# Research group

Complexity & Adaptability**Complexity & Adaptability**

Complexity is maybe one of the less properly understood concepts, and is often considered synonym of randomness and unpredictability. However, r*ecent approaches *converge toward precise definitions, considering complexity as a flexible and adaptive coordination between the multiple components in the system (Kello et al., 2010). Complexity appears midway between disorder (no coordination between components) and strict order (rigid coordination). This focus on coordination supposes that interactions among components have more influence on system’s behavior than components themselves. *In this approach, complexity determines the properties of stability and adaptability that characterize healthy, efficient and perennial systems. Complexity can be lost with aging and disease, yielding maladaptation, frailty and lack of flexibility, and regained with rehabilitation and learning. This statement represents the starting point of the scientific project of the group “Complexity & Adaptability”. *

In the former organization of the laboratory, the members of this team were disseminated among different groups (Ageing, Coordyn, and Rearm). Grouping them in a dedicated team aims to optimize their research efforts around this specific object. The scientific project of this new group is composed of three entangled axes, dedicated to basic, translational, and methodological research, respectively. These axes are not considered sequentially, nor hierarchically organized. They will enrich each other as and when they will develop.

**Fundamental research**

We consider that sensori-motor functions are produced by Complex Adaptive (sub)Systems (CAS). CAS are composed of multiple interacting components, self-similarly organized, and possess adaptive capacities (Holland, 2006; MacLennan, 2007). CAS models have been successfully applied in a number of scientific domains, including biological evolution (Whitacre, 2010), brain (Morowitz & Singer, 1995), stock market (Markose, 2004), or internet traffic (Phister, 2010). CAS present essential functional properties, and especially: (1) The capacity to produce roughly reproducible outcomes in stable environments (stability), (2) the capacity to resist to external perturbations for sustaining functional outcomes (robustness, resilience, flexibility) and (3) the capacity to adapt to changes in the environment by adopting new response modes (evolvability, plasticity, learning). These properties are obviously of central interest when considering sensorimotor functions.

The coexistence of such *a priori* antinomic properties (e.g., robustness and evolvability) remains a central theoretical challenge. Whitacre (2010) shows that this paradox can be overcome by degenerate systems. Degeneracy refers to a *partial overlap* in the functions of the multiple components within the system. In degenerate systems, structurally different components can perform similar functions under certain conditions, but can also assume distinct roles in others conditions.

Complex systems are also known to present intrinsic fluctuations, characterized by the presence of long-range correlations (LRC). This property has been evidenced in a number of physical and living systems, and especially in human movement (e.g., Gilden et al., 1995; Delignières et al., 2004; Hausdorff et al., 1995). LRC are considered to represent the hallmark of efficient and perennial systems. In the domain of living systems, they have been essentially discovered in experiments analyzing the behavior of young and healthy organisms. In contrast, the analysis of series produced by deficient systems (i.e., patients suffering from neurological diseases, elderly) revealed a clear alteration of fractal properties (Hausdorff et al., 1997).

These two lines of reasoning suggest a direct and causal link between the design principles that underlie CAS, and the statistical properties of the outcome series they produce. In turn, one can suppose that these statistical properties could represent essential markers of the internal organization of the system.

*1. System design principles and temporal structure of outcome series.*The first line of research stems from previous statements. Our goal at this level is to confirm the relationship between the complexity of systems and the statistical properties of the series they produce. Especially, we aim at deepening the degeneracy hypothesis and its links with related theories such as metastability (Kello et al., 2007) or cascade dynamics (Ihlen & Vereijken, 2010). This research line will be based on the conception of network models that could be able to simulate degeneracy, and to produce LRC series. Then, we will try to determine the optimal design principles for these models, and to reproduce experimental results that evidenced the effects of factors such as practice, learning, mental load, aging or disease on the statistical properties of outcome series.*2. Complexity as a global or specific property.*Generally, complexity is conceived as a global property of living organisms. However, recent experiments showed that LRC properties are both task- and individual-specific. This suggests that LRC reflect the complexity of the specific (but overlapping) networks that were involved in each task (Kello et al., 2007; Torre et al., 2011). This hypothesis requires further efforts for being confirmed, and for determining the true nature and the boundaries of “specific networks” and “systems” within the organism. This will require the analysis of data collected in test batteries, in order to check for the presence of eventual clusters.*3. Links between the structures of variability at different levels of observation.*Our main hypothesis suggests a close relationship between the complexity of underlying networks and that of observable behavior. This supposes that correlation structures, generated at different levels of analysis of the same behavior, for example in brain activation patterns, in electrical muscle activity, and in mechanic force output, should present strong similarities. Testing this hypothesis is essential for supporting the assumption that serial correlation properties in sensorimotor behavior reflect brain’s networks complexity.*4. Relationship between the biomechanical properties and the complexity of outcome variables.*The links between the biomechanics of physiological systems involved in posture or locomotion and the complexity of their key output variables are still not well understood. Some recent studies have explored these aspects by combining experimental manipulations, nonlinear analyses and dynamical modeling (Morrison, et al., 2007; Dingwell et al., 2010; Barbado, Murillo et al., 2012), sometimes leading to counterintuitive findings. The main objective is to investigate the relationship between biomechanical features (i.e. stability, stiffness, muscle activity, energetic cost) and the complexity of the key output variables quantified through measures of predictability and correlations. This research will include numerical simulations based on specific models as well as experimental studies.

*1.5. Synchronization processes between complex systems. *Complexity and long-range correlations play a central role in the theory of strong anticipation, which aims at explaining how complex systems synchronize and cooperate (Dubois, 2003). In contrast with traditional approaches based on local representational models, strong anticipation suggests that complexity allows a global, multiscale synchronization between systems (Marmelat & Delignières, 2012; Stephen et al., 2008). This phenomenon has to be more deeply studied, especially in order to determine the conditions that could optimize complexity matching (inter-individual coordination, synchronization with complex signals or virtual environments, etc.).

**Translational research**

Our activity in translational research will be based on three main hypotheses, directly deriving from the previous theoretical statements.

*2.1. Aging, disease and loss of complexity. **The first hypothesis states that aging and disease are characterized by a loss of complexity (Lipsitz & Goldberger, 1992). *Loss of complexity has been assumed to entail the decreased capability of elderly or patients to adapt to various constraints (Goldberger et al., 2002). Such loss of complexity has been demonstrated in the cases of several pathologies including cardiovascular diseases (Goldberger et al., 2002), neurodegenerative pathologies like Huntington’s disease (Hausdorff et al., 1997), as well as typical ageing (Vaillancourt & Newell, 2003).

Our aim is to test the clinical interest of complexity measures for assessing the emergence of frailty in elderly people (prefrailty). For example *Hausdorff et al. (1997) evidenced a whitening of walking stride interval duration series in elderly people, and showed that this effect was stronger in fallers. This kind of result suggests that complexity measures could serve as a prognostic index of frailty in elderly. A precocious diagnostic of frailty *will help to develop interventions for slowing down aging.

*This aim requires further effort for providing clinicians with efficient and reliable testing protocols. The nonlinear analysis of posture and locomotion data has produced a huge amount of literature, and often controversial results. Empirical investigations and methodological improvements are necessary for determining the best suitable tests, taking into account the limitations of elderly patients, and providing accurate results accessible for clinicians. *

*2.2. Rehabilitation and the restoration of complexity in deficient systems. **Basing on the loss of complexity hypothesis, one could consider that rehabilitation should primarily focus on the restoration of complexity in impaired systems. This idea could suggest innovative rehabilitation protocols, for example based on well-known principles in motor learning such as variability of practice or contextual interference **(Schmidt & Lee, 2005)**. Our work on strong anticipation opens interesting perspectives in this regard. Considering that synchronization between complex systems yields to a matching of complexities, *a promising rehabilitation strategy could be to instruct patients to synchronize their activity (e.g., walking) with healthy partners. We suppose that such coupling should entail an entrainment of the deficient system by the healthy one, yielding after practice a possible restoration of complexity in the former.

