Construction and performance of network codes

El principal objectiu d'aquest treball és implementar i exposar una descripció teòrica per a diferents esquemes de Physical Layer Network Coding. Utilitzant un esquema bàsic com a punt de partida, el projecte presenta la construcció i l'anàlisis de diferents esquemes de comunicació on la complexitat va augmentant a mesura que anem avançant en el projecte. El treball està estructurat en diferents parts: primer, es presenta una introducció a Physical Layer Network Coding i a Lattice Network Codes. A continuació, s'introdueixen les eines matemàtiques necessàries per entendre el CF System. Després, s'analitza i implementa el primer esquema bàsic. A partir del qual, implementem una versió vectorial del CF System i una versió codificada amb un Hamming q-ari. Finalment, s'estudien i implementen diferents estratègies per millorar la matriu de coeficients A.

A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

Les codes de l'obligations : méta-analyses pragmatologiques de l'application de méthodes en sciences sociales

Cette thèse rassemble une série de méta-analyses, c'est-à-dire d'analyses ayant pour objet des analyses produites par des sociologues (notamment celles résultant de l'application de méthodes de traitement des entretiens). Il s'agit d'une démarche réflexive visant les pratiques concrètes des sociologues. Celles-ci sont envisagées comme des activités gouvernées par des règles. Une part importante de cette thèse sera donc consacrée au développement d'un outil d'analyse « pragmatologique » (E. Durkheim), c'est-à-dire permettant l'étude des pratiques et des règles en rapport avec elles. Pour aborder les règles, la philosophie analytique d'inspiration wittgensteinienne apporte plusieurs propositions importantes. Les règles sont ainsi considérées comme des concepts d'air de famille : il n'y a pas de définitions communes recouvrant l'ensemble des règles. Pour étudier les règles, il convient alors de faire des distinctions à partir de leurs usages. Une de ces distinctions concerne la différence entre règles constitutives et règles régulatives : une règle constitutive crée une pratique (e.g. le mariage), alors qu'une règle régulative s'applique à des activités qui peuvent exister sans elle (e.g. les règles du savoir-vivre). L'activité méthodologique des sociologues repose et est contrainte par ces types de règles, qui sont pour l'essentiel implicites. Cette thèse vise donc à rendre compte, par la description et la codification des règles, du caractère normatif des méthodes dans les pratiques d'analyse de la sociologie. Elle insiste en particulier sur les limites logiques qu'instituent les règles constitutives, celles-ci rendant impossibles (et non pas interdites) certaines actions des sociologues. This thesis brings together a series of meta-analyzes, that is, analyzes that tackle analyzes produced by sociologists (notably those resulting from the application of methods in treating interviews). The approach is reflexive and aimed at the concrete practices of sociologists, considered as activities governed by rules. An important part of this thesis is therefore devoted to the development of a "pragmatological" analytical tool (Durkheim) to conduct a study of such practices and of the rules that govern them. To approach these rules, Wittgenstein-inspired analytic philosophy offers several important proposals. The rules are, at first, seen as concepts of family resemblance, assuming that there is no common definition accounting for all rules. In order to conduct the study of such rules, it is therefore necessary to discern how they are respectively used. One of these distinctions concerns the difference between constitutive rules and regulative rules: a constitutive rule creates a practice (for example marriage), while a regulative rule applies to activities that can exist outside of the rule (for example, the rules of etiquette). The methodological activity of sociologists relies on, and is constrained by these types of rules, which are essentially implicit. Through the description and codification of rules, this thesis aims to account for the normative character of methods governing analytical practices in sociology. Particular emphasis is on the logical limits established by constitutive rules, limits that render several of the sociologist's actions impossible (rather than forbidden).

