Arazo, María

idUS. Depósito de Investigación Universidad de Sevilla

On the 14th BWMCMaria ArazoUniversitat de BarcelonaEmail: maria.arazo@gmail.comAttending the 14th Brainstorming Week on Membrane Computing1 has been achallenge in many ways. A whole week in a place I had never been before, witha group of people I did not know, and learning about a topic which existence Icompletely ignored. With all that, given my initial hesitation, I am glad I decidedto go, because it was worth it. I attended the 14th BWMC with six other Physicsstudents from University of Barcelona who, like me, were interested in computa-tional physics and were curious about the workshop, that took place in Sevillefrom February 1st to 5th, 2016.First of all, I could say that in some talks I got lost almost at the beginning; theywere aimed for an audience with extensive knowledge on the topic of membranecomputing and a solid background on mathematics and/or computer science. Inother words, as a physicist and undergraduate student I felt a bit out of place.However, the tutorial sessions, that were meant to introduce membrane computingto those new to the field, were really useful and allowed me to follow the laterpresentations. It was also crucial and appreciated the patience of the workshopattendants; they answered any questions we asked them and even simplified someof the talks so students could follow them more easily.Many specific topics and applications of membrane computing to other fieldswere presented during the talks. Some of them were more accessible for me thanothers, but in any way I found it interesting to listen to them, and to see howeach attendee exposed about his/her research area. Despite the variety of topicsthat were treated, though, I would like to focus my memoir on a simple idea and aquestion: the basics of membrane computing, and how can it be applied to physics.To summarise, membrane computing is a computational model inspired by na-ture, in which certain processes defined by rules take place in a system or cell thatis hierarchically structured in compartments that are called membranes. This kindof systems, named P-systems after their creator Gheorghe Pa˘un, are composed ofmultisets of objects, membranes delimiting the regions of the system, an environ-ment, and rules that describe how a number of systems, also called machine (i.e.1 14th BWMC website: http://www.gcn.us.es/14bwmc.98 Maria Arazothe cell), works according to its objects and membranes, and how they interactwith each other. In the simplest case, it is considered that time is the same for allmembranes, so a computational step comprises a series of transitions that occurregarding to the set of rules that is applied. Furthermore, in every computationalstep the maximal number of possible rules is applied in each membrane. The ruleswill be applied in each step until no more rules can be applied, in which case thecomputation halts.An interesting characteristic element of those systems is that they presentthe possibility of adding a probabilistic factor to the rules, so a transition canfollow different rules with the corresponding probabilities that have been defined.This introduces the concept of “fuzzy logic”. Another main point of membranecomputing is that it allows us to study a system with a very large number ofinitial objects as if all of them evolved independently and in a parallel way, like ithappens on real biological systems, being the computational time proportional tothe number of steps defined by the rules.With this simple picture of the P-systems in mind, I think that it is impossiblenot to think in similar physical systems or in other problems that can be simpli-fied in order to be modeled with membrane computing. In fact, motivated by theworkshop attendants, which encouraged us to investigate how membrane comput-ing could involve physics and vice versa, and moved also by our own curiosity,we thought about the improvements that membrane computing could bring intophysics and in which cases could we apply it.An important constraint we saw was that any system defined in the continuumneeded to be discarded, because the set of objects that we consider is discrete.Nevertheless, membrane computing allows us to study certain magnitudes of asystem with no need to define neither positions nor momenta.The first case we decided to study was the Stern-Gerlach experiment of Quan-tum Mechanics. It is a simple example that can be modeled by membrane com-puting, where the magnitude under study is the third component of the spin ofa very large number of incident particles that initially we define as positive andthat after going through a Stern-Gerlach device can change or remain the samewith probabilities that depend on the angle in which the Stern-Gerlach is oriented.By using a very high number of particles, the final count of positive and negativethird components reproduces, respectively, the probabilities expected, and thus weshow that by taking a measure, the result is altered.The second example we considered is the uranium-238 decay chain, where wehad to take several simplifications in order to apply what we had learnt frommembrane computing. Initially, we start with n uranium nuclei, that naturallydecay to form thorium-234 nuclei emitting α particles. While this decay takes place,since the resulting nuclei are also radioactive, they will decay in turn followingthe decay chain, until lead-206 is reached, which is a stable nucleus. The evidentproblem that this system entails is that, as we begin with n nuclei and not with asingle nucleus, the number of disintegrations that compound the chain depend onthe amount of parent nuclei left at every step of time, so we had to consider thatOn the 14th BWMC 99a new reaction could not begin until all the parent nuclei of the step before of thechain had decayed. With that unrealistic but useful approximation, the differentdisintegrations or reactions that form the decay chain are uncoupled to each other,and the resulting system can be easily modeled with membrane computing. Asecond simplification we had to take into consideration, which derives essentiallyfrom the first one, is that the time it takes for every reaction to take place mustbe constant and proportional to a certain number of time steps.With those simplifications, all complexity and part of the interest of the systemvanish and we are left with a rather simple problem, so we tried to study it, as inthe first case, as a statistical problem: given that some nuclei can follow differentdecay modes that are weighed by some probabilities experimentally determined,membrane computing allows us to count at the end of the computation, onceall reactions have taken place, the amount of resultant particles of each kind thathave been emitted at every step. Since our nuclei decay mainly following α and β−decay, we expected alpha particles or antineutrinos and electrons, and therefore wecould see if the amounts of the different kinds of particles (that denoted the decaymode followed in each step) were the same for every initial U-238 nuclei or showedvariations. Again, this is a very simple case and with a questionable utility, but itoccurred to us that perhaps it could be described with another kind of system thatallowed us to remove the simplifications and consider the real system and how itevolved in time. For the time being, we are working on it.The attendees and organizers of the venue were, as I mentioned at the begin-ning, another remarkable element of the workshop. They not only helped us toenter into a world of which we knew little or nothing, but also made us feel likeat home and encouraged us to participate more actively in the workshop. Thatat the end of the workshop we were presenting the few ideas we had been able tocollect during the week, apart from putting us under pressure and keeping us busyeven in the sparse free hours, was also a great motivation for asking and trying tounderstand more deeply.Last but not least, I would like to emphasize how much I have learnt from mycolleagues. Even though most of us had not met before, we managed to work asa group, first to help each other to understand what was explained in the talks,and later to make motivation alive and to work together in our little contributionto the workshop. We had very similar motivations, and that encouraged us tonaturally build a team to achieve our common goal. And, at least in my case, Ihave participated much more in the workshop that what I would have participatedhad I gone alone.To conclude, I think it has been a very rewarding experience, useful to learnabout a new topic and to see how research about it was accomplished, to practicewith team work, and to motivate me to improve in my studies and to head towardsresearch.

On the 14th BWMC

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On the 14th BWMC

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idUS. Depósito de Investigación Universidad de Sevilla