Nonlinear Dynamical Systems Approach Research Articles

Unsuccessful Accommodations: Reconceptualizing the Psychopathology Attributed to Neuropsychological Deficits

This contribution proposes reframing the concept of psychopathology as it applies to the dysfunctions that individuals with neuropsychological deficits display. It suggests that labeling these dysfunctions as symptoms of an underlying condition is an incomplete way of characterizing the process that leads to that outcome. An evolutionary and nonlinear dynamic systems approach complements this position and depathologizes individuals’ efforts to deal with their disabilities. The proposed modification introduces the concept of unsuccessful accommodations to characterize these individuals’ efforts to deal with their deficits.

Flexibility Versus Routineness in Multimodal Health Indicators: A Sensor-based Longitudinal in Situ Study of Information Workers

Although some research highlights the benefits of behavioral routines for individual functioning, other research indicates that routines can reflect an individual's inflexibility and lower well-being. Given conflicting accounts on the benefits of routine, research is needed to examine how routineness versus flexibility in health-related behaviors correspond to personality traits, health, and occupational outcomes. We adopt a nonlinear dynamical systems approach to understanding routine using automatically sensed health-related behaviors collected from 483 information workers over a roughly two-month period. We utilized multidimensional recurrence quantification analysis to derive a measure of health regularity (routineness) from measures of daily step count, sleep duration, and heart rate variability (which relates to stress). Participants also completed measures of personality, health, and job performance at the start of the study and for two months via Ecological Momentary Assessments. Greater regularity was associated with higher neuroticism, lower agreeableness, and greater interpersonal and organizational deviance. Importantly, these results were independent of overall levels of each health indicator in addition to demographics. It is often believed that routine is desirable, but the results suggest that associations with routineness are more nuanced, and wearable sensors can provide insights into beneficial health behaviors.

Standing Variations Modeling Captures Inter-Individual Heterogeneity in a Deterministic Model of Prostate Cancer Response to Combination Therapy.

Simple SummaryStudying rare outcomes in cancer is challenging because observation of the rare event may require a very high number of patients or experimental animals. Here, we propose a new, predictive approach to understanding the biological mechanisms underlying such rare events in cancer treatment outcomes. We take as a case-study, the treatment of metastatic, castration-resistant prostate cancer with the live cell vaccine, sipuleucel-t (Provenge). Only a fraction of patients benefited from Provenge; that is, clinical success is a rare event. It remains an open question why Provenge conferred such a modest survival benefit. Our modeling paradigm captures the inherent heterogeneity that characterizes individuals in a population, and provides an explanation for the observed clinical outcomes of treatment with Provenge. Our approach readily generalizes to a range of emerging cancer immunotherapies, and more generally, to predicting and understanding how a population responds to any intervention targeting a human disease.Sipuleucel-T (Provenge) is the first live cell vaccine approved for advanced, hormonally refractive prostate cancer. However, survival benefit is modest and the optimal combination or schedule of sipuleucel-T with androgen depletion remains unknown. We employ a nonlinear dynamical systems approach to modeling the response of hormonally refractive prostate cancer to sipuleucel-T. Our mechanistic model incorporates the immune response to the cancer elicited by vaccination, and the effect of androgen depletion therapy. Because only a fraction of patients benefit from sipuleucel-T treatment, inter-individual heterogeneity is clearly crucial. Therefore, we introduce our novel approach, Standing Variations Modeling, which exploits inestimability of model parameters to capture heterogeneity in a deterministic model. We use data from mouse xenograft experiments to infer distributions on parameters critical to tumor growth and to the resultant immune response. Sampling model parameters from these distributions allows us to represent heterogeneity, both at the level of the tumor cells and the individual (mouse) being treated. Our model simulations explain the limited success of sipuleucel-T observed in practice, and predict an optimal combination regime that maximizes predicted efficacy. This approach will generalize to a range of emerging cancer immunotherapies.

Disentangling nonlinear geomagnetic variability during magnetic storms and quiescence by timescale dependent recurrence properties

Understanding the complex behavior of the near-Earth electromagnetic environment is one of the main challenges of Space Weather studies. This includes both the correct characterization of the different physical mechanisms responsible for its configuration and dynamics as well as the efforts which are needed for a correct forecasting of several phenomena. By using a nonlinear multi-scale dynamical systems approach, we provide here new insights into the scale-to-scale dynamical behavior of both quiet and disturbed periods of geomagnetic activity. The results show that a scale-dependent dynamical transition occurs when moving from short to long timescales, i.e., from fast to slow dynamical processes, the latter being characterized by a more regular behavior, while more dynamical anomalies are found in the behavior of the fast component. This suggests that different physical processes are typical for both dynamical regimes: the fast component, being characterized by a more chaotic and less predictable behavior, can be related to the internal dynamical state of the near-Earth electromagnetic environment, while the slow component seems to be less chaotic and associated with the directly driven processes related to the interplanetary medium variability. Moreover, a clear difference has been found between quiet and disturbed periods, the former being more complex than the latter. These findings support the view that, for a correct forecasting in the framework of Space Weather studies, more attention needs to be devoted to the identification of proxies describing the internal dynamical state of the near-Earth electromagnetic environment.

Nonlinear Nonmodal Stability Theory

This review discusses a recently developed optimization technique for analyzing the nonlinear stability of a flow state. It is based on a nonlinear extension of nonmodal analysis and, in its simplest form, consists of finding the disturbance to the flow state of a given amplitude that experiences the largest energy growth at a certain time later. When coupled with a search over the disturbance amplitude, this can reveal the disturbance of least amplitude—called the minimal seed—for transition to another state such as turbulence. The approach bridges the theoretical gap between (linear) nonmodal theory and the (nonlinear) dynamical systems approach to fluid flows by allowing one to explore phase space at a finite distance from the reference flow state. Various ongoing and potential applications of the technique are discussed.

A nonlinear dynamical system approach for the yielding behaviour of a viscoplastic material.

A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stresses recently reported in R. Sainudiin, M. Moyers-Gonzalez and T. Burghelea, Soft Matter, 2015, 11(27), 5531-5545 is presented. The predictions of the model are in fair agreement with microscopic simulations and are in very good agreement with the micro-structural semi-empirical model reported in A. M. V. Putz and T. I. Burghelea, Rheol. Acta, 2009, 48, 673-689. With only two internal parameters, the nonlinear dynamical system model captures several key features of the solid-fluid transition observed in experiments: the effect of the interactions between microscopic constituents on the yield point, the abruptness of solid-fluid transition and the emergence of a hysteresis of the micro-structural states upon increasing/decreasing external forces. The scaling behaviour of the magnitude of the hysteresis with the degree of the steadiness of the flow is consistent with previous experimental observations. Finally, the practical usefulness of the approach is demonstrated by fitting a rheological data set measured with an elasto-viscoplastic material.

Real-Time Monitoring of Non-linear Suicidal Dynamics: Methodology and a Demonstrative Case Report.

In recent years, a number of different authors have stressed the usefulness of non-linear dynamic systems approach in suicide research and suicide prevention. This approach applies specific methods of time series analysis and, consequently, it requires a continuous and fine-meshed assessment of the processes under consideration. The technical means for this kind of process assessment and process analysis are now available. This paper outlines how suicidal dynamics can be monitored in high-risk patients by an Internet-based application for continuous self-assessment with integrated tools of non-linear time series analysis: the Synergetic Navigation System. This procedure is illustrated by data from a patient who attempted suicide at the end of a 90-day monitoring period. Additionally, future research topics and clinical applications of a non-linear dynamic systems approach in suicidology are discussed.

