An artificial neural network that utilizes hip joint actuations to control bifurcations and chaos in a passive dynamic bipedal walking model

Chaos is a central feature of human locomotion and has been suggested to be a window to the control mechanisms of locomotion. In this investigation, we explored how the principles of chaos can be used to control locomotion with a passive dynamic bipedal walking model that has a chaotic gait pattern. Our control scheme was based on the scientific evidence that slight perturbations to the unstable manifolds of points in a chaotic system will promote the transition to new stable behaviors embedded in the rich chaotic attractor. Here we demonstrate that hip joint actuations during the swing phase can provide such perturbations for the control of bifurcations and chaos in a locomotive pattern. Our simulations indicated that systematic alterations of the hip joint actuations resulted in rapid transitions to any stable locomotive pattern available in the chaotic locomotive attractor. Based on these insights, we further explored the benefits of having a chaotic gait with a biologically inspired artificial neural network (ANN) that employed this chaotic control scheme. Remarkably, the ANN was quite robust and capable of selecting a hip joint actuation that rapidly transitioned the passive dynamic bipedal model to a stable gait embedded in the chaotic attractor. Additionally, the ANN was capable of using hip joint actuations to accommodate unstable environments and to overcome unforeseen perturbations. Our simulations provide insight on the advantage of having a chaotic locomotive system and provide evidence as to how chaos can be used as an advantageous control scheme for the nervous system.     

A chaotic neural network mimicking an olfactory system and its application on image recognition

1 Introduction A biological neural system is complicated and ef-ficient. People have tried for years to simulate it to per-form complex signal processing functions. For example,the artificial neural network is a kind of model derivedfrom a biological neural system. Most artificial neuralnetworks simulate some important features such as thethreshold behaviour and plasticity of synapses. However,they are primary simulations and still much simpler incomparison with specific biological neural…     

Biological Experimental Observations of an Unnoticed Chaos as Simulated by the Hindmarsh-Rose Model

An unnoticed chaotic firing pattern, lying between period-1 and period-2 firing patterns, has received little attention over the past 20 years since it was first simulated in the Hindmarsh-Rose (HR) model. In the present study, the rat sciatic nerve model of chronic constriction injury (CCI) was used as an experimental neural pacemaker to investigate the transition regularities of spontaneous firing patterns. Chaotic firing lying between period-1 and period-2 firings was observed located in four bifurcation scenarios in different, isolated neural pacemakers. These bifurcation scenarios were induced by decreasing extracellular calcium concentrations. The behaviors after period-2 firing pattern in the four scenarios were period-doubling bifurcation not to chaos, period-doubling bifurcation to chaos, period-adding sequences with chaotic firings, and period-adding sequences with stochastic firings. The deterministic structure of the chaotic firing pattern was identified by the first return map of interspike intervals and a short-term prediction using nonlinear prediction. The experimental observations closely match those simulated in a two-dimensional parameter space using the HR model, providing strong evidences of the existence of chaotic firing lying between period-1 and period-2 firing patterns in the actual nervous system. The results also present relationships in the parameter space between this chaotic firing and other firing patterns, such as the chaotic firings that appear after period-2 firing pattern located within the well-known comb-shaped region, periodic firing patterns and stochastic firing patterns, as predicted by the HR model. We hope that this study can focus attention on and help to further the understanding of the unnoticed chaotic neural firing pattern.     

Construction of an associative memory using unstable periodic orbits of a chaotic attractor

Unstable periodic orbits are the skeleton of a chaotic attractor. We constructed an associative memory based on the chaotic attractor of an artificial neural network, which associates input patterns to unstable periodic orbits. By processing an input, the system is driven out of the ground state to one of the pre-defined disjunctive areas of the attractor. Each of these areas is associated with a different unstable periodic orbit. We call an input pattern learned if the control mechanism keeps the system on the unstable periodic orbit during the response. Otherwise, the system relaxes back to the ground state on a chaotic trajectory. The major benefits of this memory device are its high capacity and low-energy consumption. In addition, new information can be simply added by linking a new input to a new unstable periodic orbit.     

