Introducing probabilistic celular automata. A versatile extension of Game of Live

The "Game of life" model was created in 1970 by the mathematician Jonh Horton Conway using cellular automata. Since then, di erent extensions of these cellular automata have been used in many applications, such as car traffic control or baggage traffic in an airport. These extensions introduce ideas not only from cellular automata models but also from neural networks theory. In this work, we introduce probabilistic cellular automata which include non-deterministic rules for transitions between successive generations of the automaton together with probabilistic decisions about life and death of the cells in next generation of the automaton. This way, more realistic situations can be modeled and the obtained results are also non-deterministic. As an example of use, an implementation of this probabilistic cellular automaton has been developed using it for simulating tissues evolution. The authors are specially interested in simulations of cancerous tissues.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A fast functional approach to personalized menus generation using set operations

The authors developed some time ago a RBES devoted to preparing personalized menus at restaurants according to the allergies, religious constraints, likes and other diet requirements as well as products availability. A first version was presented at the "Applications of Computer Algebra 2015" (ACA'2015) conference and an improved version to the "5th European Seminar on Computing" (ESCO2016). Preparing personalized menus can be specially important when traveling abroad and facing unknown dishes in a menu. Some restaurants include icons in their menu regarding their adequateness for celiacs or vegetarians and vegans, but this is not always a complete information, as it doesn't consider, for instance, personal dislikes or uncommon allergies. The tool previously developed can obtain, using logic deduction, a personalized menu for each customer, according to the precise recipes of the restaurant and taking into account the data given by the customer and the ingredients out of stock (if any). Now a new approach has been followed, using functions and set operations and the speed has been increased by three orders of magnitude, allowing to deal with huge menus instantly. Both approaches have been implemented on the computer algebra system Maple and are exemplified using the same recipes in order to compare their performances.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Computer Algebra-based RBES personalized menu generator

People have many constraints concerning the food they eat. These constraints can be based on religious believes, be due to food allergies or to illnesses, or can be derived just from personal preferences. Therefore, preparing menus at hospitals and restaurants can be really complex. Another special situation arise when travel- ing abroad. It is not always enough to know the brief description in the restaurant menu or the explanation of the waiter. For example, “calamares en su tinta” (squid in its own ink) is a delicious typical Spanish dish, not well-known abroad. Its brief description would be “squid with boiled rice in its own (black) ink”. But an in- gredient (included in a small amount, in order to thicken the sauce) is flour, a fact very important for someone suffering from celiac disease. Therefore, we have con- sidered that it would be very interesting to develop a Rule Based Expert System (RBES) to address these problems. The rules derive directly from the recipes and contain the information about required ingredients and names of the dishes. We distinguish: ingredients and ways of cooking, intermediate products (like “mayon- naise”, that doesn’t always appear explicitly in the restaurants’ menus) and final products (like “seafood cocktail”, that are the dishes listed in the restaurant menu). For each customer at a certain moment, the input to the system are: on one hand, the stock of ingredients at that moment, and on the other, the religion, allergies and restrictions due to illnesses or personal preferences of the customer. The RBES then constructs a “personalized restaurant menu” using set operations and knowl- edge extraction (thanks to an algebraic Groebner bases-based inference engine[1]). The RBES has been implemented in the computer algebra system Maple TM 18(us-ing its convenient Embedded Components) and can be run from computers and tablets using Maple TM or the Maple TM PlayerUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A RBES for Generating Automatically Personalized Menus

Food bought at supermarkets in, for instance, North America or the European Union, give comprehensive information about ingredients and allergens. Meanwhile, the menus of restaurants are usually incomplete and cannot be normally completed by the waiter. This is specially important when traveling to countries with a di erent culture. A curious example is "calamares en su tinta" (squid in its own ink), a common dish in Spain. Its brief description would be "squid with boiled rice in its own (black) ink", but an ingredient of its sauce is flour, a fact very important for celiacs. There are constraints based on religious believes, due to food allergies or to illnesses, while others just derive from personal preferences. Another complicated situation arise in hospitals, where the doctors' nutritional recommendations have to be added to the patient's usual constraints. We have therefore designed and developed a Rule Based Expert System (RBES) that can address these problems. The rules derive directly from the recipes of the di fferent dishes and contain the information about the required ingredients and ways of cooking. In fact, we distinguish: ingredients and ways of cooking, intermediate products (like sauces, that aren't always made explicit) and final products (the dishes listed in the menu of the restaurant). For a certain restaurant, customer and instant, the input to the RBES are: actualized stock of ingredients and personal characteristics of that customer. The RBES then prepares a "personalized menu" using set operations and knowledge extraction (thanks to an algebraic inference engine [1]). The RBES has been implemented in the computer algebra system MapleTM2015. A rst version of this work was presented at "Applications of Computer Algebra 2015" (ACA'2015) conference. The corresponding abstract is available at [2].Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

La tutoría en la universidad: selección, formación y práctica de los tutores: ajustes para la UCM desde el Espacio Europeo de Educación Superior

La finalidad de esta tesis consiste en plantear unas directrices para la realización de tutorías universitarias integradas en la actividad docente, en el seno de la actual universidad española y, acorde con lo exigido por la convergencia europea en materia de educación superior. De esta forma, se busca preparar el camino que permita la conformación del tutor universitario y su inclusión en la docencia

