Dynamical Systems Perspective Research Articles

Analysis of animal monitoring technologies in Germany from an innovation system perspective

In order to address societal demands (e.g., animal welfare, traceability, environmental aspects), animal monitoring (AM) technologies provide much potential for innovation in animal production. AM means the real time and on-going automatic monitoring by ‘smart’ sensors of physiological, growth and behaviour parameters of individual farming animals, integrated in various areas (e.g., animal milking, feeding, breeding, health). The literature on AM mainly focusses on technologies and their application. The available information about innovation processes in AM is still very fragmentary and not comprehensive. The present article analyses the generation, development and use of AM technologies in Germany from a dynamic innovation system perspective. The analytical framework of the article is based on the sectoral innovation system approach. Qualitative interviews, an expert workshop, and a Delphi survey were conducted to explore the roles and interactions of heterogeneous actors in innovation processes and the interlocking between innovation stages. On the basis of identified fostering and inhibiting factors, opportunities for systemic interventions are suggested to further innovations in AM and in the German animal production sector and in other countries. These interventions consider, on the one hand, recommendations to support AM technologies and their broader implementation (‘hard skill interventions’) and, on the other hand, interventions that are suitable to stimulate innovations in animal production without specific focus on a single technological regime or innovation area (‘soft skill interventions’). The ‘hard skill interventions’ refer to the need for improvements concerning system compatibility and data exchange; the special need for financial support of extensive validation of AM technologies and clear communication of benefits or constraints to farmers. ‘Soft skill interventions’ are related to innovation capacity building of actors in order to coordinate co-development processes and to improve communication: Finding of a common understanding of the innovation system and common language among actors; early involvement of all actors and the reflection of actors' roles; resource-based fostering of network management. Finally, innovation policies should be capable to gather and react appropriately to these requirements. Generally, the study contributes to a better understanding of the complexity of innovation activities in AM and their embedding in the innovation system of animal production. The opportunities for systemic intervention can be used by the sector's actors to enhance the innovativeness of the German sector and to make better use of AM potentials to address the global challenges and societal demands.

The Potential Energy of an Autoencoder.

Autoencoders are popular feature learning models, that are conceptually simple, easy to train and allow for efficient inference. Recent work has shown how certain autoencoders can be associated with an energy landscape, akin to negative log-probability in a probabilistic model, which measures how well the autoencoder can represent regions in the input space. The energy landscape has been commonly inferred heuristically, by using a training criterion that relates the autoencoder to a probabilistic model such as a Restricted Boltzmann Machine (RBM). In this paper we show how most common autoencoders are naturally associated with an energy function, independent of the training procedure, and that the energy landscape can be inferred analytically by integrating the reconstruction function of the autoencoder. For autoencoders with sigmoid hidden units, the energy function is identical to the free energy of an RBM, which helps shed light onto the relationship between these two types of model. We also show that the autoencoder energy function allows us to explain common regularization procedures, such as contractive training, from the perspective of dynamical systems. As a practical application of the energy function, a generative classifier based on class-specific autoencoders is presented.

MATHEMATICAL MODELING OF BEHÇET'S DISEASE: A DYNAMICAL SYSTEMS APPROACH

Behçet's Disease (BD) is a multi-systemic, auto-inflammatory disorder that is characterized by recurrent episodes of inflammatory manifestations affecting skin, mucosa, eyes, blood vessels, joints and several other organs. BD is classified as a multifactorial disease with an important contribution of genetics. Genetic studies suggest that there is a strong association of BD with a Class I major histocompatibility complex antigen, named HLA-B*51, along with several other weaker associations with genes encoding proteins involved in inflammation. However, pathogenic mechanisms associated with these genetic variations and their interactions with the environment have not been elucidated yet. In this paper, we present a mathematical model for BD based on a dynamical systems perspective that captures especially the relapsing nature of the disease. We propose a disease progression mechanism and construct a model, in the form of coupled ordinary differential equations (ODEs), which reveals the occurrence pattern of the disease in the population. According to our model, the disease has three distinct modes describing different phenotypes of people carrying HLA-B*51 tissue antigen, namely, the Healthy Carrier, the Potential Patient and the Active Patient. We herein present an exemplary mathematical model for BD, for the first time in the literature, that concisely captures the actions of many cell types together with genetic and environmental effects. The proposed model provides insight into this complex inflammatory disease which may lead to identification of new tools for its treatment and prevention.

