López Gerena, Juan O.

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    Closure operators, torsion theories, and radicals in a non-abelian environment
    (2009-05) López Gerena, Juan O.; Castellini, Gabriele; College of Arts and Sciences - Sciences; Walker Ramos, Uroyoán R.; Dziobiak, Wieslaw; Department of Mathematics; Castellano Rodríguez, Dorial
    In the category of abelian groups, there exists a relationship between torsion theories and idempotent radicals where we can use one to find the other. In the process we can learn of different properties that apply to the associated subclasses. We can also use a pre-radical to obtain a closure operator and a closure operator to obtain a pre-radical. The properties of the pre-radical (whether it’s idempotent or a radical) indicate corresponding properties of the closure operator and vice-versa. In this thesis, we determine how much of the relationship that exists between closure operators, torsion theories and radicals in the category of abelian groups (Ab) can be extended to the category of all groups (Grp). Once it’s clear which properties do not apply, our goal is to find, for each property, which modifications can be made so that the property still holds.
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    High precision detection of LINE-1s in human genomes
    (2022-05-20) López Gerena, Juan O.; Seguel, Jaime; College of Engineering; Vélez Rivera, Bienvenido; Schütz Schmuck, Marko; Torres García, Wandaliz; Department of Computer Science and Engineering; Isaza Brando, Clara E.
    Long interspersed elements 1 (LINE-1s or L1s) are autonomous retrotransposons that make up about 17% of the human genome. Strong correlations between abnormal L1 expression and several human diseases have been reported, which has motivated an interest in accurate quantification of the number of L1 copies present in any given biological specimen. A main obstacle towards this aim is that L1s are relatively long DNA segments with regions of high variability often with truncated or added fragments. These particularities render traditional alignment strategies, such as seed-and-extend, inefficient, as the number of segments that are similar to L1s explodes exponentially. Here, a new strategy is introduced to increase quantification efficiency, resulting in a more accurate identification of L1s. This dissertation discusses this method and experimentally validates its superiority for L1 detection over alternative methods, and also considers some additional potential applications.