Game of thrones is undoubtedly a series of success. 
But what makes it so special? Is there something that makes it different to other TV shows, and so attractive?
I will not answer those questions here. What I am going to talk about is a recent work carried out by Diambo Liu and Luca Albergante, from MIT and the University of Dundee. In this article they have applied the theory of networks to understand the success of the series and see what parameters are important to make the chapters appealing, so that people are looking forward to the following one

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Network theory
Each one of us interacts with other people around us. Family, friends, coworkers, neighbors. Each of the people we interact with in turn do so with other people. In this case each person is the node or vertex of a network, and each relationship is a link of the network. We interact with different intensity with different people, so each link has different strength.

Network theory studies the connections that are created between different nodes, and how they evolve over time. This way, knowing the details of the network, we can understand how it works, or what factors can make it change radically, or if the fact of removing a particular node from the network, will affect drastically the functionality.

Important examples of networks are the brain, where the nodes are the neurons, social networks, air traffic, where the nodes are the airports, the power grid networks.

The researchers of this study have created a network where each node is a family or house of the series: the Lannister, the Stark, the Bolton, the Tyrell, the Targerian. This with all the houses and  all the important groups , such as the Nights Watch or the Iron Bank.

Obviously, the importance of each house is directly related to the number of connections it has.

The Game of Thrones network has a certain similarity with certain marine networks. Where there are minor entities gravitating around a few entities of greater importance. Here would be the Lannister and the Stark. Although it is different from the network of scientific collaborations.

Next they have studied what kind of connections, if friendly or hostile, are between each node, and how those connections evolve, either because of changes in the alliances, because some of the nodes cease to exist, or because two nodes without interaction at first they start to interact.

They have seen that the triads are a very important subgroup. These triads are formed by three nodes and, depending on the mutual relationship (friendly or hostile), the triad may be in balance or umbalanced.

For example, suppose that the Lannister and the Stark are enemies, that the Greyjoy and the Stark get along and the Lannister and the Greyjoy are enemies. This triad is in balance. My friend's enemies are my enemies.

But things can change. For example,  the Greyjoy can become friends with the Lannisters. So, the friends of my friends are my enemies and the balance is lost.

In real political networks, it is believed that there is a tendency to make moves to minimize unbalanced triads. But that is not what happens in Game of Thrones. The fact that the balance is broken allows the series to evolve ... or maybe it breaks so to evolve.

It turns out that these changes are related to those chapters better rated by the audience and that have better acceptance, in the sense of captivating the attention.

The researchers quantify the unpredictability of the series. They use the expression,

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where T3 is a triad of type 3 (2 red links and 1 blue link), and T2 (1 red links and 2 blue link) is a triad of type 2. The denominator is the sum of all the possible triads.

According to the above, the authors claim they can predict the success of each chapter.

In any case, a series of success, which not only allows us to have a good time in front of the screen, but also to talk about science.
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May Science be with you!

Quantum Key Distribution, or how to communicate encrypted information in a totally secure manner, has gone from being an idea to being a commercial possibility in thirty years. In a recent paper in Science Advances, researchers from Duke University, Ohio State University and Oak Ridge National Laboratory have beaten a new record with their multi-dimensional qdit encoding (Islam et al., Sci. Adv. 2017;3: e1701491, 24 November 2017).

The idea of superposition, i.e., having for example 50% vertically polarized and 50% horizontally polarized, is unique to quantum mechanics. Once we measure the polarization of the photon it will be either horizontally or vertically polarized, but  we can generate photons that will be in a superposition state until it is measured.

The no-cloning theorem states that it is not possible to clone a quantum state, so we cannot observe a photon  and copy exactly the original state of the photon. This way, if Alice wants to communicate with Bob, they can use a protocol to detect any eavesdropper. But more than that, they can generate a protocol to account for possible attacks and still distill a secured key.

Bennet and Brassard described their protocol using the polarization of photons: vertical is 1, horizontal is 0. But since then other ways of encoding the information have been developed. 

The group of Islam et al. has used time-bin encoding. They encode the information in the time of arrival of the photon. They generate time bins and each one of them corresponds to one bit of information. One advantage of this is that they can encode more than two bits of information in each photon.

They have generated four time bins (see figure), so they can send pulses of photons in four different positions. Then, at the detection side, they interfere the pulses with themselves. To do this they use three unbalanced interferometers. Because the interferometers are unbalanced they interfere different time bins. This way they can track the visibility of the interference, and compare the experimental visibility with the expected one, in order to secure the communication.

The turmoil social and political recent life in Catalonia, Spain, is leading to a superposition of Independent-Republic/Part-of-a-Monarchy state. 

Spain is divided into 17 regions with their own local governments. Catalonia is one of those region, with particular historical characteristics. During the last 5 years there has been a growing feeling towards the independence of Catalonia from Spain. Spain is currently a monarchy.

