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14 December 2015

# Mathematics to Lay Siege to the Uncertainty

Crisis | Cybersecurity | Logic | Patterns

In most emergency situations it is vital to make quick decisions, which are inevitably biased by cultural contexts and personal opinions. In this scenario of paucity of information, mathematics may hold the key for reducing the margin of error. The use of probabilistic models enables subjective bias to be avoided as well as reducing uncertainty when making decisions. In April of this year, the ICMAT organized a series of talks by experts from all over the world who shared their experiences in this emerging field of research.

Andrea Arnal. We live in an increasingly complex society where political and economic decisions have acquired a global dimension and frequently give rise to unexpected consequences. Humankind must face new challenges such as climate change or terrorism, which involve a large element of uncertainty. The case of terrorism is even more complex because it poses the presence of intelligent adversaries whose intentions it is necessary to attempt to foresee, and this requires the design of new tools and strategies to enable decisions to be modified according to the action adopted by our enemies.

The decisions made in the first few hours of an emergency situation are crucial, but the information required to predict the outcome of one situation or another is normally not available, either for lack of data or lack of time. Given this uncertainty, and the need to make decisions quickly, politicians often rely on expert opinion to determine the best option open to them. However, specialists are prone to making recommendations that may be biased by their own beliefs, which in turn are determined by their own cultural and social contexts. This is where the mathematical modeling of expert judgement may be the key to mitigating biased opinions and striking a balance that makes it possible to arrive at a final decision in the most consistent and coherent manner.

“Within a framework of uncertainty,it’s vital to model expert judgements mathematically in order to provide the right support for the process of decision-making in public policy”

“Within a framework of uncertainty, it’s vital to model expert judgements mathematically in order to provide the right support for the process of decision-making in public policy,” says David Ríos, who occupies the AXA–ICMAT Chair in Adversarial Risk Analysis and is coorganizer of the “International Early Stage Researcher Training School on Applying Expert Judgement Methodologies to Real Problems” and the “Workshop on Expert Judgement for Geographical and Adversarial Problems”.

## Responding with numbers

The chief unknown quantity affecting these crisis situations may arise from two types of uncertainty: first of all, geographical, and secondly, the presence of intelligent adversaries.

In the first case, it is essential to determine the spatial and temporal data connected with the event. For example, in crises caused by natural disasters and environmental accidents, such as oil spills, flooding, gas leaks or volcanic eruptions, then information about geodynamics, orography and meteorological conditions plays a vital role. In the second case of uncertainty, in which we are confronted by a protagonist with intelligence, it is important to determine the most likely decisions that may be made by such an adversary at any given moment. In this field, mathematics is closely linked with psychology, which enables patterns of behavior to be established in order to design mathematical models for decision-making. Furthermore, the modeling of opinion is combined with Game Theory.

This is a very recent field of research that gained momentum after the 9/11 attacks and which today has many applications in national security and defense systems, cyber-security, competitive marketing, markets and auctions.

One of the fields in which these mathematical developments are applied is cyber-security. It is becoming increasingly important to develop effective strategies to deal with the threats that constantly appear on the Internet. More than 225,000 cyber attacks across the globe are reported every day and this figure continues to rise. According to the latest results in the PandaLabs Report, compiled by Panda Security, the level of infections worldwide is currently estimated at 36.5%; that is, six points higher than for the same period in 2014. In Spain, it is estimated slightly above this average at 38.7% of all computers infected, although China heads the list and is followed by Turkey and Peru.

States and institutions are not immune to this type of attack. The Spanish Centro Nacional de Inteligencia (CNI), whose task is to inform the Government on threats to national security, stability and defense of the State, receives on average four reports of critical cyber attacks per month, in addition to a further 18 classified as very serious, although so far none have been successful, according to CNI director general Félix Sanz Roldán.

As pointed out by Einar Snekkenes, professor of Information Security at Gjovik University College (Norway), one of the speakers at the meeting in April, in order to respond effectively, “the key point is to focus on the interests and motivations of the adversary.” In addition to psychology, in Snekkenes’ opinion it is “very important” in this field to include disciplines such as economics, decision theory, computational sciences, and of course mathematics, in order to bring all this information together.

As well as experts in cyber-security, the meeting was also attended by representatives from other fields, such as Alec Morton, an expert on the modeling of epidemics; Nicole Van Elst, whose research concerns the prediction of behavior; Stephanie Haywood, a specialist in the application of geographical uncertainty methods for the treatment of public health problems; Eva Chen, who coordinates a program based on the “wisdom of crowds” with the aim of forecasting global geopolitical changes, and Simon French, who collaborates with the UK Government on decision-making and risk analysis in real-world emergency situations.

In the words of David Ríos: “We live in a risk society”, an interconnected global society in which risk continues to rise. It is for this reason that we call more and more on mathematical modeling as a tool that enables us to improve our response capability when faced with challenges posed in the 21st century.

### By Andrea Arnal

for ICMAT

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