77 research outputs found
“Joie de la cort / joie de l’acort”. L’armonia degli elementi discordi nell’«Erec et Enide»
No full textL’articolo si sofferma sulla tematica delle nozze e dell’accordo degli elementi discordanti nell’Erec et Enide di Chrétien de Troyes, e sull’interpretazione allegorica della conjointure, con riferimento a Marziano Capella e a Macrobio. Una lettura allegorica viene proposta anche per il nome dell’avventura della «joie de la cort» che si può anche intendere come «joie de l’acort», in cui l’autore sintetizza come en abyme gli intenti del romanzo.The article treats the theme of the marriage and the armony of discordant elements in the Erec and Enide of Chrétien de Troyes, underlining the allegorical meaning of the conjointure, with reference to Martianus Capella and Macrobius. An allegorical interpretation is proposed also for the final adventure of the «joie de la cort» ‘Joy of the Court’, that is to be regarded also as a «joie de l’acort» ‘Joy of Agreement’, in which the author reveals and summarizes the focus of his romance.</p
A álgebra linear por trás do Google
No full textGoogle PageRank model helps evaluate the relative importance of nodes in a large graph, such as the graph of links on the World Wide Web. An important piece of the PageRank model is the damping factor d. Google relies on foundational concepts from linear algebra to evaluate and rank web pages based on their importance and relevance. In this thesis, the underlying mathematical basics for understanding how the algorithms function are provided. The concept of graphs and matrix theories are in the background, while the most important steps are in a linear algebra context especially the eigenvalue and eigenvectors of a matrix. It discusses the power iteration algorithm as an iterative method for finding the principal eigenvector, which represents PageRank scores. Google PageRank model helps evaluate the relative importance of nodes in a large graph, such as the graph of links on the World Wide Web. An important piece of the PageRank model is the damping factor d. Google relies on foundational concepts from linear algebra to evaluate and rank web pages based on their importance and relevance. In this thesis, the underlying mathematical basics for understanding how the algorithms function are provided. The concept of graphs and matrix theories are in the background, while the most important steps are in a linear algebra context especially the eigenvalue and eigenvectors of a matrix. It discusses the power iteration algorithm as an iterative method for finding the principal eigenvector, which represents PageRank scores.O modelo PageRank do Google avalia a importância das ligações entre vértices em grafos com um grande número de vértices tais como o grafo da World Wide Web. Uma peça importante do modelo PageRank é o fator de amortecimento d. A fundação do Google depende de conceitos da Álgebra Linear para avaliar e classificar páginas da web tendo em atenção a sua importância e relevância. Nesta dissertação, a matemática básica para perceber como este algoritmo funciona é apresentada. Conceitos da teoria das matrizes e teoria dos grafos são apresentados como background, enquanto que os passos mais importantes são apresentados num contexto da Álgebra Linear, dando-se destaque ao conceito de valor e vetor próprio. É discutido um método iterativo para encontrar o vetor próprio principal que é importante para classificar páginas.Mestrado em Matemática e Aplicaçõe
Chapter «Et un vergier qui fu de pris / i avoit d’eve et d’air enclos». Giardini incantati nell’Erec et Enide e nel Lai de l’oiselet (e altrove)
No full textThe author investigates the implications underlying the reprise of the enchanted garden as the setting for the story narrated in the Lai de l’oiselet and the final duel in Chrétien de Troyes’ Erec et Enide. Through comparison with other works, the main reason for this reprise is found in the character that the vergier takes on as an ‘other’ dimension, functional to the promotion of harmony between love, chivalry and community
Matrizes laplacianas: propriedades espetrais e aplicações
No full textApesar de distintas, a Teoria dos Grafos e a Teoria das Matrizes
relacionam-se, tal como sugere o facto dos grafos admitirem representações
matriciais. Dado um grafo simples, a sua matriz Laplaciana
corresponde à diferença entre a matriz diagonal dos graus dos seus
vértices e a sua matriz de adjacência. Neste trabalho estudamos propriedades
dos grafos tendo por base o conjunto dos valores próprios
das matrizes Laplacianas correspondentes. De entre estes, destacamos
o maior valor próprio, designado por índice Laplaciano, bem como
o segundo menor valor próprio, denominado por conexidade algébrica.
Através da determinação de majorantes para o índice Laplaciano conseguimos,
naturalmente, majorar todo o espetro Laplaciano e, em alguns
casos, identificar os grafos para os quais o majorante á atingido.
Por outro lado, a conexidade algébrica permite-nos medir o quão conexo
é um grafo. Adicionalmente, o vetor próprio associado à conexidade
algébrica, conhecido como vetor de Fiedler, e alvo de estudo
neste trabalho, devido à sua importância do ponto de vista prático. A
partir deste vetor conseguimos, não só, classificar grafos conexos em
um de dois tipos, mas também partir grafos conexos em exatamente
duas componentes conexas, o que se revela útil em diversos contextos.Graph Theory and Matrix Theory are related by the fact that graphs
can be represented by matrices. The study of the eigenvalues of these
matrices can determine the structure of the graph that is associated to
it. This work is related to one of these matrices, namely, the Laplacian
matrix. Given a simple graph, its Laplacian matrix corresponds to the
difference between the diagonal matrix of its vertices degrees and its
adjacency matrix. In this work we study properties of graphs, based on
the eigenvalues of its Laplacian matrices. We highlight the largest eigenvalue,
called Laplacian index, as well as the second smallest eigenvalue,
denominated by algebraic connectivity and study some of their
properties. In one hand, we study upper bounds for the Laplacian index
and, in some cases, identify the graphs for which the upper bounds
are attained. On the other hand, the algebraic connectivity gives a measure
on how connected is a graph. The eigenvector associated to
this eigenvalue, known as Fiedler vector, is very important, as it is related
to many applications. Using this vector we can, not only, classify
connected graphs in one of two types, but also partitioning connected
graphs in exactly two connected components, which is revealed to be
very important in many applications, namely in the context of spectral
partitioning.Mestrado em Matemática e Aplicaçõe
La expresión del "honneur" y de la "honte" en "Erec et Enide", "Yvain" y "Lancelot" de Chrétien de Troyes
No full textThe French terms for honneur (‘honour’) and honte (‘dishonour’) have several senses proper
of the Middle Ages that appear collected in the diverse specialized dictionaries on this
period. Nevertheless, the analysis of these terms in the novels Erec et Enide, Yvain and
Lancelot by Chrétien de Troyes will show a specialization of their meaning thanks to the
selection made by this author. Such a selection has the purpose of being more useful and
profitable for intrigue and, therefore, for the narrative structure of his novelsLos términos de honneur y honte tenían unas acepciones específicas en la Edad Media que
están recogidas en los diferentes diccionarios dedicados a este período. Sin embargo, el
análisis de estos términos en las novelas Erec et Enide, Yvain y Lancelot de Chrétien de
Troyes pondrá de manifiesto una especialización de su significado provocado por la selección, por parte de este autor, de las acepciones de estos términos que resultan más útiles y
rentables para la intriga y, por tanto, para la estructura narrativa de sus novela
Politopo de Birkhoff acíclico
No full textDoutoramento em MatemáticaNeste trabalho estabelece-se uma interpreta c~ao geom etrica, em termos
da teoria dos grafos, para v ertices, arestas e faces de uma qualquer
dimens~ao do politopo de Birkho ac clico, Tn =
n(T), onde T e uma
arvore com n v ertices. Generaliza-se o resultado obtido por G. Dahl,
[18], para o c alculo do di^ametro do grafo G(
t
n), onde
t
n e o politopo
das matrizes tridiagonais duplamente estoc asticas. Adicionalmente,
para q = 0; 1; 2; 3 s~ao obtidas f ormulas expl citas para a contagem do
n umero de qfaces do politopo de Birkho tridiagonal,
t
n, e e feito
o estudo da natureza geom etrica dessas mesmas faces. S~ao, tamb em,
apresentados algoritmos para efectuar contagens do n umero de faces de
dimens~ao inferior a de uma dada face do politopo de Birkho ac clico.In this work using graph theory, we give a geometrical interpretation
of vertices, edges, and faces of any dimension of the acyclic Birkho
polytope, Tn =
n(T), were T is a tree with n vertices. We generalize
a proposition from G. Dahl, [18], that allows the calculation of the
diameter of the graph G(
t
n), where
t
n denotes the polytope of tridiagonal
doubly stochastic matrices. Furthermore, for q = 0; 1; 2; 3 we
obtain some explicit formulae for counting the number of qfaces of
the tridiagonal Birkho polytope,
t
n, and the study of its geometrical
nature is done. For a given p-face of
t
n we determine the number of
faces of lower dimension that are contained in it and we discuss its nature.
