The Secret Ingredient of the World’s Best Apple Pie

Algorythms can predict the future, but unlike the Delphi oracle, they do it based on hard scientific methods, instead of intestines and animal bones. Finding old friends on Facebook, recomending books you might like on Amazon, or predicting the outcome of the 2012 presidential election – you name it, an algorythm does it.

So what about food? Could these same math whizzes help us bake a better pumpkin pie or mix up a tastier batch of sweet potatoes this Christmas? Lada Adamic, a computer scientist at the University of Michigan and Facebook, thinks it just might be possible. she and her team have come up with an algorithm to guess how successful a recipe will turn out. And the math works surprisingly well. It predicts with nearly 80 percent accuracy how many stars your mother's cranberry recipe will receive on allrecipes.com. Plus, it can recommend ingredient replacements to make your pie crust and potatoes more healthful.

She and her team took nearly 50,000 recipes and 2 million reviews from allrecipes.com and then hacked up an algorithm to extract out all the ingredients, cooking methods and nutritional profiles. With just these items, her algorithm could predict the recipe's rating with an accuracy of about 70 percent. But the magic happened when Adamic built a "social network" for the ingredients. She looked at how often two ingredients appear in the same recipes. Those that frequently show up together — milk and butter, nutmeg and cinnamon, basil and rosemary — sit close to each other in the network, but those that rarely appear in the same dish, such as coconut and parsley, are far from each other.



Physicists at Harvard University performed a similar network analysis on ingredients' flavors, but Adamic took it a step further and integrated the data into a recipe prediction program.

Adamic's network analysis boosted the accuracy of her recipe recommendations by about 10 percent. But it also revealed a treasure-trove of information about the way Americans mix and match ingredients, which ones we like to leave out or throw in extra.
Her algorithm analyzed reviewers' recommendations for customizing recipes, such as "I replaced the butter in the frosting by sour cream, just to soothe my conscience about all the fatty calories" and "This is a great recipe, but using fresh tomatoes only adds a few minutes to the prep time." Then the mathematics stitched together little clusters or communities of interchangeable foods and spices.

The result is a list of recipe replacements more comprehensive and scientifically accurate than anything you'll find in the Joy of Cooking or online.

Read the full article on arXiv.com, or a lighter verison on the npr blog.

Network Science of the Game of Go

You can make networks from pretty much anything. Connect music based on taste or phone calls, companies based on their ownership, spread routes of abstract movements, and lots more. It is high time to start using networks to understand games. But what of the structure of games themselves? In a paper that was recently published in EurophysicsLetters, two French scientists decided to apply network science to the game of Go.

They constructed their networks in a simple way: If one board position can lead to another, they are connected. Using a dataset of about 1,000 professional games and 4,000 amateur games, they began to construct these networks.

In a Game of Go players put black and white stones on a grid board.

Of course, the Go board is very large and so you can’t compare entire board layouts. Instead, they decided to make it much more tractable and look at the board composition surrounding a newly placed piece (a move in Go consists of putting a stone on an intersection of the grid lines of the board). In this case, they looked at the pieces immediately surrounding a newly placed piece (for a 3×3 grid). They calculated that this creates 1107 possible moves, which can be connected if the moves occur one after another, and are in the same region of the board. They also examined the frequency of moves, which obeys a heavy-tailed distribution (whether or not it is a power-law as they claim seems a bit weaker).

The network analyses in the paper are a bit odd, though they find many classic graph structures, such as a heavy-tailed link distribution and high amounts of clustering. Gratifyingly, the networks constructed from amateur and professional games are distinct, though in somewhat subtle ways. 

Read the article here, or the short version on Wired!

SNA – The Secret Weapon against Terrorism

In his forthcoming book Network Science, Albert-László Barabási has already reported about the role of social network analysis in the capturing on Saddam Hussein. Our readers know, that the blog itself is no stranger to the subject. A new American paper sums up how and why this approach can be useful in fighting political violence.

The academic community studying terrorism has changed dramatically in the past decade, and the descriptive and explanatory potentials have grown strongly. On of the reasons for its popularity is the increasing acknowledgment within the academic community of the important association between the group’s dynamic and (social)structure, and its members’ motivations and behaviors.

The Network of the Terrorist Group responsible for the Attack against WTC.