*2.3. Residual complexity as a measure of the potential of plasticity and the degree of recovery to be expected after rehabilitation. *The third hypothesis suggests that residual complexity could allow measuring the potential of plasticity, and predicting the degree of recovery to be expected after rehabilitation. This hypothesis could be tested in longitudinal protocols analyzing recovery in elderly people, but it present a specific interest in the domain of acute brain damage, for example following stroke. Beyond the localization of damages, stroke is likely to disturb interactions between components and networks in the brain, and then to dramatically alter complexity. Considering brain as a Complex Adaptive Systems, one can assume that cerebral plasticity is related to residual complexity after stroke. We hypothesize that the correlation structure of the sensorimotor behavior in stroke patients could serve as measuring a reservoir of plasticity.

*2.4. Effect of physical training on frailty in elderly people*. In a more applied perspective, we aim at determining the effects of different training modalities (postural, muscular, vibration solicitations) on the postural and locomotor capacities of elderly, especially in terms of complexity restoration. Our goal is to participate to the validation of a method associating adapted physical activities and health education, for preventing motor deconditioning and limiting the effect of aging.

**Analysis methods and modeling**

The combination of the two previous axes requires and provides opportunities for developing, improving, and assessing time series analysis techniques. The methods used to assess the temporal structure of time series include for example power spectral analysis, detrended fluctuation analysis, sample entropy, Lyapunov exponent, ARFIMA/ARMA modelling, etc., each of these methods characterizing different aspects of the complex dynamics of time series. Nonlinear analyses are known to require large data sets, implying prolonged experimental trials, which could be contaminated by factors such as fatigue or loss of concentration, especially with patients or elderly. Improving current techniques for obtaining accurate results with shorter series represents an important challenge.

It is essential for a research team working on these topics to develop a deep understanding of the methods it uses, in order to avoid blind uses and spurious conclusions. The members of the group have acquired competences in this domain, for example concerning fractal analyses (Delignieres et al., 2006; Lemoine & Delignieres, 2009; Torre et al., 2007), recurrence quantification analysis (Morana et al., 2009; Ramdani et al., in press), sample entropy (Ramdani et al., 2009a, 2009b), and system’s modeling (Delignieres et al., 2008; Delignieres & Torre, 2009; Torre et al., 2010; Torre & Delignieres, 2008a, 2008b).

References

Barbado Murillo, D., Sabido Salana, R., Vera-Garcia F.J., Gusi Fuertes, N., & Moreno, F .J. (2012). Effect of increasing difficulty in standing balance tasks with visual feedback on postural sway and EMG: Complexity and performance. Human Movement Science, 31, 1224-1237.

Delignieres, D., & Torre, K. (2009). Fractal dynamics of human gait: a reassessment of the 1996 data of Hausdorff et al. Journal of Applied Physiology, 106(4), 1272–1279.

Delignières, D., Ramdani, S., Lemoine, L., Torre, K., Fortes, M. & Ninot, G. (2006). Fractal analysis for short time series : A reassessement of classical methods. Journal of Mathematical Psychology, 50, 525-544.

Delignières, D., Torre, K., & Lemoine, L. (2008). Fractal models for event-based and dynamical timers. Acta Psychologica, 127, 382-397.

Dingwell, J.B., John, J., & Cusumano, J.P. (2010). Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking? PLOS Computational Biology, 6(7), e1000856.

Goldberger, A. L. (1996). Non-linear dynamics for clinicians: Chaos theory, fractals and complexity at the bedside. The Lancet, 347, 1312-1314.

Goldberger, A.L., Peng, C.-K., & Lipsitz, L.A. (2002). What is physiologic complexity and how does it change with aging and disease? Neurobiology of Aging, 23, 23–26.

Hausdorff, J. M., Mitchell, S. L., Firtion, R., Peng, C. K., Cudkowicz, M. E., Wei, J. Y., & Goldberger, A. L. (1997). Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington’s disease. Journal of Applied Physiology, 82, 262-269.