Performance Analysis of Two Quantum Reaction Dynamics Codes: Time-Dependent and Time-Independent Strategies

The computer simulation of reaction dynamics has nowadays reached a remarkable degree of accuracy. Triatomic elementary reactions are rigorously studied with great detail on a straightforward basis using a considerable variety of Quantum Dynamics computational tools available to the scientific community. In our contribution we compare the performance of two quantum scattering codes in the computation of reaction cross sections of a triatomic benchmark reaction such as the gas phase reaction Ne + H2+ %12. NeH++ H. The computational codes are selected as representative of time-dependent (Real Wave Packet [ ]) and time-independent (ABC [ ]) methodologies. The main conclusion to be drawn from our study is that both strategies are, to a great extent, not competing but rather complementary. While time-dependent calculations advantages with respect to the energy range that can be covered in a single simulation, time-independent approaches offer much more detailed information from each single energy calculation. Further details such as the calculation of reactivity at very low collision energies or the computational effort related to account for the Coriolis couplings are analyzed in this paper.

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

The Impact of Supervisor's Advice, Codes of Conduct, Accountability and Moral Attentiveness of Individuals on Discriminatory Behaviour Against Immigrants.

Past studies on the personnel selection demonstrated that a supervisor's advice to discriminate can lead to compliant behaviours. This study had the aim to extend past findings by examining what can overcome the powerful influence of the hierarchy. 50 Swiss managers participated to an in-basket exercise. The main task was to evaluate Swiss candidates (in-group) and foreigners (out-groups: Spanish and Kosovo Albanians) and to select two applicants for a job interview. Main results were the effect of codes of conduct to prevent discrimination against out-group applicants in the presence of a supervisor's advice to prefer in-group members. But, when participants were accountable to an audience, this beneficial effect disappears because participants followed the supervisor's advice. The second aim was to assess if the difference in responses between participants was related to their difference in moral attentiveness. Results showed some significant relationships but not always in the direction expected.

Adquisició de les codes complexes finals del català per part d'alumnat panjabi: el mètode experimental

En aquest treball estudiem l’adquisició del català per part de parlants que tenen el panjabi com a primera llengua, concretament en relació amb les codes complexes de final de mot, per a aprenents d’un nivell inicial de català

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

On Topological Solitons in The Faddeev-Skyrme Model and its Extensions

The topological solitons of two classical field theories, the Faddeev-Skyrme model and the Ginzburg-Landau model are studied numerically and analytically in this work. The aim is to gain information on the existence and properties of these topological solitons, their structure and behaviour under relaxation. First, the conditions and mechanisms leading to the possibility of topological solitons are explored from the field theoretical point of view. This leads one to consider continuous deformations of the solutions of the equations of motion. The results of algebraic topology necessary for the systematic treatment of such deformations are reviewed and methods of determining the homotopy classes of topological solitons are presented. The Faddeev-Skyrme and Ginzburg-Landau models are presented, some earlier results reviewed and the numerical methods used in this work are described. The topological solitons of the Faddeev-Skyrme model, Hopfions, are found to follow the same mechanisms of relaxation in three different domains with three different topological classifications. For two of the domains, the necessary but unusual topological classification is presented. Finite size topological solitons are not found in the Ginzburg-Landau model and a scaling argument is used to suggest that there are indeed none unless a certain modification to the model, due to R. S. Ward, is made. In that case, the Hopfions of the Faddeev-Skyrme model are seen to be present for some parameter values. A boundary in the parameter space separating the region where the Hopfions exist and the area where they do not exist is found and the behaviour of the Hopfion energy on this boundary is studied.

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Z2Z4-Additive Perdect Codes in Steganography

Steganography is an information hiding application which aims tohide secret data imperceptibly into a cover object. In this paper, we describe anovel coding method based on Z2Z4-additive codes in which data is embeddedby distorting each cover symbol by one unit at most (+-1-steganography). Thismethod is optimal and solves the problem encountered by the most e cientmethods known today, concerning the treatment of boundary values. Theperformance of this new technique is compared with that of the mentionedmethods and with the well-known rate-distortion upper bound to conclude thata higher payload can be obtained for a given distortion by using the proposedmethod.