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This thesis consists of studies in the separate fields of operator algebras and non-associative algebras. Two natural operator algebra structures, A ⊗_max B and A ⊗_min B, exist on the tensor product of two given unital operator algebras A and B. Because of the different properties enjoyed by the two tensor products in connection to dilation theory, it is of interest to know when they coincide (completely isometrically). Motivated by earlier work due to Paulsen and Power, we provide conditions relating an operator algebra B and another family {C_i}_i of operator algebras under which, for any operator algebra A, the equality A ⊗_max B = A ⊗_min B either implies, or is implied by, the equalities A ⊗_max C_i = A ⊗_min C_i for every i. These results can be applied to the setting of a discrete group G pre-ordered by a subsemigroup G⁺, where B ⊆ C*_r(G) is the subalgebra of the reduced group C*-algebra of G generated by G⁺, and C_i = A(Q_i) are digraph algebras defined by considering certain pre-ordered subsets Q_i of G. The 16-dimensional algebra A₄ of real sedenions is obtained by applying the Cayley-Dickson doubling process to the real division algebra of octonions. The classification of subalgebras of A₄ up to conjugacy (i.e. by the action of the automorphism group of A₄) was completed in a previous investigation, except for the collection of those subalgebras which are isomorphic to the quaternions. We present a classification of quaternion subalgebras up to conjugacy.

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-17Bitstream added on 2014-06-13T18:06:51Z : No. of bitstreams: 1 roque_mrd_me_sjrp.pdf: 11300361 bytes, checksum: 634655b9889665fb4488c7076d5db292 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Nesta dissertação, estuda-se estruturas matemáticas relacionadas à álgebra dos sedenions de Cayley-Dickson. O conceito de funções sedeniônicas do tipo f(z) = zn, z 2 S e n 2 N, é desenvolvido a partir da distância jf(y)¡f(x)j, com o objetivo de obter-se uma generalização. A este tipo de mapeamentos trata-se por funções quaseconformes, ou seja, mapeamentos que não preservam a magnitude dos ângulos. Em particular, através de métodos de resolução, apresenta-se e discute-se polinômios de 2n graus com coeficientes sedeniônicos com o intuito de enfatizar o valor da k-dilatação causada quando trabalha-se com o número sedeniônico em coordenadas esféricas. Por fim, ilustra-se geometricamente os cortes produzidos em hiperesferas B(x; r) quando submetidas às transformações do tipo z2 e z3. / In this work, we propose to study the mathematical construction related with algebra of Cayley-Dickson sedenions. We will present the concept of sedenions functions of f(z) = zn type, z 2 S and n 2 N, developing jf(y) ¡ f(x)j distance, with the objective of creating a generalization. This type of mappings is known as quasiconformal functions, that is, mapping that don't preserve the magnitude of angles. Specially, by means of resolution methods, we will discuss polynomials of 2n degrees with sedenions coefficients focused on highlighting the value of the k-dilation caused when we work with the sedenion number in spherical coordinates. Finally, it is illustrated geometrically the cuts produced in hiperspheres B(x; r) when submitted to the transformations of the type z2 and z3.