Making more flexible ATISMART+ model for traffic simulations using a CAS

Traffic simulations usually require the search of a path to join two different points. Dijkstra’s algorithm [1] is one of the most commonly used for this task due to its easiness and quickness. In [2, 3] we developed an accelerated time simulation of car traffic in a smart city using Dijkstra’s algorithm to compute the paths. Dijkstra’s algorithm provides a shortest path between two different points but this is not a realistic situation for simulations. For example, in a car traffic situa- tion, the driver may not know the shortest path to follow. This ignorance can be produced, among others, because one of the following two facts: the driver may not know the exact length of the lanes, or, even knowing the exact length, the driver may not know how to find the shortest path. Even more, in many cases, a mixture of both facts occurs. A more realistic simulation should therefore consider these kind of facts. The algorithm used to compute the path from one point to another in a traffic simulation might consider the possibility of not using the shortest path. In this talk, we use a new probabilistic extension of Dijkstra’s algorithm which covers the above two situations. For this matter, two different modifications in Di- jkstra’s algorithm have been introduced: using non-exact length in lanes, and the choice of a non-shortest path between two different points. Both modifications are used in a non-deterministic way by means of using probability distributions (classi- cal distributions such as Normal or Poisson distributions or even "ad hoc" ones). A precise, fast, natural and elegant way of working with such probability distributions is the use of a CAS in order to deal with exact and explicit computations. As an example of use of this extension of Dijkstra’s algorithm, we will show the ATISMART+ model. This model provides more realistic accelerated time sim- ulations of car traffics in a smart city and was first introduced in [4] and extended in [5]. This model was developed combining J AVA for the GUI and M AXIMA for the mathematical core of the algorithm. The studies developed in the above mentioned works, dealt with Poisson, Ex- ponential, Uniform and Normal distributions. In this talk we will introduce, as a novelty, the possibility of using other continuous probability distributions such as: Lognormal, Weibul, Gamma, Beta, Chi-Square, Student’s t, Z, Pareto, Lo- gistic, Cauchy or Irwin-Hall, and other discrete distributions such as: Bernouille, Rademacher, Binomial, Geometric, Negative Binomial or Hypergeometric. Even 1 more, this new version allows to deal with any “ad-hoc” continuous, discrete or mixed user’s distributions. This fact improves the flexibility of ATISMART+ model.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

New rules for improving CAS capabilities when computing improper integrals. Applications in Math Education

In many Engineering applications the computation of improper integrals is a need. In [1] we pointed out the lack of some CAS when computing some types of improper integrals. Even more, the work developed showed that some improper integrals can not be computed with CAS using their build-in procedures. In this talk we will develop new rules to improve CAS capabilities in order to compute new improper integrals We will show some examples of improper integrals that CAS asMATHEMATICA, MAPLE, DERIVE or MAXIMA can not compute. Using advance techniques as Laplace and Fourier transforms or Residue Theorem in Complex Analysis, we will be able to develop new rules schemes for these improper integrals. We will also describe the conclusions obtained after using these new rules with our Engineering students when teaching Advanced Calculus. [1] José L.Galán-García, Gabriel Aguilera-Venegas, María Á. Galán-García, Pedro Rodríguez-Cielos, Iván Atencia-Mc.Killop. Improving CAS capabilities: New rules for computing improper integrals. Applied Mathematics and Computation. Volume 316, 1 January 2018, Pages 525-540.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

An Approach to Overtaking Station Layout Diagram Design Using Graphs

The authors have approached in the past different railway engineering problems (e.g. [1,2]) and have developed software for the Spanish Railway Foundation [3], mainly using computer algebra systems (CAS). Now a CAS is used for designing and implementing a software package that allows to compare different layout diagrams for overtaking stations [4], from the point of view of its flexibility (for instance in degraded working conditions). The most common cases of overtaking stations (stations on double track lines with one or two sidings each side of the main line and one or two crossovers at the two throats of the overtaking station) are considered as illustration. It will be shown how, surprisingly, the usual position of the crossovers is not optimum from this point of view. The key idea is to use graph theory to determine the number of pairs of non conflicting itineraries (one in each direction) that can be simultaneously authorized by the railway interlocking system. The package can be applied to an overtaking station with any layout diagram. This is an important issue: for instance, the Spanish infrastructure administrator (Adif) is now planning a new track layout for Madrid Chamartín station [5] and the Iberian gauge part of Madrid Atocha station.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Random samples generation with Stata from continuous and discrete distributions

Simulations are nowadays a very important way of analyzing new improvements in different areas before the physical implementation, which may require hard resources which could only be affronted in case of a high probability of success. The use of random samples from different distributions are a must in simulations. In this talk we introduce new Stata functions for generating random samples from continuous and discrete distributions that are not considered in the defined Stata random-number generation functions. In addition, we will also introduce new Stata functions for generating random samples as an alternative of the build-in Stata functions. The goodness of the generated samples will be checked using the mean squared error (MSE) of the differences between the frequencies of the sample and the theoretical expected ones. We will also provide bar charts which will allow the user to compare graphically the sample with the exact distribution function of the random distribution which is being sampled.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec