Laguerre-Volterra Network Research Articles

A Laguerre-Volterra network model based on ant colony optimization applied to evaluate EMG-force relationship in the muscle fatigue state.

With the accuracy and convenience improvement of electromyographic (EMG) acquired by wearable devices, EMG is gradually used to evaluate muscle force signal, a non-invasive evaluation method. However, the relationship between EMG and force is a complex nonlinear relationship, even which will change with different movements and different muscle states. Therefore, it is difficult to evaluate this nonlinear EMG-force relationship, especially when the muscle state gradually transits from non-fatigue to deep fatigue. For more accurate values of force in human fatigue state, this paper proposes a dual-input Laguerre-Volterra network (LVN) model based on ant colony optimization. First, the changes in 19 EMG features are discussed with increasing fatigue. We also consider two non-Gaussian features: kurtosis and negentropy in the 19 features. Later, 11 EMG fatigue features are picked out according to the fatigue test. Then, the preprocessed EMG and a composite signal of the 11 fatigue features are simultaneously input into the LVN model. Subsequently, the ant colony optimization algorithm is selected to train the model parameters. At the same time, a penalty term that we defined is introduced into the model cost function to adjust the weight of each feature adaptively. Finally, some experiments prove that the LVN model could quick fit the accurate force signal in five fatigue stages, such as non-fatigue, slight fatigue, mild fatigue, severe fatigue, and extreme fatigue. This LVN model can quickly transform EMG into strength signal in real time, which is suitable for people to observe muscle strength by a wearable device and makes it easy to detect the muscle current state. This model has good stability and can remain effective for a long time with training once, which provides convenience for the users of wearable devices.

Modeling Nonlinear Synaptic Dynamics: A Laguerre-Volterra Network Framework for Improved Computational Efficiency in Large Scale Simulations.

Synapses are key components in signal transmission in the brain, often exhibiting complex non-linear dynamics. Yet, they are often crudely modelled as linear exponential equations in large-scale neuron network simulations. Mechanistic models that use detailed channel receptor kinetics more closely replicate the nonlinear dynamics observed at synapses, but use of such models are generally restricted to small scale simulations due to their computational complexity. Previously, we have developed an ``input-output'' (IO) synapse model using the Volterra functional series to estimate nonlinear synaptic dynamics. Here, we present an improvement on the IO synapse model using the extbf{Laguerre-Volterra network (LVN) framework. We demonstrate that utilization of the LVN framework helps reduce memory requirements and improves the simulation speed in comparison to the previous iteration of the IO synapse model. We present results that demonstrate the accuracy, memory efficiency, and speed of the LVN model that can be extended to simulations with large numbers of synapses. Our efforts enable complex nonlinear synaptic dynamics to be modelled in large-scale network models, allowing us to explore how synaptic activity may influence network behavior and affects memory, learning, and neurodegenerative diseases.

Methodology of Recurrent Laguerre-Volterra Network for Modeling Nonlinear Dynamic Systems.

In this paper, we have introduced a general modeling approach for dynamic nonlinear systems that utilizes a variant of the simulated annealing algorithm for training the Laguerre-Volterra network (LVN) to overcome the local minima and convergence problems and employs a pruning technique to achieve sparse LVN representations with l1 regularization. We tested this new approach with computer simulated systems and extended it to autoregressive sparse LVN (ASLVN) model structures that are suitable for input-output modeling of nonlinear systems that exhibit transitions in dynamic states, such as the Hodgkin-Huxley (H-H) equations of neuronal firing. Application of the proposed ASLVN to the H-H equations yields a more parsimonious input-output model with improved predictive capability that is amenable to more insightful physiological/biological interpretation.

Pattern recognition of Hodgkin-Huxley equations by auto-regressive Laguerre Volterra network

A nonparametric, data-driven nonlinear auto-regressive Volterra (NARV) [1] model has been successfully applied for capturing the dynamics in the generation of action potentials, which is classically modeled by Hodgkin-Huxley (H-H) equations. However, the compactness still need to be improved for further interpretations. Therefore, we propose a novel Auto-regressive Sparse Laguerre Volterra Network (ASLVN) model (shown in Figure ​Figure1A),1A), which is developed from traditional Laguerre Volterra Network (LVN) and principal dynamic mode (PDM) framework [2]. Figure 1 A Structure of ASLVN for modeling H-H equations, where the input x(n) is the randomly injected current and the output y*(n) is the membrane potential. B The predictions results, z(1) represents the exogenous output, z(2) represents the autoregressive ... We adopt stochastic global optimization algorithm Simulated Annealing [3] to train the ASLVN instead of Back-propagation method [2] to avoid local minima and convergence problems. We also use lasso regularization [4] to enhance the spasity of the network and prune redundant branches for parsimony. The prediction results are shown in Fig.1B, it can be seen that the exogenous output z(1) represents the subthreshold dynamics in phase III, and the autoregressive output z(2) dominates in the spike shape in phase I, and the cross term output z(x) helps to maintain the refractory period by cancelling the effect of z(1) in phase II and we also observe that refractory inhibition effect decays after initiation of AP, which explains the absolute refractory period and relative refractory period in physiology.

Cerebral hemodynamics during orthostatic stress assessed by nonlinear modeling

The effects of orthostatic stress, induced by lower body negative pressure (LBNP), on cerebral hemodynamics were examined in a nonlinear context. Spontaneous fluctuations of beat-to-beat mean arterial blood pressure (MABP) in the finger, mean cerebral blood flow velocity (MCBFV) in the middle cerebral artery, as well as breath-by-breath end-tidal CO2 concentration (P(ET(CO2))) were measured continuously in 10 healthy subjects under resting conditions and during graded LBNP to presyncope. A two-input nonlinear Laguerre-Volterra network model was employed to study the dynamic effects of MABP and P(ET(CO2)) changes, as well as their nonlinear interactions, on MCBFV variations in the very low (VLF; below 0.04 Hz), low (LF; 0.04-0.15 Hz), and high frequency (HF; 0.15-0.30 Hz) ranges. Dynamic cerebral autoregulation was described by the model terms corresponding to MABP, whereas cerebral vasomotor reactivity was described by the model P(ET(CO2)) terms. The nonlinear model terms reduced the output prediction normalized mean square error substantially (by 15-20%) and had a prominent effect in the VLF range, both under resting conditions and during LBNP. Whereas MABP fluctuations dominated in the HF range and played a significant role in the VLF and LF ranges, changes in P(ET(CO2)) accounted for a considerable fraction of the VLF and LF MCBFV variations, especially at high LBNP levels. The magnitude of the linear and nonlinear MABP-MCBFV Volterra kernels increased substantially above -30 mmHg LBNP in the VLF range, implying impaired dynamic autoregulation. In contrast, the magnitude of the P(ET(CO2))-MCBFV kernels reduced during LBNP at all frequencies, suggesting attenuated cerebral vasomotor reactivity under dynamic conditions. We speculate that these changes may reflect a progressively reduced cerebrovascular reserve to compensate for the increasingly unstable systemic circulation during orthostatic stress that could ultimately lead to cerebral hypoperfusion and syncope.

Nonlinear Modeling of the Dynamic Effects of Arterial Pressure and<tex>$rm CO_2$</tex>Variations on Cerebral Blood Flow in Healthy Humans

The effect of spontaneous beat-to-beat mean arterial blood pressure fluctuations and breath-to-breath end-tidal CO2 fluctuations on beat-to-beat cerebral blood flow velocity variations is studied using the Laguerre-Volterra network methodology for multiple-input nonlinear systems. The observations made from experimental measurements from ten healthy human subjects reveal that, whereas pressure fluctuations explain most of the high-frequency blood flow velocity variations (above 0.04 Hz), end-tidal CO2 fluctuations as well as nonlinear interactions between pressure and CO2 have a considerable effect in the lower frequencies (below 0.04 Hz). They also indicate that cerebral autoregulation is strongly nonlinear and dynamic (frequency-dependent). Nonlinearities are mainly active in the low-frequency range (below 0.04 Hz) and are more prominent in the dynamics of the end-tidal CO2-blood flow velocity relationship. Significant nonstationarities are also revealed by the obtained models, with greater variability evident for the effects of CO2 on blood flow velocity dynamics.

Modeling of nonlinear physiological systems with fast and slow dynamics. I. Methodology.

Effective modeling of nonlinear dynamic systems can be achieved by employing Laguerre expansions and feedforward artificial neural networks in the form of the Laguerre-Volterra network (LVN). This paper presents a different formulation of the LVN that can be employed to model nonlinear systems displaying complex dynamics effectively. This is achieved by using two different filter banks, instead of one as in the original definition of the LVN, in the input stage and selecting their structural parameters in an appropriate way. Results from simulated systems show that this method can yield accurate nonlinear models of Volterra systems, even when considerable noise is present, separating at the same time the fast from the slow components of these systems effectively.