Prediction of the Development of Non-Equilibrium Turbulent Boundary Layers Based on Modified Log-Wake Law

The properties of non-equilibrium turbulent boundary layers are substantially more complicated than that of equilibrium ones, and current understanding and predictive capabilities of the former are less well developed than of the latter. This paper proposed a nonlinear dynamical system approach to predict streamwise development of non-equilibrium turbulent boundary layers by means of realizing the closure of the momentum integral equation with aid of the modified log-wake law and the entrainment equation. The example calculation showed the results were in reasonable agreement with the experiment data, and demonstrated the proposed method could predict the streamwise evolution of the layers accurately and simply. Moreover, the method would be conveniently extended to the flows over rough surfaces.

A hundred years of latency: from Freudian psychosexual theory to dynamic systems nonlinear development in middle childhood.

A focus on the latency phase is used to illustrate how theory and developmental research have influenced our psychoanalytic views of development over the past hundred years. Beginning with Freud's psychosexual theory and his conception of latency, an historical overview of the major psychoanalytic contributions bearing on this developmental period over the past century is presented. Recent longitudinal research in latency supports a nonlinear dynamic systems approach to development. This approach obliges us to reconsider our linear theories and how we think about and work with our patients.

Push- and pull-based epidemic spreading in networks

Understanding the dynamics of computer virus (malware, worm) in cyberspace is an important problem that has attracted a fair amount of attention. Early investigations for this purpose adapted biological epidemic models, and thus inherited the so-called homogeneity assumption that each node is equally connected to others. Later studies relaxed this often unrealistic homogeneity assumption, but still focused on certain power-law networks. Recently, researchers investigated epidemic models inarbitrarynetworks (i.e., no restrictions on network topology). However, all these models only capturepush-basedinfection, namely that an infectious node always actively attempts to infect its neighboring nodes. Very recently, the concept ofpull-basedinfection was introduced but was not treated rigorously. Along this line of research, the present article investigates push- and pull-based epidemic spreading dynamics in arbitrary networks, using a nonlinear dynamical systems approach. The article advances the state-of-the-art as follows: (1) It presents a more general and powerful sufficient condition (also known as epidemic threshold in the literature) under which the spreading will become stable. (2) It gives both upper and lower bounds on the global mean infection rate, regardless of the stability of the spreading. (3) It offers insights into, among other things, the estimation of the global mean infection rate through localized monitoring of a smallconstantnumber of nodes,withoutknowing the values of the parameters.

Advanced Computational Methods for Security Constrained Financial Transmission Rights: Structure and Parallelism

Financial Transmission Rights (FTRs) help power market participants reduce price risks associated with transmission congestion. FTRs are issued based on a process of solving a constrained optimization problem with the objective to maximize the FTR social welfare under power flow security constraints. Security constraints for different FTR categories (monthly, seasonal or annual) are usually coupled and the number of constraints increases exponentially with the number of categories. Commercial software for FTR calculation can only provide limited categories of FTRs due to the inherent computational challenges mentioned above. In this paper, a novel non-linear dynamical system (NDS) approach is proposed to solve the optimization problem. The new formulation and performance of the NDS solver is benchmarked against widely used linear programming (LP) solvers like CPLEX™ and tested on large-scale systems using data from the Western Electricity Coordinating Council (WECC). The NDS based solver can be easily parallelized while exploiting the data structure of the revised formalism to avoid backfill of coupled blocks, maintain numerical stability, and simultaneously reducing computational complexity. The NDS is demonstrated to outperform the widely used CPLEX algorithms by over two orders of magnitude while exhibiting superior scalability.

Nonlinear ship rolling motion subjected to noise excitation

The stochastic nonlinear dynamic behavior and probability density function of ship rolling are studied using the nonlinear dynamical systems approach and probability theory. The probability density function of the rolling response is evaluated through solving the Fokker Planck Equation using the path integral method based on a Gauss-Legendre interpolation scheme. The time-dependent probability of ship rolling restricted to within the safe domain is provided and capsizing is investigated from the probability point of view. The random differential equation of ships' rolling motion is established considering the nonlinear damping, nonlinear restoring moment, white noise and colored noise wave excitation.

