A genealogical map of the concept of habit

The notion of information processing has dominated the study of the mind for over six decades. However, before the advent of cognitivism, one of the most prominent theoretical ideas was that of Habit. This is a concept with a rich and complex history, which is again starting to awaken interest, following recent embodied, enactive critiques of computationalist frameworks. We offer here a very brief history of the concept of habit in the form of a genealogical network-map. This serves to provide an overview of the richness of this notion and as a guide for further re-appraisal. We identify 77 thinkers and their influences, and group them into seven schools of thought. Two major trends can be distinguished. One is the associationist trend, starting with the work of Locke and Hume, developed by Hartley, Bain, and Mill to be later absorbed into behaviorism through pioneering animal psychologists (Morgan and Thorndike). This tradition conceived of habits atomistically and as automatisms (a conception later debunked by cognitivism). Another historical trend we have called organicism inherits the legacy of Aristotle and develops along German idealism, French spiritualism, pragmatism, and phenomenology. It feeds into the work of continental psychologists in the early 20th century, influencing important figures such as Merleau-Ponty, Piaget, and Gibson. But it has not yet been taken up by mainstream cognitive neuroscience and psychology. Habits, in this tradition, are seen as ecological, self-organizing structures that relate to a web of predispositions and plastic dependencies both in the agent and in the environment. In addition, they are not conceptualized in opposition to rational, volitional processes, but as transversing a continuum from reflective to embodied intentionality. These are properties that make habit a particularly attractive idea for embodied, enactive perspectives, which can now re-evaluate it in light of dynamical systems theory and complexity research.

Nash equilibria in multi-agent motor interactions.

Social interactions in classic cognitive games like the ultimatum game or the prisoner's dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner's dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.

Shock transmission and eigenvalue veering within a coupled system.

The operation of dynamical systems in harsh environments requires continuous monitoring. Internal sensors may be used to monitor the conditions in real time. A typical example is the sensor and electronic components used in space structures which, especially during launch, are subject to huge g force. The paper will present an experimental and theoretical study on a simplified model used to analyze the possible cause of high acceleration on the enclosed sensors and equipments due to impulsive loading. The model system consists of two beams coupled using compliant connections. An impulse hammer excites one beam, and vibrations are transmitted to the indirectly driven beam. A theoretical model is developed using a Rayleigh-Ritz approach and validated using experimental results in both the frequency and time domains. Monto Carlo simulation was done with random masses positioned on the indirectly driven beam to determine the worst-case conditions for maximum peak acceleration. Highest acceleration levels were found when mode matching in the two beams led to veering behavior in the coupled modes. The results suggest guidelines for the detailed design of internal components of a structure exposed to shock loading from its environment. [The authors thank Schlumberger Cambridge Research for financial support.].

The post-processed Galerkin method applied to non-linear shell vibrations

We present the results of a computational study of the post-processed Galerkin methods put forward by Garcia-Archilla et al. applied to the non-linear von Karman equations governing the dynamic response of a thin cylindrical panel periodically forced by a transverse point load. We spatially discretize the shell using finite differences to produce a large system of ordinary differential equations (ODEs). By analogy with spectral non-linear Galerkin methods we split this large system into a 'slowly' contracting subsystem and a 'quickly' contracting subsystem. We then compare the accuracy and efficiency of (i) ignoring the dynamics of the 'quick' system (analogous to a traditional spectral Galerkin truncation and sometimes referred to as 'subspace dynamics' in the finite element community when applied to numerical eigenvectors), (ii) slaving the dynamics of the quick system to the slow system during numerical integration (analogous to a non-linear Galerkin method), and (iii) ignoring the influence of the dynamics of the quick system on the evolution of the slow system until we require some output, when we 'lift' the variables from the slow system to the quick using the same slaving rule as in (ii). This corresponds to the post-processing of Garcia-Archilla et al. We find that method (iii) produces essentially the same accuracy as method (ii) but requires only the computational power of method (i) and is thus more efficient than either. In contrast with spectral methods, this type of finite-difference technique can be applied to irregularly shaped domains. We feel that post-processing of this form is a valuable method that can be implemented in computational schemes for a wide variety of partial differential equations (PDEs) of practical importance.

An organizing center in a planar model of neuronal excitability

This paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the classical FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables. © 2012 Society for Industrial and Applied Mathematics.

Nonlinear drillstring dynamics analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control. © 2009 Society for Industrial and Applied Mathematics.

Analysis of interconnected oscillators by dissipativity theory

This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. Oscillators are regarded as open systems that satisfy a particular dissipation inequality. It is shown that this characterization has implications for the global stability analysis of limit cycle oscillations: i) in isolated oscillators, ii) in interconnections of oscillators, and iii) for the global synchrony analysis in interconnections of identical oscillators. © 2007 IEEE.

Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet

The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to T{double-struck}2 quasiperiodicity via a torus-birth bifurcation; and then (ii) from T{double-struck}2 quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled. © 2013 Cambridge University Press.

Bayesian inference and learning in Gaussian process state-space models with Particle MCMC

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and, instead, infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

An adaptive controller for a class of nonlinear system using direction basis function

For a class of nonlinear dynamical systems, the adaptive controllers are investigated using direction basis function (DBF) in this paper. Based on the criterion of Lyapunov' stability, DBF is designed which guarantees that the output of the controlled system asymptotically tracks the reference signals. Finally, the simulation shows the good tracking effectiveness of the adaptive controller.

