regulate healthy blood cell production and are disrupted during leukaemia. Competition models of cellular species help to elucidate stem cell dynamics in the bone marrow microenvironment (or niche), and to determine how these dynamics impact leukaemia progression. Here we develop two models that target acute myeloid leukaemia with particular focus on the mechanisms that control proliferation via feedback signalling. It is within regions of parameter space permissive of coexistence that the effects of competition are most subtle and the clinical outcome least certain. Steady state and linear stability analyses identify parameter regions that allow for coexistence to occur, and allow us to characterise behaviour near critical points. Where analytical expressions are no longer informative, we proceed statistically and sample parameter space over a coexistence region. We find that the rates of proliferation and differentiation of healthy progenitors exert key control over coexistence. We also show that inclusion of a regulatory feedback onto progenitor cells promotes healthy haematopoiesis at the expense of leukaemia, and that – somewhat paradoxically – within the coexistence region feedback increases the sensitivity of the system to dominance by one lineage over another.

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Models of competition between cell populations can describe the progression of acute myeloid leukaemia.

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We identify regions of coexistence in which leukaemia and healthy haematopoietic species can coexist in the niche.

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The dynamics of progenitor cells exert key control over species coexistence.

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The introduction of regulatory feedback can promote healthy haematopoiesis and suppress leukaemia.

Learning stochastic process-based models of dynamical systems from knowledge and data

Background

Identifying a proper model structure, using methods that address both structural and parameter uncertainty, is a crucial problem within the systems approach to biology. And yet, it has a marginal presence in the recent literature. While many existing approaches integrate methods for simulation and parameter estimation of a single model to address parameter uncertainty, only few of them address structural uncertainty at the same time. The methods for handling structure uncertainty often oversimplify the problem by allowing the human modeler to explicitly enumerate a relatively small number of alternative model structures. On the other hand, process-based modeling methods provide flexible modular formalisms for specifying large classes of plausible model structures, but their scope is limited to deterministic models. Here, we aim at extending the scope of process-based modeling methods to inductively learn stochastic models from knowledge and data.

Results

We combine the flexibility of process-based modeling in terms of addressing structural uncertainty with the benefits of stochastic modeling. The proposed method combines search trough the space of plausible model structures, the parsimony principle and parameter estimation to identify a model with optimal structure and parameters. We illustrate the utility of the proposed method on four stochastic modeling tasks in two domains: gene regulatory networks and epidemiology. Within the first domain, using synthetically generated data, the method successfully recovers the structure and parameters of known regulatory networks from simulations. In the epidemiology domain, the method successfully reconstructs previously established models of epidemic outbreaks from real, sparse and noisy measurement data.

Conclusions

The method represents a unified approach to modeling dynamical systems that allows for flexible formalization of the space of candidate model structures, deterministic and stochastic interpretation of model dynamics, and automated induction of model structure and parameters from data. The method is able to reconstruct models of dynamical systems from synthetic and real data.

PeTTSy: a computational tool for perturbation analysis of complex systems biology models

Background

Over the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models. However, many of the currently available toolboxes have either used parameter sampling, been focused on a restricted set of model observables of interest, studied optimisation of a objective function, or have not dealt with multiple simultaneous model parameter changes where the changes can be permanent or temporary.

Results

Here we introduce our new, freely downloadable toolbox, PeTTSy (Perturbation Theory Toolbox for Systems). PeTTSy is a package for MATLAB which implements a wide array of techniques for the perturbation theory and sensitivity analysis of large and complex ordinary differential equation (ODE) based models. PeTTSy is a comprehensive modelling framework that introduces a number of new approaches and that fully addresses analysis of oscillatory systems. It examines sensitivity analysis of the models to perturbations of parameters, where the perturbation timing, strength, length and overall shape can be controlled by the user. This can be done in a system-global setting, namely, the user can determine how many parameters to perturb, by how much and for how long. PeTTSy also offers the user the ability to explore the effect of the parameter perturbations on many different types of outputs: period, phase (timing of peak) and model solutions. PeTTSy can be employed on a wide range of mathematical models including free-running and forced oscillators and signalling systems.

To enable experimental optimisation using the Fisher Information Matrix it efficiently allows one to combine multiple variants of a model (i.e. a model with multiple experimental conditions) in order to determine the value of new experiments. It is especially useful in the analysis of large and complex models involving many variables and parameters.