Rotations of the 2B sub-domain of E. coli UvrD helicase/translocase coupled to nucleotide and DNA binding

Escherichia coli UvrD is a superfamily 1 DNA helicase and single-stranded DNA (ssDNA) translocase that functions in DNA repair and plasmid replication and as an anti-recombinase by removing RecA protein from ssDNA. UvrD couples ATP binding and hydrolysis to unwind double-stranded DNA and translocate along ssDNA with 3′-to-5′ directionality. Although a UvrD monomer is able to translocate along ssDNA rapidly and processively, DNA helicase activity in vitro requires a minimum of a UvrD dimer. Previous crystal structures of UvrD bound to a ssDNA/duplex DNA junction show that its 2B sub-domain exists in a “closed” state and interacts with the duplex DNA. Here, we report a crystal structure of an apo form of UvrD in which the 2B sub-domain is in an “open” state that differs by an ∼ 160° rotation of the 2B sub-domain. To study the rotational conformational states of the 2B sub-domain in various ligation states, we constructed a series of double-cysteine UvrD mutants and labeled them with fluorophores such that rotation of the 2B sub-domain results in changes in fluorescence resonance energy transfer. These studies show that the open and closed forms can interconvert in solution, with low salt favoring the closed conformation and high salt favoring the open conformation in the absence of DNA. Binding of UvrD to DNA and ATP binding and hydrolysis also affect the rotational conformational state of the 2B sub-domain, suggesting that 2B sub-domain rotation is coupled to the function of this nucleic acid motor enzyme.     

Segregation of micron-scale membrane sub-domains in live murine sperm

Lipid rafts, membrane sub-domains enriched in sterols and sphingolipids, are controversial because demonstrations of rafts have often utilized fixed cells. We showed in living sperm that the ganglioside G(M1) localized to a micron-scale membrane sub-domain in the plasma membrane overlying the acrosome. We investigated four models proposed for membrane sub-domain maintenance. G(M1) segregation was maintained in live sperm incubated under non-capacitating conditions, and after sterol efflux, a membrane alteration necessary for capacitation. The complete lack of G(M1) diffusion to the post-acrosomal plasma membrane (PAPM) in live cells argued against the transient confinement zone model. However, within seconds after cessation of sperm motility, G(M1) dramatically redistributed several microns from the acrosomal sub-domain to the post-acrosomal, non-raft sub-domain. This redistribution was not accompanied by movement of sterols, and was induced by the pentameric cholera toxin subunit B (CTB). These data argued against a lipid-lipid interaction model for sub-domain maintenance. Although impossible to rule out a lipid shell model definitively, mice lacking caveolin-1 maintained segregation of both sterols and G(M1), arguing against a role for lipid shells surrounding caveolin-1 in sub-domain maintenance. Scanning electron microscopy of sperm freeze-dried without fixation identified cytoskeletal structures at the sub-domain boundary. Although drugs used to disrupt actin and intermediate filaments had no effect on the segregation of G(M1), we found that disulfide-bonded proteins played a significant role in sub-domain segregation. Together, these data provide an example of membrane sub-domains extreme in terms of size and stability of lipid segregation, and implicate a protein-based membrane compartmentation mechanism.     