Some algorithms allowing an exhaustive account on the number
of edges and faces of the acyclic Birkho polytope are presented
Comutadores de matrizes
No full textMestrado em MatemáticaO estudo de comutadores aditivos de matrizes ao longo da década de 50 e de
comutadores multiplicativos de matrizes ao longo da década de 60 estão na
base deste trabalho, que pretende apresentar os resultados mais abrangentes
sobre os dois tipos de comutadores.
São caracterizados os comutadores aditivos de matrizes em corpos quaisquer
e apresentadas algumas propriedades particulares válidas em corpos
algebricamente fechados.
São apresentadas condições para que uma matriz com entradas em GF(2),
GF(3) e num corpo distinto dos anteriores, seja um comutador multiplicativo de
matrizes.
Finalmente, apresentam-se condições para que uma matriz seja um comutador
multiplicativo de matrizes com determinantes quaisquer prescritos.The study of additive matrix commutators along the decade of 50 and
multiplicative matrix commutators along the decade of 60 are the basis of this
work, which intends to present the most including results on the two types of
commutators.
We characterize additive matrix commutators over a general field and present
some particular properties valid in algebraically closed fields.
We present conditions so that a matrix with elements in GF(2), GF(3) and in a
field different from the previous is a multiplicative matrix commutator.
Finally, we present conditions so that a matrix is a multiplicative matrix
commutator with any prescribed determinants
Faces of faces of the tridiagonal Birkhoff polytope
No full textAbstractThe tridiagonal Birkhoff polytope, Ωnt, is the set of real square matrices with nonnegative entries and all rows and columns sums equal to 1 that are tridiagonal. This polytope arises in many problems of enumerative combinatorics, statistics, combinatorial optimization, etc. In this paper, for a given a p-face of Ωnt, we determine the number of faces of lower dimension that are contained in it and we discuss its nature. In fact, a 2-face of Ωnt is a triangle or a quadrilateral and the cells can only be tetrahedrons, pentahedrons or hexahedrons
Combinatorial Fiedler Theory and Graph Partition
No full textPartition problems in graphs are extremely important in applications, as
shown in the Data science and Machine learning literature. One approach is
spectral partitioning based on a Fiedler vector, i.e., an eigenvector
corresponding to the second smallest eigenvalue of the Laplacian matrix
of the graph . This problem corresponds to the minimization of a
quadratic form associated with , under certain constraints involving the
-norm. We introduce and investigate a similar problem, but using the
-norm to measure distances. This leads to a new parameter as the
optimal value. We show that a well-known cut problem arises in this approach,
namely the sparsest cut problem. We prove connectivity results and different
bounds on this new parameter, relate to Fiedler theory and show explicit
expressions for for trees. We also comment on an -norm
version of the problem
Combinatorial Perron values of trees and bottleneck matrices
No full textThe algebraic connectivity of a graph is an important parameter, defined as the second smallest eigenvalue of the Laplacian matrix of . If is a tree, is closely related to the Perron values (spectral radius) of so-called bottleneck matrices of subtrees of . In this setting we introduce a new parameter called the {\em combinatorial Perron value} . This value is a lower bound on the Perron value of such subtrees; typically is a good approximation to . We compute exact values of for certain special subtrees. Moreover, some results concerning when the tree is modified are established, and it is shown that, among trees with given distance vector (from the root), is maximized for caterpillars
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