Matemáticahttp://hdl.handle.net/10669/2802020-10-30T11:37:10Z2020-10-30T11:37:10ZOn the kinematics of the last Wigner particlehttp://hdl.handle.net/10669/817652020-10-29T16:06:27Z2019-01-01T00:00:00ZOn the kinematics of the last Wigner particle
Wigner's particle classification provides for "continuous spin" representations of the Poincaré group, corresponding to a class of (as yet unobserved) massless particles. Rather than building their induced realizations by use of "Wigner rotations" in the textbooks' way, here we exhibit a scalar-like first-quantized form of those (bosonic) Wigner particles directly, by combining wave equations proposed by Wigner long ago with a recent prequantized treatment employing Poisson structures.
2019-01-01T00:00:00ZVariations of Hodge Structures of Rank Three k-Higgs Bundles and Moduli Spaces of Holomorphic Tripleshttp://hdl.handle.net/10669/817322020-10-27T12:14:37Z2020-01-01T00:00:00ZVariations of Hodge Structures of Rank Three k-Higgs Bundles and Moduli Spaces of Holomorphic Triples
There is an isomorphism between the moduli spaces of σ-stable holomorphic triples
and some of the critical submanifolds of the moduli space of k-Higgs bundles of
rank three, whose elements (E, ϕk
) correspond to variations of Hodge structure,
VHS. There are special embeddings on the moduli spaces of k-Higgs bundles of
rank three. The main objective here is to study the cohomology of the critical
submanifolds of such moduli spaces, extending those embeddings to moduli spaces
of holomorphic triples.
2020-01-01T00:00:00ZStratifications on the Nilpotent Cone of the moduli space of Hitchin pairshttp://hdl.handle.net/10669/817312020-10-27T12:14:35Z2020-01-01T00:00:00ZStratifications on the Nilpotent Cone of the moduli space of Hitchin pairs
We consider the problem of finding the limit at infinity (corresponding to
the downward Morse flow) of a Higgs bundle in the nilpotent cone under the natural
C
∗
-action on the moduli space. For general rank we provide an answer for Higgs bundles
with regular nilpotent Higgs field, while in rank three we give the complete answer. Our
results show that the limit can be described in terms of data defined by the Higgs field,
via a filtration of the underlying vector bundle
2020-01-01T00:00:00ZClustering binary data by application of combinatorial optimization heuristicshttp://hdl.handle.net/10669/815932020-09-22T12:16:32Z2019-08-09T00:00:00ZClustering binary data by application of combinatorial optimization heuristics
We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior combinatorial optimization metaheuristics: first ones are simulated annealing, threshold accepting and tabu search, and the others are a genetic algorithm and ant colony optimization.
The methods are implemented, performing the proper calibration of parameters in the case of heuristics, to ensure good results. From a set of 16 data tables generated by a quasi-Monte Carlo experiment, a comparison is performed for one of the aggregations using L1 dissimilarity, with hierarchical clustering, and a version of k-means: partitioning around medoids or PAM.
Simulated annealing perform very well, especially compared to classical methods.
Artículo será publicado en Springer Verlag, como capítulo del libro "Data Analysis and Rationality in a Complex World".
2019-08-09T00:00:00Z