Conclusions

PeTTSy is a comprehensive tool for analysing large and complex models of regulatory and signalling systems. It allows for simulation and analysis of models under a variety of environmental conditions and for experimental optimisation of complex combined experiments. With its unique set of tools it makes a valuable addition to the current library of sensitivity analysis toolboxes. We believe that this software will be of great use to the wider biological, systems biology and modelling communities.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-0972-2) contains supplementary material, which is available to authorized users.

Combining optogenetic stimulation and fMRI to validate a multivariate dynamical systems model for estimating causal brain interactions

State-space multivariate dynamical systems (MDS) (Ryali et al. 2011) and other causal estimation models are being increasingly used to identify directed functional interactions between brain regions. However, the validity and accuracy of such methods are poorly understood. Performance evaluation based on computer simulations of small artificial causal networks can address this problem to some extent, but they often involve simplifying assumptions that reduce biological validity of the resulting data. Here, we use a novel approach taking advantage of recently developed optogenetic fMRI (ofMRI) techniques to selectively stimulate brain regions while simultaneously recording high-resolution whole-brain fMRI data. ofMRI allows for a more direct investigation of causal influences from the stimulated site to brain regions activated downstream and is therefore ideal for evaluating causal estimation methods in vivo. We used ofMRI to investigate whether MDS models for fMRI can accurately estimate causal functional interactions between brain regions. Two cohorts of ofMRI data were acquired, one at Stanford University and the University of California Los Angeles (Cohort 1) and the other at the University of North Carolina Chapel Hill (Cohort 2). In each cohort, optical stimulation was delivered to the right primary motor cortex (M1). General linear model analysis revealed prominent downstream thalamic activation in Cohort 1, and caudate-putamen (CPu) activation in Cohort 2. MDS accurately estimated causal interactions from M1 to thalamus and from M1 to CPu in Cohort 1 and Cohort 2, respectively. As predicted, no causal influences were found in the reverse direction. Additional control analyses demonstrated the specificity of causal interactions between stimulated and target sites. Our findings suggest that MDS state-space models can accurately and reliably estimate causal interactions in ofMRI data and further validate their use for estimating causal interactions in fMRI. More generally, our study demonstrates that the combined use of optogenetics and fMRI provides a powerful new tool for evaluating computational methods designed to estimate causal interactions between distributed brain regions.

Exploratory Approaches for Studying Social Interactions, Dynamics, and Multivariate Processes in Psychological Science

In this article, I argue for the need of more use of exploratory techniques to identify dynamics in social interactions. I describe several approaches as they are applied to multivariate time series data. The first approach is an algorithm that searches for periods of variability and stability at the individual level as well as for patterns of overlap in such periods between the two individuals in a couple. These patterns describe the daily ups and downs in the couples' affect and are predictive of the state of the couples 1 to 2 years later. The second approach, hierarchical segmentation, is based on the idea of partitioning the time series in segments with distinct data patterns. In the case of data from dyads, as in the illustration, the patterns can be compared in terms of coherence between the 2 individuals in the dyad. The third approach is based on network analysis, and its use is shown as a method to examine data transitions at the individual and dyadic level as well as system-wide coherence in multivariate systems. For each approach, I provide examples of its use with empirical data. The article ends with general guidelines and recommendations for researchers interested in using exploratory methods as a way to examine psychological processes.

Comparing dynamical systems concepts and techniques for biomechanical analysis

Traditional biomechanical analyses of human movement are generally derived from linear mathematics. While these methods can be useful in many situations, they do not describe behaviors in human systems that are predominately nonlinear. For this reason, nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature. These analysis techniques have provided new insights into how systems (1) maintain pattern stability, (2) transition into new states, and (3) are governed by short- and long-term (fractal) correlational processes at different spatio-temporal scales. These different aspects of system dynamics are typically investigated using concepts related to variability, stability, complexity, and adaptability. The purpose of this paper is to compare and contrast these different concepts and demonstrate that, although related, these terms represent fundamentally different aspects of system dynamics. In particular, we argue that variability should not uniformly be equated with stability or complexity of movement. In addition, current dynamic stability measures based on nonlinear analysis methods (such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics, but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored. Finally, systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.

