Biologically inspired rate control of chaos

The overall intention of chaotic control is to eliminate chaos, and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes, and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision, and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems, or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade

Criticality in biocomputation

Complexity in biological computation is one of the recognised means by which biological systems manage to function in a complex chaotic world. The ability to function and solve problems irrespective of scale and relative complexity, including higher-order interactions, is essential to the efficacy of biological systems. However, it has been unclear how the required complexity can be introduced to allow these functions to be realised. Nonlinear local interactions are required to combine into a global stable system. The property of criticality, that is exhibited by many nonlinear physical systems, can be exploited to allow local nonlinear oscillators to interact, resulting in a globally stable system. This concept introduces robustness, as well as, a means to control global stability

Controlled bio-inspired self-organised criticality

Complex biological systems are considered to be controlled using feedback mechanisms. Reduced systems modelling has been effective to describe these mechanisms, but this approach does not sufficiently encompass the required complexity that is needed to understand how localised control in a biological system can provide global stable states. Self-Organised Criticality (SOC) is a characteristic property of locally interacting physical systems, which readily emerges from changes to its dynamic state due to small nonlinear perturbations. These small changes in the local states, or in local interactions, can greatly affect the total system state of critical systems. It has long been conjectured that SOC is cardinal to biological systems, that show similar critical dynamics, and also may exhibit near power-law relations. Rate Control of Chaos (RCC) provides a suitable robust mechanism to generate SOC systems, which operates at the edge of chaos. The bio-inspired RCC method requires only local instantaneous knowledge of some of the variables of the system, and is capable of adapting to local perturbations. Importantly, connected RCC controlled oscillators can maintain global multi-stable states, and domains where power-law relations may emerge. The network of oscillators deterministically stabilises into different orbits for different perturbations, and the relation between the perturbation and amplitude can show exponential and power-law correlations. This can be considered to be representative of a basic mechanism of protein production and control, that underlies complex processes such as homeostasis. Providing feedback from the global state, the total system dynamic behaviour can be boosted or reduced. Controlled SOC can provide much greater understanding of biological control mechanisms, that are based on distributed local producers, with remote consumers of biological resources, and globally defined control

The spike generation processes: a case for low level computation

Over the last couple of years, it can be said that the focus of the computational aspects of neurons has moved from synaptic weight and firing rate encoding to temporal firing encoding. On the other hand, several elements of these models have been based on some conceptual assumptions that imply relative simple dynamic behaviour of neuronal membrane activity in an active-passive process. In line with recent advances that have produced a better understanding of the biochemical processes that occur within cells, it is proposed that the processes that are involved in a membrane depolarisation cascade are less static than have been assumed so far. In particular, the possibilities of low level computation at the membrane level need to be explored more extensively. In this chapter some computational properties of the spike generation processes are explored using phenomenological models

Dynamic Hebbian Cross-Correlation Learning Resolves the Spike Timing Dependent Plasticity Conundrum

Spike Timing-Dependent Plasticity has been found to assume many different forms. The classic STDP curve, with one potentiating and one depressing window, is only one of many possible curves that describe synaptic learning using the STDP mechanism. It has been shown experimentally that STDP curves may contain multiple LTP and LTD windows of variable width, and even inverted windows. The underlying STDP mechanism that is capable of producing such an extensive, and apparently incompatible, range of learning curves is still under investigation. In this paper, it is shown that STDP originates from a combination of two dynamic Hebbian cross-correlations of local activity at the synapse. The correlation of the presynaptic activity with the local postsynaptic activity is a robust and reliable indicator of the discrepancy between the presynaptic neuron and the postsynaptic neuron's activity. The second correlation is between the local postsynaptic activity with dendritic activity which is a good indicator of matching local synaptic and dendritic activity. We show that this simple time-independent learning rule can give rise to many forms of the STDP learning curve. The rule regulates synaptic strength without the need for spike matching or other supervisory learning mechanisms. Local differences in dendritic activity at the synapse greatly affect the cross-correlation difference which determines the relative contributions of different neural activity sources. Dendritic activity due to nearby synapses, action potentials, both forward and back-propagating, as well as inhibitory synapses will dynamically modify the local activity at the synapse, and the resulting STDP learning rule. The dynamic Hebbian learning rule ensures furthermore, that the resulting synaptic strength is dynamically stable, and that interactions between synapses do not result in local instabilities. The rule clearly demonstrates that synapses function as independent localized computational entities, each contributing to the global activity, not in a simply linear fashion, but in a manner that is appropriate to achieve local and global stability of the neuron and the entire dendritic structure

