Nature has produced a video to explain our research and my most recent article on causal deconvolution
as part of the Algorithmic Information Dynamics programme and the field that we have introduced
I was invited to an Ask Me Anything session available here
​and was in the top 10 all time Reddit/PLOS Science AMAs in 2018
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At Christ Church College, Oxford
short bio
I consider myself a 'computational natural scientist' (Greg Chaitin described me as a "new kind of practical theoretician").  ​I co-lead the Algorithmic Dynamics Lab at the Karolinska Institute (one of the institutions that awards the Nobel Prize) in Stockholm, Sweden, where I team up with experimental scientists such as molecular biologists, immunologists, oncologists, toxicologists, and other mathematicians to understand biological processes and living systems. We approach these problems in very innovative ways such as with a new cryptocurrency Automacoin that, unlike others, performs only useful computation. The coin came as one of several projects led by my students from our course on Algorithmic Information Dynamics at the Santa Fe Institute Complexity Explorer.

I also lead the Algorithmic Nature Group, the Paris-based lab that started the Online Algorithmic Complexity Calculator and the Human Randomness Perception and Generation Project (triggering wide media coverage), an inverse Turing test performed on ~3.4K people.​  Previously, I was a Research Associate at the Behavioural and Evolutionary Theory Lab at the Department of Computer Science at the University of Sheffield in the UK before joining the Department of Computer Science at the University of Oxford as a Senior Researcher (faculty member) and director of Oxford Immune Algorithmics. I am also a member of the Mexican National System of Researchers (SNI II), and an elected member of the London Mathematical Society in the UK. 

I am also the Managing Editor of Complex Systems, the first journal in the field founded by Stephen Wolfram in 1987. I am member of the Editorial Board of publications and book series such as the Springer series on Emergence, Complexity and Computation, the journals Philosophies and Frontiers in Robotics and AI for its Computational Intelligence section, among other journals. I also serve as consultant/advisor for labs and organisations such as Wolfram Research, the Living Systems Lab, Intuition Machine, and Veda Data.

When not traveling, I spend must of my time in Oxford, London-Reading and Stockholm. 

My Research in a Nutshell
​
My current aims are:
  1. to find ways to reprogram natural and synthetic systems such as biological cells as we do computers, e.g. to reprogram immune cells to differentiate into more specialised cells to fight specific diseases,
  2. to establish strong formal and numerical connections between the discrete and the continuous by way of computational and equational dynamical systems key to connect fundamental science such as information theory and applications to areas such as genetics, and
  3. to introduce symbolic computation to statistical machine learning and differentiable programming (such as deep learning) by exploiting aspects of algorithmic information theory into a form of hybrid computation to better deal with causation and produce more robust approaches to machine learning circumventing trivial statistical adversarial attacks. 

By introducing model-based approaches my team and I are thus merging some of the most exciting areas in science such as dynamical systems, complexity science and artificial intelligence in application to another set of exciting areas such as molecular, genetic, evolutionary and behavioural biology (cognition).
​One year before passing away, Marvin Minsky, widely considered the founding father of Artificial Intelligence, made an astonishing claim describing what turns out to be exactly my research aim and purpose in a closing statement at a prime venue (video on the right):
​"It seems to me that the most important discovery since Gödel was the discovery by Chaitin, Solomonoff and Kolmogorov of the concept called Algorithmic Probability which is a fundamental new theory of how to make predictions given a collection of experiences and this is a beautiful theory, everybody should learn it, but it’s got one problem, that is, that you cannot actually calculate what this theory predicts because it is too hard, it requires an infinite amount of work. However, it should be possible to make practical approximations to the Chaitin, Kolmogorov, Solomonoff theory that would make better predictions than anything we have today. Everybody should learn all about that and spend the rest of their lives working on it."