Understanding the motives and the processes that led the group to engage in political violence requires a look beyond the apparent causal relations between the causes of the violence and the violent activities. Since September 11th, growing numbers of media outlets have increased their coverage of terrorist incidents and groups. This, combined with the striking increase in the efforts and resources invested in data collection about these groups by academic and governmental agencies in recent years.

An IRA statement.

Violence or political action is a result of collective action, i.e., an output of a process, which is an action of a group of actors who interact with each other on some level, so SNA seems like an obvious analyzing tool. The sizes of these gropus varies widely (from 2 man groups to milites like the IRA), so an instrumental approach in bigger newtorks focus on command and information channels and the roles of leaders.

After drawing the networks of terrorist organizations, measuring the influence and power of individual actors becomes relatively easy, with the help of centrality and betweenness measures. Unveiling the hierarchy could also help authorities in dismantling them, making targeting a lot less complicated.

You can read the whole article at the academia homepage.

Ckeck out the original article for more.

Research is the New Discovery

A software called Livaplasma helps you discover new music you might like, with music you already do. 

This is what a music search looks like, if you look for music like Led Zeppelin, bands from the are and the genre become part of the network. Cream, The Who and Pink Floyd are the top recommendations.

The crator of the site Frédéric Vavrille, made the site back in 2004. But music recommendations is not all Liveplasma can do. It also works for books and movies.

With Inception as a key word, the network consist of other Cristopher Nolan movies, and genre specific works like The Girl With the Dragon Tattoo and The Matrix.

Jane Eyre's networks include Jane Austen's other works, books by Dickens and the Bronte sisters.

Curious? Check out the site for yourself at liveplasma.com !

The Global Super-Entity - The Economic Ruling Class of The World

A small, tightly woven network of companies, mostly banks, wields disproportionate control over the global economy, according to a new study. The findings shed some light on the intimate ways 21st century capitalism works — and how those functions can undermine the entire system.

A trio of systems theorists at ETH Zurich examined the world’s 43,060 transnational corporations and studied their share ownerships, searching for commonalities that tie the companies together. They worked with techniques used to study complex systems in nature to construct a model of which companies controlled which other companies, and through which networks.

Ultimately, Stefania Vitali, James Glattfelder and Stefano Battiston identified a core of 1,318 companies with interwoven ownerships, each with ties to two or more other companies. They were connected to an average of 20 each, the researchers found. The network forms a “giant bow-tie structure,” with a small, tight knot in the middle and connections spanning outward in an increasingly nebulous pattern. The knot is very small and dense compared to the other sections, and the researchers dubbed it an economic “super-entity.” It is also very closely held — about three-quarters of the ownership remains in the hands of the core itself.

While the authors note that there’s no example of this core intentionally acting as a bloc — in other words, there’s no vast economic conspiracy — that doesn’t mean it can’t act that way. “Globally, top holders are at least in the position to exert considerable control, either formally (e.g., voting in shareholder and board meetings) or via informal negotiations,” they write.

“Nearly [40 percent] of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of 147 TNCs in the core, which has almost full control over itself,” the authors explain. Unsurprisingly, three-quarters of these companies are banks.

The Core of the Network

They add that domestic anti-trade strictures prevent the core from acting as some kind of cash cartel.

Concentrated power in the hands of a few has clear implications for global financial stability — which everyone already knows, given what the world went through starting in 2008. But this study puts it in empirical terms. Further studies that build upon the assumptions made in this paper could potentially help policymakers and economists studying ways to stabilize financial markets.

The Top 20 Corporation in the Core of the Network:

1. Barclays plc2. Capital Group Companies Inc
3. FMR Corporation

4. AXA

5. State Street Corporation

6. JP Morgan Chase & Co 

7. Legal & General Group plc 

8. Vanguard Group Inc

9. UBS AG

10. Merrill Lynch & Co Inc 

11. Wellington Management Co LLP

12. Deutsche Bank AG

13. Franklin Resources Inc

14. Credit Suisse Group

15. Walton Enterprises LLC

16. Bank of New York Mellon Corp

17. Natixis

18. Goldman Sachs Group Inc

19. T Rowe Price Group Inc

20. Legg Mason Inc

Source: New Scientist

The Dark Side of Hospitals

After virtual threats and food poisoning, a new study takes a closer look at viruses in hospitals.

Hospitals shouldn’t make you sicker. But plenty of people acquire illnesses while hospitalized—in some countries, such so-called nosocomial infections afflict more than 10 percent of patients.

