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'm = 1 retrieves the linear case. Figure 6.25 explains the concept of a nonlinear response.,When the sum of all trend-following behaviors is expressed in a non- linear form so that the net order size is proportional to a power of the difference between the logarithm of the price today and the logarithm of the price yesterday with an exponent larger than 1, by the same reasoning as in the technical inset entitled “Intuitive explanation of the creation of a inite-time singularity at tc ” in chapter 5, the price exhibits a inite-time'
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m=1检索线性情况。图6.25解释了非线性响应的概念。,当所有趋势跟踪行为的总和以非线性形式表示，使得净订单大小与今天价格的对数和昨天价格的对数之间的差的幂成比例，且指数大于1时，根据与第5章题为“在tc处创建初始时间奇点的直观解释”的技术插图中相同的推理，价格显示了初始时间。
'Trend following (in various elaborated forms) was (and probably still is) one of the major strategies used by so-called technical analysts (see [6] for a review and references therein). In its simplest form, trend following amounts to taking the net order size as proportional to the past trend, that is, to the difference between the logarithm of the price today and the logarithm of the price yesterday. Trend-following strategies thus exert a positive feedback on prices, since previous price increases (decreases) lead to buy (sell) orders, thus enhancing the previous trend. Taken alone, this implies that the difference in the logarithm of the price between tomorrow and today is proportional to the logarithm of the price between today and yesterday. This simple relationship expresses the existence of a constant growth rate, leading to an exponential growth of the logarithm of the price. This means that the price increases as the exponential of the exponential of time.'
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趋势跟踪（以各种详细形式）是（可能仍然是）所谓的技术分析师使用的主要策略之一（参见[6]中的回顾和参考资料）。在最简单的形式中，趋势跟踪相当于将净订单规模与过去的趋势成比例，即今天价格的对数与昨天价格的对数之差。因此，趋势跟踪策略对价格产生正反馈，因为先前的价格上涨（下跌）导致买入（卖出）订单，从而增强了先前的趋势。单独来看，这意味着明天和今天的价格对数之差与今天和昨天的价格对数成正比。这个简单的关系表示存在一个恒定的增长率，导致价格对数的指数增长。这意味着价格随着时间的指数而增长。。
'else at an even higher price in some future. As an illustration, it has been reported [142] that Henry Ford was taking the elevator to his penthouse one day in 1929, and the operator said, “Mr. Ford, a friend of mine who knows a lot about stocks recommended that I buy shares in X, Y, and Z. You are a person with a lot of money. You should seize this opportunity.” Ford thanked him, and as soon as he got into his penthouse, he called his broker, and told him to sell everything. He explained afterwards: “If the elevator operator recommends buying, you should have sold long ago.” More generally, this refers to the following cascade [309]: New demographic, technological, or economic developments prompt sponta- neous innovation in inancial markets and the irst wave of investors and innovators become wealthy. Then, imitators arrive and overdo the new techniques. In the ensuing crises, latecomers lose big before regulators and academics put out the ires.'
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否则在未来的某个时候，价格会更高。举个例子，据报道[142]，1929年的一天，亨利·福特乘电梯去他的顶楼，接线员说，“我的一个朋友福特先生非常了解股票，他建议我买X、Y和Z的股票。你是个有钱人。你应该抓住这个机会。”福特感谢他，他一走进顶楼，他打电话给经纪人，让他把所有东西都卖掉。他后来解释说：“如果电梯运营商建议购买，你早就应该卖出了。”更一般地说，这指的是以下一连串的情况[309]：新的人口、技术或经济发展促进了金融市场的自发创新，第一批投资者和创新者变得富有。然后，模仿者到来并过度使用新技术。在随后的危机中，后来者在监管者和学者发出ires之前损失惨重。。
'Consider a network of agents positioned at the nodes of the hierarchical diamond lattice shown in Figure 6.2 and interacting with their nearest neighbors through the links in a noisy imitative fashion according to expression (6) on page 102. We recall that this expression (6) embodies the competition between the ordering effect of imitation and the dis- ordering forces of idiosyncratic signals modeled as random noise. This network as well as different extensions turns out to be exactly solvable [106, 9]. The extensions of the network shown in Figure 6.2 comprise networks constructed by substituting any link of a given generation by a set of q branches, each containing a series of r bonds. The construction of Figure 6.2 corresponds to q = r = 2.Erdös number is 15, while the average value is about 4.7 [179, 33].'
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考虑一个位于图6.2所示分层菱形晶格节点处的代理网络，并根据第102页的表达式（6），通过链路与它们的最近邻居进行交互。我们记得，这个表达式（6）体现了模仿的有序效应和建模为随机噪声的特殊信号的无序力之间的竞争。这个网络以及不同的扩展证明是完全可解的[106，9]。图6.2所示的网络扩展包括通过将给定一代的任何链路替换为一组q分支构成的网络，每个分支包含一系列r键。图6.2的结构对应于q=r=2。埃尔德数为15，平均值约为4.7[179，33]。。