当前位置：文档之家 › On the Dynamical Complexity of Small-World Networks of Spiking Neurons

On the Dynamical Complexity of Small-World Networks of Spiking Neurons

  • 格式：pdf
  • 大小：1.66 MB
  • 文档页数：17

Submitted for publication June 2008On the Dynamical Complexity of Small-World Networks ofSpiking NeuronsMurray ShanahanDepartment of Computing, Imperial College London, 180 Queen’s Gate, London SW72AZ, UK.PACS area: 87.18.SnAbstractA computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected clusters and then applying a probabilistic rewiring method reminiscent of the Watts-Strogatz procedure to make inter-cluster connections. Causal density, which counts the number of independent significant interactions among a system’s components, is used to assess dynamical complexity. This measure was chosen because it employs lagged observations, and is therefore more sensitive to temporally smeared evidence of segregation and integration than its alternatives. The results broadly support the hypothesis that small-world topology promotes dynamical complexity, but reveal a narrow parameter range within which this occurs for the network topology under investigation, and suggest an inverse correlation with phase synchrony inside this range.The existence of both functional and structural networks with small-world properties in the brains of a variety of animals is now well established [1,19], and the evolutionary, metabolic, and computational constraints likely to favour neural networks with small-world topologies have been the subject of much recent discussion [20, 23]. At the same time, the theme of dynamical complexity – the extent to which both segregated and integrated activity are present in the same system – has become important in the attempt to understand how sophisticated cognition emerges from the activity of large numbers of neurons [16, 21]. In pursuit of this theme, Sporns, et al. [18] report a computer experiment with an evolutionary algorithm in which an initial population of randomly connected networks evolved towards small-world topologies when subject to a selection criterion that favoured dynamical complexity (according to one of several formal measures of that concept). Further support for the thesis that small-world topology promotes dynamical complexity in neural networks is provided by Roxin and colleagues, who describe the simulation of a specific class of small-world networks of integrate-and-fire neurons with constant conduction delays [12, 14].The class of networks investigated by Roxin and colleagues are constructed using the well-known Watts-Strogatz procedure [22], in which the short-range connections in a ring lattice are replaced by long-range connections with a given probability p. In [12], these authors demonstrate a variety of different behaviours for their spiking neuron networks depending on p. In particular, they show that if p lies within a certain critical range, the resulting networks tend to generate self-sustaining activity. They also show that, given a sufficiently long conduction delay, higher values of p within this rangesupport a form of chaotic behaviour which is suggestive of increased dynamical complexity. As Riecke, et al.point out [12], the network topology generated by the Watts-Strogatz procedure is a reasonable approximation of a mid-sized patch of cortex that comprises abundant short (less than 100µmm) connections among nearby neurons with proportionally fewer longer-range projections to sites several millimetres away. However, there is strong evidence that cortical anatomy also enjoys small-world properties on a more global scale [1, 19], where it may be characterised as a network of anatomically distinct regions that are densely intra-connected at the level of grey matter and interact with each other through relatively sparse long-range white matter projections [5]. This kind of small-world topology is not well modeled by the Watts-Strogatz procedure, which produces networks whose density of short-range connections is uniform, and in which markedly segregated areas therefore do not exist.The present paper reports an experiment whose aim was to deepen our understanding of the relationship between dynamical complexity and connectivity in so-called “modular” small-world networks [2, 9]. These networks, which comprise a number of densely intra-connected clusters linked by a small set of inter-cluster connections, are better approximations of cortical structure at a global scale than those produced by the Watts-Strogatz procedure. However, echoing the Watts-Strogatz procedure, the network construction method employed here includes a probabilistic rewiring phase to establish inter-cluster connections, and it can therefore be parameterised by the rewiring probability p. So in the experiment p was used to capture each network’s structure, along with its small-world index. Causal density – which assesses the extent to which eachvariable in a system exercises independent influence on the others – was the chosen measure of dynamical complexity since, as well as being able to distinguish between individual and systemic dependencies in multivariate data, it is sensitive to temporally smeared evidence of segregation and integration thanks to its use of lagged observations [16]. This feature turns out to be essential for detecting the complexity trend that is the main result of the paper.In line with the findings of Sporns et al. [18] and Riecke, et al. [12], we would expect dynamical complexity to correlate positively with small-world index. Intuitively, a high small-world index (assuming sparse connectivity) indicates that distinct portions of the network enjoy considerable structural segregation yet remain significantly interconnected, and it is reasonable to expect this balance to manifest in the dynamics as loosely coupled islands of largely independent activity. The results of the experiment broadly support this hypothesis. However, contrary to expectations, they show that a high small-world index does not guarantee dynamical complexity. Rather, there is a narrow parameter range within which the balance in question is struck, because networks with too much inter-cluster connectivity, though still enjoying a high small-world index, tend towards entrainment, a dynamical regime which is highly integrated but lacks segregation. High dynamical complexity only occurs with sparsely inter-connected clusters, although this is indetectable without the use of lagged observations because such networks only exhibit integration over time. Since dynamical complexity is a plausible prerequisite for flexible cognition this suggests that the structural connectivity matrices oflarge-scale cortical networks will conform to a tighter set of constraints than was previously realised.Each randomly generated network in the experiment comprised 1000 spiking neurons with variable conduction delays, of which 800 (80%) were excitatory and 200 (20%) inhibitory. The spiking neuron model used was that of Izhikevich [8]. The model is defined by the following three equations.