On F-algebroids and Dubrovin’s duality

Abstract

In this note we introduce the concept of F-algebroid, and give its elementary properties and some examples. We provide a description of the almost duality for Frobenius manifolds, introduced by Dubrovin, in terms of a composition of two anchor maps of a unique cotangent F-algebroid.

Factors associated with viremia in people living with HIV on antiretroviral therapy in Guatemala

“…Of 929 participants enrolled in the cohort, 664 had a recent viral load and had completed at least six months of ART. The median age was 39 years [interquartile range (IQR) [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], 356 (53.6%) were male, 493 (74.2%) were heterosexual and 99 (14.9%) self-identified with indigenous ethnicity. Almost half of the participants (49.2%) had less than or equal to primary education and only 60 (9.0%) had a bachelor's degree or higher.…”

“…Lower individual income, low educational attainment, engaging in risk behaviors, bisexual orientation and perceived difficulty attending healthcare exclusively had an impact on viremia in men. Individual income may be less relevant in women due to differences in workforce participation in the cohort (23.7% in women vs 42.6% in men) [41]. Other studies have examined the interplay between gender, HIV and risk behaviors and have observed that the prevalence of heavy alcohol consumption is higher in men with HIV than in women [42], at-risk drinking in men is predictive of virologic failure [43], and MSM who engage in higher risk drinking are more likely to engage in HIV risk behaviors [44].…”

F-algebroids and deformation quantization via pre-Lie algebroids

“…Remark 2.8. Cruz Morales and Torres-Gomez [11] had already defined an Falgebroid. There is a slight difference between the above definition of an F-algebroid and that one.…”

“…There is a slight difference between the above definition of an F-algebroid and that one. In [11], it is assumed that the base manifold has an F-manifold structure (M, • ). An F-algebroid defined in [11] is a vector bundle A over M equipped with a bilinear operation…”

“…In this paper, we introduce the notion of F-algebroids, which is a generalization of F-manifold algebras and F-manifolds. There is a slight difference between this Falgebroid and the one introduced in [11]. We introduce the notion of pre-Lie formal deformations of commutative associative algebroids and show that F-algebroids are the corresponding semiclassical limits.…”