Motivation for participation or non-participation in group tasks: A dynamic systems model of task-situated willingness to communicate

Abstract The effectiveness of group tasks in L2 classes relies in large part on individual students' Willingness to Communicate (WTC) during the duration of the task. Dornyei (2009) suggested four conglomerates of task motivation from a dynamic systems perspective, but these conglomerates may not include all possible factors affecting task-situated WTC. Focus group based research was used to explore what English language learners at two universities in Macau, a Special Administrative Region of China, say motivates them to participate or not participate in group tasks. Interest, perceived effectiveness, good groupmates, good classroom social situation, personal vision and self-confidence were themes identified as both motivating and also, when in inverse form or absent in student experience, demotivating. Marks were also identified as a motivating influence. Overall, Macau students mentioned that social factors and task-related factors significantly influenced task-situated WTC in addition to self-confidence and L2 learning motivation, which are part of general L2 WTC models. In light of these findings, recommendations are made to adjust and add to Dornyei's (2009) conglomerates to create a model of task-situated WTC. Some suggestions for further research and implications for L2 teachers in arranging group tasks are given.

Dynamical analysis and visualization of tornadoes time series.

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.

Motor control of rhythmic dance from a dynamical systems perspective: a review.

While dancers and dance educators express great interest in motor control as it relates to rhythmic dance, the subject remains largely uninvestigated. In order to advance our understanding of motor control, a theoretical framework called the dynamical systems approach (DSA) has been used. The DSA was originally developed to describe mathematically the principle of synchronization patterns in nature and their change over time. In recent decades, researchers studying human motor control have attempted to describe the synchronization of rhythmic movement using a DSA. More recently, this approach has been applied specifically to rhythmic dance movements. A series of studies that used the DSA revealed that when people synchronize rhythmic movement of a body part 1. with a different body part, 2. with other people's movement, or 3. with an auditory beat with some phase differences, unintentional and autonomous entrainment to a specific synchronization pattern occurs. However, through practice dancers are able to overcome such entrainment and dance freely. These findings provide practical suggestions for effective ways of training in dance education. The DSA can potentially be an effective tool for furthering our understanding of the motor control utilized in rhythmic dance.

Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

Abstract In this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

The tongue as an excitable medium

Geographic tongue (GT) is a medical condition affecting approximately 2% of the population, whereby the papillae covering the upper part of the tongue are lost due to a slowly expanding inflammation. The resultant dynamical appearance of the tongue has striking similarities with well known out-of-equilibrium phenomena observed in excitable media, such as forest fires, cardiac dynamics, chemically driven reaction-diffusion systems and morphogenesis in multicellular organisms. Here we identify GT as a novel example of excitable media dynamics and explore the evolution of the condition from a dynamical systems perspective. We focus on two characteristic aspects of GT in particular: anisotropic expansion of lesions and re-entry of the inflammation into recovering regions. Our investigation sheds light on the evolution of the inflammation and suggests a practical way to classify the severity of the condition, based on the characteristic patterns observed in GT patients.

State space analysis of forest fires

This paper studies forest fires from the perspective of dynamical systems. Burnt area, precipitation and atmospheric temperatures are interpreted as state variables of a complex system and the correlations between them are investigated by means of different mathematical tools. First, we use mutual information to reveal potential relationships in the data. Second, we adopt the state space portrait to characterize the system’s behavior. Third, we compare the annual state space curves and we apply clustering and visualization tools to unveil long-range patterns. We use forest fire data for Portugal, covering the years 1980–2003. The territory is divided into two regions (North and South), characterized by different climates and vegetation. The adopted methodology represents a new viewpoint in the context of forest fires, shedding light on a complex phenomenon that needs to be better understood in order to mitigate its devastating consequences, at both economical and environmental levels.

Power Law Behavior and Self-Similarity in Modern Industrial Accidents

Advances in technology have produced more and more intricate industrial systems, such as nuclear power plants, chemical centers and petroleum platforms. Such complex plants exhibit multiple interactions among smaller units and human operators, rising potentially disastrous failure, which can propagate across subsystem boundaries. This paper analyzes industrial accident data-series in the perspective of statistical physics and dynamical systems. Global data is collected from the Emergency Events Database (EM-DAT) during the time period from year 1903 up to 2012. The statistical distributions of the number of fatalities caused by industrial accidents reveal Power Law (PL) behavior. We analyze the evolution of the PL parameters over time and observe a remarkable increment in the PL exponent during the last years. PL behavior allows prediction by extrapolation over a wide range of scales. In a complementary line of thought, we compare the data using appropriate indices and use different visualization techniques to correlate and to extract relationships among industrial accident events. This study contributes to better understand the complexity of modern industrial accidents and their ruling principles.

A Kalman Filtering Perspective for Multiatlas Segmentation.