˙ v =0.04v2+5v+140"u+I(1)˙ u =a(bv"u)(2)if v"30then v#cu#u+d$%&(3) where v is the neuron’s membrane potential, I is its input current, and u is a variable that regulates the recovery time of the neuron after spiking. Eqn. (3) describes the way the neuron is reset after spiking, which is assumed to occur when its membrane potential reaches 30mV. Following Izhikevich [8], the parameters of the neuron model were assigned non-uniformly to endow the population with a variety of signalling behaviours. For excitatory neurons, the values used were a = 0.02, b = 0.2, c = -65 + 16r2, and d = 8-6r2, where r is a uniformly distributed random variable in the interval [0,1]. For inhibitory neurons, the values used were a = 0.02 + 0.08r, b = 0.250-0.05r, c = -65, and d = 2, with r as above.Consider a time t and a neuron i, and let Φ be the set of all neurons j that fired at time t–δwhere δ is the conduction delay from neuron j to i. Then the input current I for neuron i at time t is given by:I (t )=Si ,j j "#$F (4)where S i,j is the synaptic weight of the connection from neuron j to i and F is a scaling factor. F was set to 30 in all the experiments described here.The wiring regime was as follows (Fig. 1). Every excitatory neuron had 20 synaptic connections, of which 16 (80%) were to other excitatory neurons and 4 (20%) were to inhibitory neurons. Synaptic weights were randomly assigned, drawn from a uniform distribution over the interval [0,0.7] for excitatory connections and from a uniform distribution over the interval [-2,0] for inhibitory connections. Two experiments were carried out. In the first, the 800 excitatory neurons were organised into 8 clusters of 100, while in the second they were organised into 10 clusters of 80. Excitatory connections were established using a two-phase procedure reminiscent of the Watts-Strogatz method.FIG 1. Small-world network construction. The first phase of wiring (A) produces a set of separate but densely intra-connected clusters. In the second phase (B), a small subset of the connections established in the first phase is replaced with “long-range” inter-cluster connections.In the first phase, for every excitatory neuron in the network 16 connections were made to randomly chosen excitatory neurons within the same cluster. Conduction delays in the range 1ms to 20ms were assigned randomly to each connection. In the second phase, a rewiring decision was made for every excitatory connection established in the first phase. With probability p, an established intra-cluster connection was replaced with a connection to a randomly chosen neuron within a randomly chosen different cluster (preserving the original conduction delay). A method for constructing a very similar class of networks is described by Pan and Sinha [9], but their method does not use a separate rewiring phase.As with the Watts-Strogatz procedure, the present wiring regime ensures that various statistics are preserved across a population of randomly generated networks whatever the value of p, including the number of nodes, the number of connections, the mean synaptic weight averaged over the whole network, and the mean conduction delay averaged over the whole network. Note that if p = 1 a fully randomised network results, while if p = 0 the resulting network comprises eight disconnected sub-networks. The inhibitory neurons were also organised into eight clusters, one per excitatory cluster, and connections between excitatory and inhibitory neurons within corresponding clusters were established randomly in both directions. Connections to and from inhibitory neurons were unaffected by the rewiring phase.A series of 1000 trials were conducted: 500 with 8-cluster networks and 500 with 10-cluster networks. For each trial, the probability p was drawn from a uniform distributionover the interval [0,0.15] and a new network was generated using this value. The resulting network was then run for 60s of simulation time. In each run, a single neuron was forced to spike at t = 500ms. Since the neurons received no input current prior to 500ms, the network remained quiescent until then. But following the injection of this spike, a period of self-sustaining network activity ensued. In some runs this activity died out before t = 60s, but in many cases (depending on the value of p , as we shall see) it lasted for the entire duration of the run. Figure 2 shows a raster plot of all neuron firings during the last second of a representative 8-cluster trial.The small-world index of each network generated was computed. This is defined as follows. Consider a graph G graph with n nodes and k edges per node on average. The path length between any pair of nodes in G is the number of edges in the shortest path between those nodes, and G ’s mean path length ! "G is the path length averaged over every pair of nodes in G . The clustering coefficient of a node P in G is the fraction of theset of all possible edges between immediate neighbours of P that are actual edges, and theclustering coefficient "G of the whole graph G is the clustering coefficient averaged overFIG 2. Raster plot of the last 1000ms of a representative trial (number 21). Neurons numbered 1 to 800 are excitatory, and organised into 8 sequentially numbered clusters (1 to 100, 101 to 200, etc.). Neurons numbered above 800 are inhibitory.the set of all its nodes. A sparsely connected graph (where k << n) is said to be small-world if its mean path length is comparable to that of a randomly connected graph with the same n and k but its clustering coefficient is higher. This property can be quantified asthe small-world index!"Gof G [6], which is defined as!"G=#G/#rand$G/$randwhere !"randand!"randcan be approximated as k/n and ln(n)/ln(k) respectively [22].In addition to the small-world index, an estimate of the causal density of the interactions among the network’s eight clusters was computed for each trial [15, 16]. The concept of causal density is based on that of Granger-causality [3], which is a measure of the causal influence among the variables of a dynamical system. To grasp the idea of Granger-causality, consider a trio of time series X1(t), X2(t), and X3(t), and suppose X1(t)isdescribed by the following autoregressive model:X 1(t)=Ajj=1m"X1(t#j)+B j X2(t#j)+C j X3(t#j)+$ABC(t)where m(the model order) is the maximum observation lag, A, B, and C are vectors containing the coefficients of the model (indexed by observation lag), and "ABCis theprediction error. This can be compared with the following model of X1(t), in which theX2term is absent:X 1(t)=Ajj=1m"X1(t#j)+C j X3(t#j)+$AC(t)Now, X2 is said to Granger-cause X1if the variance of "ABCis significantly less than thevariance of "AC , that is to say if the inclusion of the X2term helps to predict X1.Assuming X1 to X3are covariance stationary, this significance can be determined usingan F-test. Note that for X2 to Granger-cause X1, it must exercise an influence over andabove that of X3. Clearly X2and X3can be treated symmetrically, and the extension toany number of variables is straightforward. The causal density of a system of variablesX 1 (X)nis then defined as "/n(n#1), where αis the number of pairs of variablesXi ,Xjsuch that XiGranger-causes Xj. In other words, causal density measures theproportion of all possible causal relations among system variables that is statistically significant.In each run, firing data was gathered for the network’s 800 excitatory neurons, resulting in an 800 by 59000 binary matrix, each element of which represents the occurrence or non-occurrence of a spiking event for the relevant neuron at the specified time point (the first 1000ms of each run was ignored). It would be infeasible to apply a causal density analysis directly to so much data. But knowing the large-scale topology of the network we can reduce it to a small set of time series, one per network cluster. In practice, each such time series was obtained by calculating the mean number of firings per neuron in the cluster per millisecond over a moving 50ms window sampled at 20ms intervals, yielding 8 or 10 time series (depending on the number of clusters) each of length 2950. For causal density analysis to be valid, the time series to which it is applied must be covariance stationary. This can be established using the Augmented Dickey-Fuller (ADF) test. A raw time series obtained by the above method invariably fails the ADF test. So first-order temporal differencing was deployed, generating a new set of 8 (resp. 10) time series of length 2950, in effect representing the change in mean firing rate over time. Since 100%of the differenced time series passed the ADF test in the 8-cluster experiment and 99.75% passed the test in the 10-cluster experiment, these were the subject of the causal density analysis, which was carried out using a model order of 10.The results for the 8-cluster experiment are summarised in Fig. 3. Causal density peaks at around 0.38, when the rewiring probability p is approximately 0.05 (Fig. 3A), and tails off for values of p greater than 0.05. Note that causal density is only assessed for runs that exhibit sustained activity for the full 59.5s following the introduction of the initial spike at 500ms. A run in which this is not achieved is deemed a “failure”. There were 265 successful runs out of 500 trials in the 8-cluster experiment. Causal density was notFIG. 