Details on the deterministic and stochastic stabilization of an inverted pendulum

In this work a quantitative and qualitative analysis of the dynamical stabilization of an inverted pendulum with a sinusoidal external perturbation applied at the suspension point is made. Initially, the external perturbation is composed of a single cosine, then a generalization is made using a sum of N cosines with different amplitudes and frequencies. Approximations are tested, and the time for which the inverted pendulum remains stable is explored when N is large, in order to recover the pattern of the case when N = 1. The specific case of periodic and almost periodic oscillations, when N = 2, is analysed and stability diagrams considering different frequencies and amplitudes are studied. Later, an additive Gaussian noise is added to the system so the degradation of the stability diagrams generated by different variances can be studied. All points of this work are corroborated by simulations, which numerically integrate the system’s equation of motion through a fourth order Runge-Kutta method. Algorithms and extra details on the integration methods used are explored in a publication of this work, which is presented in this thesis as an appendix.Neste trabalho, uma análise quantitativa e qualitativa para a estabilização dinâmica de um pêndulo invertido com uma força externa senoidal aplicada no ponto de suspensão é feita. Inicialmente, a perturbação externa é composta de um único cosseno, então uma generalização é feita, usando uma soma de N cossenos com diferentes amplitudes e frequências. Aproximações são testadas e o tempo durante o qual o pêndulo invertido permanece estável é explorado quando N é grande, a fim de recuperar o padrão do caso onde N = 1. O caso específico de oscilações periódicas e quase periódicas, quando N = 2, é analisado e diagramas de estabilidade considerando diferentes frequências e amplitudes são estudados. Depois, um ruído Gaussiano additivo é adicionado ao sistema para que a degradação dos diagramas de estabilidade gerados por variâncias diferentes possam ser estudados. Todos os pontos deste trabalho são corroborados por simulações, as quais integram numericamente as equações de movimento do sistema através do método de Runge-Kutta de quarta ordem. Os algoritmos e detalhes extras dos métodos de integração usados são explorados numa publicação deste trabalho, a qual está apresentada, nesta dissertação, como um apêndice

Uma discussão sobre algumas interpretações do "tempo de tunelamento quântico"

Nesta monografia apresentaremos uma breve discussão sobre a relação da incerteza energia-tempo que é baseada no princípio da incerteza da posição-momentum de Heisenberg. Mostraremos aqui como essa relação pode ser aplicada para estimar o tempo que uma partícula leva para atravessar uma barreira de potencial.In this monograph we present a brief discussion on the time-energy uncertainty relation which is based on Heisenberg’s momentum-space uncertainty principle. It is shown here how this relation can be applied to estimate the time it takes a particle to go through a potential barrier

Uma discussão sobre algumas interpretações do "tempo de tunelamento quântico"

Nesta monografia apresentaremos uma breve discussão sobre a relação da incerteza energia-tempo que é baseada no princípio da incerteza da posição-momentum de Heisenberg. Mostraremos aqui como essa relação pode ser aplicada para estimar o tempo que uma partícula leva para atravessar uma barreira de potencial.In this monograph we present a brief discussion on the time-energy uncertainty relation which is based on Heisenberg’s momentum-space uncertainty principle. It is shown here how this relation can be applied to estimate the time it takes a particle to go through a potential barrier

The impact of tau deposition and hypometabolism on cognitive impairment and longitudinal cognitive decline

Introduction: Tau and neurodegeneration strongly correlate with cognitive impairment, as compared to amyloid. However, their contribution in explaining cognition and predicting cognitive decline in memory clinics remains unclarified. Methods: We included 94 participants with Mini-Mental State Examination (MMSE), tau positron emission tomography (PET), amyloidPET, fluorodeoxyglucose (FDG)PET, and MRI scans from Geneva Memory Center. Linear regression and mediation analyses tested the independent and combined association between biomarkers, cognitive performance, and decline. Linear mixed-effects and Cox proportional hazards models assessed biomarkers’ prognostic values. Results: Metabolism had the strongest association with cognition (r = 0.712; p < 0.001), followed by tau (r = -0.682; p < 0.001). Neocortical tau showed the strongest association with cognitive decline (r = -0.677; p < 0.001). Metabolism mediated the association between tau and cognition and marginally mediated the one with decline. Tau positivity represented the strongest risk factor for decline (hazard ratio = 32). Discussion: Tau and neurodegeneration synergistically contribute to global cognitive impairment while tau drives decline. The tauPET superior prognostic value supports its implementation in memory clinics.ISSN:1552-5279ISSN:1552-526

Impact of Image Processing Settings for Radiomic Features in Alzheimer's Disease Using 18F-FDG and 11C-PIB PET Scans

&lt;p&gt;Radiomics is an established method for calculating features for computer-aided diagnosis and has been vastly applied to oncological studies. This study aimed to assess the impact of image processing in radiomic features in neuroimaging. Fifteen Alzheimer's disease subjects and 18 healthy individuals underwent [18F]-2-fluoro-2-deoxy-D-glucose (FDG) and 11C-labelled Pittsburgh Compound B (PIB) PET scans. T1-MRI scans were used for cerebellar and grey matter (GM), and white matter (WM) tissue delineation. PET images were registered to MRI (MR space) and transformed to MNI space. All images were normalized to cerebellar uptake (SUVR). All possible combinations of the following settings were considered to extract feature values: (1)tracer: FDG or PIB; (2)space: MR or MNI space; (3)discretization: fixed bin number (BN) of 64, fixed bin sizes (BS) of 0.05 or 0.25; and (4)volume of interest (VOI): GM, WM, or BRAIN (GM+WM). Features that correlated (&gt;0.9) to traditional metrics (average VOI SUVR and volume) in any configuration were removed. Correlation of feature values between configurations, redundancy, and harmonization of feature values were tested. Image processing settings highly affect radiomic feature values and should be carefully taken into consideration during study design and should be properly reported.&lt;/p&gt;&lt;p&gt;&nbsp;&lt;/p&gt;&lt;p&gt;The enclosed datasets refer to the work developed at the University Medical Center Groningen and consists of extracted feature values used in the publication.&lt;/p&gt