1) Stage 1 of the Experiment: The Referendum. On October 1st was the first attempt in this unprecedented quantum experiment. On one side, the Catalan president summoned the catalans (citizens of Catalonia) to a referendum to determine if they wanted or not Catalonia to be an independent Republic. On the other side, Spanish president claimed that it was not going to be a referendum, or at least a binding one. 

This is the way they were creating the quantum superposition of Referendum/non-referendum. And they really succeeded in having the citizens and the media confused on whether a referendum took place or not. Of course, there were lots of observers, which some claimed that the wave-function had collapsed into a yes and some into a no referendum. Experimental results were not robust enough, but there was no room for a second run of the experiment, at least from an independent research team.

2) Stage 2 of the Experiment: The Declaration of Independence. On October 10th, in agreement with the Catalan interpretation of Quantum Mechanics, the Catalan president summoned the Catalan House of Representatives. He was going to declare the independence. Did he do it? Well, he did and he did not, in the purest Schrödinger style. But high resolution measurements of his declaration could see that there had been a flow in his which path experiment. He had declared the independence but cancelled right after 6 seconds.

3) Stage 3 of the Experiment: Protocol 155. After one week of disagreement with the experimental results, and not knowing the uncertainty of the measurements, the Spanish president demanded the Catalan one the raw data and the analyzed data. Catalan experimentalists published a quick letter (fast editing) which was not clear enough (reviewers fault?). This made the Spanish part of the research team to perform a different measurement. They decided to apply technique 155 from the constitutional protocol. This would dissolve the government of Catalonia, giving a clear result of the superposition experiment.

4) Stage 4 of the Experiment: Call for Elections. After one week of fighting with the numbers and many-worlds interpretations of quantum mechanics, the Catalan president went one step forward and announced that he would make a call for elections. Then he didn't, trying to create a new superposition state to see if the experiment can still be saved.

5) Stage 5 of the Experiment: New Declaration of Independence. The last measurement did not create the desired superposition, so he has now announced a new declaration of independence, just to make it coincide with the Spanish application of the 155 protocol to the experiment.

Will they finally attain the Quantum Superposition of States, having a Republic and a Monarchy at the same time. Well, as far a nobody looks, that might work, but we will have to look and collapse the wave-function. We will have more information as the experiment is developed, which seems to be a long experiment.

It's Nobel prize announcement week. Today we just were announced the expected Physics one for the gravitational waves, but yesterday, the one on physiology was a well deserved one, also.

The Nobel prize in physiology was awarded for their discoveries of molecular mechanisms controlling the circadian rhythm. This circadian rhythms are internal clocks that all living creatures have and that control most of our internal mechanisms such as protein production, gene expression, ...

We are ruled by the 24 hours of the sun light, and we have evolved adapted to it. Even though our natural clock works for 25 hours, it seems to be more robust than the 24 hors one, due to interactions with many other circadian clocks. Our body has many different internal clocks that make it work properly. They are all interconnected, so some of them depend on others.

Also, because we are being in interaction with other animals, plants, and their clocks, ours have been adapted to the whole system. 

Understanding these circadian rhythms is tantamount for many reasons. On the one hand, it can help us understand interactions in the complex nature of ecology, but also in social networks. We can see which phenomena (which clocks) are the most relevant ones in interactions to know and forecast the effects of one of the clocks weaken, for example. But on the other hand, it can improve how we administrate medicines to sick people, in order for it to synchronize with the suitable clock to make it reach its destiny in the most efficient manner.
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It was expected, is was a loud secret, but it is well deserved prize.
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The detection and verification of the Gravitational Waves predicted by Einstein in 2016 has been awarded with the Physics Nobel prize 2017.

​Science might look less exciting in real life than in movies, as there everything is so fast, so stressful, that it seems that you only need seconds to revolutionize life.

But that is far from truth. I remember studying General Relativity in my last year in college. It was one of the courses that I most enjoyed, time dilation, gravitational pull that distorts space and time, black holes, cosmology. Gravitational waves, GW, was one chapter that I did not expect, I though that was going to be a rough mathematical one with minor implications. But it wasn't. It was surprising to imagine that we could see beyond light by using GW. Indeed, in the final project that I had to do in that course I was asked to figure out a way to detect them. I related that to the solid state course that I was taking at the same time. But I was off by several orders of magnitude.
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At that time the LIGO project was a baby just newborn.

The discovery of GW is not just one more of hundreds of demonstrations that Einstein's General Relativity works (I'd say rules), but it is the opening of new eyes to the Universe.

I was socked when the first announcement of their detection on Earth, I was waiting for the LISA project. The LIGO experiment, that triangulates with three detectors now (two in the U.S. and one in Italy) is able to see were the light can't reach. It is able to study phenomena that can't otherwise be studied.

It is the opening of a new astronomy, and I am proud and happy that Carleton College has contributed to that achievement.

Next Monday October 16th LIGO will make a new announcement, probably detection of neutron star merger? We better stay tuned.

Here and here you can find the last of the publications of the LIGO team on September 2017.​