nÃo hà / Desde o princÃpio, as sequÃncias e sÃries numÃricas geraram interesse entre os matemÃticos. Sua aplicabilidade atual à extensa e inclui o cÃlculo refinado da Ãrea da superfÃcie e do volume de uma variedade de sÃlidos. Neste trabalho usaremos as diferenÃas entre os elementos de uma sequÃncia finita a fim de encontrar leis que expressem as tendÃncias nela contidas. Veremos tambÃm como um estudo simples sobre progressÃes aritmÃticas de ordens diversas à capaz de fornecer funÃÃes paramÃtricas de curvas passando por pontos prÃ-definidos, de superfÃcies contendo curvas prÃ-definidas ou, atà mesmo, de regiÃes do R situadas entre duas superfÃcies dadas. AlÃm disso, poderemos, com o auxÃlio do programa computacional Winplot, visualizar as curvas, superfÃcies ou regiÃes obtidas em cada exemplo de nosso estudo, alÃm de, eventualmente, verificar pontos de mÃximo e mÃnimo relativos de uma curva ou calcular a Ãrea de uma superfÃcie e o volume de uma regiÃo limitada do RÂ, tudo isto com um devido e prÃvio embasamento teÃrico. / From the beginning, the numeric sequences and series generated interest among mathematicians. Your present applicability is extensive and includes the refined calculation of the surface area and volume of a variety of solids. In this work we will use the differences between the elements of a finite sequence in order to find laws that express the trends contained therein. We will also see how a simple study about arithmetic progressions of various orders is able to provide curves's parametric functions through predefined points, of surfaces containing predefined curves or even regions of the R localized between two given surfaces. Moreover, we will can, with the aid of the computational program Winplot, visualize the curves, surfaces, or regions obtained in each example of our study, in addition to eventually check points of relative maximum and minimum of a curve or calculate the area of a surface and the volume of a limited region of RÂ, all of this with a necessary and previous theoretical background.

Small animal positron emission tomography (PET) image analysis can be particularly challenging with heavily-lesioned animal disease models with limited tracer uptake such as the 6-hydroxydopamine (OHDA) lesioned rat model of Parkinson's disease. Methodology-related variations in measured values of 10% or 15% can obscure meaningful biological differences, so accurate analysis methods are essential. However, placing regions of interest (ROIs) on these images without additional guidance is unreliable, and can lead to significant errors in results. To address this problem, this work develops a partly atlas-guided method place ROIs on structures that lack specific binding with presynaptic dopaminergic tracers. The method is tested by correlation of PET binding potential (BP) with autoradiographic binding measurements, and with repeated PET scans of the same subjects, both with the presynaptic tracer ¹¹C-dihydrotetrabenazine (DTBZ). The method is found to produce reliable results. When directly comparing PET images of the same subject to detect changes, it is essential to minimize variations due to analysis method. To this end, a masking method for automated image registration (AIR) of PET images with dopaminergic tracer rat images is developed. Coregistration with AIR and separate ROI placement are compared and tested with repeated scans of the same rat with DTBZ, and are found to be equivalent. Kinetic modelling algorithms may also introduce bias or scatter to binding potentials (BP) calculated from TACs or in parametric images. To determine the optimal method for this step, algorithms for dopaminergic tracers are compared for small animal DTBZ, ¹¹C-methylphenidate (MP), and ¹¹C-raclopride (Rac) data. Among the tested methods is a new variant of the Logan graphical kinetic modelling method, developed in this work, that issignificantly less biased by target tissue TAC noise than the standard Logan approach. The modified graphical method is further compared with the Logan graphical algorithms with added-noise simulations. The simplified reference tissue model (SRTM) is found to have the best method for ROI TAC data, while the modified graphical algorithm may be preferred when generating parametric images. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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A FORTRAN program has been developed in order to investigate the process of modal parameter estimation and non-parametric system identification. The theory underlying the process of modal parameter estimation is reviewed and the decoupling of a MIMO system into several SISO systems is demonstrated. Modal filtering is shown to be useful in the field of non-parametric system identification and it is shown that it may also be of some use in the field of signal processing. The program is documented. It simulates the output of a n-th order system from which a smaller order subsystem can be decoupled. The modal parameters of a subsystem output signal and its first two derivatives and the modal parameters of a second subsystem output and its first derivative are calculated. The unit step response of the theoretical system and the subsystem are then calculated. The signals are then modal filtered to produce the periodic unit step response and the periodic unit square wave response. Finally, the discrete Fourier coefficients of the periodic unit step response are calculated. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The delayed matching‐to‐sample (DMTS) procedure involves the insertion of a delay between the offset of a sample stimulus and the onset of an array of comparison stimuli; one of which is designated as the “correct” match for the sample on each trial. The procedure has served as the base preparation in which the effects of environmental variables on short‐term remembering and is, in many ways, responsible for a refined understanding of the phenomenon. Despite its utility, however, there are a few problems with the DMTS procedure – first, the procedure doesn’t adjust for individual differences and second, the conventional dependent measure, percent of correct trials, is not as sensitive as one might like. The titrating-delay matching to sample (TDMTS) procedure is a variant of the DMTS procedure in which the delays between sample and comparison are adjusted as a function of the subject’s performance. Stable measures of adjusted delay are not only sensitive measures of the performance of interest but they are also automatically tuned to differences across individuals. The study reported here continues our efforts to understand the dynamics of the TDMTS procedure so that it can be used to ask important questions related to short‐term remembering.

Indiana University-Purdue University Indianapolis (IUPUI) / Within the aerospace design, analysis and optimization community, there is an increasing demand to finalize the preliminary design phase of the wing as quickly as possible without losing much on accuracy. This includes rapid generation of designs, an early adaption of higher fidelity models and automation in structural analysis of the internal structure of the wing. To perform the structural analysis, the aerodynamic load can be transferred to the wing using many different methods. Generally, for preliminary analysis, indirect load transfer method is used and for detailed analysis, direct load transfer method is used. For the indirect load transfer method, load is discretized using shear-moment-torque (SMT) curve and applied to ribs of the wing. For the direct load transfer method, the load is distributed using one-way Fluid-Structure Interaction (FSI) and applied to the skin of the wing. In this research, structural analysis is performed using both methods and the nodal displacement is compared. Further, to optimize the internal structure, iterative changes are made in the number of structural members. To accommodate these changes in geometry as quickly as possible, the parametric design method is used through Engineering SketchPad (ESP). ESP can also provide attributions the geometric feature and generate multi-fidelity models consistently. ESP can generate the Nastran mesh file (.bdf) with the nodes and the elements grouped according to their geometric attributes. In this research, utilizing the attributions and consistency in multi-fidelity models an API is created between ESP and Nastran to automatize the multi-fidelity structural optimization. This API generates the design with appropriate parameters and mesh file using ESP. Through the attribution in the mesh file, the API works as a pre-processor to apply material properties, boundary condition, and optimization parameters. The API sends the mesh file to Nastran and reads the results file to iterate the number of the structural member in design. The result file is also used to transfer the nodal deformation from lower-order fidelity structural models onto the higher-order ones to have multi-fidelity optimization. Here, static structural optimization on the whole wing serves as lower fidelity model and buckling optimization on each stiffened panel serves as higher fidelity model. To further extend this idea, a parametric model of the whole aircraft is also created. / 2021-08-17

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