On Lie groups and algebras

Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2014, Director: Ricardo García LópezThe objectives of this work are fundamentally three: the first is to give the basic definitions of Lie groups, Lie algebras, the exponential map and the morphisms relating them. The second is to give an elementary introduction to Lie group representation theory as well as some criteria on how to classify certain Lie groups. The third and final goal is to study a couple of specific Lie groups, namely SU(2) and SO(3), in order to apply all the concerning theory and have an insight into the applications of Lie groups into Physics

Clinical validation of eye vergence as an objective marker for diagnosis of ADHD in children

Objective: ADHD youth show poor oculomotor control. Recent research shows that attention-related eye vergence is weak in ADHD children. Method: To validate vergence as a marker to classify ADHD, we assessed the modulation in the angle of vergence of children (n = 43) previously diagnosed with ADHD while performing an attention task and compared the results with age-matched clinical controls (n = 19) and healthy peers (n = 30). Results: We observed strong vergence responses in healthy participants and weak vergence in the clinical controls. ADHD children showed no significant vergence responses. Machine-learning models classified ADHD patients (n = 21) from healthy controls (n = 21) with an accuracy of 96.3% (false positive [FP]: 5.12%; false negative [FN]: 0%; area under the curve [AUC]: 0.99) and ADHD children (n = 11) from clinical controls (n = 14) with an accuracy of 85.7% (FP: 4.5%; FN: 19.2%, AUC: 0.90). Conclusion: In combination with an attention task, vergence responses can be used as an objective marker to detect ADHD in children.Peer ReviewedPostprint (author's final draft

Un acostament a les quàrtiques projectives planes

Treballs Finals de Grau de Matemàtiques de la Facultat de Matemàtiques de la Universitat de Barcelona, Any: 2012 , Director: Juan Carlos Naranjo del ValThis work, which consists in two separate parts, will attempt to build an equation for a non-singular plane projective quartic over an algebraically closed eld, namely C. In the course of this trail, algebric and geometric theory will be introduced and discussed here, taking special care in subjects such as Bézout's theorem, the divisor language, Riemann-Roch's theorem and some matters about symplectic algebra. This path will lead us to Steiner-Hesse's theorem which provides a way to write an equation for a non-singular quartic. Finally, we will use those methods in order to attempt the development of an equation for the Klein quartic. An appendix lies at the end of the work talking about a pair of questions which can be investigated parting from the subjects in the main text, and a brief historical background for the things shown on it

Clinical validation of eye vergence as an objective marker for diagnosis of ADHD in children

Objective: ADHD youth show poor oculomotor control. Recent research shows that attention-related eye vergence is weak in ADHD children. Method: To validate vergence as a marker to classify ADHD, we assessed the modulation in the angle of vergence of children (n = 43) previously diagnosed with ADHD while performing an attention task and compared the results with age-matched clinical controls (n = 19) and healthy peers (n = 30). Results: We observed strong vergence responses in healthy participants and weak vergence in the clinical controls. ADHD children showed no significant vergence responses. Machine-learning models classified ADHD patients (n = 21) from healthy controls (n = 21) with an accuracy of 96.3% (false positive [FP]: 5.12%; false negative [FN]: 0%; area under the curve [AUC]: 0.99) and ADHD children (n = 11) from clinical controls (n = 14) with an accuracy of 85.7% (FP: 4.5%; FN: 19.2%, AUC: 0.90). Conclusion: In combination with an attention task, vergence responses can be used as an objective marker to detect ADHD in children.Peer Reviewe

Eye vergence responses during an attention task in adults with ADHD and clinical controls

Objective: ADHD patients show poor oculomotor control and recent studies show that attention-related eye vergence is weak in ADHD children. We aimed to assess vergence as a potential diagnostic biomarker for ADHD in adults. Method: We assessed the modulation in the angle of vergence while performing an attention task (N = 144), comparing the results for adults previously diagnosed with ADHD (N = 108) with age-matched clinical controls (N = 36). Results: Significant differences in eye vergence response modulation between clinical controls and ADHD patients were documented. Diagnostic test accuracy was 79%. Conclusion: In combination with an attention task, eye vergence responses could be used as an objective marker to support the clinical diagnosis of adult ADHDPeer ReviewedPostprint (author's final draft

Clinical validation of eye vergence as an objective marker for diagnosis of ADHD in children

Objective: ADHD youth show poor oculomotor control. Recent research shows that attention-related eye vergence is weak in ADHD children. Method: To validate vergence as a marker to classify ADHD, we assessed the modulation in the angle of vergence of children (n = 43) previously diagnosed with ADHD while performing an attention task and compared the results with age-matched clinical controls (n = 19) and healthy peers (n = 30). Results: We observed strong vergence responses in healthy participants and weak vergence in the clinical controls. ADHD children showed no significant vergence responses. Machine-learning models classified ADHD patients (n = 21) from healthy controls (n = 21) with an accuracy of 96.3% (false positive [FP]: 5.12%; false negative [FN]: 0%; area under the curve [AUC]: 0.99) and ADHD children (n = 11) from clinical controls (n = 14) with an accuracy of 85.7% (FP: 4.5%; FN: 19.2%, AUC: 0.90). Conclusion: In combination with an attention task, vergence responses can be used as an objective marker to detect ADHD in childre

Clinical validation of eye vergence as an objective marker for diagnosis of ADHD in children

Objective: ADHD youth show poor oculomotor control. Recent research shows that attention-related eye vergence is weak in ADHD children. Method: To validate vergence as a marker to classify ADHD, we assessed the modulation in the angle of vergence of children (n = 43) previously diagnosed with ADHD while performing an attention task and compared the results with age-matched clinical controls (n = 19) and healthy peers (n = 30). Results: We observed strong vergence responses in healthy participants and weak vergence in the clinical controls. ADHD children showed no significant vergence responses. Machine-learning models classified ADHD patients (n = 21) from healthy controls (n = 21) with an accuracy of 96.3% (false positive [FP]: 5.12%; false negative [FN]: 0%; area under the curve [AUC]: 0.99) and ADHD children (n = 11) from clinical controls (n = 14) with an accuracy of 85.7% (FP: 4.5%; FN: 19.2%, AUC: 0.90). Conclusion: In combination with an attention task, vergence responses can be used as an objective marker to detect ADHD in childre