An avian-only Filippov model incorporating culling of both susceptible and infected birds in combating avian influenza

Depopulation of birds has always been an effective method not only to control the transmission of avian influenza in bird populations but also to eliminate influenza viruses. We introduce a Filippov avian-only model with culling of susceptible and/or infected birds. For each susceptible threshold level [Formula: see text], we derive the phase portrait for the dynamical system as we vary the infected threshold level [Formula: see text], focusing on the existence of endemic states; the endemic states are represented by real equilibria, pseudoequilibria and pseudo-attractors. We show generically that all solutions of this model will approach one of the endemic states. Our results suggest that the spread of avian influenza in bird populations is tolerable if the trajectories converge to the equilibrium point that lies in the region below the threshold level [Formula: see text] or if they converge to one of the pseudoequilibria or a pseudo-attractor on the surface of discontinuity. However, we have to cull birds whenever the solution of this model converges to an equilibrium point that lies in the region above the threshold level [Formula: see text] in order to control the outbreak. Hence a good threshold policy is required to combat bird flu successfully and to prevent overkilling birds.

The coordination dynamics of mobile conjugate reinforcement

What we know about infant learning and memory is founded largely on systematic studies by the late Carolyn Rovee-Collier (1942-2014) and her associates of a phenomenon called mobile conjugate reinforcement. Experiments show that when a ribbon is attached from a 3-month-old infant's foot to a mobile suspended overhead the baby quickly realizes it can make the mobile move. The mobile, which offers interesting sights and sounds, responds conjugately to the baby's vigorous kicks which increase in rate by a factor of 3-4. In this paper, using the concepts, methods and tools of coordination dynamics, we present a theoretical model which reproduces the experimental observations of Rovee-Collier and others and predicts a number of additional features that can be experimentally tested. The model is a dynamical system consisting of three equations, one for the baby's leg movements, one for the jiggling motion of the mobile and one for the functional coupling between the two. A key mechanism in the model is positive feedback which is shown to depend sensitively on bifurcation parameters related to the infant's level of attention and inertial properties of the mobile. The implications of our model for the dynamical (and developmental) origins of agency are discussed.

A Mechanistic Neural Field Theory of How Anesthesia Suppresses Consciousness: Synaptic Drive Dynamics, Bifurcations, Attractors, and Partial State Equipartitioning

With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus on how the molecular properties of anesthetic agents lead to the observed macroscopic property that defines the anesthetic state, that is, lack of responsiveness to noxious stimuli. In this paper, we use dynamical system theory to develop a mechanistic mean field model for neural activity to study the abrupt transition from consciousness to unconsciousness as the concentration of the anesthetic agent increases. The proposed synaptic drive firing-rate model predicts the conscious-unconscious transition as the applied anesthetic concentration increases, where excitatory neural activity is characterized by a Poincaré-Andronov-Hopf bifurcation with the awake state transitioning to a stable limit cycle and then subsequently to an asymptotically stable unconscious equilibrium state. Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions. This is done by focusing on a postulated subset of inhibitory neurons that are not themselves connected to other inhibitory neurons. Finally, several numerical experiments are presented to illustrate the different aspects of the proposed theory.

Modeling HIV-1 viral capsid nucleation by dynamical systems

There are two stages generally recognized in the viral capsid assembly: nucleation and elongation. This paper focuses on the nucleation stage and develops mathematical models for HIV-1 viral capsid nucleation based on six-species dynamical systems. The Particle Swarm Optimization (PSO) algorithm is used for parameter fitting to estimate the association and dissociation rates from biological experiment data. Numerical simulations of capsid protein (CA) multimer concentrations demonstrate a good agreement with experimental data. Sensitivity and elasticity analysis of CA multimer concentrations with respect to the association and dissociation rates further reveals the importance of CA trimer-of- dimers in the nucleation stage of viral capsid self- assembly.

A glycemia-structured population model

Structured models are population models in which the individuals are characterized with respect to the value of some variable of interest, called the structure variable. In the present paper, we propose a glycemia-structured population model, based on a linear partial differential equation with variable coefficients. The model is characterized by three rate functions: a new-adult population glycemic profile, a glycemia-dependent mortality rate and a glycemia-dependent average worsening rate. First, we formally analyze some properties of the solution, the transient behavior and the equilibrium distribution. Then, we identify the key parameters and functions of the model from real-life data and we hypothesize some plausible modifications of the rate functions to obtain a more beneficial steady-state behavior. The interest of the model is that, while it summarizes the evolution of diabetes in the population in a completely different way with respect to previously published Monte Carlo aggregations of individual-based models, it does appear to offer a good approximation of observed reality and of the features expected in the clinical setting. The model can offer insights in pharmaceutical research and be used to assess possible public health intervention strategies.

Philosophy for the rest of cognitive science

Cognitive science has always included multiple methodologies and theoretical commitments. The philosophy of cognitive science should embrace, or at least acknowledge, this diversity. Bechtel's (2009a) proposed philosophy of cognitive science, however, applies only to representationalist and mechanist cognitive science, ignoring the substantial minority of dynamically oriented cognitive scientists. As an example of nonrepresentational, dynamical cognitive science, we describe strong anticipation as a model for circadian systems (Stepp & Turvey, 2009). We then propose a philosophy of science appropriate to nonrepresentational, dynamical cognitive science.

Investigating Conversational Dynamics: Interactive Alignment, Interpersonal Synergy, and Collective Task Performance

This study investigates interpersonal processes underlying dialog by comparing two approaches, interactive alignment and interpersonal synergy, and assesses how they predict collective performance in a joint task. While the interactive alignment approach highlights imitative patterns between interlocutors, the synergy approach points to structural organization at the level of the interaction-such as complementary patterns straddling speech turns and interlocutors. We develop a general, quantitative method to assess lexical, prosodic, and speech/pause patterns related to the two approaches and their impact on collective performance in a corpus of task-oriented conversations. The results show statistical presence of patterns relevant for both approaches. However, synergetic aspects of dialog provide the best statistical predictors of collective performance and adding aspects of the alignment approach does not improve the model. This suggests that structural organization at the level of the interaction plays a crucial role in task-oriented conversations, possibly constraining and integrating processes related to alignment.

Conversation and coordinative structures

People coordinate body postures and gaze patterns during conversation. We review literature showing that (1) action embodies cognition, (2) postural coordination emerges spontaneously when two people converse, (3) gaze patterns influence postural coordination, (4) gaze coordination is a function of common ground knowledge and visual information that conversants believe they share, and (5) gaze coordination is causally related to mutual understanding. We then consider how coordination, generally, can be understood as temporarily coupled neuromuscular components that function as a collective unit known as a coordinative structure in the motor control literature. We speculate that the coordination of gaze and body sway found in conversation may be understood as a cross-person coordinative structure that embodies the goals of the joint action system.

Sagittal plane coordination dynamics of typically developing gait

BACKGROUND

Individuals who undergo an instrumented gait analysis often have an aberrant gait pattern due to neuromuscular impairments that adversely affect their coordination. Conventional instrumented gait analysis descriptors fail to capture the complex coordination dynamics of gait. This paper presents a straightforward methodology for generating descriptors of coordination dynamics based on dynamical systems theory and provides the largest reported dataset of sagittal plane coordination measures, including adjacent and non-adjacent segment pairings, from individuals free of gait pathology walking over-ground.

METHODS

Tri-planar marker trajectories from 104 unimpaired subjects between the ages of 8 and 66 years were collected as they walked at a self-selected speed on a level surface. Phase portraits for the pelvis, thigh, shank, and foot and continuous relative phase diagrams for the segment pairs of pelvis-thigh, thigh-shank, shank-foot, and thigh-foot were calculated.

FINDINGS

The low coefficients of variation for each coordination curve are comparable to inter-subject coefficients of variation for kinematic curves, narrow confidence intervals for relative phase angles at four essential footfall conditions, and small standard deviation bands of the continuous relative phase diagrams are evidence that these curves characterize the coordination dynamics of normal gait.

INTERPRETATION

These findings support the use of this normative dataset as a reference for coordination studies in the clinic or research laboratory. Improving our understanding of gait strategies from the level of coordination and characterizing the natural variability in gait patterns offer a means to enhance our understanding of atypical gait patterns.

CauseMap: fast inference of causality from complex time series

Background. Establishing health-related causal relationships is a central pursuit in biomedical research. Yet, the interdependent non-linearity of biological systems renders causal dynamics laborious and at times impractical to disentangle. This pursuit is further impeded by the dearth of time series that are sufficiently long to observe and understand recurrent patterns of flux. However, as data generation costs plummet and technologies like wearable devices democratize data collection, we anticipate a coming surge in the availability of biomedically-relevant time series data. Given the life-saving potential of these burgeoning resources, it is critical to invest in the development of open source software tools that are capable of drawing meaningful insight from vast amounts of time series data. Results. Here we present CauseMap, the first open source implementation of convergent cross mapping (CCM), a method for establishing causality from long time series data (≳25 observations). Compared to existing time series methods, CCM has the advantage of being model-free and robust to unmeasured confounding that could otherwise induce spurious associations. CCM builds on Takens' Theorem, a well-established result from dynamical systems theory that requires only mild assumptions. This theorem allows us to reconstruct high dimensional system dynamics using a time series of only a single variable. These reconstructions can be thought of as shadows of the true causal system. If reconstructed shadows can predict points from opposing time series, we can infer that the corresponding variables are providing views of the same causal system, and so are causally related. Unlike traditional metrics, this test can establish the directionality of causation, even in the presence of feedback loops. Furthermore, since CCM can extract causal relationships from times series of, e.g., a single individual, it may be a valuable tool to personalized medicine. We implement CCM in Julia, a high-performance programming language designed for facile technical computing. Our software package, CauseMap, is platform-independent and freely available as an official Julia package. Conclusions. CauseMap is an efficient implementation of a state-of-the-art algorithm for detecting causality from time series data. We believe this tool will be a valuable resource for biomedical research and personalized medicine.

Implications of polychronous neuronal groups for the continuity of mind

Is conceptual space continuous? The answer to this question depends on how concepts are represented in the brain. Vector space representations, which ground conceptual states in the instantaneous firing rates of neurons, have successfully captured cognitive dynamics in a broad range of domains. There is a growing body of evidence, however, that conceptual information is encoded in spatiotemporal patterns of neural spikes, sometimes called polychronous neuronal groups (PNGs). The use of PNGs to represent conceptual states, rather than employing a continuous vector space, introduces new challenges, including issues of temporally extended representations, meaning through symbol grounding, compositionality, and representational similarity. In this article, we explore how PNGs support discontinuous transitions between concepts. While the continuous dynamics of vector space approaches require such transitions to activate intermediate and blended concepts, PNGs offer the means to change the activation of concepts discretely, introducing a form of conceptual dynamics unavailable to vector space models.

Some mathematical models of intermolecular autophosphorylation

Intermolecular autophosphorylation refers to the process whereby a molecule of an enzyme phosphorylates another molecule of the same enzyme. The enzyme thereby catalyses its own phosphorylation. In the present paper, we develop two generic models of intermolecular autophosphorylation that also include dephosphorylation by a phosphatase of constant concentration. The first of these, a solely time-dependent model, is written as one ordinary differential equation that relies upon mass-action and Michaelis-Menten kinetics. Beginning with the enzyme in its dephosphorylated state, it predicts a lag before the enzyme becomes significantly phosphorylated, for suitable parameter values. It also predicts that there exists a threshold concentration for the phosphorylation of enzyme and that for suitable parameter values, a continuous or discontinuous switch in the phosphorylation of enzyme are possible. The model developed here has the advantage that it is relatively easy to analyse compared with most existing models for autophosphorylation and can qualitatively describe many different systems. We also extend our time-dependent model of autophosphorylation to include a spatial dependence, as well as localised binding reactions. This spatio-temporal model consists of a system of partial differential equations that describe a soluble autophosphorylating enzyme in a spherical geometry. We use the spatio-temporal model to describe the phosphorylation of an enzyme throughout the cell due to an increase in local concentration by binding. Using physically realistic values for model parameters, our results provide a proof-of-concept of the process of activation by local concentration and suggest that, in the presence of a phosphatase, this activation can be irreversible.