In multiatlas segmentation, one typically registers several atlases to the novel image, and their respective segmented label images are transformed and fused to form the final segmentation. In this work, we provide a new dynamical system perspective for multiatlas segmentation, inspired by the following fact: The transformation that aligns the current atlas to the novel image can be not only computed by direct registration but also inferred from the transformation that aligns the previous atlas to the image together with the transformation between the two atlases. This process is similar to the global positioning system on a vehicle, which gets position by inquiring from the satellite and by employing the previous location and velocity-neither answer in isolation being perfect. To solve this problem, a dynamical system scheme is crucial to combine the two pieces of information; for example, a Kalman filtering scheme is used. Accordingly, in this work, a Kalman multiatlas segmentation is proposed to stabilize the global/affine registration step. The contributions of this work are twofold. First, it provides a new dynamical systematic perspective for standard independent multiatlas registrations, and it is solved by Kalman filtering. Second, with very little extra computation, it can be combined with most existing multiatlas segmentation schemes for better registration/segmentation accuracy.

Discussion on the Complicated Topological Dynamic System of Ordinary Differential Equation (ODE)

The dynamical system of ODEs is about closed-form researches into the field of ODEs from the perspective of dynamical systems. This paper, starting with the research of path in autonomous differential equations and discussion on Poincaré’s viewpoints, probes into the complicated topological dynamic system of ODEs.

The Psychology of Dynamic Balance and Peak Performance in Sport: Correction Theory

This article introduces a new approach to understanding peak performance and dysfunctional performance in sport, correction theory. Correction theory, based within a control theory and dynamical systems perspective, assumes that dynamic balance (a state in which a robust complex system will self-correct in response to imbalance) underwrites individual functioning. The central thesis presented in this article is that an interdependent relationship exists between peak performance and dysfunctional performance in sport. Peak performance is, in part, a (corrective) response to dysfunctional performance and vice versa. An overview of correction theory is presented, based on two propositions relating to balance. Implications of correction theory for understanding sporting performance are briefly considered.

Female same-sex sexuality from a dynamical systems perspective: sexual desire, motivation, and behavior.

Fluidity in attractions and behaviors among same-sex attracted women has been well-documented, suggesting the appropriateness of dynamical systems modeling of these phenomena over time. As dynamical systems modeling offer an approach to explaining the patterns of complex phenomena, it may be apt for explaining variability in female same-sex sexuality. The present research is the first application of this analytical approach to such data. Dynamical systems modeling, and specifically generalized local linear approximation modeling, was used to fit daily diary data on same-sex attractions and behaviors over a 21 day period among a group of 33 sexual minority women characterized as lesbian, bisexual or "fluid" based on their identity histories. Daily measures of women's reported same-sex attractions were fit using a linear oscillator model and its parameters estimated the cyclicity in these attractions. Results supported the existence of a "core sexual orientation" for women in this sample, regardless of how they identified and despite a high degree of variability in daily same-sex attractions. Thus, modeling individual differences in the variability of attractions and behaviors of sexual minority women may be critical to furthering our understanding of female same-sex sexuality and human sexual orientation more broadly.

Microdevelopment of Daily Well-Being through Mental Imagery Practice

In this study, we present a qualitative approach to changes in daily well-being as a function of mental imagery practice. Each morning for a period of 1 week, participants practiced a brief (approximately 1- to 2-minute long) mental imagery practice designed to facilitate well-being. Upon completing each exercise, they provided brief written reflections on their well-being. Qualitative analysis of these subjective reports revealed significant patterns that correspond to three of the four major components of well-being (positive affect, vitality, negative affect) examined by researchers from a Self-Determination Theory perspective. All participants reported immediate well-being benefits of mental imagery practice, and these benefits reflected several patterns that we identified. As these changes take place in seconds and minutes, this study reflects a microdevelopmental approach to well-being from a Dynamic Systems perspective. The value of exploring short-term imagery-related improvements in well-being in combination with long-term influences is discussed.

Dynamic analysis and pattern visualization of forest fires.

This paper analyses forest fires in the perspective of dynamical systems. Forest fires exhibit complex correlations in size, space and time, revealing features often present in complex systems, such as the absence of a characteristic length-scale, or the emergence of long range correlations and persistent memory. This study addresses a public domain forest fires catalogue, containing information of events for Portugal, during the period from 1980 up to 2012. The data is analysed in an annual basis, modelling the occurrences as sequences of Dirac impulses with amplitude proportional to the burnt area. First, we consider mutual information to correlate annual patterns. We use visualization trees, generated by hierarchical clustering algorithms, in order to compare and to extract relationships among the data. Second, we adopt the Multidimensional Scaling (MDS) visualization tool. MDS generates maps where each object corresponds to a point. Objects that are perceived to be similar to each other are placed on the map forming clusters. The results are analysed in order to extract relationships among the data and to identify forest fire patterns.

