Hierarchical random cellular neural networks for system-level brain-like signal processing

Partial-Neurons-Based Proportional-Integral Observer Design for Artificial Neural Networks: A Multiple Description Encoding Scheme

This article is concerned with a new partial-neurons-based proportional-integral observer (PIO) design problem for a class of artificial neural networks (ANNs) subject to bounded disturbances. For the purpose of improving the reliability of the data transmission, the multiple description encoding mechanisms are exploited to encode the measurement data into two identically important descriptions, and the encoded data are then transmitted to the decoders via two individual communication channels susceptible to packet dropouts, where Bernoulli-distributed stochastic variables are utilized to characterize the random occurrence of the packet dropouts. An explicit relationship is discovered that quantifies the influences of the packet dropouts on the decoding accuracy, and a sufficient condition is provided to assess the boundedness of the estimation error dynamics. Furthermore, the desired PIO parameters are calculated by solving two optimization problems based on two metrics (i.e., the smallest ultimate bound and the fastest decay rate) characterizing the estimation performance. Finally, the applicability and advantage of the proposed PIO design strategy are verified by means of an illustrative example.

Modelling brain dynamics by Boolean networks

Understanding the relationship between brain architecture and brain function is a central issue in neuroscience. We modeled realistic spatio-temporal patterns of brain activity on a human connectome with a Boolean networks model with the aim of computationally replicating certain cognitive functions as they emerge from the standardization of many fMRI studies, identified as patterns of human brain activity. Results from the analysis of simulation data, carried out for different parameters and initial conditions identified many possible paths in the space of parameters of these network models, with normal (ordered asymptotically constant patterns), chaotic (oscillating or disordered) but also highly organized configurations, with countless spatial–temporal patterns. We interpreted these results as routes to chaos, permanence of the systems in regimes of complexity, and ordered stationary behavior, associating these dynamics to cognitive processes. The most important result of this work is the study of emergent neural circuits, i.e., configurations of areas that synchronize over time, both locally and globally, determining the emergence of computational analogues of cognitive processes, which may or may not be similar to the functioning of biological brain. Furthermore, results put in evidence the creation of how the brain creates structures of remote communication. These structures have hierarchical organization, where each level allows for the emergence of brain organizations which behave at the next superior level. Taken together these results allow the interplay of dynamical and topological roots of the multifaceted brain dynamics to be understood.

Nonfragile H∞ State Estimation for Recurrent Neural Networks With Time-Varying Delays: On Proportional-Integral Observer Design

In this article, a novel proportional-integral observer (PIO) design approach is proposed for the nonfragile H_∞ state estimation problem for a class of discrete-time recurrent neural networks with time-varying delays. The developed PIO is equipped with more design freedom leading to better steady-state accuracy compared with the conventional Luenberger observer. The phenomena of randomly occurring gain variations, which are characterized by the Bernoulli distributed random variables with certain probabilities, are taken into consideration in the implementation of the addressed PIO. Attention is focused on the design of a nonfragile PIO such that the error dynamics of the state estimation is exponentially stable in a mean-square sense, and the prescribed H_∞ performance index is also achieved. Sufficient conditions for the existence of the desired PIO are established by virtue of the Lyapunov-Krasovskii functional approach and the matrix inequality technique. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed PIO design scheme.

Proportional-Integral Observer Design for Multidelayed Sensor-Saturated Recurrent Neural Networks: A Dynamic Event-Triggered Protocol

In this article, the design problem of the proportional-integral observer (PIO) is investigated for a class of discrete-time multidelayed recurrent neural networks (RNNs). In the addressed RNN model, the delays occurring in the information interconnections are allowed to be different, and the phenomenon of sensor saturation is taken into consideration in the measurement model. A novel dynamic event-triggered protocol is employed in the data transmission from sensors to the observer with hope to improve the efficiency of resource utilization, where the threshold parameters are adaptive to the dynamical environment. By virtue of the Lyapunov-like approach, a general framework is established for examining the boundedness of the estimation errors in mean-square sense, and the ultimate bound of the error dynamics is also acquired. Subsequently, the explicit expression of the desired PIO is parameterized by using the matrix inequality techniques. Finally, a simulation example is utilized to verify the effectiveness and superiority of the proposed PIO design scheme.

Conflicting emergences. Weak vs. strong emergence for the modelling of brain function

The concept of "emergence" has become commonplace in the modelling of complex systems, both natural and man-made; a functional property" emerges" from a system when it cannot be readily explained by the properties of the system's sub-units. A bewildering array of adaptive and sophisticated behaviours can be observed from large ensembles of elementary agents such as ant colonies, bird flocks or by the interactions of elementary material units such as molecules or weather elements. Ultimately, emergence has been adopted as the ontological support of a number of attempts to model brain function. This manuscript aims to clarify the ontology of emergence and delve into its many facets, particularly into its "strong" and "weak" versions that underpin two different approaches to the modelling of behaviour. The first group of models is here represented by the "free energy" principle of brain function and the "integrated information theory" of consciousness. The second group is instead represented by computational models such as oscillatory networks that use mathematical scalable representations to generate emergent behaviours and are then able to bridge neurobiology with higher mental functions. Drawing on the epistemological literature, we observe that due to their loose mechanistic links with the underlying biology, models based on strong forms of emergence are at risk of metaphysical implausibility. This, in practical terms, translates into the over determination that occurs when the proposed model becomes only one of a large set of possible explanations for the observable phenomena. On the other hand, computational models that start from biologically plausible elementary units, hence are weakly emergent, are not limited by ontological faults and, if scalable and able to realistically simulate the hierarchies of brain output, represent a powerful vehicle for future neuroscientific research programmes.

Event-Triggered State Estimation for Discrete-Time Multidelayed Neural Networks With Stochastic Parameters and Incomplete Measurements

In this paper, the event-triggered state estimation problem is investigated for a class of discrete-time multidelayed neural networks with stochastic parameters and incomplete measurements. In order to cater for more realistic transmission process of the neural signals, we make the first attempt to introduce a set of stochastic variables to characterize the random fluctuations of system parameters. In the addressed neural network model, the delays among the interconnections are allowed to be different, which are more general than those in the existing literature. The incomplete information under consideration includes randomly occurring sensor saturations and quantizations. For the purpose of energy saving, an event-triggered state estimator is constructed and a sufficient condition is given under which the estimation error dynamics is exponentially ultimately bounded in the mean square. It is worth noting that the ultimate boundedness of the error dynamics is explicitly estimated. The characterization of the desired estimator gain is designed in terms of the solution to a certain matrix inequality. Finally, a numerical simulation example is presented to illustrate the effectiveness of the proposed event-triggered state estimation scheme.

Cinematic Operation of the Cerebral Cortex Interpreted via Critical Transitions in Self-Organized Dynamic Systems

Measurements of local field potentials over the cortical surface and the scalp of animals and human subjects reveal intermittent bursts of beta and gamma oscillations. During the bursts, narrow-band metastable amplitude modulation (AM) patters emerge for a fraction of a second and ultimately dissolve to the broad-band random background activity. The burst process depends on previously learnt conditioned stimuli (CS), thus different AM patterns may emerge in response to different CS. This observation leads to our cinematic theory of cognition when perception happens in discrete steps manifested in the sequence of AM patterns. Our article summarizes findings in the past decades on experimental evidence of cinematic theory of cognition and relevant mathematical models. We treat cortices as dissipative systems that self-organize themselves near a critical level of activity that is a non-equilibrium metastable state. Criticality is arguably a key aspect of brains in their rapid adaptation, reconfiguration, high storage capacity, and sensitive response to external stimuli. Self-organized criticality (SOC) became an important concept to describe neural systems. We argue that transitions from one AM pattern to the other require the concept of phase transitions, extending beyond the dynamics described by SOC. We employ random graph theory (RGT) and percolation dynamics as fundamental mathematical approaches to model fluctuations in the cortical tissue. Our results indicate that perceptions are formed through a phase transition from a disorganized (high entropy) to a well-organized (low entropy) state, which explains the swiftness of the emergence of the perceptual experience in response to learned stimuli.

Random graph theory and neuropercolation for modeling brain oscillations at criticality

Mathematical approaches are reviewed to interpret intermittent singular space-time dynamics observed in brain imaging experiments. The following aspects of brain dynamics are considered: nonlinear dynamics (chaos), phase transitions, and criticality. Probabilistic cellular automata and random graph models are described, which develop equations for the probability distributions of macroscopic state variables as an alternative to differential equations. The introduced modular neuropercolation model is motivated by the multilayer structure and dynamical properties of the cortex, and it describes critical brain oscillations, including background activity, narrow-band oscillations in excitatory-inhibitory populations, and broadband oscillations in the cortex. Input-induced and spontaneous transitions between states with large-scale synchrony and without synchrony exhibit brief episodes with long-range spatial correlations as observed in experiments.