Jack Nicholson's life might not be the only one threatened by a nurse.

To investigate transmission pathways, European researchers of the SocioPatterns collaboration fitted 119 people in a ward of the Bambino Gesù Children's Hospital with radio-frequency identification (RFID) badges. The tags registered face-to-face interactions—and the potential spreading of airborne pathogens.

The map.

Nurses interacted with the widest variety of individuals across the ward—patients, doctors, other nurses, and so on. The study indicates that nurses should take priority in strategies for preventing or controlling hospital outbreaks.

Different groups of the hospital.

The scientific method used in the analysis was developed in the MIT Media Lab. The sociometric badges aim to eliminate behavioral changes that occure because they are participating in an experiment. The devices are capable of  capturing face-to-face interactions, extracting social signals from speech and body movement and can also measure proximity and location of the users. The invention was listed as on of the top 10 innovations by the Harvard Business Review.

Check out the interactive map on Scientific American! For more about the method, we recommend the company's page.

Can Social Media Become the Saviour of Democracy ?

An article in Nature claims to have proven the  direct impact of  social media on political activity. Researchers at the University of Carolina along with people from Facebook run a gigantic experiment.

On Nov. 2, 2010, the day of the nationwide Congressional elections, nearly every Facebook member who signed on — 61 million in all — received a nonpartisan “get out the vote” message at the top of the site’s news feed. It included a reminder that “today is Election Day”; a link to local polling places; an option to click an “I Voted” button, with a counter displaying the total number of Facebook users who had reported voting; and as many as six pictures of the member’s friends who had reported voting. The results: 340,000 additional votes nationwide! Pretty amazing, but how can we be sure these people would not have voted by themselves?

Two randomly chosen control groups, of 600,000 Facebook members each, did not receive the pictures. One group received just the “get out the vote” message; the other received no voting message at all.By examining public voter rolls, the researchers were able to compare actual turnout among the groups. They determined that the message showing friends who had voted was directly responsible for 60,000 more votes nationwide and indirectly responsible for 280,000 that were spurred by friends of friends — what they called “social contagion” effect.

Significantly if not surprisingly, the voting study showed that patterns of influence were much more likely to be demonstrated among close friends, suggesting that “strong ties” in cyberspace are more likely than “weak ties” to influence behavior. It also found an indirect impact from the messages: friends of friends were influenced as well.

Fun fact, they also discovered that about 4 percent of those who claimed they had voted were not telling the truth.Because only about 1 percent of Facebook users openly state their political orientation, the researchers said they could not determine whether political leanings had any influence on social networking and voting behavior.Past studies have shown that a variety of methods for mobilizing potential voters have a disappointing effect. Knocking on doors is the most effective technique; e-mail is one of the least.

A New Frontier for Organizational Network Analysis

Find out more about ONA online.

The Key Opinion Leaders of Music

The evidence that ideas and fashions spread through society like viruses or like wildfire is compelling. Numerous studies have examined the networks in which this spread takes place and with increasingly large data sets to work with, researchers have become increasingly confident in their network-centric view of the world. These tools are teasing apart the large scale behaviour of humanity in ever increasing resolution. Our frequent viewers are well aware of the fact, the popculture is a futile ground for network analysis, whether it comes to movies, comics or music. 

Last.fm is interesting because it publishes lists of the most listened to artists divided geographically. So Lee and Cunningham have studied the way these charts vary in time and looked to see whether some cities consistently lead others in terms of listening habits. The researchers studied the Last.fm data for 200 cities around the world dating back to 2003. This is compiled from some 60 billion pieces of data the site collects from its users. 

Edges represent cities following.

The results are interesting. They show that certain cities appear to lead others for various genres of music. For example, Montreal seems to lead North American in indie music listening habits and the leader for hip hop is Atlanta. In Europe, Paris leads for indie music whereas Oslo leads for music as a whole. 

It's easy to imagine that the biggest cities ought to be those furthest ahead of the curve because they have biggest populations from which new and interesting bands can emerge. That doesn't seem to be the case in this data--big cities such as New York, LA and London do not lead. "We find only weak support for this hypothesis," say Lee and Cunningham. 

That may cause some alarm bells to ring. An interesting body of work has recently suggested that big cities benefit disproportionally for their size since qualities such as efficiency, productivity and innovation all scale super linearly with population. 