Hausdorff, J.M. (2009). Gait dynamics in Parkinson’s disease: Common and distinct behavior among stride length, gait variability, and fractal-like scaling. Chaos, 19, DOI: 10.1063/1.3147408

Holland, J. H. (2006). Studying Complex Adaptive Systems. *Journal of Systems Science and Complexity*, *19*(1), 1–8. doi:10.1007/s11424-006-0001-z

Kello, C.T., Brown, G.D.A., Ferrer-i-Cancho, R., Holden, J.G., Linkenkaer-Hansen, K., Rhodes, T., & Van Orden, G. (2010). Scaling laws in cognitive sciences. Trends in Cognitive Sciences, 14, 223-232.

Lipsitz, L.A. & Goldberger, M.D. (1992). Loss of ‘complexity’ and aging. Journal of the American Medicine Association, 267, 1806-1809.

MacLennan, B. (2007). Evolutionary Psychology, Complex Systems, and Social Theory. Soundings: An Interdisciplinary Journal, 90(3/4), 169-189.

Markose, S.M. (2004). Novelty in Complex Adaptive Systems (CAS) dynamics : a computational theory of actor innovation. Physica A, 344, 41-49.

Morana, C., Ramdani, S., Perrey, S., & Varray, A. (2009). Recurrence quantification analysis of surface electromyographic signal: Sensitivity to potentiation and neuromuscular fatigue. Journal of Neuroscience Methods, 177(1), 73–79.

Morowitz, H. & Singer, J. (1995, Eds.). The Mind, the Brain, and Complex Adaptive Systems. Reading, MA: Addison-Wesley.

Morrison, S., Hong, S.L., & Newell, K.M. (2007). Inverse relations in the patterns of muscle and center of pressure dynamics during standing still and movement postures. Experimental Brain Research, 181, 347–358.

Phister, P.W. (2010). Cyberspace : The Ultimate Complex Adaptive System. The International C2 Journal, 4(2), 1-30.

Ramdani, S., Bouchara, F., & Caron, O. (2012). Detecting high-dimensional determinism in time series with application to human movement data. Nonlinear Analysis-Real World Applications, 13(4), 1891–1903.

Ramdani, S., Bouchara, F., & Lagarde, J. (2009). Influence of noise on the sample entropy algorithm. Chaos, 19(1). doi:10.1063/1.3081406

Ramdani, S., Seigle, B., Lagarde, J., Bouchara, F., & Bernard, P. L. (2009). On the use of sample entropy to analyze human postural sway data. Medical Engineering & Physics, 31(8), 1023–1031.

Ramdani, S., Tallon, G., Bernard, P.L., Blain, H. (in press). *Recurrence quantification analysis of human postural fluctuations in older fallers and non-fallers.* Annals of Biomedical Engineering.

Torre, K, Balasubramaniam, R., & Delignieres, D. (2010). Oscillating in Synchrony with a Metronome: Serial Dependence, Limit Cycle Dynamics, and Modeling. Motor Control, 14(3), 323–343.

Torre, K, Delignières, D., & Lemoine, L. (2007). Detection of long-range dependence and estimation of fractal exponents through ARFIMA modeling. British Journal of Mathematical and Statistical Psychology, 60, 85-106.

Torre, K. & Delignières, D. (2008). Distinct ways for timing movements in bimanual coordination tasks: The contribution of serial correlation analysis and implications for modelling. Acta Psychologica, 129, 284-296.

Torre, K., & Delignières, D. (2008a). Unraveling the finding of 1/fβ noise in self-paced and synchronized tapping: A unifying mechanistic model. Biological Cybernetics, 99, 159-170.

Turvey, M. T. (2007) Action and perception at the level of synergies. *Human Movement Science, 26*, 657-697.

Vaillancourt, D. E., & Newell, K. M. (2003). Aging and the time and frequency structure of force output variability. Journal of Applied Physiology, 94, 903-912.

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