Certain fibered hyperbolic 3-manifolds admit a layered veering triangulation, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. In the first part of this work, we obtain experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold. Among other things, our experimental results strongly suggest that typical veering triangulations are non-geometric, i.e., they cannot be realized as a union of isometrically embedded hyperbolic tetrahedra. In the second part, we prove that veering triangulations are in fact generically non-geometric. / Mathematics / Accompanied by two .py files. A Python interpreter is required to run a PY script in Windows.

No andar, o risco de quedas em idosos é maior. O objetivo é estudar o risco de quedas na locomoção sem visão e a relação entre orientação espacial, veering e controle postural. Participaram 27 adultos (25,2±4,5 anos, 1,68±0,10m, 63,8±10,3kg); 27 idosos AF (72,1±4,3 anos, 1,60±0,09m, 68,5±13kg); 12 idosos RQ (72,3±6 anos, 1,57±0,08m, 67,4±10,9kg). Eles caminharam 15m sem visão com um acelerômetro fixo entre L1 e L2. Variáveis: grupo; variabilidade do desvio; erro absoluto e variável; DFA; Tc; HST; DLT. O idoso RQ teve maior variabilidade do desvio (F(2,63)=4,6, p=0,01), erro absoluto (F(2,63)=16,64, p<0,0001) e variável (F(2,63)=4,5, p=0,01). Grupo (F(2,652)=48,9, p<0,0001) e direção (F(1,652)=444,5, p<0,0001) afetaram o DFA, e foi maior nos idosos e em AP (p<0,0001). O grupo (F(2,652)=29,3, p<0,0001) e direção (F(1,652)=605, p<0,0001) afetaram o HST, no idoso RQ e na ML (p<0,0001). O grupo (F(2,652)=30,8, p<0,0001) e direção (F(1,652)=178, p<0,0001) afetaram HLT,que foi maior nos idosos e em ML (p<0,0001). A forma como o indivíduo caminha nas direções ML e AP são diferentes. O controle da oscilação é anti-persistente na direção ML e persistente na AP. Os idosos dependem mais da visão na estabilização ML na locomoção. Os idosos RQ apresentam maior veering, os idosos AF e adultos têm veering semelhante. A AF pode retardar o envelhecimento quanto à estabilidade dinâmica e à memória espacial durante a locomoção sem visão, diminuindo o risco de quedas / For elderly, the risk to fall increases during walking. The aim of this project is to study the risk to fall in elderly during gait without vision and its relation to spatial orientation, veering and postural control. The subjects were 27 adults (25.2±4.5 years old, 1.68±0,10 m height, 63.8±10.3 kg weight); 27 elderly AF (72.1±4.3 years old, 1.60±0.09 m height, 68.5±13 kg weight); 12 elderly RQ (72.3±6 years old, 1.57±0.08m height, 67.4±10.9 kg weight). The subjects were instructed to walk straight ahead with their eyes closed for 15 m, with an accelerometer fixed between L1 and L2. The variables were: group; target variability; absolute and variable error; DFA; Tc; HST; DLT. The elderly RQ showed the highest target variability (F(2,63)=4.6, p=0.01), absolute (F(2,63)=16.6, p<0,0001) and variable error (F(2,63)=4.5, p=0.01). Group (F(2,652)=48.9, p<0.0001) and direction (F(1,652)=444, p<0.0001) affected DFA, AP and elderly showed the highest values (p<0.0001). Group (F(2,652)=29.3, p<0.0001) and direction (F(1,652)=605, p<0.0001) affected HST, elderly RQ and ML showed the highest values (p<0.0001). Group (F(2,652)=30.8, p<0.0001) and direction (F(1,652)=178, p<0.0001) affected HLT, all elderly and ML showed the highest values (p<0.0001). The direction affects gait control, it is anti-persistent for ML direction and persistent for AP direction. The lack of visual information affects more the elderly in ML direction. The elderly RQ showed larger veering; while the others were similar. Physical activity may slow down the aging process by affecting the dynamic stability and spatial memory during gait without vision, leading to reduce the risk of fall