Introdução. A prática regular do exercício de força (EF) está associada a adaptações metabólicas, neuromusculares e cardiovasculares que repercutem de maneira positiva sobre a saúde e qualidade de vida de seus praticantes. No entanto, Indivíduos sedentários apresentam comprometimentos agudos na função endotelial após EF de alta intensidade. Objetivo. Avaliar a função endotelial de indivíduos sedentários de meia idade em resposta a diferentes intensidades do EF. Métodos. 11 indivíduos sedentários (40,1±3,9 anos; 27,3±1,4 kg/m2) realizaram EF em três condições experimentais: extensão de joelhos a 50% de 1RM (MI), 80% de 1RM (AI) e repouso na condição controle (CON). Foi realizada avaliação da vasodilatação mediada pelo fluxo (FMD) antes, 30 minutos após e 60 minutos após os protocolos. A quantificação das concentrações de NO2 e NO3 (NOx), endotelina-1 (ET-1) e TBARS foram realizadas antes, imediatamente após e 60 minutos após os protocolos. A pressão arterial foi mensurada antes e após os protocolos Resultados. A FMD aumentou significativamente 30 minutos após o exercício na condição MI (12,5± 4,10 para 17,2±3,9 %; p=0,01) bem como os níveis de NOx (6,8± 3,3 vs. 12,6± 4,2μM; p= 0,007). A concentração de ET-1 aumentou imediatamente após na condição AI (20,02±2,2 vs. 25,4± 2,1pg/ml; p= 0,004). A elevação da pressão arterial não diferiu entre as condições MI e AI. As concentrações de TBARS não se alteraram ao longo dos protocolos. Conclusão. O EF de moderada intensidade aumenta a FMD e os níveis NOx após uma sessão aguda de exercício em indivíduos sedentários de meia idade, estes resultados sugerem que menores intensidades do EF são mais seguras ao iniciar um programa de exercícios. / Regular resistance exercise (RE) is associated with metabolic, neuromuscular and cardiovascular adaptation that results in improvement of quality of life and health. However, sedentary subjects have been showing an acute impairment on endothelial function after high intensity resistance exercise. The aim of this study was to evaluate the endothelial function in sedentary middle age men after RE in different intensities. Methods. Eleven middle age sedentary men (40,1±3,9 years; 27,3±1,4 kg/m2) performed RE in three different conditions: knee extension at 50% of one 1RM (MI), at 80% of 1RM (HI) and rest in the control group (CON). Flow mediated dilation (FMD) was assessed before, 30 and 60 minutes of exercise. Venus plasma concentration of ET-1 NOx and TBARS were measured before, immediately after and 60 minutes after exercise. Blood pressure was evaluated before and after exercise. Results. There was a significant improvement in FMD 30 minutes after exercise in the MI condition (12,5± 4,10 vs 17,2±3,9%; p= 0,016; p=0,01). The plasma NOx concentration was significant higher immediately after MI (6,8± 3,3 vs. 12,6± 4,2μM; p= 0,007). There was a significant improvement in the plasma ET-1 concentration immediately after HI (20,02±2,2 vs. 25,4± 2,1pg/ml; p= 0,004). There was no significant difference in the BP between the experimental conditions (MI vs HI) and TBARS throughout the experimental conditions. Conclusions. Resistance exercise performed in moderate intensity improve endothelial function in sedentary middle aged men, there results suggest that lower intensities of RE could be safe for this population in the beginning of the exercise programs.

Introdução. A prática regular do exercício de força (EF) está associada a adaptações metabólicas, neuromusculares e cardiovasculares que repercutem de maneira positiva sobre a saúde e qualidade de vida de seus praticantes. No entanto, Indivíduos sedentários apresentam comprometimentos agudos na função endotelial após EF de alta intensidade. Objetivo. Avaliar a função endotelial de indivíduos sedentários de meia idade em resposta a diferentes intensidades do EF. Métodos. 11 indivíduos sedentários (40,1±3,9 anos; 27,3±1,4 kg/m2) realizaram EF em três condições experimentais: extensão de joelhos a 50% de 1RM (MI), 80% de 1RM (AI) e repouso na condição controle (CON). Foi realizada avaliação da vasodilatação mediada pelo fluxo (FMD) antes, 30 minutos após e 60 minutos após os protocolos. A quantificação das concentrações de NO2 e NO3 (NOx), endotelina-1 (ET-1) e TBARS foram realizadas antes, imediatamente após e 60 minutos após os protocolos. A pressão arterial foi mensurada antes e após os protocolos Resultados. A FMD aumentou significativamente 30 minutos após o exercício na condição MI (12,5± 4,10 para 17,2±3,9 %; p=0,01) bem como os níveis de NOx (6,8± 3,3 vs. 12,6± 4,2μM; p= 0,007). A concentração de ET-1 aumentou imediatamente após na condição AI (20,02±2,2 vs. 25,4± 2,1pg/ml; p= 0,004). A elevação da pressão arterial não diferiu entre as condições MI e AI. As concentrações de TBARS não se alteraram ao longo dos protocolos. Conclusão. O EF de moderada intensidade aumenta a FMD e os níveis NOx após uma sessão aguda de exercício em indivíduos sedentários de meia idade, estes resultados sugerem que menores intensidades do EF são mais seguras ao iniciar um programa de exercícios. / Regular resistance exercise (RE) is associated with metabolic, neuromuscular and cardiovascular adaptation that results in improvement of quality of life and health. However, sedentary subjects have been showing an acute impairment on endothelial function after high intensity resistance exercise. The aim of this study was to evaluate the endothelial function in sedentary middle age men after RE in different intensities. Methods. Eleven middle age sedentary men (40,1±3,9 years; 27,3±1,4 kg/m2) performed RE in three different conditions: knee extension at 50% of one 1RM (MI), at 80% of 1RM (HI) and rest in the control group (CON). Flow mediated dilation (FMD) was assessed before, 30 and 60 minutes of exercise. Venus plasma concentration of ET-1 NOx and TBARS were measured before, immediately after and 60 minutes after exercise. Blood pressure was evaluated before and after exercise. Results. There was a significant improvement in FMD 30 minutes after exercise in the MI condition (12,5± 4,10 vs 17,2±3,9%; p= 0,016; p=0,01). The plasma NOx concentration was significant higher immediately after MI (6,8± 3,3 vs. 12,6± 4,2μM; p= 0,007). There was a significant improvement in the plasma ET-1 concentration immediately after HI (20,02±2,2 vs. 25,4± 2,1pg/ml; p= 0,004). There was no significant difference in the BP between the experimental conditions (MI vs HI) and TBARS throughout the experimental conditions. Conclusions. Resistance exercise performed in moderate intensity improve endothelial function in sedentary middle aged men, there results suggest that lower intensities of RE could be safe for this population in the beginning of the exercise programs.