Dynamic patterns of flow in the workplace: Characterizing within‐individual variability using a complexity science approach

AbstractAs a result of the growing interest in studying employee well‐being as a complex process that portrays high levels of within‐individual variability and evolves over time, this present study considers the experience of flow in the workplace from a nonlinear dynamical systems approach. Our goal is to offer new ways to move the study of employee well‐being beyond linear approaches. With nonlinear dynamical systems theory as the backdrop, we conducted a longitudinal study using the experience sampling method and qualitative semi‐structured interviews for data collection; 6981 registers of data were collected from a sample of 60 employees. The obtained time series were analyzed using various techniques derived from the nonlinear dynamical systems theory (i.e., recurrence analysis and surrogate data) and multiple correspondence analyses. The results revealed the following: 1) flow in the workplace presents a high degree of within‐individual variability; this variability is characterized as chaotic for most of the cases (75%); 2) high levels of flow are associated with chaos; and 3) different dimensions of the flow experience (e.g., merging of action and awareness) as well as individual (e.g., age) and job characteristics (e.g., job tenure) are associated with the emergence of different dynamic patterns (chaotic, linear and random). Copyright © 2011 John Wiley & Sons, Ltd.

Emotions are emergent processes: they require a dynamic computational architecture

Emotion is a cultural and psychobiological adaptation mechanism which allows each individual to react flexibly and dynamically to environmental contingencies. From this claim flows a description of the elements theoretically needed to construct a virtual agent with the ability to display human-like emotions and to respond appropriately to human emotional expression. This article offers a brief survey of the desirable features of emotion theories that make them ideal blueprints for agent models. In particular, the component process model of emotion is described, a theory which postulates emotion-antecedent appraisal on different levels of processing that drive response system patterning predictions. In conclusion, investing seriously in emergent computational modelling of emotion using a nonlinear dynamic systems approach is suggested.

Language learning from the perspective of nonlinear dynamic systems

This article outlines a nonlinear dynamic systems approach to language learning on the basis of developmental cognitive neuroscience. Language learning, on this view, is a process of experience-dependent shaping and selection of broadly defined domain-general and domain-specific genetic predispositions. The central concept of development is (neuro) cognitive growth in terms of self-organization. Linguistic structure-building is synergetic and emergent insofar as the acquisition of a critical mass of elements on a local level (e.g., words) results in the emergence of novel qualities and units on a macroscopic level (e.g., syntax). We argue that language development does not take a linear path but comes in phases of intermittent turbulence, fluctuation, and stability, along a chaotic itinerary. We review qualitative, quantitative and computational applications of this concept in the lexical, morphological, and syntactic domain. We identify as the most significant property of the dynamic approach the temporal nature of language learning. As a medium-term forecast we anticipate a further diversification of the dynamic approach, an increase in more formal approaches, and a stronger interest in issues of embodiment and embeddedness.

Pedodiversity, connectance and spatial variability of soil properties, what is the relationship?

The concept of diversity and its measurement is becoming increasingly attractive to soil scientists. This theme is explored using a terrace chronosequence in the Henares River valley, NE Madrid. Pedodiversity was computed at different hierarchical levels (Great Group, Subgroup and family of Soil Taxonomy) using appropriate indices including abundance and the Shannon diversity index. Taxonomic pedodiversity, i.e., the diversity of soil types, increased with time (from low to high terraces) at high hierarchical levels but no clear relationship was found at family level. Richness–area analysis showed that a logarithmic function fitted data from the low and middle terraces, while the high terrace data could be fitted with a power model. The geostatistical analysis revealed a decrease in the variability of soil properties from young to old deposits. This study showed that, at the Henares site, diversity and spatial variability of soil properties are not synonymous concepts. Indeed, the terrace with the highest taxonomic pedodiversity at Great Group and Subgroup levels, showed a low spatial variability of soil properties. Also, the same terrace exhibited the lowest connectance values. A non-linear dynamical system approach can be useful to explain these apparently contradictory results.

