Efficient gradient computation for dynamical models

Data assimilation is a fundamental issue that arises across many scales in neuroscience — ranging from the study of single neurons using single electrode recordings to the interaction of thousands of neurons using fMRI. Data assimilation involves inverting a generative model that can not only explain observed data but also generate predictions. Typically, the model is inverted or fitted using conventional tools of (convex) optimization that invariably extremise some functional — norms, minimum descriptive length, variational free energy, etc. Generally, optimisation rests on evaluating the local gradients of the functional to be optimized. In this paper, we compare three different gradient estimation techniques that could be used for extremising any functional in time — (i) finite differences, (ii) forward sensitivities and a method based on (iii) the adjoint of the dynamical system. We demonstrate that the first-order gradients of a dynamical system, linear or non-linear, can be computed most efficiently using the adjoint method. This is particularly true for systems where the number of parameters is greater than the number of states. For such systems, integrating several sensitivity equations – as required with forward sensitivities – proves to be most expensive, while finite-difference approximations have an intermediate efficiency. In the context of neuroimaging, adjoint based inversion of dynamical causal models (DCMs) can, in principle, enable the study of models with large numbers of nodes and parameters.

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We compare three methods to compute gradients in dynamical systems.

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The methods are finite-differences, forward sensitivity and reverse adjoints.

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The adjoint method is 50–70 folds more efficient.

Coupling angle variability in healthy and patellofemoral pain runners

BACKGROUND

Patellofemoral pain is hypothesized to result in less joint coordination variability. The ability to relate coordination variability to patellofemoral pain pathology could have many clinical uses; however, evidence to support its clinical application is lacking. The aim was to determine if vector coding's coupling angle variability, as a measure of joint coordination variability, was less for runners with patellofemoral pain than healthy controls as is commonly postulated.

METHODS

Nineteen female recreational runners with patellofemoral pain and eleven healthy controls performed a treadmill acclimation protocol then ran at a self-selected pace for 15min. 3-D kinematics, force plate kinetics, knee pain and rating of perceived exertion were recorded each minute. Data were selected for the: pain group at the highest pain reached (pain≥3/10) in a non-exerted state (exertion<14/20), and; non-exerted healthy group from the eleventh minute. Coupling angle variability was calculated over several portions of the stride for six knee-ankle combinations during five non-consecutive strides.

FINDINGS

46 of 48 coupling angle variability measures were greater for the pain group, with 7 significantly greater (P<.05).

INTERPRETATION

These findings oppose the theory that less coupling angle variability is indicative of a pathological coordinate state during running. Greater coupling angle variability may be characteristic of patellofemoral pain in female treadmill running when a larger threshold of pain is reached than previously observed. A predictable and directional response of coupling angle variability measures in relation to knee pathology is not yet clear and requires further investigation prior to considerations for clinical utility.

Evolving Boolean regulatory networks with epigenetic control

The significant role of epigenetic mechanisms within natural systems has become increasingly clear. This paper uses a recently presented abstract, tunable Boolean genetic regulatory network model to explore aspects of epigenetics. It is shown how dynamically controlling transcription via a DNA methylation-inspired mechanism can be selected for by simulated evolution under various single and multicellular scenarios. Further, it is shown that the effects of such control can be inherited without detriment to fitness.

A dynamical system perspective to understanding badminton singles game play

By altering the task constraints of cooperative and competitive game contexts in badminton, insights can be obtained from a dynamical systems perspective to investigate the underlying processes that results in either a gradual shift or transition of playing patterns. Positional data of three pairs of skilled female badminton players (average age 20.5±1.38years) were captured and analyzed. Local correlation coefficient, which provides information on the relationship of players' displacement data, between each pair of players was computed for angle and distance from base position. Speed scalar product was in turn established from speed vectors of the players. The results revealed two patterns of playing behaviors (i.e., in-phase and anti-phase patterns) for movement displacement. Anti-phase relation was the dominant coupling pattern for speed scalar relationships among the pairs of players. Speed scalar product, as a collective variable, was different between cooperative and competitive plays with a greater variability in amplitude seen in competitive plays leading to a winning point. The findings from this study provide evidence for increasing stroke variability to perturb existing stable patterns of play and highlights the potential for speed scalar product to be a collective variable to distinguish different patterns of play (e.g., cooperative and competitive).