Human Brain Networks: Spiking Neuron Models, Multistability, Synchronization, Thermodynamics, Maximum Entropy Production, and Anesthetic Cascade Mechanisms

Advances in neuroscience have been closely linked to mathematical modeling beginning with the integrate-and-fire model of Lapicque and proceeding through the modeling of the action potential by Hodgkin and Huxley to the current era. The fundamental building block of the central nervous system, the neuron, may be thought of as a dynamic element that is “excitable”, and can generate a pulse or spike whenever the electrochemical potential across the cell membrane of the neuron exceeds a threshold. A key application of nonlinear dynamical systems theory to the neurosciences is to study phenomena of the central nervous system that exhibit nearly discontinuous transitions between macroscopic states. A very challenging and clinically important problem exhibiting this phenomenon is the induction of general anesthesia. In any specific patient, the transition from consciousness to unconsciousness as the concentration of anesthetic drugs increases is very sharp, resembling a thermodynamic phase transition. This paper focuses on multistability theory for continuous and discontinuous dynamical systems having a set of multiple isolated equilibria and/or a continuum of equilibria. Multistability is the property whereby the solutions of a dynamical system can alternate between two or more mutually exclusive Lyapunov stable and convergent equilibrium states under asymptotically slowly changing inputs or system parameters. In this paper, we extend the theory of multistability to continuous, discontinuous, and stochastic nonlinear dynamical systems. In particular, Lyapunov-based tests for multistability and synchronization of dynamical systems with continuously differentiable and absolutely continuous flows are established. The results are then applied to excitatory and inhibitory biological neuronal networks to explain the underlying mechanism of action for anesthesia and consciousness from a multistable dynamical system perspective, thereby providing a theoretical foundation for general anesthesia using the network properties of the brain. Finally, we present some key emergent properties from the fields of thermodynamics and electromagnetic field theory to qualitatively explain the underlying neuronal mechanisms of action for anesthesia and consciousness.

A dynamical system perspective on plant hydraulic failure

AbstractPhotosynthesis is governed by leaf water status that depends on the difference between the rates of transpiration and water supply from the soil and through the plant xylem. When transpiration increases compared to water supply, the leaf water potential reaches a more negative equilibrium, leading to water stress. Both high atmospheric vapor pressure deficit and low soil moisture increase the water demand while decreasing the supply due to lowered soil‐to‐root conductance and xylem cavitation. Therefore, dry conditions may eventually reduce the leaf water potential to the point of collapsing the plant hydraulic system. This “hydraulic failure” is shown to correspond to a fold bifurcation where the environmental parameters (vapor pressure deficit and soil moisture) trigger the loss of a physiologically sustainable equilibrium. Using a minimal plant hydraulic model, coordination among plant hydraulic traits is shown to result in increased resilience to environmental stresses, thereby impeding hydraulic failure unless hydraulic traits deteriorate due to prolonged water shortage or other damages.

Qualitative analysis of Kantowski-Sachs metric in a generic class of f(R) models

In this paper we investigate, from the dynamical systems perspective, the evolution of a Kantowski-Sachs metric in a generic class of f(R) models. We present conditions (i.e., differentiability conditions, existence of minima, monotony intervals, etc.) for a free input function related to the f(R), that guarantee the asymptotic stability of well-motivated physical solutions, specially, self-accelerated solutions, allowing to describe both inflationary- and late-time acceleration stages of the cosmic evolution. We discuss which f(R) theories allows for a cosmic evolution with an acceptable matter era, in correspondence to the modern cosmological paradigm. We find a very rich behavior, and amongst others the universe can result in isotropized solutions with observables in agreement with observations, such as de Sitter, quintessence-like, or phantom solutions. Additionally, we find that a cosmological bounce and turnaround are realized in a part of the parameter-space as a consequence of the metric choice.

Lagrangian coherent structures analysis of gas-liquid flow in a bubble column

The objective of this paper is to apply a new identifying method to investigating the gas-liquid two-phase flow behaviors in a bubble column with air injected into water. In the numerical simulations, the standard k-ɛ turbulence model is employed to describe the turbulence phenomenon occurring in the continuous fluid. The Finite-Time Lyapunov Exponent (FTLE) and Lagrangian Coherent Structures (LCS) are applied to analyze the vortex structures in multiphase flow. Reasonable agreements are obtained between the numerical and experimental data. The numerical results show that the evolution of gas-liquid in the column includes initial and periodical developing stages. During the initial stage, the bubble hose is forming and extending along the vertical direction with the vortex structures formed symmetrically. During the periodical developing stage, the bubble hose starts to oscillate periodically, and the vortexes move along the bubble hose to the bottom of column alternately. Compared to the Euler-system-based identification criterion of a vortex, the FTLE field presents the boundary of a vortex without any threshold defined and the LCS represents the divergence extent of infinite neighboring particles. During the initial stage, the interfaces between the forward and backward flows are highlighted by the LCS. As for the periodical developing stage, the LCS curls near the vortex centers, providing a method of analyzing a flow field from a dynamical system perspective.