​​​Marvin Minsky
Panel discussion on The Limits of Understanding
World Science Festival, NYC, Dec 14, 2014
ffwd to 1h30m02s
On the other hand, these excerpts from a review article by Sydney Brenner — the 2002 Nobel prize in Physiology or Medicine laureate awarded by the Karolinska Institute -- completes the picture of what I and my lab at the Karolinska Institute strive: 
"[on biological research] in Alan Turing’s work there is much to guide us 
​.  .  .  Although many believe that ‘more is better’, history tells us that ‘least is best’. We need theory and a firm grasp on the nature of the objects we study to predict the rest . . .   The concept of the gene as a symbolic representation of the organism — a code script — is a fundamental feature of the living world and must form the kernel of biological theory."  (my brackets)
Sydney Brenner
'Turing centenary: Life's code script'
​Nature 482(7386):461, 2012
"AI is currently split. First, there are those who are intoxicated by the success of machine learning and deep learning and neural nets. They don’t understand what I’m talking about. They want to continue to fit curves. But when you talk to people who have done any work in AI outside statistical learning, they get it immediately. I have read several papers written in the past two months about the limitations of machine learning."

The way you talk about curve fitting, it sounds like you’re not very impressed with machine learning.
"No, I’m very impressed, because we did not expect that so many problems could be solved by pure curve fitting. It turns out they can. But I’m asking about the future — what next? Can you have a robot scientist that would plan an experiment and find new answers to pending scientific questions? That’s the next step. We also want to conduct some communication with a machine that is meaningful ...
Judea Pearl
To Build Truly Intelligent Machines, Teach Them Cause and Effect
Interview in Quanta Magazine, May 2018.
My research consists in cracking the universe (quite literally) based on algorithmic and computation based on the theory of algorithmic complexity producing candidate computer programs as generative models of natural phenomena built from small pieces of code as the result of conducting the largest ever search of the space of computer programs with some of the fastest supercomputers in the world. We then try to match those computable models to data by literally putting the pieces together (we call it, the Block Decomposition method). Algorithmic Information Dynamics (or Algorithmic Dynamics in short) is the name of the field that we came up with that allow us to do all this and is based on a new type of discrete calculus (that we are also trying to connect to the continuous world). This new body of literature helps us study causation by algorithmic modelling to reveal possible first principles behind natural processes building-up the next generation of algorithmic data analysis, algorithmic machine learning and algorithmic cognition. Teaming up with immunologists, bioinformaticians, toxicologists, oncologists, cognitive scientists and molecular biologists, the lab I co-lead applies this new theory and methods to areas such as behavioural, evolutionary and molecular biology.
Inspired by a twit from Moshe Vardi, one of the most celebrated contemporary computer scientists, this is the state of one of the most successful areas in AI, that of machine and deep learning explained as a job interview:

Interviewer (Human): What is you greatest strength?
Deep Neural Network (DNN): I am an expert in Machine and Deep Learning
Human: What's 10 + 2?
DNN: Zero
Interviewer: Nowhere near, it's 12.
DNN: OK, 12
Interviewer: What's 10 + 5?
DNN: 12

Without denying the success of machine and deep learning in some areas, especially in tasks of classification that have proven to be so prosperous especially in industrial applications. Computers, are much better than humans at doing math and making logical inferences, so how did we manage to make computers this dumb out of logically and mathematically highly literate calculators?
One of my research aims at combining symbolic computation and machine learning to alleviate current limitations in areas such as deep learning. Here is a video produced by Nature explaining my research in the context of our most recent paper on causal deconvolution combining what Sydney Brenner, Marvin Minsky and Judea Pearl think is the way forward for science and artificial intelligence:
I got interested in neural networks from the standpoint of computability and complexity theory in my early 20s when writing my final year memoir for my BSc in math degree​​ at UNAM. Today I am trying to help revolutionise the area by reintroducing the theories of computability and algorithmic randomness back into the field of neural networks, in particular, to machine and deep learning.

​On the right is an image showing how a deep neural network trained with a large set of fine art paintings 'sees' me. My current research consists in helping machine and deep learning see beyond statistical patterns in more clever ways than simple pattern matching. By introducing algorithmic probability to artificial intelligence we aim at helping traditional deep learning to incorporate more abstract thinking of the type needed to understand the basic concept of cause and effect.
 