3: The relationship between rewiring probability, causal density, neuralcomplexity, failure count, and small-world index for the 8-cluster experiment. See text for details.A BC Dcomputed for failed runs. The absence of data points close to the Y-axis in Fig. 3A indicates that networks generated with p less than 0.01 are very rarely capable of sustained activity for 60s. The leftmost column of the histogram in Fig. 3B confirms that although 30 networks were generated with p ≤0.01 they all produced failed runs. Moreover, as Fig. 3B shows, the proportion of networks capable of sustained activation decreases with p > 0.05. In other words, when p falls outside a certain narrow range, from approximately 0.01 to approximately 0.09, it typically generates networks that either fail or have low causal density. For comparison, Fig. 3C shows the contrasting results of computing an approximation to the “neural complexity” of the same data, using the information-theoretic formulation given in [21]. With hindsight (see below) it is no surprise that this measure fails to see significant complexity in runs with high causal density, because it is insensitive to integration or segregation that is smeared over time. Only when activity in the clusters begins to synchronise does it detect complexity, which is exactly when the dynamical complexity of the system is starting to tail off according to causal density.Fig. 3D suggests that networks with higher small-world indices (> 3.3) give rise to runs with greater causal density (> 0.25). (Although this trend is obscured by considerable trial-to-trial variation, it should be borne in mind that the number of data points is much larger for higher small-world indices because these yield fewer failed runs.) However, the small-world index for networks generated with p > 0.1 is still high (significantly greater than 1). Fig. 4 summarises the results for the 10-cluster experiment, which yielded 251 successful runs. As with the 8-cluster experiment, these show that causal density tails offas p increases, and that self-sustained activation is most likely to occur when pis within a narrow range (close to 0.04). In sum, to the extent that causal density is acceptable as a measure of dynamical complexity these findings support the conclusion that, for the class of networks under consideration, a sufficiently high small-world index promotes both self-sustained activation and complexity. However, they also indicate that networks that are small-world but that enjoy only modest small-world indices tend not to be capable of self-sustained complex behaviour.Some insight into the underlying reasons for these results can be gained by looking into the rhythmic behaviour of the networks. Visual inspection of the raster plots shows that the level of activitation within each cluster is highly rhythmic, waxing and waning at a frequency of approximately 4Hz (corresponding to the theta band in EEG terms). This is to be expected because, due to their dense connectivity, there is a tendency for activation to spread rapidly within a cluster, causing all its neurons to hyperpolarise together. So, within a given cluster, periods of intense activation tend to be followed by periods of totalFIG. 4: The relationship between rewiring probability, causal density, and failure count for the 10-cluster experiment. As with the 8-cluster experiment, causal density tails off as rewiring probability increases.quiescence while all the neurons recover in concert. But thanks to their connections to other clusters – the very connections that confer small-world topology on the network – there is always a significant number of incoming spikes during these quiescent periods which can reignite activity in the cluster when it has recovered. A similar phenomenon is reported by Roxin, et al. [14].Although theta-band activity is common to networks exhibiting both high and low causal density, a visual comparison of typical raster plots suggests a difference in their phase characteristics. In particular, one hallmark of networks with high causal density is the absence of a stable phase difference between the theta waves generated by each cluster, while clusters in networks with low causal density are far more likely to entrain, producing synchronous theta waves. A plausible explanation for this is that an excess of inter-cluster connections (produced with high values of p) leads to such strong coupling between clusters that the phenomenon of simultaneous hyperpolarisation extends across cluster boundaries. This causes the clusters to become entrained [4], making each cluster a good predictor for activity in every other cluster and bringing down the causal density accordingly. If this coupling is too strong, the entire network can become quiescent simultaneously, causing self-sustained activation to be extinguished entirely, a frequent occurrence with high values of p (Fig. 3B).It is possible to quantify the phenomenon in question by assessing the level of globalphase synchrony among the clusters. Let X1(t) and X2(t) be two scalar signals and let" 1(t)and "2(t)respectively denote their instantaeous phases according to the Hilberttransform. Then, followingRosenblum, et al . [13], an estimate of the phase synchrony between X 1(t ) and X 2(t ) is given by"=cos #(t )2+sin #(t )2wheref (t ) denotes the average of f over time, and "(t )=#1(t )$#2(t )()mod2%.The synchronisation index among a system of variablesX 1...X n may then be defined as the phase synchrony estimate Γ averaged over all pairs of distinct variables X i ,X j . As Figure 5 (left) illustrates for the 8-cluster experiment, phasesynchrony increases monotonically with rewiring probability, which accords with the above explanation. (Comparable results are reported by Masuda & Aihara [8] and Percha, et al . [11] for small-world networks of neurons with topologies different from that used here, and by Park, et al . [10] and Guan, et al . [4] for small-word networks of coupled oscillators with a topology similar to that used here.) Figure 5 (right) also shows, while phase synchrony is prevalent in all complete runs, phase synchrony indices above 0.4 (corresponding roughlyFIG. 5: The relationship between rewiring probability, synchronisation index, and causal density for the 8-cluster experiment. See text for details.with rewiring probabilities > 0.05) are inversely correlated with causal density (cf: Fig. 3A), which again accords with the above explanation.References1. D.S.Bassett and E.Bullmore, The Neuroscientist 12, 512 (2006).2.M.Girvan and M.E.J.Newman, Proc. Natl. Acad. Sci. USA 99, 7821 (2002).3. C.W.J.Granger, Econometrica 37, 424 (1969).4.S.Guan, X.Wang, i and i, Phys. Rev. E 77, 046211 (2008).5.P.Hagmann, L.Cammoun, X.Gigandet, R.Meuli, C.J.Honey, V.J.Wedeen andO.Sporns, PLoS Biology 6, e159 (2008).6.M.D.Humphries, K.Gurney and T.J.Prescott, Proc. Roy. Soc. B 273, 503 (2006).7. E.M.Izhikevich, IEEE Trans. Neural Networks 14, 1569 (2003).8.N.Masuda and K.Aihara, Biological Cybernetics 90, 302 (2004).9.R.K.Pan and S.Sinha, arXiv:0802.3671v1 [physics.bio-ph], 2008 (unpublished).10.K.Park, Y.-C. Lai , S.Gupte and J.-W.Kim, Chaos 16, 015105 (2006).11.B.Percha, R.Dzakpasu, M.Zochowski and J.Parent, Phys. Rev. E 72, 031909 (2005).12.H.Riecke, A.Roxin, S.Madruga and S.A.Solla, Chaos 17, 026110 (2007).13.M.Rosenblum, A.Pikovsky, J.Kurths, C.Schäfer and P.A.Tass, in Handbook ofBiological Physics, Vol. 4: Neuro-Informatics and Neuromodelling, edited by F.Moss and S.Gielen (Elsevier, 2001), Chapter 9, pp. 279–321.14.A.Roxin, H.Riecke and S.A.Solla, Phys. Rev. Lett. 92, 198101 (2004).15.A.K.Seth, Cognitive Neurodynamics 2, 49 (2008).16.A.K.Seth, E.M.Izhikevich, G.N.Reeke and G.M.Edelman, Proc. Natl. Acad. Sci. USA103, 10799 (2006).17.M.Shanahan, Consciousness and Cognition 17, 288 (2008).18.O.Sporns, G.Tononi and G.M.Edelman, Cerebral Cortex 10, 127 (2000).19.O.Sporns and J.D.Zwi, Neuroinformatics 2, 145 (2004).20.G.F.Striedter, Principles of Brain Evolution (Sinauer Associates, 2005).21.G.Tononi, G.M.Edelman and O.Sporns, Trends in Cognitive Sciences 2, 474 (1998).22.D.J.Watts and S.H.Strogatz, Nature 393, 440 (1998).23.Q.Wen and D.B.Chklovskii, PLoS Computational Biology 1, 0617 (2006).。

合集下载

Complex_Dynamical_Systems_Theory

Complex_Dynamical_Systems_Theory

Complex Dynamical Systems Theory This article was written by Professor Alicia Juarrero, author of Dynamics in action:intentional behavior as a complex system.Complex Dynamical Systems TheoryComplexity is a systemic property. Adaptive evolving systems like ethnic cliques or complex social situations such as “knife crimes” are best understood as dynamic networks of interactions and relationships, not mere aggregates of static entities that can by analyzed by separately identifying and enumerating them. By definition, relata do not exist in individual particles, only in their inter-relationships. In short, dynamic relations, not isolated agents, constitute the basis from which complex dynamical systems theory takes its start. Thus, instead of attempting to construct the identity and dynamics of a self-organizing network from the bottom up by identifying separate individuals and only afterwards grouping them into what the investigator hopes is the appropriate aggregate, complex systems theory proceeds by letting the dynamic patterns produced by the flows and processes involved identify the specific architecture in question. Because complex systems aredi ff erentiated into interlinked levels of organization – with no preferred level of granularity - the appropriate coarseness on which to ground a model is determined by the functional task of interest.Whether in the physical or social realms, if individuals are independent or even weakly interdependent no complex physical or social structure will emerge; connectivity and interaction are necessary conditions for the emergence of complexity. No closed system can spontaneously become di ff erentiated and show complex organization, form or structure. Stated di ff erently, complexity is the order that results from the interaction among multiple agents; while particles remain separate from each other, no increase in their number will ever produce organization (Brooks and Wiley 1988). In contrast to collections of isolated elements that generate Gaussian (normal) distributions that can be understood and modeled in the traditional manner, a complex system is identified by the signature “relations among components, whether static or dynamic, that constitute a composite unity as a unity of a particular kind” (Maturana 1980). The rich interactions between real complex adaptive systems and their environment also mean that because a given domain “is connected to other domains in various ways, the e ff ects of those changes might propagate through the system and out into other domains in the world, inducing changes of various degrees on all scales… . Those e ff ects might eventually travel back and lead to the disappearance of the original domain or transform its dynamics” (Chu et al. 2003).Therefore only complex dynamical systems theory and its related disciplines and tools - network theory, agent-based modeling - provide the appropriate prism through which interdependent systems such as social groups can be understood, and coherent, integrated policy recommended.BoundariesA complex dynamical system’s internal structure consists in the patterns that result from particular objects and the interactions among them. But unlike those systems characterized by linear processes that can be e ff ectively isolated from environmental influence, the external structure or boundary conditions of complex systems are as much as part of the complex system as the internal structure; the interactions between the components and the environment, that is, “the set of all [interactions not components of the system] that act or are acted on by components of [the system]” (Bunge 1979) provides the system with a causally e ff ective external structure. Although the environment of interest is thus not the total environment but the environment that a ff ects and is a ff ected by the thing in question, the feedback provides complex systems with a contextual embeddedness that makes the boundaries of complex systems typically fuzzy and di ffi cult to demarcate.From a complexity science point of view, therefore, ethnic cliques and situations such as “knife crime”, understood as dynamic “structures of process,” are not bounded by physical or geographic boundaries. In the case of ethnicity, for example, the dynamic structure of a group no doubt extends spatially into both the group’s diaspora a well as the local communities; insofar as ancient traditions, rites and rituals continue to inform and influence present practices, the dynamical system we identify as an ethnic group also extends back in time to pre-diaspora and tribal culture.The Causality of Complex SystemsThis deep contextual embeddedness of complex systems presents additionaldi ffi culties for researchers: feedback and interactions to/from embedding domains can spread causally (not as e ffi cient causes but as context-sensitive constraints), thereby expanding the domain of the system in question and propagating unforeseen side-e ff ects uncontrollably (Chu et al.). Due to the interactions that constitute them, complex adaptive systems show not only nonlinear e ff ects, but also what is often called causal spread (Wheeler and Clark 1999), a form of causalitydi ff erent from that of the more commonly understood e ffi cient causality.The connectivity and interaction required for complex systems to self-organize, and which provides them with their contextuality and causal e ffi cacy, are best understood in terms of context-sensitive constraints (Juarrero 1999) not classical billiard-ball-like (e ffi cient) causality. First order, context-dependent constraints such as nonlinear interactions like positive feedback loops and catalysts make individuals or particles strongly interdependent by altering their marginal probability. Feedback relations with the environment recalibrate the internal dynamics of complex systems to incoming signals. Doing so embeds the system in its contextual setting by e ff ectively importing the environment into the system’s very dynamical structure. Positive feedback is a temporal context-dependent constraint insofar as it incorporates the past into a system’s present structure. Because the presence of a catalyst changes the probability of a reaction’s occurrence, catalysts also function as contextual constraints insofar as they incorporate the environment into a system’s present structure. Thus individuals or organizations who play the role of social catalysts and serve as media for feedback loops are physical embodiments of bottom-up constraints that link other individuals and organizations together and embed –tightly link—their dynamic organization to its environment and its history such that the newly formed global structure is no longer independent of either.By embodying context-sensitive dependencies, feedback and catalysts are bottom-up constraints that render a system constrained by its own past experience and its environment. Complex dynamical systems thus embody the initial conditions under which they were created; their origin and trajectory constrains their future development and evolution. Because such exquisite sensitivity to initial conditions is one of the hallmarks of complex adaptive systems, these dynamical processes are also essentially historical; in Prigogine’s words, “they carry their history on their backs,” that is, their internal structure reflects their history. Accordingly, self-organizing networks are “path-dependent.” Any methodology that purports to understand a given complex system while at the same time ignoring or not fully understanding either its trajectory or the overall context in which it is embedded is bound to fail. The e ff ects of context-dependent constraints, therefore, are described by conditional, not marginal, probabilities. They are, in other words, functional constraints.Once closure of first-order context sensitive constraints occurs, the resulting global dynamics presents characteristics that aggregates or sums of individuals do not; in technical terms, context-sensitive constraints are enabling constraints insofar as they precipitate the emergence of a global dynamics with an expanded phase space. The dynamic whole has greater degrees of freedom than its components individually – a narrative can tell you more than a Q&A form can. Self-organizing networks described in stories are thus multi-level dynamical systems with emergent properties that are irreducible to their component particles. These characteristics will be ignored and missed if the analytic focus is limited solely to compartmentalized components studied in isolation from each other.Qua emergent wholes, complex systems function as the boundary conditions that actively influence the behavior of their components. Insofar as individuals – children or adults - envision themselves as caught up in a particular narrative structure, we will be able to foresee their constrained behavior. Top down, narratives act as limiting constraints that restrict the degrees of freedom of their components. Whereas from a traditional mechanistic, atomistic point of view such influence was impossible, complex dynamical systems theory allows us to understand such interlevel causal relationships – ubiquitous in social systems - in a scientifically respectable way. In complex adaptive systems, interactions among individuals weave together a story; and once a narrative coalesces in the minds of an individual, or a culture in turn, and as a global system, it actively influences the behavior of the components that make it up. Only complexity science theory provides the tools to understand this kind of bottom-up and top-down causation typical of the collective behavior of human organizations. When combined with narratives as Cognitive-Edge’s SenseMaker® allows, policy