Chaotic attractor in two-prey one-predator system originates from interplay of limit cycles

We investigate the appearance of chaos in a microbial 3-species model motivated by a potentially chaotic real world system (as characterized by positive Lyapunov exponents (Becks et al., Nature 435, 2005). This is the first quantitative model that simulates characteristic population dynamics in the system. A striking feature of the experiment was three consecutive regimes of limit cycles, chaotic dynamics and a fixed point. Our model reproduces this pattern. Numerical simulations of the system reveal the presence of a chaotic attractor in the intermediate parameter window between two regimes of periodic coexistence (stable limit cycles). In particular, this intermediate structure can be explained by competition between the two distinct periodic dynamics. It provides the basis for stable coexistence of all three species: environmental perturbations may result in huge fluctuations in species abundances, however, the system at large tolerates those perturbations in the sense that the population abundances quickly fall back onto the chaotic attractor manifold and the system remains. This mechanism explains how chaos helps the system to persist and stabilize against migration. In discrete populations, fluctuations can push the system towards extinction of one or more species. The chaotic attractor protects the system and extinction times scale exponentially with system size in the same way as with limit cycles or in a stable situation.     

Chaotic neural network applied to two-dimensional motion control

Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.     

An adaptive and robust biological network based on the vacant-particle transportation model

A living system reveals local computing by referring to a whole system beyond the exploration-exploitation dilemma. The slime mold, Physarum polycephalum, uses protoplasmic flow to change its own outer shape, which yields the boundary condition and forms an adaptive and robust network. This observation suggests that the whole Physarum can be represented as a local protoplasmic flow system. Here, we show that a system composed of particles, which move and are modified based upon the particle transformation that contains the relationship between the parts and the whole, can emulate the network formed by Physarum. This system balances the exploration-exploitation trade-off and shows a scale-free sub-domain. By decreasing the number of particles, our model, VP-S, can emulate the Physarum adaptive network as it is attracted to a food stimulus. By increasing the number of particles, our model, VP-D, can emulate the pattern of a growing Physarum. The patterns produced by our model were compared with those of the Physarum pattern quantitatively, which showed that both patterns balance exploration with exploitation. This model should have a wide applicability to study biological collective phenomena in general.     

Study of a Bionic Pattern Classifier Based on Olfactory Neural System

Simulating biological olfactory neural system, KIII network, which is a high-dimensional chaotic neural network, is designed in this paper. Different from conventional artificial neural network, the KⅢ network works in its chaotic trajectory. It can simulate not only the output EEG waveform observed in electrophysiological experiments, but also the biological intelligence for pattern classification. The simulation analysis and application to the recognition of handwriting numerals are presented here. The classification performance of the KⅢ network at different noise levels was also investigated.     

Multivariate analysis of conserved sequence-structure relationships in kinesins: coupling of the active site and a tubulin-binding sub-domain

An extensive computational analysis of available sequence and crystal structure data was used to identify functionally important residue interactions within the motor domain of the kinesin molecular motor. Principal component analysis revealed that all current kinesin crystal structures reside in one of two main conformations, which differ at the active site, and in the position of a microtubule-binding sub-domain relative to a rigid central core. This sub-domain consists of secondary structure elements alpha4-loop12-alpha5-loop13 and contains a conserved hydrophilic surface patch that may be involved in strong binding to microtubules. A hinge point for the sub-domain motion lies near a conserved glycine at position 292. Statistical coupling analysis revealed a network of co-evolving positions that link this region to the nucleotide-binding site, via a highly conserved histidine in the switch I loop. The data are consistent with a model in which the nucleotide status of the active site shifts kinesin between weak and strong binding conformations via reconfiguration of the identified sub-domain. Our data provide a statistically supported framework for further examination of this and other structure-function relationships in the kinesin family.     

Structural insights into the functional role of the Hcn sub-domain of the receptor-binding domain of the botulinum neurotoxin mosaic serotype C/D

Botulinum neurotoxin (BoNT), the causative agent of the deadly neuroparalytic disease botulism, is the most poisonous protein known for humans. Produced by different strains of the anaerobic bacterium Clostridium botulinum, BoNT effects cellular intoxication via a multistep mechanism executed by the three modules of the activated protein. Endocytosis, the first step of cellular intoxication, is triggered by the ∼50 kDa, heavy-chain receptor-binding domain (HCR) that is specific for a ganglioside and a protein receptor on neuronal cell surfaces. This dual receptor recognition mechanism between BoNT and the host cell's membrane is well documented and occurs via specific intermolecular interactions with the C-terminal sub-domain, Hcc, of BoNT–HCR. The N-terminal sub-domain of BoNT–HCR, Hcn, comprises ∼50% of BoNT–HCR and adopts a β-sheet jelly roll fold. While suspected in assisting cell surface recognition, no unambiguous function for the Hcn sub-domain in BoNT has been identified. To obtain insights into the potential function of the Hcn sub-domain in BoNT, the first crystal structure of a BoNT with an organic ligand bound to the Hcn sub-domain has been obtained. Here, we describe the crystal structure of BoNT/CD–HCR determined at 1.70 Å resolution with a tetraethylene glycol (PG4) moiety bound in a hydrophobic cleft between β-strands in the β-sheet jelly roll fold of the Hcn sub-domain. The PG4 moiety is completely engulfed in the cleft, making numerous hydrophilic (Y932, S959, W966, and D1042) and hydrophobic (S935, W977, L979, N1013, and I1066) contacts with the protein's side chain and backbone that may mimic in vivo interactions with the phospholipid membranes on neuronal cell surfaces. A sulfate ion was also observed bound to residues T1176, D1177, K1196, and R1243 in the Hcc sub-domain of BoNT/CD–HCR. In the crystal structure of a similar protein, BoNT/D–HCR, a sialic acid molecule was observed bound to the equivalent residues suggesting that residues T1176, D1177, K1196, and R1243 in BoNT/CD may play a role in ganglioside binding.     

神经起步点自发放电节律及节律转化的分岔规律

在神经起步点的实验中观察到了复杂多样的神经放电([Ca^2 ]o)节律模式,如周期簇放电、周期峰放电、混沌簇放电、混沌峰放电以及随机放电节律等。随着细胞外钙离子浓度的降低,神经放电节律从周期l簇放电,经过复杂的分岔过程(包括经倍周期分岔到混沌簇放电、混沌簇放电经激变到混沌峰放电、以及混沌峰放电经逆倍周期分岔到周期峰放电)转化为周期l峰放电。在神经放电理论模型——Chay模型中,调节与实验相关的参数(Ca^2 平衡电位),可以获得与实验相似的神经放电节律和节律转换规律。这表明复杂的神经放电节律之间存在着一定的分岔规律,它们是理解神经元信息编码的基础。     

嗅觉系统神经网络模型的模拟与动力学特性分析

在哺乳动物嗅觉系统的拓扑结构及生理实验的基础上建立了一套非线性动力学神经网络模型．此模型在模拟嗅觉神经系统方面有着突出的优点,同时在信号处理以及模式识别中表现出了奇异的混沌特性．着重描述了K系列模型的非线性动力学特性,并通过数值模拟进行分析．     

Nonlinear transient computation as a potential "kernel trick" in cortical processing

Evidence has been found for the presence of chaotic dynamics at all levels of the mammalian brain. This has led to some searching questions about the potential role that nonlinear dynamics may have in neural information processing. We propose that chaos equips the brain with the equivalent of a kernel trick for solving hard nonlinear problems. The approach presented, which is described as nonlinear transient computation, uses the dynamics of a well known chaotic attractor. The paper provides experimental results to show that this approach can be used to solve some challenging pattern recognition tasks. The paper also offers evidence to suggest that the efficacy of nonlinear transient computation for nonlinear pattern classification is dependent only on the generic properties of chaotic attractors and is not sensitive to the particular dynamics of specific sub-regions of chaotic phase space. If, as this work suggests, nonlinear transient computation is independent of the particulars of any given chaotic attractor, then it could be offered as a possible explanation of how the chaotic dynamics that have been observed in brain structures contribute to neural information processing tasks.     

