Fuzzy set Theory and Quantum Chemistry

Es discuteixen breument algunes consideracions sobre l'aplicació de la Teoria dels Conjunts difusos a la Química quàntica. Es demostra aqui que molts conceptes químics associats a la teoria són adequats per ésser connectats amb l'estructura dels Conjunts difusos. També s'explica com algunes descripcions teoriques dels observables quàntics es potencien tractant-les amb les eines associades als esmentats Conjunts difusos. La funció densitat es pren com a exemple de l'ús de distribucions de possibilitat al mateix temps que les distribucions de probabilitat quàntiques

Inside the competences evaluation, the stress tolerance of students. An empirical study based on conservation of resources theory

Competence development is considered a preventive strategy of burnout. At an organizational context some competences could be linked as precursors or consequences. In self-assessment of competence development, students perceive stress tolerance as a priority competence to ameliorate. Moreover employers and recruitment consultants agree that this is a new authentic challenge for organizations. The main reasons of this result are debated, this study should consider the importance of competence development from a holistic point of view. In addition it considers the exploration of the relationship between stress tolerance and competence development, according to Conservation Resources (COR) theory (Hobfoll 1988, 1989, 1998, 2004) where the resource loss is considered the principal component in the stress process

Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

Quantified set inversion with applications to control

This paper describes a new reliable method, based on modal interval analysis (MIA) and set inversion (SI) techniques, for the characterization of solution sets defined by quantified constraints satisfaction problems (QCSP) over continuous domains. The presented methodology, called quantified set inversion (QSI), can be used over a wide range of engineering problems involving uncertain nonlinear models. Finally, an application on parameter identification is presented

Prediction of the bulking phenomenon in wastewater treatment plants

The control and prediction of wastewater treatment plants poses an important goal: to avoid breaking the environmental balance by always keeping the system in stable operating conditions. It is known that qualitative information — coming from microscopic examinations and subjective remarks — has a deep influence on the activated sludge process. In particular, on the total amount of effluent suspended solids, one of the measures of overall plant performance. The search for an input–output model of this variable and the prediction of sudden increases (bulking episodes) is thus a central concern to ensure the fulfillment of current discharge limitations. Unfortunately, the strong interrelation between variables, their heterogeneity and the very high amount of missing information makes the use of traditional techniques difficult, or even impossible. Through the combined use of several methods — rough set theory and artificial neural networks, mainly — reasonable prediction models are found, which also serve to show the different importance of variables and provide insight into the process dynamics

A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

L'herència deweyana: la Philosophy for Children de Matthew Lipman i les bases del coneixement

