处在临界值上的大脑

2015-09-30 约 2817 字预计阅读 6 分钟

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本文作者为傅渥成《写在物理边上》作者

本文内容基于（Chialvo, D. R. (2010). Emergent complex neural dynamics. Nature physics,6(10), 744-750. 或

http://arxiv.org/abs/1010.2530）

什么是生命的临界状态

所谓临界状态，直观地来理解，就是指一个系统既具有相当稳定性，但与此同时又能具有适应环境的特性。临界点不是水处在99度时的状态，而是类似沙堆再加一粒沙子就要倒塌的状态。具体的说，“临界性”是指复杂系统不像通常以为的那样遵循一种平缓的、渐进的演化方式，而是在不平衡的状态运行，临近一个雪崩式的巨大不平衡以改变原有的运行方式、从而进入到新的不平衡运行状态的性质。这种临界性或者说市场从一种状态到另一种状态的改变，并不是由人们通常以为的外在因素的干扰，而实际上是系统内部（如大脑神经元间）各种力量相互作用的结果，也就是它是系统内部的（自组织），而不是系统外部的（所有外部的因素都要先转化为内部因素，从而再影响到整个系统）。这样的系统，通常有下面一些特性：关联长度非常长，（例如位于左耳的一个神经元仅仅通过几个连接就能与位于右耳处的神经元“通信”）系统的弛豫时间也会变得发散（不确定需要多少时间由暂态趋于某种稳定态），同时，描述该系统的多个物理量之间可能存在许多标度关系(相比与无标度的幂率关系）。

为什么要研究大脑中的临界性

A better understanding of these critical dynamics could shed light on what happens when the brain malfunctions. Self-organized criticality also holds promise as a unifying theoretical framework. Most of the current models in neuroscience apply only to single experiments; to replicate the results from other experiments, scientists must change the parameters — tune the system — or use a different model entirely. Self-organized criticality providing a broader, more fundamental theory for neuroscientists, like those found in physics.

生命的临界性是怎样起源的？

下面所说的几种现象可能可以建立起生命系统与临界性之间的一些关联：

生命也是动力系统，而如果作为动力系统，系统始终保持在分岔点附近进行演化，这就有可能形成临界性。
在集体行为中有可能形成这种临界性。
生命系统中的缓慢弛豫的动力学也有可能与临界性相关。
生命体系中的大偏差和多样性可能与临界性相关。
生命系统同时具有稳定性与可塑性，即适应性有可能与这种临界性有关。

以上回答来自于东京大学复杂生命系统研究中心的主任金子邦彦

在 Kunihiko 的回答的基础上，还有一点值得补充的就是，因为生命本身就是从自然中演化出来的，而我们的自然本身也是临界的（地震、太阳耀斑等现象）。当然，演化在生命形成的历程中起到了重要的作用，但这种临界性的形成有些与演化相关，有些只是因为我们同样也只是自然的一部分。

有什么证据支持大脑处于临界状态

大脑中神经的firing符合指数分步 Most notably, the smaller avalanches were more frequent than the larger ones, following the expected power law distribution. That is, if there were 100 small avalanches involving only 10 grains during a given time frame, there would be 10 avalanches involving 100 grains in the same period, but only a single large avalanche involving 1,000 grains.

该图中，大大小小的神经firing在log处理后分布在2/3的直线上Size distribution of neuronal avalanches in mature cortical cultured networks follows a p ower law with an exp onent close to 3/2 (dashed line) and exhibits finite size scaling. The relative probability of observing an avalanche covering a given numb er of electro des is shown for three sets of grid sizes

为什么我们需要神经元网络处于临界状态

There can be no phase transitions without a critical point, and without

transitions, a complex system — like Bak’s sand pile, or the brain — cannot adapt. That is why avalanches only show up at criticality, a “sweet

spot” where a system is perfectly balanced between order and disorder,

according to Plenz. They typically occur when the brain is in its normal resting state. Avalanches are a mechanism by which a complex system

avoids becoming trapped, or “phase-locked,” in one of two extreme cases. At one extreme, there is too much order, such as during an epileptic

seizure; the interactions among elements are too strong and rigid, so

the system cannot adapt to changing conditions. At the other, there is

too much disorder; the neurons aren’t communicating as much, or aren’t as broadly interconnected throughout the brain, so information

can’t spread as efficiently and, once again, the system is unable to

adapt. A complex system that hovers between “boring randomness and boring regularity” is surprisingly stable overall, If you spark avalanches all the time, you’ve used up all the fuel, so to speak, and so there is no opportunity for large avalanches.