周期激励下FHN模型的两种多峰分布放电节律

文章揭示了外界周期脉冲激励下神经元系统产生的随机整数倍和混沌多峰放电节律的关系.随机节律统计直方图呈多峰分布、峰值指数衰减、不可预报且复杂度接近1;混沌节律统计直方图呈不同的多峰分布,峰值非指数衰减、有一定的可预报性且复杂度小于1.混沌节律在激励脉冲周期小于系统内在周期且刺激强度较大时产生,参数范围较小;而随机节律在激励脉冲周期大于系统内在周期且脉冲刺激强度小时,可与随机因素共同作用而产生,产生的参数范围较大.上述结果揭示了两类节律的动力学特性,为区分两类节律提供了实用指标.     

Pattern recall in networks of chaotic neurons

This research investigates the potential utility of chaotic dynamics in neural information processing. A novel chaotic spiking neural network model is presented which is composed of non-linear dynamic state (NDS) neurons. The activity of each NDS neuron is driven by a set of non-linear equations coupled with a threshold based spike output mechanism. If time-delayed self-connections are enabled then the network stabilises to a periodic pattern of activation. Previous publications of this work have demonstrated that the chaotic dynamics which drive the network activity ensure that an extremely large number of such periodic patterns can be generated by this network. This paper presents a major extension to this model which enables the network to recall a pattern of activity from a selection of previously stabilised patterns.     

Sub-domains of the dystrophin rod domain display contrasting lipid-binding and stability properties

Dystrophin is a muscle scaffolding protein that establishes a structural link between the cytoskeleton and the extracellular matrix. Despite the large body of knowledge about the dystrophin gene and its interactions, the functional importance of the large central rod domain remains highly controversial. It is composed of 24 spectrin-like repeats interrupted by four hinges that delineate three sub-domains. We express repeat 1-3 and repeat 20-24 sub-domains, delineated by hinges 1-2 and 3-4 and the single repeats 2 and 23. We determine their lipid-binding properties, thermal and urea stabilities and refolding velocities. By using intrinsic tryptophan fluorescence spectroscopy and size exclusion chromatography, we show that repeat 2 and the repeat 1-3 sub-domain strongly interact with anionic lipids. By contrast, repeat 23 and the repeat 20-24 sub-domain do not interact with lipids. In addition, the repeat 1-3 sub-domain and repeat 2 are dramatically less stable and refold faster than the repeat 20-24 sub-domain and repeat 23. The contrasting properties of the two sub-domains clearly indicate that they make up two units of the rod domain that are not structurally interchangeable, thus providing molecular evidence supporting the observations on the biological function of dystrophin.     

Chaotic synchronization using a network of neural oscillators

Synchronization of chaotic low-dimensional systems has been a topic of much recent research. Such systems have found applications for secure communications. In this work we show how synchronization can be achieved in a high-dimensional chaotic neural network. The network used in our studies is an extension of the Hopfield Network, known as the Complex Hopfield Network (CHN). The CHN, also an associative memory, has both fixed point and limit cycle or oscillatory behavior. In the oscillatory mode, the network wanders chaotically from one stored pattern to another. We show how a pair of identical high-dimensional CHNs can be synchronized by communicating only a subset of state vector components. The synchronizability of such a system is characterized through simulations.     

Complex Generalized Synchronization and Parameter Identification of Nonidentical Nonlinear Complex Systems

In this paper, generalized synchronization (GS) is extended from real space to complex space, resulting in a new synchronization scheme, complex generalized synchronization (CGS). Based on Lyapunov stability theory, an adaptive controller and parameter update laws are designed to realize CGS and parameter identification of two nonidentical chaotic (hyperchaotic) complex systems with respect to a given complex map vector. This scheme is applied to synchronize a memristor-based hyperchaotic complex Lü system and a memristor-based chaotic complex Lorenz system, a chaotic complex Chen system and a memristor-based chaotic complex Lorenz system, as well as a memristor-based hyperchaotic complex Lü system and a chaotic complex Lü system with fully unknown parameters. The corresponding numerical simulations illustrate the feasibility and effectiveness of the proposed scheme.