Global bifurcation structure of chaotic neural networks and its application to traveling salesman problems

This paper studies global bifurcation structure of the chaotic neural networks applied to solve the traveling salesman problem (TSP). The bifurcation analysis clarifies the dynamical basis of the chaotic neuro-dynamics which itinerates a variety of network states associated with possible solutions of TSP and efficiently ‘searches’ for the optimum or near-optimum solutions. By following the detailed merging process of chaotic attractors via crises, we find that the crisis-induced intermittent switches among the ruins of the previous localized chaotic attractors underly the ‘chaotic search’ for TSP solutions. On the basis of the present study, efficiency of the ‘chaotic search’ to optimization problems is discussed and a guideline is provided for tuning the bifurcation parameter value which gives rise to efficient ‘chaotic search’.     

在人工神经网络中引入混沌的必要性

本文从Freeman的生理学实验和仿真实验的结果出发,综合了Freeman和Tsuda对生物神经网络中混沌动力学的解释,从信息流动的角度论述了在生物神经网络中混沌存在的必要性和引入混沌机制的人工神经网络模型所具有的信息处理的潜力,指出认知系统对外界输入的反应是其动力学行为性质的改变而不仅是静态的数值输出.并认为具有混沌动力学性质的神经网络应同时具有模式分类器和解释器的双重作用.这一结合来自于系统的混沌动力性质.描述了混沌在模式识别中的作用,指出了其相对ART等传统神经网络模型的一些优势.部分结论在仿真实验中得到了证实.     

Correlation dimension analysis of the artificial circulation

Artificial circulation has been analyzed by decomposing it into parts. However, the sum of the decomposed parts is not equal to the whole system, especially in nonlinear dynamic systems such as biological systems. To evaluate prosthetic circulation as an entity, not as decomposed parts, nonlinear mathematical analytic techniques, including fractal dimension analyzing theory, were used. Two pneumatically actuated ventricular assist devices were implanted as biventricular bypasses (BVB) in chronic animal experiments using four healthy adult goats. For comparison between natural and prosthetic circulation in the same experimental animals, the BVB-type complete prosthetic circulation model with ventricular fibrillation was adopted. All hemodynamic parameters with natural and prosthetic circulation were recorded under awake conditions and calculated by a personal computer system. By the use of nonlinear mathematical techniques, time-series data of the hemodynamics were embedded into the phase space, and correlation dimension analysis was performed to evaluate the reconstructed attractor. Our results suggest that the correlation dimension of the arterial blood pressure does not linearly increase according to the increase of the embedding dimension, even during artificial circulation, suggesting those are the fractal time series data. Dimensional analysis of the hemodynamics revealed that lower dimensional fractal dynamics were observed during prosthetic circulation. Fractal time series data are suggested to have robustness and error resistance. Thus, our results suggest that the circulatory regulatory system with the artificial heart may have these desirable characteristics. Accepted: July 14, 1995     

Chaos and control in mass-action binding of endogenous compounds

Endogenous compounds, such as hormones and neurotransmitters, interact with cellular receptors in controlled reactions governed by the mass-action law. Autoreceptors, a subset of the receptor pool, when activated by the endogenous ligand, result in a negative feedback that reduces the further release of ligand. This paper discusses and illustrates this control system when the concentrations (free and bound) are near or slightly beyond the limits of effective feedback control. Specifically, a forced periodic input function, simulating periodic release of the ligand, is used in the simulation of this controlled binding reaction in which a parameter representing the upper limit of control is varied. The solution of the system differential equations, representing free and bound ligand, is shown to pass from periodic to chaotic as the parameter is varied.     

Stochastic and Coherence Resonance in an In Silico Neural Model

We show that it is possible for chaotic systems to display the main features of stochastic and coherence resonance. In particular, a model of coupled nonlinear oscillators which emulates the transmembrane voltage activities in CA3 neurons, operating in a chaotic regime and in the presence of noise, can exhibit coherence resonance and stochastic resonance. Certain firing frequencies become more "rhythmic" for some optimal values of noise intensity. The effect of noise in different coupling pathways is investigated. We found that the effect of coherence resonance and stochastic resonance are more prominent if noise is presented in either electric field or gap junction coupling pathways. Frequency sensitivity of the model is investigated as a preliminary step in illustrating the principles of possible epileptic seizure control strategies using "chaos control" concepts. Significant effects of stochastic resonance are observed in the 4-8 Hz range. Weaker effects can be found in the 1-4 Hz and 8-10 Hz ranges whereas 0.5 Hz does not exhibit any resonance phenomenon. Our results suggest that: (a) Stochastic resonance could enhance the intrinsic 4-8 Hz rhythms in CA3 neurons more prominently via field coupling pathways. It could also help explain why some reported seizure control strategies using pulse-trains would only be effective at 0.5 Hz. (b) Stochastic resonance-like behavior can occur in the gamma range only if noise is presented via chemical synaptic pathways.     