Towards the identification of scaling relations in drainage basin sediment budgets

Drainage basin sediment budgets concern inputs, storages and outputs of sediments, and solutes through monitored cross-sections at the mouth of basins or at the base of individual slopes. The question under consideration is whether, and to what extent, it is possible to transfer knowledge from one spatial scale to another. The answer hinges on the question of scale invariance of (a) individual processes of sediment and solute transfer and (b) aggregate sediment budgets. Scale invariance of a number of hydrologic parameters has been established but, in general, with a few exceptions, geomorphic parameters are subject to scale distortion. By inference, but not yet established by experimental or field evidence, scale invariance of sediment budgets is improbable. There is therefore a priority to explore scaling relations in sediment budgets so as to determine the precise extent of scale distortion that is present. In this paper, five ways of identifying scaling relations in drainage basin sediment budgets are identified: (1) a fractal approach; (2) a theory hierarchy approach; (3) a non-linear dynamic systems approach; (4) a panarchy approach; and, (5) a hybrid approach. There are no “a priori” bases for selection of any one of these approaches until further field research and modeling of sediment and solute fluxes has been completed.

A non‐linear dynamical system approach to finite amplitude Taylor‐Vortex flow of shear‐thinning fluids

AbstractThe effect of shear thinning on the stability of the Taylor–Couette flow is explored for a Carreau–Bird fluid in the narrow‐gap limit. The Galerkin projection method is used to derive a low‐order dynamical system from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional non‐linear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the circular Couette flow, becomes lower as the shear‐thinning effect increases. That is, shear thinning tends to precipitate the onset of Taylor vortex flow, which coincides with the onset of a supercritical bifurcation. Comparison with existing measurements of the effect of shear thinning on the critical Taylor and wave numbers show good agreement. The Taylor vortex cellular structure loses its stability in turn, as the Taylor number reaches a critical value. At this point, an inverse Hopf bifurcation emerges. In contrast to Newtonian flow, the bifurcation diagrams exhibit a turning point that sharpens with shear‐thinning effect. Copyright © 2004 John Wiley & Sons, Ltd.

Hierarchical Bayesian air conditioning load prediction—A nonlinear dynamical systems approach

AbstractThis paper considers the energy demand prediction problem and formulates it in the framework of hierarchical Bayesian nonlinear time series prediction with a neural net. As a practical problem, the method is applied to thermal load prediction of a formal energy storage system and the results are presented. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(11): 101–110, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.1217

Simulating mother-child interaction: exploring two varieties of a non-linear dynamic systems approach

In theoretical analyses of early mother–child interaction, it has been argued that interaction should be studied in its flow over time, and that the behaviour of each interactant is likely to be non-linearly determined. The mother–child dyad can be seen as a non-linear dynamic system, the development of which is determined by the mutual relations between its elements. The present study is based on the idea that computer simulations can be used to find out what kind of empirical implication these ideas have. Accordingly, we describe two non-linear dynamic systems-based models for simulating mother–child interaction, i.e. a connectionist network model and a logistic growth model. Three determinants of the nature of the interaction, i.e. the child's irritability, the mother's sensitive responsiveness, and the intensity of an external stressor bothering the child, are varied systematically. Although the results of both simulations differed considerably, they shared the fact that small changes in stressor intensity produced abrupt changes from one type of interaction to another. In addition, increasing stressor intensity sometimes had the paradoxical effect of resulting in less, rather than more, distress on the side of the child. Though irritability and responsiveness were varied in a less fine-grained way than stressor intensity, the results suggest that similarly small differences in these dimensions at different parts of the dimension's scale range have differentially strong effects on the nature of the interaction. It is concluded that these simulations help us to specify the nature of empirically researchable phenomena that are to be expected, given the assumptions listed above. Further elaboration of the models and comparison with longitudinal empirical data is needed to answer further theoretical and practical questions. Copyright © 2000 John Wiley & Sons, Ltd.