abstract: Cardiovascular disease (CVD) is the number one cause of death in the United States and type 2 diabetes (T2D) and obesity lead to cardiovascular disease. Obese adults are more susceptible to CVD compared to their non-obese counterparts. Exercise training leads to large reductions in the risk of CVD and T2D. Recent evidence suggests high-intensity interval training (HIT) may yield similar or superior benefits in a shorter amount of time compared to traditional continuous exercise training. The purpose of this study was to compare the effects of HIT to continuous (CONT) exercise training for the improvement of endothelial function, glucose control, and visceral adipose tissue. Seventeen obese men (N=9) and women (N=8) were randomized to eight weeks of either HIT (N=9, age=34 years, BMI=37.6 kg/m2) or CONT (N=8, age=34 years, BMI=34.6 kg/m2) exercise 3 days/week for 8 weeks. Endothelial function was assessed via flow-mediated dilation (FMD), glucose control was assessed via continuous glucose monitoring (CGM), and visceral adipose tissue and body composition was measured with an iDXA. Incremental exercise testing was performed at baseline, 4 weeks, and 8 weeks. There were no changes in weight, fat mass, or visceral adipose tissue measured by the iDXA, but there was a significant reduction in body fat that did not differ by group (46±6.3 to 45.4±6.6%, P=0.025). HIT led to a significantly greater improvement in FMD compared to CONT exercise (HIT: 5.1 to 9.0%; CONT: 5.0 to 2.6%, P=0.006). Average 24-hour glucose was not improved over the whole group and there were no group x time interactions for CGM data (HIT: 103.9 to 98.2 mg/dl; CONT: 99.9 to 100.2 mg/dl, P>0.05). When statistical analysis included only the subjects who started with an average glucose at baseline > 100 mg/dl, there was a significant improvement in glucose control overall, but no group x time interaction (107.8 to 94.2 mg/dl, P=0.027). Eight weeks of HIT led to superior improvements in endothelial function and similar improvements in glucose control in obese subjects at risk for T2D and CVD. HIT was shown to have comparable or superior health benefits in this obese sample with a 36% lower total exercise time commitment. / Dissertation/Thesis / Ph.D. Exercise and Wellness 2013