makers acquire an indispensible tool with which to map current social patterns and anticipate future trends. Without an appreciation of such global dynamics it is impossible to fully understand the inter-level organizational dynamics of social groups: interacting individuals create stories which then loop back down and alter the behavior of the very individuals that constitute them.Power LawsThe relationship between (on the one hand) the context-sensitive constraints that make complex self organization possible, and the power laws that describe such systems on the other has become clearer thanks to the research of e.g. Barabasi (2002, 2003). Since many complex systems give evidence of the same dynamics atwork on multiple levels of organization (i.e., they tend to be self-similar across levels), scalability is often a central element of complexity science. Through children’s narratives it is therefore possible to capture the dynamics of an overall ethnic or social group. Because power laws are frequently “indicative of correlated, cooperative phenomena between groups of interacting agents” (Cook et al. 2004), students of complex human systems recognize that in lieu of Gaussian statistics, linear regression models, normal distributions, etc., they must model their subject matter using the more unfamiliar tools of organizational dynamics, including Pareto distributions, fractal geometries, and the like. Since extreme cases and situations are much more important than average cases and situations to most students of the human sciences, managers, policy makers, analysts and social scientists ignore power laws (which show fat or long tails, infinite variance, unstable confidence intervals, etc.) at their own peril.Game TheoryApplying game theory to human complex systems, exploring rational choice strategies over time, and investigating the basis of social cooperation, are just a few examples of the increasing pervasiveness of the complexity approach. In each case, the situation is treated as an evolving dynamical system with global properties that emerge from the local interactions among the participants, and between the participants and the context in which they are embedded. Such simulation modeling can capture otherwise intractable nonlinear e ff ects and thereby reveal global patterns that would have been previously out of reach.Once the usefulness of simulation models became clear, the Asian Development Bank, for example, dropped its opposition to a centuries-old management practice when Lansing’s computer model of the complex Balinese irrigation system showed the functional role of traditional water temples bore a “close resemblance to computer simulations of optimal solutions” (Lansing 2000).AttractorsAttractors are typical patterns of dynamical, interdependent behaviors of limited dimensionality and carved out from a much larger space of possible patterns and dimensions. These global structural patterns, which emerge from interactions among the system’s components through phase space, can be characterized as emergent collectives. Social networks can be characterized and studied as attractors.Ergodic behavior patterns describe what are called a system’s attractors. Only two attractors were thought to exist: (1) The dynamics of a grandfather clock’s pendulum describe a point attractor that draws the bob to a single point in phase space regardless of its original position. Equilibrium models assume that all systems they describe are of this sort; traditional economic models were equilibrium models. Not all processes can be understood as near-equilibrium and drawn into a point attractor; ecological research revealed that predator-prey relationships described a di ff erent type of attractor, (2) a periodic attractor. Unlike phenomena characterized by point attractors, predator-prey distribution, for example, typically repeat regularly in a continuous, periodic loop. It was not until the last quarter of the twentieth century that a third type of attractor, so-called strange, chaotic or complex attractors, were discovered: patterns of behavior so convoluted that it is di ffi cult todiscern any order at all; complex human systems can often be characterized as complex attractors, of which social networks are one example.Complex attractors surprised scientists when they discovered that far from being chaotic in the old sense of the word, these complex systems are characterized by a high-dimensional degree of order. Never exactly repeating, the trajectories they trace nevertheless stay within certain bounds. Far from being chaotic in the old sense of the term, these complex behavior patterns provide evidence of highly complex, context-dependent dynamic forms of organization.Attractor LandscapesIn the 1930s biologist Sewall Wright (1932) developed a model of fitness landscapes intended to capture the processes natural selection by visualizing the “switch and trigger mechanisms” that precipitate a change in a system’s evolutionary trajectory. More recently, thanks to the development of computer simulation models, the dependencies and constraints embodied by attractors can also be visualized as three dimensional adaptive landscapes depicting a series of changes in a system’s relative stability and instability over time. The increased probability that a system will occupy a particular state can be represented visually as a landscape’s wells, dips or valleys that embody attractor states and behaviors; the deeper the valley the greater the propensity of its being visited and the stronger the entrainment its attractor represents. In contrast sharp peaks are saddle points representing states and behaviors from which the system shies away. These landscape features capture the impact of context-sensitive constraints over time. The set of all states that end up in a particular attractor constitutes the attractor basin; di ff erent basins are separated from each other by basin boundaries or separatrices. A system’s identity at a particular point in time captures the signature probability distribution of its dynamics – its unique adaptive landscape, so to speak. The most useful image of complex systems is its phase space portrait: its state space carved up into basins of attraction and changing over time.Since all social phenomena are complex systems it becomes extremely important for makers of social policy to be able to map these convoluted relationships as accurately as possible. Doing so allows policy makers to map a situation’s relative volatility, as well as to explore which changes to which parameters will make the situation more or less stable. Complex dynamical mapping of this sort thus provides an invaluable visual aid in phase shift prediction. Although by their very naturecomplex systems resist precise predictability,dynamical landscapes and the mathematicalsoftware that create these visual aids alsoshow decision-makers the range of “adjacentpossible” successor states an unstablesituation is likely to tip into.Dynamic landscapes depicting a series ofchanges of relative stability and instabilityover time provide a very useful way ofvisualizing the contextual and historicalconstraints embodied in the convolutedbehavior patterns described by strangeattractors. By tweaking the various parametersand filters that produce the landscapes,dynamical mapping with SenseMaker®software can provide decision-makers, forexample, with evidence of the presence of “astable pattern overall, except for those groupsthat rank high on the combination of two scales, “retributive justice” and “anger.” These dynamical landscapes also provide evidence of probable and improbable “successor states” to a given situation, information that can be invaluable, for example, for designing a particular governmental advertisement campaigns on crime prevention etc. Dynamical mapping can prove that the intended network is possible, that it can be built; it can also providing guidance on the most appropriate criteria with which to design the most e ff ective network – or disrupt a noxious one. For example, one city’s current landscape might show that it is possible to build a particular network that assists community leaders in precipitating a particular desirable phase change with respect to criminal activity– or, conversely, it can provide decision makers with information that aids and enhances the status quo. Because complex dynamical systems are uniquely individuated, dynamical systems mapping can also provide decision makers with information about whether or not the same advertisement campaign will be as e ff ective in a di ff erent city, or a di ff erent country.If a system could access every alternative with the same frequency as every other – that is, randomly – its landscape would be smooth and flat, portraying an object or a situation with no propensities or dispositions, that is, with no attractors. In contrast, the increased probability that a real system will occupy a particular state can be represented as wells – dips or valleys in a landscape – that embody attractor states and behaviors that the system is more likely to occupy. The deeper the valley the greater the propensity of being visited and the stronger the entrainment of its attractor. Dynamic landscapes thus provide governmental leaders with information about how entrenched a set of attitudes or behavior patterns are, and how best to go about preserving or changing them.Topologically, ridges separating basins of attraction are called separatrices or repellers. Sharp peaks are saddle points representing states and behaviors from which the system shies away and in all likelihood will not access; the probability of their occurrence is low or nonexistent. But if a decision-maker discovers that a system is perched on a saddle point, he can rest assured that it won’t remain in that condition very long. The height of the saddle point separating one attractor from another thus also represents the unlikelihood that the system will switch to another attractor given its history, current dynamics, and the environment. Landscape valleys thus provide decision-makers with a very good indication of whether or not a systemis locked-in to that particular condition, and what the likely “adjacent possibles” might be. The steeper the attractor’s separatrix walls, the greater the improbability of the system’s making the transition. On the other hand, the deeper the valley, the stronger the attractor’s pull, and so the stronger the perturbation that would be needed to dislodge the system from that behavior pattern. Similarly, the broader the floor of a valley the greater the variability in states and behaviors that the attractor allows under its control; conversely, the narrower the valley the more specific the attractor, that is, the fewer the states and behaviors it countenances.Complex systems theory tells us that a landscape’s valleys and peaks are neither static givens nor external control mechanisms through which we can force change. They are not determinants operating as Newtonian forces. Instead they represent constrained pathways that have been constructed and continue to be modified as a result of persistent interactions between the dynamical system and its environment. Landscapes that incorporate dynamics also provide decision makers with information about the likely direction of change, and of the critical parameters that can influence the direction of that change.Co-evolutionPredator-prey relationships taught us that the dynamical landscape of a complex system, to continue with the topographical metaphor, is not fixed. A predator will evolve better eyesight to see its prey, but the prey will evolve a disguise, negating the eyesight advantage. Thus “the landscape peak the predator attempted to climb has moved from under its feet, the fitness peak has shifted, the landscape has deformed due to the changes in the prey. This “coevolution” means that the fitness landscape seen by one creature is a dynamic, ever changing map dependent upon the actions of everything else in its surroundings. This is true for occupants of an ecosystem or a social group. It is a highly non-linear, closely coupled system - attractors that vary in both shape and position over time” (Lucas). Co-evolution with their natural and social environment is even more so of human systems than it is of animals. In the case of human beings we are always referring, therefore, to complex adaptive systems.In other words, since fitness is a relative term (relative to an environmental niche), changes in a (natural, social) niche alter the fitness of the individuals and species within it; in turn, changes in the relative distribution of types of individuals and species within a niche will alter the characteristics of the niche. Thus complex adaptive systems are best characterized as adapting and co-evolving with their environment.Stability versus Resilience: The Importance of Micro-diversityComplex dynamical systems theory explains the di ff erence between stability and resilience. A stable system fluctuates minimally outside its stable attractor, to which it quickly returns when perturbed. Stable systems are typically brittle; they disintegrate if highly stressed. Resilient systems, on the other hand, might fluctuate wildly but have the capacity to modify their structure so as to adapt and evolve. Resilient, robust systems are also called meta-stable. Co-evolution selects for resilience, not stability.Complex adaptive systems are typically resilient. And notoriously robust to random perturbations – but exquisitely vulnerable to targeted interventions, as we will see below.Understanding what causes resilience or robustness is a central issue for analysts and policy makers. For purposes of Cultural Mapping it is particularly important to understand which specific features of the dynamical relationships that make up the knife crime statistics in the city of XYZ make the situation robust or resilient; it is important, that is, to identify the system’s dynamics that allow likely participants to adapt in response to either their own dynamics or perturbations from the outside, and thereby to evolve and persist as a network, despite the removal or incarceration of many of their members. This understanding also points to avenues for intervention by the appropriate authorities. Although still a young science, complex adaptive systems theory has begun to make inroads into understanding (1) the conditions that allow these structures evolve over time in response both to their own internal dynamics and in interaction with the environment; (2) the conditions that facilitate robustness and resilience; and (3) the most e ff ective points of intervention. Jackson & Watts (2002) note that in a network context, path resistance or network resilience is equivalent to “how many errors or mutations are needed to get from some given network to an improving path leading to another network.” Peter Allen defines microdiversity more broadly than simply errors or mutations, as “a measure of the number of qualitatively di ff erent types of entity present corresponding to individuals with di ff erent attributes.” (Garnsey & McGlade 2006, 23). Chu et al. (2003) call such systemic di ff erentiation “inhomogeneity”; they too consider it a hallmark of complexity, as do Carlson & Doyle (2002). In an important article that echoes this general point, the U.S. Naval Academy’s Robert Artigiani demonstrates through two military examples that the best way to deal with unpredictable complex systems is by organizing the system so it is maximally adaptive – when leadership cannot solve the problem in advance because no one knows what the problems will be, it is important to build systems that can solve the problem for themselves. Microdiversity in the sense of internal di ff erentiation is one way to do just that. Allen, who worked extensively with Nobel Laureate Ilya Prigogine in Brussels during the earliest years of this science, has also extensively studied how micro-diversity within a natural or social system drives the qualitative changes that occur in these systems and structures over time. Allen demonstrates that if a particular variation increases an organism’s fitness, natural selection will favor that variation; following the landscape metaphor, evolutionary change – i.e., increased adaptation to the environment - is tantamount to hill-climbing.Allen’s early experiments demonstrated that hill-climbing occurs “as a result of processes of ‘di ff usion’ in character space. Using di ff usion models, Allen’s research also establishes that it is micro-diversity or internal di ff erentiation that confers resilience. Further experiments conducted by Allen and his team at Cranfield University (UK) subsequently confirmed that successful “evolution will be driven by the amount of diversity generation to which it leads. Evolution selects for an appropriate capacity to evolve [more exploration and innovation in novel situations; less exploration in established conditions], and this will be governed by the balance between the costs of experimental ‘failures’… and the improved performance capabilities discovered by the exploration.” The conclusion Allen draws from the research is that “organizations or individuals that can adapt and transform themselves, do so as a result of the generation of micro-diversity and the interactions with micro-contextualities” (emphasis added). The system’s complex regulatory feedback and dynamics also stop cascading failures and enable thesystem to survive (Carlson & Doyle 2002). Incorporating narrative research into dynamical landscapes is a unique and powerful tool to understand and influence social systems.Understanding how information and influence disseminate throughout a social group is a key component that cuts across storylines and issues. To the extent thatdi ff usion processes identify a property that is the inverse of robustness (both pertain to the way influence or information disseminates through, or is blocked, within particular communities by components that are di ff erent – by social mavericks, ine ff ect), identifying features in a social landscape that promote desirable robustness and resilience is a central task of any decision-maker’s mission.Fail-Safe versus Safe-FailThinkers in the field of public policy have traditionally counseled what might be called a fail-safe strategy. From Plato to Marx, the goal was always to design forms of social organization that, because they were ideal, would remain forever in equilibrium. The traditional goal of public policy makers, in other words, has been stability, the minimization of fluctuations. In stark contrast to this approach, ecologist C. S. Holling argues convincingly that if the notion of resilience applies to society at all, it counsels instead a safe-fail strategy that assumes from the outset that failures will occur despite the best-laid plans. A safe-fail strategy is one “that optimizes a cost of failure and even assures that there are periodic ‘minifailures’ to prevent evolution of inflexibility” (Holling 1976; Juarrero-Roque 1991). It is clear that Allen’s thesis - that evolution evolves to maximize evolvability - is another way of making the same point. Social policy should pursue a goal of resilience, not stability. As this new science develops, valuable lessons are derived from studying dynamical landscapes and the networks described in cluster graphs for the way weak ties, high betweenness links, micro-diversity, and other similar features contribute to the robustness and resilience of complex adaptive networks. In turn, these insights are can inform social organization management.。

研究生英语阅读教程答案-重庆大学出版社Unit3Technology

研究生英语阅读教程答案-重庆大学出版社Unit3Technology

Unit 3 Technology课后练习答案Passage ARethinking What Leads the Way: Science, or New Technology?KEYS TO EXERCISESI. Reading comprehension1. D2. B3. A4. A5. B6. B7. B8. A9. D 10. DII. Vocabulary1. A2. A3. B4. B5. B6. C7. D8. B9. C 10. A11. D 12. A 13.D 14.A 15.A 16.C 17.A 18. B 19. A 20. AIII. Word bank1.cautious2. discrete3. arrive at4. prognostication5. reassessment6. inspiration7. endow8. automated9. elusive 10. theoreticalIV. Cloze1. A2. B3. D.4. D5. B6. A7. B8. A9. C 10. B1. A 12. B 13. C 14. D 15. CV. Translation1.Happiness is an illusion for some people and elusive to others, but for families who get theirrecipes right, happiness is an all-pervasive emotion that follows them wherever they go and whatever they do.2.Psychologists have also found that if you sleep after thinking about your problems there is abetter chance that you arrive at a solution the next day.3.Setbacks can help you accumulate experience, and experience can, in return, enrich your mind.4.His talk was evocative of the bygone days.5.In this world, what is it to set apart people who love each other?6.What can't be denied is that technology, no matter its faults, makes life a whole lot easier. Itallows us to communicate with more people in less time; it can make conversation simple—no small talk required. It can be therapeutic: robots are now used to help care for the elderly.But it can also be seductive, providing more stimulation than our natural lives. But is anyone of those feelings on par with the kind we feel when engaged in real, face-to-face intimacy?Online, you can ignore others' feelings. In a text message, you can avoid eye contact. That doesn't spell disaster, but it does mean we might want to start thinking about the way we want to live.VI. Discussion1.How does technology influence our life?2.How do you think about the issue of food safety?课文参考译文重新考量孰先孰后：科学还是技术？设想一下如果没有显微镜、望远镜以及像DNA自动测序这样更为先进的新进技术的话，科学会是什么状态？这样的科学仍然植根于人类的感知和推理。

高考英语(北师大)新探究大一轮精练(含新题)：Unit 11 知能演练 轻松闯关 Word含解析

高考英语(北师大)新探究大一轮精练(含新题)：Unit 11 知能演练 轻松闯关 Word含解析

课时练1阅读理解提速练[学生用书P283(单独成册)]Ⅰ阅读理解A(2019·湖北重点中学模拟)Don’t have plenty of time for reading？If you are interested in non-fiction books，here are good choices for you.A Room of One’s O w nThis essay by English writer Virginia Woolf is based on her several lectures given to two women’s colleges at Cambridge University in 1928. In it，Woolf describes that it’s circumstance not talent alone that allows men to be more successful at writing. Women，in other words，spend so much time cooking，cleaning，and tending to their children that they have no time left for art. To write well，therefore，a woman must have “a room of her own”. While on its surface，this essay appears to be only about writing，it is actually about wealth and class，freedom and imprisonment，and the power struggle between sexes.The Art of WarWritten by ancient Chinese military strategist Sun Zi，The Art of War is widely considered to be one of the best books about military strategy(军事战略) in human history. Consisting of 13 chapters，each dealing with a separate aspect about how to fight a war，the book has been translated into many languages and has thousands of editions. For centuries，it has been used to train military leaders for its detailed study of military strategy and effective leadership.Letter to My DaughterThis book of essays and poems by Maya Angelou，a respectable American poet，is written for “the daughter she neve r had”—the millions of women，both young and old，who she considers to be her “family”. From the viewpoint of a caring，older relative，this book contains lessons selected from her own life experiences，including the birth of her only child，a son，as well as the development and loss of friendship.A Brief History of TimeIf you’re short on time，then why not read about，well，the creation of time？This book，first published in 1998 from brilliant scientist and mathematician Stephen Hawking，explores mind-bending questions about the creation of the universe，including if and when it will end，and if so，how. Despite its heavy subject matter，Hawking addresses these questions in a way that’s easy to understand，even for those who know little about physics.【解题导语】本文主要介绍了四本纪实类文学作品。

2017年大学英语六级阅读考前押题(1)附答案

2017年大学英语六级阅读考前押题(1)附答案

2017年大学英语六级阅读考前押题(1)附答案Questions 61 to 65 are based on the following passage.Small increases in temperature found to add power to storms in the Atlantic.Hurricanes that form in the Atlantic Ocean are expected to gain considerable strength asthe global temperature continues to rise, a new study has found.Using modeling data focused on the conditions in which hurricanes form, a group ofinternational researchers based at Beijing Normal University found that for every 1.8°F ( 1℃)rise of the Earth's temperature, the number of hurricanes in the Atlantic that are as strong orstronger than Hurricane Katrina will increase twofold to sevenfold.Hurricane strength is directly related to the heat of the water where the storm forms. Morewater vapor in the air from evaporating ocean water adds fuel to hurricanes that build strengthand head toward land.Hurricane Katrina is widely considered the measure for a destructive storm, holding themaximum Category 5 designation for a full 24 hours in late August 2005. It lost strength as itpassed over the Florida peninsula,but gained destructive power fight before colliding withNew Orleans, killing more than 200 people and causing $ 80 billion in damage.The study points to a gradual increase of Katrina-like events. The warming experiencedover the 20th century doubled the number of such debilitating(将人类摧垮的)storms. But theongoing warming of the planet into the 21st century could increase the frequency of theworst kinds of storms by 700 percent, threatening coastlines along the Atlantic Ocean withmuitiple Category 5 storms every year."Our results support the idea that changes in regional sea surface temperatures is theprimary cause of hurricane variability," said Aslak Girnstead, a researcher with the Center forIce and Climate at the University of Copenhagen. The large impact of smallsea-surfacetemperature increases was more than Girustead and his colleagues had anticipated. Theentire study was published in the Proceedings of the National Academy of Sciences.Global temperatures have steadily increased, making the past decade the warmest onrecord. Earlier this year, climate researchers reported that the Earth's temperatures have risenfaster in the last century than at any point since the last ice age, 11,300 years ago. Theprimary cause, a couseusus of scientists has said, is the rising emissions of greenhousegases like carbon dioxide and methane.Past hurricanes have supported the study's finding that global temperature rise is linkedto more destructive storms. According to the National Center for Atmospheric Research, whilethe frequency of storms doesn't appear to have increased, the percentage of strong ones hasrisen sharply over the past few decades. The trend may be similar further back in time, butcomprehensive hurricane data doesn't exist.61. According to the team of international researchers based at Beijing Normal University,the rise of the Earth's temperature is likely to causeA.the coming of ice ageC.more Katrina-like or worse hurricanesB.less intense hurricanesD.more greenhouse gases in the atmosphere62. The ocean water in the region where the storm formsA.is heating the hurricanesB.evaporates and becomes fuelC.heads toward landD.turns into water vapor that makes hurricanes stronger63. Which of the following statement is TRUE about Hurricane Katrina?A.It did not lose its strength as it moved.B.It claimed over 200 people's lives.C.It caused 80 billion dollars loss for Florida peninsula.D.It lasted for full 24 hours.64. What result can regional sea surface temperature changes produce?A.Hurricane changes.C.Global warming.B.Increasing greenhouse gas emissions.D.Destructive hurricanes.65. It can be inferred from the passage thatA.there is no link between greenhouse gas emissions and destructive stormsB.reduction of greenhouse gas emissions may reduce destructive stormsC.the higher percentage of strong ones rose as more hurricanes appearedD.past records on hurricanes included everything needed参考答案61.C)。