Selective disinhibition: A unified neural mechanism for predictive and post hoc attentional selection

The natural world presents us with a rich and ever-changing sensory landscape containing diverse stimuli that constantly compete for representation in the brain. When the brain selects a stimulus as the highest priority for attention, it differentially enhances the representation of the selected, "target" stimulus and suppresses the processing of other, distracting stimuli. A stimulus may be selected for attention while it is still present in the visual scene (predictive selection) or after it has vanished (post hoc selection). We present a biologically inspired computational model that accounts for the prioritized processing of information about targets that are selected for attention either predictively or post hoc. Central to the model is the neurobiological mechanism of "selective disinhibition" - the selective suppression of inhibition of the representation of the target stimulus. We demonstrate that this mechanism explains major neurophysiological hallmarks of selective attention, including multiplicative neural gain, increased inter-trial reliability (decreased variability), and reduced noise correlations. The same mechanism also reproduces key behavioral hallmarks associated with target-distracter interactions. Selective disinhibition exhibits several distinguishing and advantageous features over alternative mechanisms for implementing target selection, and is capable of explaining the effects of selective attention over a broad range of real-world conditions, involving both predictive and post hoc biasing of sensory competition and decisions.

A model for spatio-temporal dynamics in a regulatory network for cell polarity

Cell polarity in Myxococcus xanthus is crucial for the directed motility of individual cells. The polarity system is characterised by a dynamic spatio-temporal localisation of the regulatory proteins MglA and MglB at opposite cell poles. In response to signalling by the Frz chemosensory system, MglA and MglB are released from the poles and then rebind at the opposite poles. Thus, over time MglA and MglB oscillate irregularly between the poles in synchrony but out of phase. A minimal macroscopic model of the Mgl/Frz regulatory system based on a reaction-diffusion PDE system is presented. Mathematical analysis of the steady states derives conditions on the reaction terms for formation of dynamic localisation patterns of the regulatory proteins under different biologically-relevant regimes, i.e. with and without Frz signalling. Numerical simulations of the model system produce either a stationary pattern in time (fixed polarity), periodic solutions in time (oscillating polarity), or excitable behaviour (irregular switching of polarity).

A control systems engineering approach for adaptive behavioral interventions: illustration with a fibromyalgia intervention

The term adaptive intervention has been used in behavioral medicine to describe operationalized and individually tailored strategies for prevention and treatment of chronic, relapsing disorders. Control systems engineering offers an attractive means for designing and implementing adaptive behavioral interventions that feature intensive measurement and frequent decision-making over time. This is illustrated in this paper for the case of a low-dose naltrexone treatment intervention for fibromyalgia. System identification methods from engineering are used to estimate dynamical models from daily diary reports completed by participants. These dynamical models then form part of a model predictive control algorithm which systematically decides on treatment dosages based on measurements obtained under real-life conditions involving noise, disturbances, and uncertainty. The effectiveness and implications of this approach for behavioral interventions (in general) and pain treatment (in particular) are demonstrated using informative simulations.

Multistate network model for the pathfinding problem with a self-recovery property

In this study, we propose a continuous model for a pathfinding system. We consider acyclic graphs whose vertices are connected by unidirectional edges. The proposed model autonomously finds a path connecting two specified vertices, and the path is represented by a stable solution of the proposed model. The system has a self-recovery property, i.e., the system can find a path when one of the connections in the existing path is suddenly terminated. Further, we demonstrate that the appropriate installation of inhibitory interaction improves the search time.

Analyzing feed-forward loop relationship in aging phenotypes: physical activity and physical performance

We present evidence of feed-forward loop relationships and positive association between physical activity and performance levels, which are components of frailty, using measures from 431 high functioning women initially aged 70-79 years followed over 7 visits. Physical activity levels were assessed using a questionnaire. Grip strength was measured using a handheld dynamometer and usual walking speed was measured over 4-m. The results suggest that a reduction in physical activity would not only degrade physical performance, but it would further reduce physical activity through declines in physical performance. As both physical activity and physical performance impact frailty, improvement of physical activity could help reduce frailty directly as well as indirectly via improved physical performance. Our findings support a priori hypothesis that feed-forward loops are present in the phenotype of frailty, which is due to dysregulated energetics. A methodologically broader implication is that we introduce modeling and analysis of feed-forward loop data here. The feed-forward loop, as we define it, is different from the concept of feedback loops used in biochemical systems. Generalizing our model of two-variable feed-forward loop, three, four or multivariable feed-forward loop can be applied to other biological systems.