处于临界状态意味着什么？

The generality of the scenario of ferromagneticparamagnetic phase transition is used, without implying that the brain would

reach criticality in this way. As an iron magnet is heated, the magnetization decreases until it reaches zero beyond a critical temperature Tc. Individual spins orientations are, at high temperatures, changing continuously in small groups. As a

consequence, the mean magnetization, expressing the collective behavior, vanishes. At low temperature the system

will be very ordered exhibiting large domains of equally oriented spins, a state with negligible variability over time. In between these two homogeneous states, at the critical temperature Tc, the system exhibits very different properties both in time and space. The temporal fluctuations of the magnetization are known to be scale invariant. Similarly, the spatial distribution of correlated spins show long-range (power law) correlations. It is only close enough to Tc that large correlated structures (up to the size of the system) emerge, even though interactions are with nearest neighbor elements. In addition, the largest fluctuations in the magnetization are observed at Tc. At this point the system is at the highest susceptibility, a single spin perturbation has a small but finite chance to start an avalanche that reshapes the entire systems state, something unthinkable on a non-critical state. Many of these dynamical properties, once properly translated to neural terms, exhibit striking analogies to brain dynamics. Neuro-modulators, which are known to alter brain states acting globally over nonspecific targets, could be thought as control parameters, as is temperature in this case.

我们的大脑为何会是处在临界状态的？

It is self-evident that the brains we see today are those that inherited an edge useful to survive. In light of this, how consistent with Darwinian constraints could it be to suggest that the brain should evolve to be near a critical point? The answer, in short, is that brains should be critical because the world in which they must survive is to some degree critical as well. Let us see the alternatives: in a subcritical world, everything would be simple and uniform and there would be nothing to learn; a brain would be completely superfluous. At the other extreme, in a supercritical world, everything would be changing continuously; under these circumstances there would not be sufficient regularity to make learning possible or valuable. Thus, brains are only needed to navigate a complex, critical world, where surprising events still have a finite chance of occurring. In other words, animals need a brain because the world is critical. Furthermore, a brain not only has to remember, but also has to forget and adapt. In a subcritical brain, memories would be frozen. In a supercritical brain, patterns change continuously so no long-term memory would be possible. To be highly susceptible, the brain itself has to be in an in-between, critical state.

Which generic features of systems at criticality should be expected in brain experiments?

1. At relatively large scale: cortical long-range correlations in space and time, correlation length divergence; near-zero magnetization or, equivalently, the presence of anticorrelated cortical states.

2. At relatively small scale: cortical circuits exhibit neuronal avalanches, cascades of activity obeying inverse-power-law statistics as well as long-range correlations.

3. At behavioural level: adaptive human behaviour should be bursty, seeming unstable, as it is always at the ‘edge of failure’. Life-long learning continuously ‘raises the bar’ to more challenging tasks, making performance critical as well.

处于临界态，意味着大脑中的神经网络的连接不应该是随机的。

下图来自论文

The non-random brain: efficiency, economy, and complex dynamics (2011) by Olaf Sporns

这幅图表明我们的大脑应该如B中的第三幅图那样。下面是图后的文字解释。

The initial population of graphs in generation 1 consisted of 10 randomized graphs similar to the ones shown in Figure 3B, with 47 nodes and 505 edges. Simple linear dynamics (Galán, 2008) was run on these graphs and the graph generating the highest neural complexity (Tononi et al., 1994) was selected and copied forward to the next generation, as described in Sporns et al. (2000). Then, small random“mutations” were introduced in the graph’s “offspring” and the process of selecting for complex dynamics was continued for a total of 50,000 generations. (A) Plots show the increase in complexity and a parallel increase in modularity. (B) Examples of graphs obtained at the end of the simulations exhibit non-random topologies, including high modularity and hub nodes.

具有Non-random的特性，使我们的大脑能时刻处在临界态

Modern circuit mapping and neural recording studies unequivocally

show that the brain is not a random network. Instead, at different levels of scale, network studies have identified a number of specific

non-random structural attributes, particularly the existence of network

communities interlinked by hub regions. The modular small world of

brain networks simultaneously promotes their economy and efficiency, by enabling their physical realization at low cost of wiring volume and metabolic energy, while also allowing efficient information flow.

Non-random structure leads to the emergence of complex dynamics,

generating a diverse repertoire of brain states that are differentially

engaged during ongoing neural activity as well as in response to

stimulation and task demands.

补充一点，作者在这篇文章中还说明 “some evidence suggests that degraded functional performance of brain networks may be the outcome of a process of randomization affecting their nodes and edges.”

如果您对本文所介绍的一些内容感兴趣，除了前面提到的论文之外，还欢迎您阅读下面链接中的文章。这篇文章介绍了生命系统中「临界性」概念的提出以及整个的历史：https://www.quantamagazine.org/20140403-a-fundamental-theory-to-model-the-mind/ ；这篇文章中介绍到了 Bak 的生平，而 Bak 本人的著作《大自然如何工作》也是非常值得一读的作品，本公众号曾推出三篇关于这本书的书评，长按以下的二维码，你可以直接跳转到之前的文章中。

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自然的启示