L'objectiu d'aquest treball s'emmarca dintre del que tradicionalment s'ha anomenat teoria del coneixement, perquè pretén examinar alguns conceptes bàsics que fonamenten i participen en el procés de coneixement. Tot això, des duna perspectiva clarament pragmatista i, més específicament, deweyana. Optar per una perspectiva clarament deweyana suposa una reformulació de nocions tradicionalment emprades per la filosofia en general i per la teoria del coneixement en particular. Els primers conceptes afectats són els de "filosofia" i "coneixement", que hauran de ser reconstruïts. Però si la noció de coneixement ha de ser replantejada, també ho haurà de ser la qüestió de les seves bases: en el millor dels casos, les bases tradicionals del coneixement no podran ser interpretades com fins ara; en el pitjor dels casos, caldrà substituir-les per noves bases. És evident que no es pot construir un nou edifici sobre vells fonaments. Així, l'anàlisi de les bases del coneixement haurà d'incidir en les diferències respecte a la interpretació tradicional del coneixement. Aquesta investigació estableix, com a hipòtesi inicial, que la noció reconstruïda de coneixement té com a condicions de possibilitat - el que hem anomenat "bases del coneixement" - l'experiència, la comunitat de recerca i el judici. Si és cert que són condicions de possibilitat del coneixement, aleshores haurien d'aparèixer com a nocions fonamentals de qualsevol teoria del coneixement - sempre que s'acceptin d'entrada els pressupòsits pragmatistes. D'altra banda, el coneixement sempre ha estat vinculat a l'educació. Així, segons la visió tradicional, el coneixement era substancial, mentre que l'educació (identificada amb la instrucció) era el procés pel qual s'adquiria aquesta fi-en-si. Ara bé, que el coneixement ja no sigui substancial sinó instrumental no significa que desaparegui la seva íntima relació amb l'educació, sinó que - necessàriament - es replantegi: l'educació passa a ser el procés obert, social, de diàleg, en el qual es desenvolupa el coneixement; un coneixement que ja no és un fi-en-si sinó que retroalimenta el mateix procés "educatiu", enriquint-lo. Hem dit que les condicions de possibilitat del coneixement són l'experiència, la comunitat de recerca i el judici. Però, alhora, aquests resulten ser també els fonaments filosòfics de l'educació; respondre realment a les necessitats dels individus i de la societat. Experiència, recerca, diàleg i judici sorgeixen tant de la mateixa naturalesa de la filosofia com de la naturalesa de l'educació. Són alhora elements d'una filosofia reconstruïda i assumpcions del paradigma reflexiu en l'educació. Així doncs, podríem dir que el judici, l'experiència de l'individu i la comunitat de recerca (aquesta en tant que context en què es donen el diàleg filosòfic i la recerca) esdevenen pressupòsits inevitables de la "nova" filosofia i de la "nova educació. "Aprendre a pensar pel propi compte" - que apareix com a l'objectiu de l'educació - suposa atendre a totes i cadascuna d'aquestes bases. En aquest context, la filosofia o teoria de l'educació esdevé una teoria filosòfica del coneixement: una reflexió sobre el coneixement i el pensament, sobre les condicions de possibilitat del coneixement, sobre els seus límits. Aquest plantejament s'enfronta explícitament a altres alternatives força més comunes i que volem intentar d'evitar: -un estudi de la filosofia de l'educació i/o de la teoria del coneixement simplement historicista, com a mer compendi de teories i autors ordenats més o menys cronològicament; -una reflexió abstracta sobre el coneixement, sense cap mena de contrastació empírica; -una investigació sociològica sobre el coneixement en el qual es privilegiïn els condicionaments sociològics (que no vol dir necessàriament socials) de l'adquisició del coneixement basant-se en realitats culturals i educatives existents però oblidant tot fonament filosòfic; o -una teoria sobre el coneixement de caire marcadament psicologista. Per tal d'evitar fer hipòtesis i reflexions en el buit, concretem el nostre estudi en un projecte concret: Philosophy for Children, perquè entenem que és una teoria del coneixement portada a la pràctica filosòfica; que posa en joc, doncs, les mateixes bases que garanteixen el coneixement. Així, aquesta investigació no és solament una reflexió sobre les bases epistemològiques de Philosophy for Children, ni una apologia del projecte, sinó que pretén posar i analitzar les bases d'una visió més global del coneixement prenent en consideració totes les seves vessants. En aquest sentit, Philosophy for Children en és útil en la mesura que serveix de suport concret per a la nostra anàlisi. Així doncs, establim que les bases del coneixement - en la seva acceptació pragmatista - són tres: experiència, comunitat de recerca i judici. Alhora, aquests elements són també condicions d'una educació reflexiva. Queden així estretament vinculades la filosofia i l'educació. Confirmar aquestes hipòtesis suposa una sèrie de passos: 1r. Analitzar la noció de filosofia que hi ha al darrera d'aquesta concepció del coneixement. No pretenem que les nostres conclusions siguin vàlides universalment (trairíem el mateix esperit pragmatista!) sinó solament que ho són en l'espai que queda delimitat per una determinada manera d'entendre la filosofia. 2n. Investigar cadascuna de les bases del coneixement en el context de les filosofies de Dewey i , especialment, de Lipman per tal d'oferir-ne una interpretació i veure en quina mesura es vinculen amb el coneixement. Això suposarà, en algun cas, recórrer a algun altre autor, per tal d'afinar més en la demarcació del concepte en qüestió. 3r. Clarificar el concepte d'educació relacionat amb el coneixement i establir els lligams corresponents amb cadascuna de les bases analitzades. Un cop fets aquests passos esperem que quedarà manifest que l'experiència, la comunitat de recerca i el judici són bases del coneixement i, alhora, elements essencials de qualsevol procés educatiu. Tot això, a més, ha d'anar acompanyat de l'exigència d'un paper actiu del filòsof en el procés educatiu. No n'hi ha prou amb "baixar la filosofia del cel a la terra"; cal que, a més, aquest descens repercuteixi en la manera com l'home es relaciona amb els altres i amb el seu entorn. Només així podrà ser superat el vell dualisme entre pensament i acció.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.