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Mangue's school ou por uma pedagogia rizomática
Lins, Daniel;
Educa??o & Sociedade , 2005, DOI: 10.1590/S0101-73302005000400008
Abstract: a rizomatic pedagogy whose main axiom is a nomadic or itinerant science and could act as a counterpoint to the royal science is embedded into the ethics and aesthetics of existence, into immanence. as life, thus. it rises out as pure resistance, as pure becoming. here is one of the axes of a school following a rizomatic dynamic: resisting, contaminating, and vitalizing what has become established. in a nomadic pedagogy knowledge turns to be flavors because it allows intelligence to access another world. knowledge as flavor does not change the finite reality of human beings, but attributes to the inexplicable an artistic and creative reality.
Um passaporte húngaro, de Sandra Kogut: cinema polí-tico e intimidade
Consuelo Lins
Galáxia , 2008,
Abstract: Um passaporte húngaro, da cineasta e videoartista brasileira Sandra Kogut, é um filme que utiliza diferentes tecnologias para construir uma narrativa em que a diretora está fortemente presente. Trata-se de um filme em que a esfera da vida privada está em primeiro plano, indo ao encontro de uma realidade midiática que esvazia cada vez mais a esfera pública em favor da intimidade. Contudo, diferentemente do que assistimos na televis o, o filme articula de maneira singular experiências pessoais com a história e a memória coletivas, imprimindo deslocamentos importantes tanto em rela o í produ o midiática quanto ao documentário clássico polí-tico e aos filmes autobiográficos mais correntes. Palavras-chave cinema, documentário, intimidade, memória, polí-tico Abstract A Hungarian Passport, a film by Sandra Kogut, a Brazilian film-maker and video artist, makes use of different technologies in order to construct a narrative in which the director is strongly present. The private life circle is quite evident in the film, conforming to a media reality that progressively does without a public context in favour of the intimate. However, different from what we see on television, this film, in such special manner, articulates personal experiences with collective history and memory, imprinting important displacements both in relation to the mediatic production and the classical political documentary as well as the more common autobiographical films. Key words cinema, documentary, intimacy, memory, politics
Combinatorial Dehn-Lickorish Twists and Framed Link Presentations of 3-Manifolds Revisited
Sostenes Lins
Mathematics , 2007,
Abstract: From a pseudo-triangulation with $n$ tetrahedra $T$ of an arbitrary closed orientable connected 3-manifold (for short, {\em a 3D-space}) $M^3$, we present a gem $J '$, inducing $\IS^3$, with the following characteristics: (a) its number of vertices is O(n); (b) it has a set of $p$ pairwise disjoint couples of vertices $\{u_i,v_i\}$, each named {\em a twistor}; (c) in the dual $(J ')^\star$ of $J '$ a twistor becomes a pair of tetrahedra with an opposite pair of edges in common, and it is named {\em a hinge}; (d) in any embedding of $(J ')^\star \subset \IS^3$, the $\epsilon$-neighborhood of each hinge is a solid torus; (e) these $p$ solid tori are pairwise disjoint; (f) each twistor contains the precise description on how to perform a specific surgery based in a Denh-Lickorish twist on the solid torus corresponding to it; (g) performing all these $p$ surgeries (at the level of the dual gems) we produce a gem $G '$ with $|G '|=M^3$; (h) in $G '$ each such surgery is accomplished by the interchange of a pair of neighbors in each pair of vertices: in particular, $|V(G ')=|V(J ')|$. This is a new proof, {\em based on a linear polynomial algorithm}, of the classical Theorem of Wallace (1960) and Lickorish (1962) that every 3D-space has a framed link presentation in $\IS^3$ and opens the way for an algorithmic method to actually obtaining the link by an $O(n^2)$-algorithm. This is the subject of a companion paper soon to be released.
A state sum invariant for regular isotopy of links having a polynomial number of states
Sostenes Lins
Mathematics , 2008,
Abstract: The state sum regular isotopy invariant of links which I introduce in this work is a generalization of the Jones Polynomial. So it distinguishes any pair of links which are distinguishable by Jones'. This new invariant, denoted {\em VSE-invariant} is strictly stronger than Jones': I detected a pair of links which are not distinguished by Jones' but are distinguished by the new invariant. The full VSE-invariant has $3^n$ states. However, there are useful specializations of it parametrized by an integer k, having $O(n^k)=\sum_{\ell=0}^k {n \choose \ell} 2^\ell $ states. The link with more crossings of the pair which was distinguished by the VSE-invariant has 20 crossings. The specialization which is enough to distinguish corresponds to k=2 and has only 801 states, as opposed to the $2^{20} = 1,048,576$ states of the Jones polynomial of the same link. The full VSE-invariant of it has $3^{20} = 3,486,784,401$ states. The VSE-invariant is a good alternative for the Jones polynomial when the number of crossings makes the computation of this polynomial impossible. For instance, for $k=2$ the specialization of the VSE-invariant of a link with $n=500$ crossings can be computed in a few minutes, since it has only $2 n^2+1 = 500,001$ states.