The ultimate test, of course, is whether their discovery has any predictive value. For example, could they predict how listening habits will change in the near future? "We have not yet demonstrated that our models have this predictive power, although we plan to attempt this validation in future work," they say.

Hooked already? Read the whole article on Cornell University's Library page.

If Achilles Used Facebook...

In a study published in Europhysics Letters, scientists use a mathematical approach to examine the social networks in three narratives: “The Iliad”, “Beowulf” and the Irish epic “Tain BoCuailnge.” If the social networks depicted appeared realistic, they surmised, perhaps they would reflect some degree of historical reality.

When we pick up a mythological text like “The Iliad” or “Beowulf,” we like to imagine that the societies they describe existed. Even if the stories are fiction, we believe that they tell us something about ancient Greece or the Anglo-Saxons, and that some of the characters and events were based on reality.

1.Howard David Johnson - Victorious Achilles

“Beowulf” is an Anglo-Saxon heroic epic, set in Scandinavia. Notwithstanding obvious embellishments, archaeology supports the historical authenticity associated with some of its characters. The main character, Beowulf, is believed to be fictional. “The Iliad,” is an epic poem attributed to Homer dating from the eighth century B.C. Some archaeological evidence suggests that the story is based on an actual conflict. We contrasted those two narratives with the Irish epic “Tain Bo Cuailnge” (usually called the “Tain”), which most believe to be completely fictional. The “Tain,” which survives in three manuscripts from between the 12th and 14th centuries, concerns a conflict between Connaught and Ulster, Ireland’s western and northern provinces.

2.Hans W. Schmidt Beowulf Illustration

To construct the social networks in each of the narratives, researchers created databases for the characters and their interactions, and categorized their relationships as hostile or friendly. The myth networks were found to have some of the characteristics, including the small-world property and structural balance (related to the idea that the enemy of my enemy is my friend), typical of real-world networks.

3.Táin Bó Cúailnge

The results showed, that all three were scale-free, unlike any of the intentionally fictional narratives they have examined. However, in the Irish myth, the top six characters are all unrealistically well connected. There are 398 other characters in the “Tain,” but after remove the weakest links (or single, direct encounters) between these characters and the Top 6, the narrative becomes as realistic as “Beowulf” from a social-network view. Perhaps these characters are amalgams of a number of entities that were fused as the narrative was passed down orally.

The studies approach is different from traditional approaches to comparative mythology. It is not literary analysis; it tells us nothing about events or the human condition. Instead, it promises a new way to analyze old material and find striking new perspectives and evidence — in this case, that which we call “myths” may not be as mythical as we thought.

Read the full article on NY Times.

The Web of Modernism - How Abstract Movements Spread Across The Globe

The Museum Of Modern Art (MoMA) in New York is currently hosting an exhibition called Inventing Abstraction: 1920-5. They took the opportunity to unreaval a graphic representation of the birth of modern art. 

The image, which was designed for their upcoming show Inventing Abstraction: 1910-1925 (December 23, 2012–April 15, 2013), is an obvious node to Alfred H. Barr Jr.’s important Cubism and Abstract Art chart that accompanied a show of the same name at the MoMA in 1936.

1. Barr's Original for the 1936 Exhibition 

This web of relationships goes beyond visual art to incorporate musicians like Claude Debussy, writers like Guillaume Apollinaire, and choreographers like Vaslav Nijinsky, and gives us the most complete picture of abstractions transcontinental roots we’ve ever seen.

2. Info Graphic for the 2012 Exhibition (Click Here to Enlarge)

The Americans, centered on photographer Alfred Stieglitz, branch out to include Max Weber, Marsden Hartley, and others. There are obvious Italian, Russian, British, Dutch and other clusters but the image connects the dots between figures we may not know were in contact. The Hungarian hub includes painter Sándor Bortnyik, and Bauhaus pioneer László Moholy-Nagy.The chart shows all known relationships that including those who have shared studios and even slept together.

For more, go to Hyperallergic or the MoMA homepage.

CNN's War On Cyber Terrorism - A Fictional Drama Set in the Situation Room

In February 2010 the cable network ran a live simulation under the name 'We Were Warned - Cyber Shockwave", where Wolf Blitzer guided viewers through a fictional scenario of digital terrorism.

To avoid a War Of the Worlds-like panic, CNN made it very clear, that is was only a product of fiction; but how far were they from the truth? A situation like this could easily happen tomorrow: a Russian computer infects smarthphones via the application 'March Madness', and the virus goes viral within a few hours. Soon it shuts down communication channels, power networks, and due to the blackouts, telecommunication and traffic get shut down as well. Hospitals have only 12 hours left on their backup generators, and the governments hands are tied, the president has no other choice but to declare martial law.

You can watch the whole show on YouTube, or read the transcript on the CNN homepage.

What CNN is trying to reenact, is the 'War Room', reserved for the President of The United States, that comes with a bunch of military personel and a group of advisers (probably a red phone too), for situations involving national security and requiring military action. The most infamous depiction of this roundtable was in Stanley Kubrick's Dr.Strangelove, accompanied by a brilliant performance of Peter Sellers. Entertainment however, was not the only goal of CNN, since their team included experts like the former director of the CIA General Michael Hayden among other high ranking security experts and former advisers.

The event was organised by the Bipartisan Policy Center, but the meaning behind it goes further than politics.  We have reported earlier, that closely linked systems, like the world food trade network, can serve as transmitters for certain viruses, causing a rapid failure of the whole system. Take any countries online network, and you get the same result. One computer is enough to infect and eventually take down the whole system. In 2010 researchers from Boston published a paper in the scientific journal Nature, that pointed out the Achilles heal of strongly interconnected networks. The failure of one point in the system can take down all the others, so the bigger the network is, the more vulnerable it gets.

Hooked already? Read on about the networks of networks on ScienceNews!

The Paradox Of Friendship – Why do our friends have more friends than we do?

What may look like a psychological phenomenon, is actually basic maths.

In a colossal study of Facebook by Johan Ugander, Brian Karrer, Lars Backstrom and Cameron Marlow,  examined all of Facebook’s active users, which at the time included 721 million people — about 10 percent of the world’s population — with 69 billion friendships among them. They found that a user’s friend count was less than the average friend count of his or her friends, 93 percent of the time. Next, they measured averages across Facebook as a whole, and found that users had an average of 190 friends, while their friends averaged 635 friends of their own.

Studies of offline social networks show the same trend. It has nothing to do with personalities; it follows from basic arithmetic. For any network where some people have more friends than others, it’s a theorem that the average number of friends of friends is always greater than the average number of friends of individuals.

This phenomenon has been called thefriendship paradox. Its explanation hinges on a numerical pattern — a particular kind of “weighted average” — that comes up in many other situations. Understanding that pattern will help you feel better about some of life’s little annoyances.

In this hypothetical example, Ross, Chandler, Phoebe and Rachel are four friends. Lines signify reciprocal friendships between them; two people are connected if they’ve named each other as friends.

Ross’s only friend is Chandler, a social butterfly who is friends with everyone. Phoebe and Rachel are friends with each other and with Chandler. So Ross has 1 friend, Chandler has 3, Phoebe has 2 and Rachel has 2. That adds up to 8 friends in total, and since there are 4 girls, the average friend count is 2 friends per girl. This average, 2, represents the “average number of friends of individuals” in the statement of the friendship paradox. Remember, the paradox asserts that this number is smaller than the “average number of friends of friends” — but is it? Part of what makes this question so dizzying is its sing-song language. Repeatedly saying, writing, or thinking about “friends of friends” can easily provoke nausea. So to avoid that, I’ll define a friend’s “score” to be the number of friends she has. Then the question becomes: What’s the average score of all the friends in the network?

Imagine each person calling out the scores of his/her friends. Meanwhile an accountant waits nearby to compute the average of these scores.

Ross: “Chandler has a score of 3.”

Chandler: “Ross has a score of 1. Phoebe has 2. Rachel has 2.”

Phoebe: “Chandler has 3. Rachel has 2.”

Rachel: “Chandler has 3. Phoebe has 2.”

These scores add up to 3 + 1 + 2 + 2 + 3 + 2 + 3 + 2, which equals 18. Since 8 scores were called out, the average score is 18 divided by 8, which equals 2.25.

Notice that 2.25 is greater than 2. The friends on average do have a higher score than the girls themselves. That’s what the friendship paradox said would happen.