基于复合离散混沌动力系统的序列密码算法

利用复合离散混沌系统的特性,提出了两个基于复合离散混沌系统的序列密码算法.算法的加密和解密过程都是同一个复合离散混沌系统的迭代过程,取迭代的初始状态作为密钥,以明文序列作为复合系统的复合序列,它决定了迭代过程中迭代函数的选择(或明文与密钥),然后将迭代轨迹粗粒化后作为密文.由于迭代对初始条件的敏感性和迭代函数选择的随机性,密钥、明文与密文之间形成了复杂而敏感的非线性关系,而且密文和明文的相关度也很小,从而可以有效地防止密文对密钥和明文信息的泄露.复合离散混沌系统均匀的不变分布还使密文具有很好的随机特性.经分析表明,系统具有很高的安全性.

陡坡带砂砾岩体油气成藏模式研究——以东营凹陷西北部陡坡带为例

Based on the study of sequence stratigraphy, modern sedimentary, basin analysis, and petroleum system in abrupt slop of depression, this paper builds sedimentary system and model, sandy bodies distribution, and pool-forming mechanism of subtle trap. There are some conclusions and views as follows. By a lot of well logging and seismic analysis, the author founded up the sequence stratigraphic of the abrupt slope, systematically illustrated the abrupt slope constructive framework, and pointed out that there was a special characteristics which was that south-north could be divided to several fault block and east-west could be carved up groove and the bridge in studying area. Based all these, the author divided the studying area to 3 fault block zone in which because of the groove became the basement rock channel down which ancient rivers breathed into the lake, the alluvial fan or fan delta were formed. In the paper, the author illustrated the depositional system and depositional model of abrupt slope zone, and distinguished 16 kinds of lithofacies and 3 kinds of depositional systems which were the alluvial fan and fan-delta system, lake system and the turbidite fan or turbidity current deposition. It is first time to expound completely the genetic pattern and distributing rule of the abrupt slope sandy-conglomeratic fan bodies. The abrupt slope sandy-conglomeratic fan bodies distribute around the heaves showing itself circularity shape. In studying area, the sandy-conglomeratic fan bodies mainly distribute up the southern slope of Binxian heave and Chenjiazhuang heave. There mainly are these sandy-conglomeratic fan body colony which distributes at a wide rage including the alluvial fan, sub-water fluvial and the turbidite fan or the other turbidity current deposition in the I fault block of the Wangzhuang area. In the II fault block there are fan-delta front and sub-water fluvial. And in the Binnan area, there mainly are those the alluvial fan (down the basement rock channel) and the sandy-conglomeratic fan body which formed as narrowband sub-water fluvial (the position of bridge of a nose) in the I fault block, the fan-delta front sandy-conglomeratic fan body in the H fault block and the fan-delta front and the turbidity current deposition sandy-conglomeratic fan body in the m fault block. Based on the reservoir outstanding characteristics of complex classic composition and the low texture maturity, the author comparted the reservoir micro-structure of the Sha-III and Sha-IV member to 4 types including the viscous crude cementation type, the pad cementation type, the calcite pore-funds type and the complex filling type, and hereby synthetically evaluated 4 types sandy- conglomeratic fan body reservoir. In the west-north abrupt slope zone of Dongying Depression, the crude oil source is belonging to the Sha-III and Sha-IV member, the deep oil of Lijin oilfield respectively come from the Sha-III and Sha-IV member, which belongs to the autogeny and original deposition type; and the more crude oil producing by Sha-IV member was migrated to the Wangzhuan area and Zhengjia area. The crude oil of Binnan oil-field and Shanjiasi oil-field belongs to mixed genetic. It is the first time to illustrate systematically the genetic of the viscous crude that largely being in the studying area, which are that the dissipation of the light component after pool-forming, the biological gradation action and the bath-oxidation action, these oil accumulation belonging to the secondary viscous crude accumulation. It is also the first time to compart the studying area to 5 pool-forming dynamical system that have the characteristic including the common pressure and abnormal pressure system, the self-fountain and other-fountain system and the closing and half-closing system etc. The 5 dynamical systems reciprocally interconnected via the disappearance or merger of the Ethology and the fluid pressure compartment zone, the fault and the unconformity surface, hereby formed duplicated pattern oil-gas collecting zone. Three oil-gas pool-forming pattern were founded, which included the self-fountain side-direction migrated collecting pattern, the self-fountain side-direction ladder-shape pool-forming pattern and the other-fountain pressure releasing zone migrated collecting pattern. A series of systemic sandy-conglomeratic fan bodies oil-gas predicting theory and method was founded, based on the groove-fan corresponding relation to confirm the favorable aim area, according as the characteristic of seismic-facies to identify qualitatively the sandy-conglomeratic fan bodies or its scale, used the temporal and frequency analysis technique to score the interior structure of the sandy- conglomeratic fan bodies, applied for coherent-data system analysis technology to describe the boundary of the sandy-conglomeratic fan bodies, and utilized the well logging restriction inversion technique to trace quantificational and forecast the sandy-conglomeratic fan bodies. Applied this technique, totally 15 beneficial sandy-conglomeratic fan bodies were predicted, in studying area the exploration was preferably guided, and the larger economic benefit and social benefit was acquired.

Non-commutative symbolic coding

Gohm, Rolf; Kummerer, B.; Lang, T., (2006) 'Non-commutative symbolic coding', Ergodic Theory and Dynamical Systems 26(5) pp.1521-1548 RAE2008