A 3-Variable Bracket
Sostenes Lins
Mathematics , 2008,
Abstract: Kauffman's bracket is an invariant of regular isotopy of knots and links which since its discovery in 1985 it has been used in many different directions: (a) it implies an easy proof of the invariance of (in fact, it is equivalent to) the Jones polynomial; (b) it is the basic ingredient in a completely combinatorial construction for quantum 3-manifold invariants; (c) by its fundamental character it plays an important role in some theories in Physics; it has been used in the context of virtual links; it has connections with many objects other objects in Mathematics and Physics. I show in this note that, surprisingly enough, the same idea that produces the bracket can be slightly modified to produce algebraically stronger regular isotopy and ambient isotopy invariants living in the quotient ring $R/I$, where the ring $R$ and the ideal $I$ are: \begin{center} $R=\Z[\alpha,\beta,\delta]$, $I=< p_1, p_2 >$, with $p_1=\alpha^2 \delta + 2 \alpha \beta \delta ^2 -\delta ^2+\beta ^2 \delta, p_2=\alpha \beta \delta ^3+\alpha ^2 \delta ^2+\beta ^2 \delta ^2+\alpha \beta \delta -\delta.$ \end{center} It is easy to prove that any pair of links distinguished by the usual bracket is also distinguishable by the new invariant. The contrary is not necessarily true. However, a explicit example of a pair of knots not distinguished by the bracket and distinguished by this new invariant is an open problem.
A subtle new invariant for framed knots and links
Sostenes Lins
Mathematics , 2012,
Abstract: We produce a facial state sum on plane diagrams of a knot or a link which admits an invariant specialization under Polyak's recent set of generating of 4 Reidemeister moves. Thus an isotopy invariant of framed links is obtained. Each state is a complete coloring of the faces of the diagram into white and black faces so that no two black faces share an edge. Each state induces a monomial in a ring of 16 variables. The sum of the states, properly specialized defines the new invariant. In despite of its simplicity it complements Jones invariant in distinguishing mirror pairs of links. In particular it proves that $9_{42}$ is distinct from its mirror image. For this pair of knots both the Jones Polynomial and Kauffman 2-variable polynomial fail.
Graphs of Maps
Sostenes Lins
Mathematics , 2003,
Abstract: This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as planar abstract duality, and is characterized topologically. An extension of the Gauss code problem treating together the cases in which the surface involved is the plane or the real projective plane is established. The problem of finding a minimum transversal of orientation-reversing circuits in graphs on arbitrary surfaces is proved to be NP-complete and is algorithmically solved for the special case where the surface is the real projective plane.
A challenge to 3-manifold topologists and group algebraists
Sostenes L. Lins,Lauro D. Lins
Mathematics , 2013,
Abstract: This paper poses some basic questions about instances (hard to find) of a special problem in 3-manifold topology. "Important though the general concepts and propositions may be with the modern industrious passion for axiomatizing and generalizing has presented us...nevertheless I am convinced that the special problems in all their complexity constitute the stock and the core of mathematics; and to master their difficulty requires on the whole the harder labor." Hermann Weyl 1885-1955, cited in the preface of the first edition (1939) of \cite{whitehead1997}.
All the shapes of spaces: a census of small 3-manifolds
Sóstenes L. Lins,Lauro D. Lins
Mathematics , 2013,
Abstract: In this work we present a complete (no misses, no duplicates) census for closed, connected, orientable and prime 3-manifolds induced by plane graphs with a bipartition of its edge set (blinks) up to $k=9$ edges. Blinks form a universal encoding for such manifolds. In fact, each such a manifold is a subtle class of blinks, \cite{lins2013B}. Blinks are in 1-1 correpondence with {\em blackboard framed links}, \cite {kauffman1991knots, kauffman1994tlr} We hope that this census becomes as useful for the study of concrete examples of 3-manifolds as the tables of knots are in the study of knots and links.
PHORMA: Perfectly Hashed Order Restricted Multidimensional Array
Lauro Lins,Sostenes Lins,Silvio Melo
Computer Science , 2003,
Abstract: In this paper we propose a simple and efficient strategy to obtain a data structure generator to accomplish a perfect hash of quite general order restricted multidimensional arrays named {\em phormas}. The constructor of such objects gets two parameters as input: an n-vector a of non negative integers and a boolean function B on the types of order restrictions on the coordinates of the valid n-vectors bounded by a. At compiler time, the phorma constructor builds, from the pair a,B, a digraph G(a,B) with a single source s and a single sink t such that the st-paths are in 1-1 correspondence with the members of the B-restricted a-bounded array A(a,B). Besides perfectly hashing A(a,B), G(a,B) is an instance of an NW-family. This permits other useful computational tasks on it.
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