Flexible effects of quantified cigarette-smoke delivery on EEG dimensional complexity

A quantified smoke delivery system (QSDS) was used to experimentally control the administration of inhaled cigarette smoke to 28 male smokers. One puff (2 s, 35 cc) was taken every 30 s on a cigarette (nicotine yield 1.0 mg) until the char line reached 3 mm from the filter wrap. The smoke was inhaled for 5 s. Resting eyes-closed and eyes-open EEG was recorded from F3, F4, P3, and P4 before and after quantified smoke delivery (QSD). EEG dimensional complexity (DC _x, a measure derived from chaos theory) was computed using the Takens-Ellner method. QSD appeared to have a flexible effect on EEGDC _x, primarily lowering it in subjects whose pre-smoking level was high, not affecting it in subjects whose pre-smoking level was intermediate, and tending to raise it in subjects whose pre-smoking level was low. This replicates previous results obtained with ad libitum smoking, suggesting the hypothesis that smoking may have an optimizing effect on the complexity of brain dynamics.     

Buckling Sensitivity of Tow-Steered Plates Subjected to Multiscale Defects by High-Order Finite Elements and Polynomial Chaos Expansion

It is well known that fabrication processes inevitably lead to defects in the manufactured components. However, thanks to the new capabilities of the manufacturing procedures that have emerged during the last decades, the number of imperfections has diminished while numerical models can describe the ground truth designs. Even so, a variety of defects has not been studied yet, let alone the coupling among them. This paper aims to characterise the buckling response of Variable Stiffness Composite (VSC) plates subjected to spatially varying fibre volume content as well as fibre misalignments, yielding a multiscale sensitivity analysis. On the one hand, VSCs have been modelled by means of the Carrera Unified Formulation (CUF) and a layer-wise (LW) approach, with which independent stochastic fields can be assigned to each composite layer. On the other hand, microscale analysis has been performed by employing CUF-based Mechanics of Structure Genome (MSG), which was used to build surrogate models that relate the fibre volume fraction and the material elastic properties. Then, stochastic buckling analyses were carried out following a multiscale Monte Carlo analysis to characterise the buckling load distributions statistically. Eventually, it was demonstrated that this multiscale sensitivity approach can be accelerated by an adequate usage of sampling techniques and surrogate models such as Polynomial Chaos Expansion (PCE). Finally, it has been shown that sensitivity is greatly affected by nominal fibre orientation and the multiscale uncertainty features.     

Connectionist networks learn to transmit chaos

Evidence presented in the preceding paper indicates that the activity of some neurons during the generation of coordinated motor patterns may be attributable to chaos. Because even "simple" biological systems are difficult to control, we have used connectionist networks in order to inquire into the question of whether a chaotic signal originating in one part of the nervous system can be learned and transmitted by another. We have examined a number of different architectures, and report here the findings for a simple network consisting of one input unit, four hidden units, and one output unit. During training sessions, the input of the circuit was given analog values of either the 3.60 or 3.95 logistic equation, or of one variable of the three-variable R?ssler attractor. The backpropagated error in the learning algorithm was a function of the difference between the input value and the output at each iteration. Iterations involving small changes in analog value resulted in good similarity between the input and output signals, but little learning occurred because of the small error propagated back to the synapses. With larger differences in the analog values (and larger feedback error) at each iteration, we found that networks learned to transmit different chaotic attractors. Once the network learned one input, it could transmit another without changing the synapses. Increasing the number of hidden units increased the rate of learning.(ABSTRACT TRUNCATED AT 250 WORDS)     

Effect of nortriptyline and paroxetine on measures of chaos of heart rate time series in patients with panic disorder

Tricyclic antidepressants have notable cardiac side effects, and this issue has become important due to the recent reports of increased cardiovascular mortality in patients with depression and anxiety. Several previous studies indicate that serotonin reuptake inhibitors (SRIs) do not appear to have such adverse effects. Apart from the effects of these drugs on routine 12-lead ECG, the effects on beat-to-beat heart rate (HR) and QT interval time series provide more information on the side effects related to cardiac autonomic function. In this study, we evaluated the effects of two antidepressants, nortriptyline (n=13), a tricyclic, and paroxetine (n=16), an SRI inhibitor, on HR variability in patients with panic disorder, using a measure of chaos, the largest Lyapunov exponent (LLE) using pre- and posttreatment HR time series. Our results show that nortriptyline is associated with a decrease in LLE of high frequency (HF: 0.15–0.5 Hz) filtered series, which is most likely due to its anticholinergic effect, while paroxetine had no such effect. Paroxetine significantly decreased sympathovagal ratios as measured by a decrease in LLE of LF/HF. These results suggest that paroxetine appears to be safer in regards to cardiovascular effects compared to nortriptyline in this group of patients.     

From chaos to complex order: personal values and resources in the process of psychotherapy

TOPIC: Chaos as a scientific metaphor for the therapeutic relationship. PURPOSE: To provide an approach to psychotherapy of a psychotic experience through aspects of a single case. SOURCES: Selective literature review and author's clinical work. CONCLUSIONS: Appreciation of the water metaphor, and its deployment within Eastern philosophy and psychology, may help Western therapists develop further traditional interpersonal relations today.