How visual information influences coordination dynamics when following the leader

Coordinating one's movements with others is an important aspect of human interactions. Regulating the distance to other moving agents is often necessary to achieve specific task goals such as in invasion sports. This study aimed to examine how distance regulation is mediated by different sources of information that are typically available when humans coordinate their actions to others. Participants followed a virtual leader that moved backwards and forwards, and were instructed to maintain the initial distance. In one condition, participants were presented with a life-size fully animated human avatar as the leader, displaying both segmental (limb motion) and global (optical expansion) motion information. In the other condition, participants had to follow an expanding and receding sphere in which segmental motion information was absent. Optical expansion rates revealed that participants regulated distance equally effective in both conditions. Given the phase relation and response times to direction changes however, the timing to the leader appeared to be more accurate in the avatar condition. These results provide support that forward-backward following can indeed be successfully mediated through global information, but that detection of segmental information allows for earlier tuning to another person's movement intentions.

A spatial model with pulsed releases to compare strategies for the sterile insect technique applied to the mosquito Aedes aegypti

We present a simple mathematical model to replicate the key features of the sterile insect technique (SIT) for controlling pest species, with particular reference to the mosquito Aedes aegypti, the main vector of dengue fever. The model differs from the majority of those studied previously in that it is simultaneously spatially explicit and involves pulsed, rather than continuous, sterile insect releases. The spatially uniform equilibria of the model are identified and analysed. Simulations are performed to analyse the impact of varying the number of release sites, the interval between pulsed releases and the overall volume of sterile insect releases on the effectiveness of SIT programmes. Results show that, given a fixed volume of available sterile insects, increasing the number of release sites and the frequency of releases increases the effectiveness of SIT programmes. It is also observed that programmes may become completely ineffective if the interval between pulsed releases is greater that a certain threshold value and that, beyond a certain point, increasing the overall volume of sterile insects released does not improve the effectiveness of SIT. It is also noted that insect dispersal drives a rapid recolonisation of areas in which the species has been eradicated and we argue that understanding the density dependent mortality of released insects is necessary to develop efficient, cost-effective SIT programmes.

Differences in plantarflexor function during a stretch-shortening cycle task due to limb preference

Most healthy humans move symmetrically at gross limb level but large kinetic and kinematic asymmetries have been observed at joint level during locomotion. The aim of this study was to assess muscle function asymmetries in healthy, active adults using an adapted force sledge apparatus which isolates the plantarflexors during a stretch-shortening cycle (SSC) task. Peak force, rate of force development and SSC function of preferred and non-preferred limbs were assessed in 21 healthy, active individuals using the adapted sledge and three-dimensional motion analysis. Between-limb differences and relationships were determined using paired t-tests/Wilcoxon Signed-rank test, Cohen's dz, absolute symmetry index and Pearson's r/Spearman's rho. Significant differences with moderate effect size (ES) were observed in peak force (ES: 0.66), rate of peak force development (ES: 0.78), rate of force development in the first 50 ms (ES: 0.76), flight time (ES: 0.64) and SSC function (0.68), with no difference in contact time or duration of eccentric loading. A small ES (0.56) was observed in rate of force development in the first 30 ms. The upper range of asymmetry observed (up to 44.6%) was larger than previously reported for healthy individuals, indicating compensations occur at proximal joints during locomotion to ensure symmetrical movement.

Asymmetric interpersonal coupling in a cyclic sports-related movement task

In interactive sports, teammates and/or opponents mutually tune their behavior. Expert performance thus implies certain interactive abilities, which critically depend on perceptual coupling. To illustrate this assertion, we examined the coordination dynamics with asymmetric interaction of dyads performing a sports-related cyclical movement task. In pairs, basketball players performed lateral defensive slides in in-phase, until a cue prompted them to switch to antiphase coordination. We assessed how these switches were mediated by phase adaptations of each agent under bidirectional (i.e., agents facing one another) and unidirectional (i.e., one agent facing the back of the other) visual interaction conditions. This imposed asymmetry in visual coupling exemplified an imbalance in the interaction (or 'interact-ability') between two agents. The results concurred the asymmetric coupling: during the switch the agent facing the other adapted his phasing more than the other agent. Furthermore, also in the bidirectional condition the coupling revealed dyad-intrinsic asymmetries (e.g., related to implicit follower-leader strategies). Together, this illustrates that interpersonal coordination is characterized by asymmetric coupling between the agents, and highlights how mutual perception of pertinent information mediates interpersonal coordination. This study offered a first step towards analyzing interpersonal coordination dynamics in relation to 'interact-ability'.