No andar, o risco de quedas em idosos é maior. O objetivo é estudar o risco de quedas na locomoção sem visão e a relação entre orientação espacial, veering e controle postural. Participaram 27 adultos (25,2±4,5 anos, 1,68±0,10m, 63,8±10,3kg); 27 idosos AF (72,1±4,3 anos, 1,60±0,09m, 68,5±13kg); 12 idosos RQ (72,3±6 anos, 1,57±0,08m, 67,4±10,9kg). Eles caminharam 15m sem visão com um acelerômetro fixo entre L1 e L2. Variáveis: grupo; variabilidade do desvio; erro absoluto e variável; DFA; Tc; HST; DLT. O idoso RQ teve maior variabilidade do desvio (F(2,63)=4,6, p=0,01), erro absoluto (F(2,63)=16,64, p<0,0001) e variável (F(2,63)=4,5, p=0,01). Grupo (F(2,652)=48,9, p<0,0001) e direção (F(1,652)=444,5, p<0,0001) afetaram o DFA, e foi maior nos idosos e em AP (p<0,0001). O grupo (F(2,652)=29,3, p<0,0001) e direção (F(1,652)=605, p<0,0001) afetaram o HST, no idoso RQ e na ML (p<0,0001). O grupo (F(2,652)=30,8, p<0,0001) e direção (F(1,652)=178, p<0,0001) afetaram HLT,que foi maior nos idosos e em ML (p<0,0001). A forma como o indivíduo caminha nas direções ML e AP são diferentes. O controle da oscilação é anti-persistente na direção ML e persistente na AP. Os idosos dependem mais da visão na estabilização ML na locomoção. Os idosos RQ apresentam maior veering, os idosos AF e adultos têm veering semelhante. A AF pode retardar o envelhecimento quanto à estabilidade dinâmica e à memória espacial durante a locomoção sem visão, diminuindo o risco de quedas / For elderly, the risk to fall increases during walking. The aim of this project is to study the risk to fall in elderly during gait without vision and its relation to spatial orientation, veering and postural control. The subjects were 27 adults (25.2±4.5 years old, 1.68±0,10 m height, 63.8±10.3 kg weight); 27 elderly AF (72.1±4.3 years old, 1.60±0.09 m height, 68.5±13 kg weight); 12 elderly RQ (72.3±6 years old, 1.57±0.08m height, 67.4±10.9 kg weight). The subjects were instructed to walk straight ahead with their eyes closed for 15 m, with an accelerometer fixed between L1 and L2. The variables were: group; target variability; absolute and variable error; DFA; Tc; HST; DLT. The elderly RQ showed the highest target variability (F(2,63)=4.6, p=0.01), absolute (F(2,63)=16.6, p<0,0001) and variable error (F(2,63)=4.5, p=0.01). Group (F(2,652)=48.9, p<0.0001) and direction (F(1,652)=444, p<0.0001) affected DFA, AP and elderly showed the highest values (p<0.0001). Group (F(2,652)=29.3, p<0.0001) and direction (F(1,652)=605, p<0.0001) affected HST, elderly RQ and ML showed the highest values (p<0.0001). Group (F(2,652)=30.8, p<0.0001) and direction (F(1,652)=178, p<0.0001) affected HLT, all elderly and ML showed the highest values (p<0.0001). The direction affects gait control, it is anti-persistent for ML direction and persistent for AP direction. The lack of visual information affects more the elderly in ML direction. The elderly RQ showed larger veering; while the others were similar. Physical activity may slow down the aging process by affecting the dynamic stability and spatial memory during gait without vision, leading to reduce the risk of fall

Thesis advisor: Julia E. Grigsby / "Ozsváth, Stipsicz and Szabó define a one-parameter family {ϒᴋ(t)}t∈[₀,₂] of Heegaard Floer knot invariants for knots K ⊂ S³ . We generalize ϒᴋ (t) to knots in any" "rational homology sphere. We study the ϒ−invariant of a fibered knot. We prove that the ϒ−invariant can never reach its minimum slope if the monodromy of the fibration is not right-veering. / Thesis (PhD) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

Individuals with Parkinson’s disease (PD) present with motor and non-motor symptoms, including in the visuospatial domain. Correction of walking abnormalities through application of visual cues in the environment has been reported in PD, but the mechanisms of action are poorly understood. The present project examined competing explanations of the effects of visual guidance on multiple aspects of gait in PD. Comfortable over-ground walking was performed by 9 participants with left-side motor onset (LPD), 11 with right-side motor onset (RPD), and 13 age-matched normal control participants (NC). Study 1 examined whether veering in PD is predominantly induced by asymmetrical perception of the visual environment or by motor asymmetry between relatively affected and relatively non-affected body side. Walking conditions were eyes-open, vision-occluded, and egocentric reference point (walk toward the perceived center of a distant target). The visual hypothesis predicted that LPD, with a known tendency toward left spatial hemineglect, would veer rightward, whereas RPD would veer leftward. The motor hypothesis predicted the opposite pattern of results because the more affected body side has shorter step length. The results supported the visual hypothesis. In Study 2, visually-cued gait was examined to establish whether the key variable to improvement is attention to pattern rhythmicity, or instead if improvement may arise from perception of dynamic flow. Floor patterns included transverse lines (attention; 3 frequencies) and randomly-placed squares (dynamic; 3 densities). Relative to baseline, both transverse lines and random squares, especially at higher frequency/density, resulted in gait improvements and induced more stable interlimb coordination, especially for LPD, the subgroup known to have greater visual dependence. Effects lasted after the cues were removed. The success of the random-squares cuing indicates that the mechanism of improvement may be dynamic flow of visual texture rather than attention, and further suggests that vision-based interventions need not be restricted to transverse lines. Taken together, the studies lay the foundation for the development of treatments for walking disturbances in PD by addressing critical issues that could influence the outcomes of therapeutic interventions, including the role of visual input and the differential effects on PD subgroups. / 2017-07-01T00:00:00Z

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