Emotion is thought to modulate the long-term fate of memories. Experiences that elicit an emotional response tend to be better remembered than comparatively unemotional events, while the emotional charge associated with these memories diminishes over time. Sleep – in particular rapid-eye movement (REM) and slow-wave sleep (SWS) - has been implicated in both the selective strengthening and affective uncharging of emotional memories. According to the sleep to forget, sleep to remember (SFSR) hypothesis, both processes occur in parallel during REM sleep. Although evidence strongly supports a role of REM sleep in the selective consolidation of emotional memories, it is far less clear to what extent sleep is involved in the development of emotional charge. While some studies support a primary role of REM in habituation (i.e. the decrease of emotional charge), others suggest a more central role of SWS. Further, existing literature indicates that the physiological (bottom-up) and cognitive (top-down) components of emotional responses may be differentially processed across sleep. Chapter 2 proposes complementary functions of REM and SWS in emotional memory processes based on a combination of evidence from rodent and human research. The experiments presented in this thesis employed polysomnography (PSG), subjective arousal testing, pupillometry, targeted memory reactivation (TMR), and transcranial alternating current stimulation (tACs) to investigate the respective roles of REM and SWS in the overnight development of subjective and autonomic arousal in response to negative emotional and neutral stimuli. In Chapter 3 I assessed how subjective and autonomic responses to neutral and negative stimuli develop across 12 hours containing either nocturnal sleep or daytime wakefulness. I found that autonomic reactivity – indexed by pupil dilation – decreased across sleep but not wake, while subjective arousal did not change across either interval. In a further experiment, I investigated whether the placement of sleep within a 24 hour interval would affect habituation. Once again, autonomic arousal decreased significantly. Subjective arousal towards negative stimuli was found to decrease more if sleep followed rather than preceded daytime wakefulness within the 24 hour interval. In Chapter 4 I explored the role of REM sleep in emotional habituation by applying 5 Hz tACs in an attempt to entrain endogenous cortical theta (4-7 Hz) activity, which has previously been associated with emotional memory consolidation in humans. Surprisingly, I found that stimulation was associated with a reduction in theta power and no change in subjective or autonomic habituation compared to the sham control night. In Chapters 5 and 6, I addressed the contribution of memory reactivations during SWS and REM sleep, respectively, in emotional habituation using TMR. In Chapter 5, I found that TMR was associated with a decrease and simultaneous increase in autonomic habituation towards negative and neutral stimuli, respectively, without affecting overnight changes in subjective arousal. In contrast, in Chapter 6, TMR during REM sleep was associated with an increase in subjective habituation towards both neutral and negative stimuli without affecting autonomic responses. In conclusion, my results provide new insights to the role of sleep in emotional habituation. I have provided evidence that targeted memory reactivation during REM sleep can modulate the development of cognitive evaluations of emotion, while TMR during SWS may interfere with autonomic habituation. This suggests distinct emotional processing during REM and SWS, as well as a dissociation between subjective and autonomic habituation across sleep. These results are discussed in the light of previous research and the model of sleep-dependent emotional memory processing proposed in Chapter 2.

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The concept of attention is complex and multifaceted and can be approached from many perspectives. One such perspective is of attention as a limited pool of resources. Kahneman’s (1973) model of limited capacity provides a basis for understanding constraints on attention, including the costs of divided attention. In the same vein as Kahneman’s model, the Framework for Understanding Effortful Listening (FUEL; Pichora-Fuller et al., 2016) applies the concept of limited attentional capacity to the demands of listening in a variety of contexts. The current work examines novel combinations of the methods commonly used in the field of Cognitive Hearing Science to address questions about the nature of attention allocation when listening in noise and under the constraints of divided attention. I first combined listening in noise with a secondary continuous working memory task and measured pupillary response as an index of cognitive work and listening effort. Here, I found that listening task demands affect performance on the working memory task. The shared demands of listening and working memory were not, however, evident in the pupil dilation patterns. As a result, I followed these findings by employing a different divided attention method. With the use of a temporally discrete secondary task that either closely overlapped with the listening task or did not closely overlap, I found the same carryover effects of listening demands on secondary task. Most importantly, I found that these demands interacted and were clearly present in the pupil dilation patterns, demonstrating the importance of the timing of the task demands. Together, the studies in this thesis provide evidence that these two secondary tasks access the same attentional resources as those accessed in the primary listening task and that this overlapping demand for resources can be seen in the pupillary response. / Thesis / Doctor of Philosophy (PhD) / Listening to speech in a noisy environment is a cognitively difficult and effortful task. Attending to more than one task at a time is similarly demanding and effortful. These two kinds of tasks are assumed to use the same limited pool of cognitive resources that we have available to us. This thesis combines listening in noise with divided attention tasks to demonstrate this overlap in demands for cognitive resources using novel combinations of these kinds of tasks. Additionally, this thesis uses the pupillary response—a well-studied index of cognitive effort—to further examine the nature of these overlapping task demands. These studies found that the demands of these tasks do, in fact, overlap, and contribute evidence to the current literature supporting the underlying assumption that these two tasks, and the pupillary response as a measure of effort, are accessing the same pool of limited resources.

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