The key point is why this happens. It’s because popular friends like Chandler contribute disproportionately to the average, since besides having a high score, they’re also named as friends more frequently. Watch how this plays out in the sum that became 18 above: Ross was mentioned once, since she has a score of 1 (there was only 1 friend to call her name) and therefore she contributes a total of 1 x 1 to the sum; Chandler was mentioned 3 times because she has a score of 3, so she contributes 3 x 3; Phoebe and Rachel were each mentioned twice and contribute 2 each time, thus adding 2 x 2 apiece to the sum. Hence the total score of the friends is (1 x 1) + (3 x 3) + (2 x 2) + (2 x 2), and the corresponding average score is

 Each individual’s score is multiplied by itself before being summed. In other words, the scores are squared before they’re added. That squaring operation gives extra weight to the largest numbers (like Chandler’s 3 in the example above) and thereby tilts the weighted average upward.

So that’s intuitively why friends have more friends, on average, than individuals do. The friends’ average — a weighted average boosted upward by the big squared terms — always beats the individuals’ average, which isn’t weighted in this way.

Like many of math’s beautiful ideas, the friendship paradox has led to exciting practical applications unforeseen by its discoverers. It recently inspired an early-warning system for detecting outbreaks of infectious diseases. In a study conducted at Harvard during the H1N1 flu pandemic of 2009, the network scientists Nicholas Christakis and James Fowler monitored the flu status of a large cohort of random undergraduates and found that people with more connections were infected faster.

For more analogies check out the whole article at a New York Times blog.

In the Mist of Drugs

A research from India takes a closer look at what our medicine cabinet is made of, with the help of network analysis.

It is a well-known phenomenon, that the demand on medicine increases year to year (the market produces an annual growth of 6%!). The industry has an income sum of 800 billion dollars per year, with India and China as the fastest growing markets, and an annual increase in demand over 15%. The top consumers are of course overseas. The Americans with their 320 billion dollar annual drug spending are responsible for more than one third of the industries income, a sum about three times larger than in Germany. Its hardly a coincident, that the number prescription drug abuse victims is growing as well. Last year only, about 27.000 people died prescription medicine related deaths, one in every 19 minutes. Livestock drugs are pretty common too, since factory farming procedures require to use antibiotics on animals.

The goal of the research was to understand drug consumption from a network point of view, and to learn what drugs consist of. American drug label databases served as sources of information, making over 70 thousand chemicals subjects of the analysis.

The picture above shows the whole network of ingredients, with 16,444 dots and 32,627 edges. You can notice at first sight, that clustering is present. the most common chemicals include Octinoxate, Titaniumdioxide, Octisalate, Oxybenzone and Avobenzone, that are ingredients in drugs and chemicals, sometimes even food colouring materials. Another center point is Triclozan, a commonly used antibacterial and antifungus chemical.

Alcohol is number 3 in the centrailty top 10.For more cool pictures and the top10 check out the original aricle at Web 2.0.

The Fromula Of Doom

A recent interdisciplinary study shows how food poisoning might be the end of us all.

The collaboration – including the University of Notre Dame and the Budapest Corvinus University – took a closer look at a darker future, with a serious methodological background. With Earth’s population exceeding 7 billion people, sustainable and safe food raise some serious concerns. The high demand for nutrition turned the food world trade into a very complex system, with seven countries in central positions, and the ability to reach 77% of the planet’s population on an everyday basis. But there is a serious price to be paid for stuffed grocery shelves: the risk. The door is not only open for goods and services, but infections as well. A massive food poisoning epidemic – like the Escherichia coli virus in Germany last year – could do serious damages, and claim human lives.

The United Nations monitors food trade since the sixties, focusing on networks, qualities, and trends of the goods being transferred. An interesting development of the past decades was the fact that the amound of food transfer is now larger than production itself. The main exports shifted from raw agricultural materials to processed and branded foods. The research itself used a 2007 UN database as a source. The density of the network increased by 33% in the last ten years, its most vulnerable parts are dots (countries) in the centre with the most edges (connections). Through these countries, viruses could spread vastly within a few days, reaching millions, and making it virtually impossible to locate the source of an infection (in the case of Germany, it took 3 weeks). Surprisingly, the most vulnerable dot was not an agricultural giant like the USA, but the Netherlands (based on per capita trade activity).Other weak links are the seven giants including the USA, Germany, France, Italy, China and Spain.

For those of you interested in the numbers, the research was based on graph theory, that used factors like consumption, population and production figures in order to make a dynamic model, ranking the danger level of individual countries. We already mentioned that the Nederlands came out on top. They also calculated how fast a virus could spread in a country, and how vulnerably they are.

For more figures and numbers check out the original article.