A novel criticality analysis technique for detecting dynamic disturbances in human gait

The application of machine learning (ML) has made an unprecedented change in the field of medicine, showing a significant potential to automate tasks and to achieve objectives that are closer to human cognitive capabilities. Human gait, in particular, is a series of continuous metabolic interactions specific for humans. The need for an intelligent recognition of dynamic changes of gait enables physicians in clinical practice to early identify impaired gait and to reach proper decision making. Because of the underlying complexity of the biological system, it can be difficult to create an accurate detection and analysis of imbalanced gait. This paper proposes a novel Criticality Analysis (CA) methodology as a feasible method to extract the dynamic interactions involved in human gait. This allows a useful scale-free representation of multivariate dynamic data in a nonlinear representation space. To quantify the effectiveness of the CA methodology, a Support Vector Machine (SVM) algorithm is implemented in order to identify the nonlinear relationships and high-order interactions between multiple gait data variables. The gait features extracted from the CA method were used for training and testing the SVM algorithm. The simulation results of this paper show that the implemented SVM model with the support of the CA method increases the accuracy and enhances the efficiency of gait analysis to extremely high levels. Therefore, it can perform as a robust classification tool for detection of dynamic disturbances of biological data patterns and creates a tremendous opportunity for clinical diagnosis and rehabilitation

Developing a dynamic bio-inspired intelligent system to support diabetic patients

This paper proposes a new biologically-inspired phenomenological model of insulin release that can be used to continuously monitor a person with diabetes and therefore recommend insulin dose and predict events. Given all the parameters and conditions that have to be met in order to achieve stability, the proposed insulin-release system will be considered as highly non-linear and dynamical. The resulting model will study the mechanisms that keep the system from reaching a chaotic state (diabetes), based on the property of self-organised criticality. This property was selected since it has been previously identified and studied in other dynamical biological systems. The proposed model will then be used as part of a model-based reasoning system that aims to support patients with diabetes

Harmonic Versus Chaos Controlled Oscillators in Hexapedal Locomotion

The behavioural diversity of chaotic oscillator can be controlled into periodic dynamics and used to model locomotion using central pattern generators. This paper shows how controlled chaotic oscillators may improve the adaptation of the robot locomotion behaviour to terrain uncertainties when compared to nonlinear harmonic oscillators. This is quantitatively assesses by the stability, changes of direction and steadiness of the robotic movements. Our results show that the controlled Wu oscillator promotes the emergence of adaptive locomotion when deterministic sensory feedback is used. They also suggest that the chaotic nature of chaos controlled oscillators increases the expressiveness of pattern generators to explore new locomotion gaits

A novel criticality analysis method for assessing obesity treatment efficacy

Human gait is a significant indicator of overall health and well-being due to its dependence on metabolic requirements. Abnormalities in gait can indicate the presence of metabolic dysfunction, such as diabetes or obesity. However, detecting these can be challenging using classical methods, which often involve subjective clinical assessments or invasive procedures. In this work, a novel methodology known as Criticality Analysis (CA) was applied to the monitoring of the gait of teenagers with varying amounts of metabolic stress who are taking part in an clinical intervention to increase their activity and reduce overall weight. The CA approach analysed gait using inertial measurement units (IMU) by mapping the dynamic gait pattern into a nonlinear representation space. The resulting dynamic paths were then classified using a Support Vector Machine (SVM) algorithm, which is well-suited for this task due to its ability to handle nonlinear and dynamic data. The combination of the CA approach and the SVM algorithm demonstrated high accuracy and non-invasive detection of metabolic stress. It resulted in an average accuracy within the range of 78.2% to 90%. Additionally, at the group level, it was observed to improve fitness and health during the period of the intervention. Therefore, this methodology showed a great potential to be a valuable tool for healthcare professionals in detecting and monitoring metabolic stress, as well as other associated disorders