Skill transfer, affordances and dexterity in different climbing environments

This study explored how skills in one region of a perceptual-motor landscape of performance, created in part by previous experience in rock climbing, can shape those that emerge in another region (ice climbing). Ten novices in rock climbing and five intermediate rock climbers were observed climbing an icefall. Locations of right and left ice tools and crampons were videotaped from a frontal camera. Inter-individual variability of upper and lower limb couplings and types of action regarding icefall properties were assessed by cluster hierarchical analysis, distinguishing three clusters. Pelvis vertical displacement, duration and number of pelvis pauses were also analyzed. Experienced rock climbers were grouped in the same cluster and showed the highest range and variability of limb angular locations and coordination patterns, the highest vertical displacement and the shortest pelvis plateaux durations. Non-fluent climbers (clusters 2 and 3) showed low range and variability of limb angular locations and coordination patterns. In particular, climbers of cluster 3 exhibited the lowest vertical displacement, the longest plateaux durations and the greatest ratio between tool swinging and definitive anchorage. Our results exemplified the positive influence of skills in rock climbing on ice climbing performance, facilitated by the detection of affordances from environmental properties.

In vitro regulatory models for systems biology

The reductionist approach has revolutionized biology in the past 50 years. Yet its limits are being felt as the complexity of cellular interactions is gradually revealed by high-throughput technology. In order to make sense of the deluge of "omic data", a hypothesis-driven view is needed to understand how biomolecular interactions shape cellular networks. We review recent efforts aimed at building in vitro biochemical networks that reproduce the flow of genetic regulation. We highlight how those efforts have culminated in the rational construction of biochemical oscillators and bistable memories in test tubes. We also recapitulate the lessons learned about in vivo biochemical circuits such as the importance of delays and competition, the links between topology and kinetics, as well as the intriguing resemblance between cellular reaction networks and ecosystems.

Acquisition of expertise in cricket fast bowling: perceptions of expert players and coaches

OBJECTIVES

Experiential knowledge of elite athletes and coaches was investigated to reveal insights on expertise acquisition in cricket fast bowling.

DESIGN

Twenty-one past or present elite cricket fast bowlers and coaches of national or international level were interviewed using an in-depth, open-ended, semi-structured approach.

METHODS

Participants were asked about specific factors which they believed were markers of fast bowling expertise potential. Of specific interest was the relative importance of each potential component of fast bowling expertise and how components interacted or developed over time.

RESULTS

The importance of intrinsic motivation early in development was highlighted, along with physical, psychological and technical attributes. Results supported a multiplicative and interactive complex systems model of talent development in fast bowling, in which component weightings were varied due to individual differences in potential experts. Dropout rates in potential experts were attributed to misconceived current talent identification programmes and coaching practices, early maturation and physical attributes, injuries and lack of key psychological attributes and skills.

CONCLUSIONS

Data are consistent with a dynamical systems model of expertise acquisition in fast bowling, with numerous trajectories available for talent development. Further work is needed to relate experiential and theoretical knowledge on expertise in other sports.

Parameter uncertainty in biochemical models described by ordinary differential equations

Improved mechanistic understanding of biochemical networks is one of the driving ambitions of Systems Biology. Computational modeling allows the integration of various sources of experimental data in order to put this conceptual understanding to the test in a quantitative manner. The aim of computational modeling is to obtain both predictive as well as explanatory models for complex phenomena, hereby providing useful approximations of reality with varying levels of detail. As the complexity required to describe different system increases, so does the need for determining how well such predictions can be made. Despite efforts to make tools for uncertainty analysis available to the field, these methods have not yet found widespread use in the field of Systems Biology. Additionally, the suitability of the different methods strongly depends on the problem and system under investigation. This review provides an introduction to some of the techniques available as well as gives an overview of the state-of-the-art methods for parameter uncertainty analysis.

Mathematical model of the dynamics of psychotherapy

The success of psychotherapy depends on the nature of the therapeutic relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters of the model. Previously Gottman et al. used a very similar approach (physical-sciences paradigm) for modeling and making predictions about husband–wife relationships. Given that this novel approach shed light on the dyadic interaction between couples, we have applied it to the study of the relationship between therapist and client. The results of our computations provide a new perspective on the therapeutic relationship and a number of useful insights. Our goal is to create a model that is capable of making solid predictions about the dynamics of psychotherapy with the ultimate intention of using it to better train therapists.

Health behavior models in the age of mobile interventions: are our theories up to the task?

Mobile technologies are being used to deliver health behavior interventions. The study aims to determine how health behavior theories are applied to mobile interventions. This is a review of the theoretical basis and interactivity of mobile health behavior interventions. Many of the mobile health behavior interventions reviewed were predominately one way (i.e., mostly data input or informational output), but some have leveraged mobile technologies to provide just-in-time, interactive, and adaptive interventions. Most smoking and weight loss studies reported a theoretical basis for the mobile intervention, but most of the adherence and disease management studies did not. Mobile health behavior intervention development could benefit from greater application of health behavior theories. Current theories, however, appear inadequate to inform mobile intervention development as these interventions become more interactive and adaptive. Dynamic feedback system theories of health behavior can be developed utilizing longitudinal data from mobile devices and control systems engineering models.