Understanding the key properties of complex systems can help us clarify and deal with many new and existing global challenges, from pandemics to poverty . . . A recent study in Nature Physics found transitions to orderly states such as schooling in fish (all fish swimming in the same direction), can be caused, paradoxically, by randomness, or ‘noise’ feeding back on itself. That is, a misalignment among the fish causes further misalignment, eventually inducing a transition to schooling. Most of us wouldn’t guess that noise can produce predictable behaviour. The result invites us to consider how technology such as contact-tracing apps, although informing us locally, might negatively impact our collective movement. If each of us changes our behaviour to avoid the infected, we might generate a collective pattern we had aimed to avoid higher levels of interaction between the infected and susceptible, or high levels of interaction among the asymptomatic.
Complex systems also suffer from a special vulnerability to events that don’t follow a normal distribution or ‘bell curve’. When events are distributed normally, most outcomes are familiar and don’t seem particularly striking. Height is a good example: it’s pretty unusual for a man to be over 7 feet tall; most adults are between 5 and 6 feet, and there is no known person over 9 feet tall. But in collective settings where contagion shapes behaviour – a run on the banks, a scramble to buy toilet paper – the probability distributions for possible events are often heavy-tailed. There is a much higher probability of extreme events, such as a stock market crash or a massive surge in infections. These events are still unlikely, but they occur more frequently and are larger than would be expected under normal distributions.
What’s more, once a rare but hugely significant ‘tail’ event takes place, this raises the probability of further tail events. We might call them second-order tail events; they include stock market gyrations after a big fall and earthquake aftershocks. The initial probability of second-order tail events is so tiny it’s almost impossible to calculate – but once a first-order tail event occurs, the rules change, and the probability of a second-order tail event increases.
The dynamics of tail events are complicated by the fact that they result from cascades of other unlikely events. When COVID-19 first struck, the stock market suffered stunning losses followed by an equally stunning recovery. Some of these dynamics are potentially attributable to former sports bettors, with no sports to bet on, entering the market as speculators rather than investors. The arrival of these new players might have increased inefficiencies and allowed savvy long-term investors to gain an edge over bettors with different goals. . . .
One reason a first-order tail event can induce further tail events is that it changes the perceived costs of our actions and changes the rules that we play by. This game-change is an example of another key complex systems concept: nonstationarity. A second, canonical example of nonstationarity is adaptation, as illustrated by the arms race involved in the coevolution of hosts and parasites [in which] each has to ‘run’ faster, just to keep up with the novel solutions the other one presents as they battle it out in evolutionary time.
To solve this question, we need to identify which inference is not supported by the given passage. This involves checking each option against the information provided in the passage.
Therefore, the correct answer is the fourth option, as it incorrectly enlarges the role of displaced sports bettors as the single cause of the pandemic rebound.
Step 1: Understand what the passage actually says about each option.
Option (1): Supported.
The passage explicitly uses runs on banks and toilet paper buying to illustrate contagion-driven cascades that produce extreme, unintended system-wide behaviour.
Hence, this inference is supported.
Option (2): Supported.
The passage discusses no stationarity — how a first-order tail event changes the rules of the system, altering perceived costs and raising the probability of a second-order tail event.
This matches the inference stated.
Option (3): Supported.
The passage stresses that heavy-tailed distributions produce more frequent and larger extreme outcomes than normal distributions, especially in contagion-driven systems.
This is directly stated and therefore supported.
Option (4): Not supported (EXCEPT).
The passage gives the example that former sports bettors might have contributed to market inefficiencies and movements during the COVID–19 rebound.
It does not claim:
that they were the sole cause, nor
that their entry was the overriding cause of market recovery.
The authors clearly treat this factor as one potential contributor, not the decisive explanation.
Thus, Option (4) states something the passage does not support and is therefore the correct answer to an EXCEPT question.
The question requires us to identify the best summary of the provided passage. To determine the correct option, we will carefully analyze each part of the passage and compare it with the given options.
The passage discusses how understanding complex systems can illuminate global challenges. It particularly focuses on how noise can paradoxically create order in such systems. It mentions the example of fish schooling to illustrate how randomness can lead to predictable patterns. The text also highlights the vulnerability of complex systems to events that do not follow a normal distribution, such as stock market crashes and pandemics, which have 'heavy-tailed' distributions where extreme events are more probable.
Additionally, the passage explains that once a first-order 'tail event' occurs, it increases the likelihood of further tail events. This idea is expanded with the example of the COVID-19 pandemic and its impact on the stock market, where the entry of new, speculative players created inefficiencies. It concludes by discussing the concept of nonstationarity, meaning changes in conditions can alter rules, similar to evolutionary adaptations.
We will now analyze the given options:
After evaluating all options, Option 2 is the most accurate summary of the passage as it comprehensively encompasses all the key concepts discussed, including the role of randomness, the nature of heavy-tailed events, and the influence of nonstationarity with real-world examples.
Step 1: Identify the major themes of the passage.
The passage covers three core ideas:
Noise (randomness) in complex systems can surprisingly create orderly collective behaviour.
Complex systems with contagion dynamics are prone to heavy-tailed cascades and extreme events.
Nonstationarity explains how early shocks change the rules of the system, illustrated with stock-market behaviour during COVID-19.
A correct summary must incorporate all three ideas.
Step 2: Evaluate each option.
Option (1): Incorrect.
This contradicts the passage. The passage explicitly argues that complex systems do not follow normal distributions and that extreme events are important, not negligible.
Option (2): Correct.
This option accurately reflects:
the surprising emergence of order from noise,
the vulnerability of contagion-driven systems to heavy-tailed events,
the idea of nonstationarity and how early shocks change rules,
the COVID-19 market example used in the passage.
It is the only option that captures the full scope of the passage.
Option (3): Incorrect.
This overstates the passage. The text says speculative entrants might have contributed to market movements; it emphatically does not say that speculative entrants always cause inefficiency or that long-term investors always profit.
Option (4): Incorrect.
This misrepresents the passage entirely. The passage does not reject applying nonstationarity to markets or public health; in fact, it explicitly applies it to those contexts. The parasite–host example is merely an analogy.
Thus, the best summary is Option (2).
The question is about identifying which observation most supports the passage's assertion that in complex systems, a first-order tail event increases the probability of subsequent tail events. Let us analyze each option to determine which one aligns with this claim.
Therefore, the correct answer is Option 3:
After a major equity crash, researchers find dense clusters of large daily moves for several weeks, with extreme days occurring far more often than in normal circumstances for assets with customarily low volatility profiles.
This option supports the passage's assertion by illustrating that after a first-order tail event (equity crash), there is an increased probability and occurrence of further tail events.
Step 1: Recall the passage’s claim.
The passage states that:
A first-order tail event (a large, rare shock)
raises the probability of second-order tail events,
meaning that after the initial shock, extreme events become more frequent.
Thus, we must choose the option showing clusters of extreme events after an initial extreme event.
Step 2: Evaluate each option.
Option (1): Weakens the claim.
Says tail events remain isolated with no increase afterward — the opposite of what we want.
Option (2): Irrelevant.
Describes a normal distribution with thin tails; nothing about successive extreme events.
Option (3): Strongly supports the claim.
After a major stock market crash, there are:
dense clusters of large daily moves,
extreme events appearing far more often,
a sustained period of elevated tail risk.
This directly confirms that a first-order tail event increases the probability of further tail events.
Option (4): Weakens the claim.
Says seismic activity returns to baseline with no aftershocks — contradicting the idea of second-order tail events.
Thus the best answer is Option (3).
To solve this problem, we need to determine which assumption is most crucial for the suggestion that contact-tracing apps could inadvertently increase risky interactions by affecting local behavior.
The passage highlights the complexity of systems and how small individual changes can collectively contribute to larger patterns. Particularly, it focuses on how technological interventions like contact-tracing apps can have unintended effects on group behavior.
The suggested phenomenon relates to the idea that individual behaviors influenced by these apps may inadvertently cause an increase in risky interactions, which is certainly not the intended purpose of these apps.
Now, let’s consider the provided options:
Given the context, the assumption that is most crucial is the second option. It aligns with the passage's emphasis on complex system dynamics where local, behavior-driven interactions can inadvertently lead to larger, unintended consequences, such as increased risky interactions.
Conclusion: The assumption that "Individuals base movement choices partly on observed infections and on the behavior of others. So, local responses interact, which turns many small adjustments into large scale patterns that can frustrate the intended aim of risk reduction." is the most necessary for the suggestion in the passage to hold.
The passage argues that contact-tracing apps, though designed to help individuals avoid risk, could inadvertently create collective patterns that increase risky interactions.
This can only happen if:
This is the hallmark of a complex system with interdependent behaviour.
Option (2) states exactly this assumption:
\(\textit{Individuals change behaviour based on infection data and the behaviour of others, and these interactions scale up.}\)
Without this interdependence, individual actions would stay local, and no large-scale unintended pattern could emerge — which the passage says can happen.
Thus, (2) is the necessary assumption.
Therefore, the assumption most necessary for the passage’s argument is Option (2).
Write any four problems faced by the animals that thrive in forests and oceans: 
Verbal to Non-Verbal:
A stain is an unwanted mark of discolouration on a fabric caused due to contact with another substance which cannot be removed by the normal washing process. Stains can be grouped on the basis of their origin, e.g. tea, coffee and fruits come from vegetable source. Stains from shoe polish, tar, oil paints come under grease stains. Animal stains comprise of stains formed by milk, blood and eggs, whereas marks on your clothes after sitting on an iron bench are those of rust and come under mineral stains. Then there are stains that are formed due to dye, into perspiration which can be categorised under miscellaneous stains. Read the given passage and complete the table. Suggest a suitable title. 