Known to underperform in tasks requiring abstraction and logical inference, current approaches to deep neural networks are very limited. An example of our research in this direction is our paper published in Nature Machine Intelligence that can be read here for free (no paywall).
As reported in  our paper published in the journal of Cellular Automata (also available in the arXiv), by exhaustive exploration of rule composition, two 4-colour cellular automata that we've proved to be Turing universal.
This means that these CAs can, in principle, run MS Windows and any other software.
These new CAs helped us show how the Boolean composition of two and three ECA rules can emulate rule 110.
This also means that these new CAs can be decomposed into simpler rules and thus illustrates the process of causal composition and decomposition. It also constitutes a form of sophisticated causal coarse-graining that I have explored in other papers such as this one. In the same paper we also introduced a minimal set of ECA rules that can generate all others by Boolean composition.
CAs that we have proven to be Turing-universal using novel methods, they are able to run any computable function and are the result of combining the power of extremely simple computer programs (ECAs):
Composition of ECA rules 50 ◦ 37 with colour remapping leading to a 4-colour Turing universal CA emulating rule 110.
Composition of ECA rules 170 ◦ 15 ◦ 118 with colour re-mapping mapping leading to a 4-colour Turing universal CA emulating rule 110.

Latest news

AUTOMATA 2020
I am the organiser and chair of the prestigious AUTOMATA 2020 that has been running for about 2 decades now and next year will be held in Stockholm. The website is now available but it is being updated constantly. More details will be announced on the website.
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A new kind of research-based cryptocurrency:
​My students and I are developing a new more responsible and eco-friendly cryptocurrency to help science reveal models of the world. We are creating and developing the first coin whose purpose is to perform the most meaningful computation (all possible useful computations). It provides a sense and meaning to crypto-mining and, in a sense, is thus the most eco-friendly coin possible as every computation involved contributes to a specific scientific calculation. It aims at using crypto-mining as a force for research rather than wasting precious resources, it will implement incremental lossless compression too. It is also the first coin purely based on the most basic computational principles that are behind all other cryptocurrencies but in a purely transparent fashion. Click on the banner to see the new website of the project. AUTOMATA 2020 is the first conference that will accept Automacoins as partial payment for conference fees.
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Conference Speaking & Organising:
  • I am chair organiser of AUTOMATA 2020, one of the main conferences in cellular automata and discrete complex systems. The conference will be host in Stockholm, Sweden in 2020. Website to be announced soon.
  • I am also closing a nice workshop in Barcelona on 'real patterns' with a talk on the algorithmic nature of the world/universe, click on it to get the full-res poster.
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Journal Anniversary:
  • The journal Complex Systems for which I was recently made its editor-in-chief. Founded 30 years ago it was the first journal in the field founded by Stephen Wolfram. To celebrate we commissioned a very nice poster that you can download and print in high resolution by clicking on it:
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Online course:
  • We have closed the first course on Algorithmic Information Dynamics---A Computational Approach to Causality and Molecular Biology: From Complex Networks to Reprogramming Cells​. More than 1200 students were enrolled and 10% of them are currently pursuing projects or became AID ambassadors and collaborators. The course will be open next year and you can register here.
Course poster, trailer and content module dependencies:
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Module dependencies of the course and of the new field of Algorithmic Information Dynamics. Orange link means conceptual/motivational dependency. Pink link means weak dependency. Blue link means strong dependency.
You can start watching and following the course (for free) online here !
Special issue on Philosophy and Epistemology of Deep Learning:
​Book season time, four books coming out in the next months:
  • Our book Algorithmic Information Dynamics: A Computational Approach to Causality and Molecular Biology. From Networks to Cells has been approved for publication by Cambridge University Press and will be available later this year (with N.A. Kiani and J. Tegnér)
  • Our book Methods and Applications of Algorithmic Complexity: From Sequences to Graphs is also coming out soon published by Springer Verlag later this year (with F. Soler-Toscano and N. Gauvrit).
  • Two more books will see the light next year: Algorithmic Cognition (with N. Gauvrit and J. Tegnér) and Graph Complexity (with N.A. Kiani and  J. Tegnér), both to be published by Springer Verlag.​ Here the line-up:

Other authored and edited books:

'Lo que cabe en el espacio' a short book I prepared right after my BSc degree, is available for Kindle and for free in mobi and pdf.

As contributor:

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I contributed to the final materialization of the Leibniz-Chaitin medallion after Leibniz' original design 300 years ago to celebrate his discovery of binary arithmetic
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The Leibniz-Chaitin medallion story in celebration of the works of Greg Chaitin and the discovery of binary arithmetic from which, according to Leibniz, everything can be created
I have visited more than 250 cities in about 50 countries giving talks related to my
research in about half of them, ​and as invited speaker in 13:
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Histograms of countries and continents: