42 research outputs found
A Hybrid High-Order method for Leray-Lions elliptic equations on general meshes
In this work, we develop and analyze a Hybrid High-Order (HHO) method for
steady non-linear Leray-Lions problems. The proposed method has several assets,
including the support for arbitrary approximation orders and general polytopal
meshes. This is achieved by combining two key ingredients devised at the local
level: a gradient reconstruction and a high-order stabilization term that
generalizes the one originally introduced in the linear case. The convergence
analysis is carried out using a compactness technique. Extending this technique
to HHO methods has prompted us to develop a set of discrete functional analysis
tools whose interest goes beyond the specific problem and method addressed in
this work: (direct and) reverse Lebesgue and Sobolev embeddings for local
polynomial spaces, -stability and -approximation properties for
-projectors on such spaces, and Sobolev embeddings for hybrid polynomial
spaces. Numerical tests are presented to validate the theoretical results for
the original method and variants thereof
Visual Computing Tools for Studying Micro-scale Diffusion
In this dissertation, we present novel visual computing tools and techniques to facilitate the exploration, simulation, and visualization of micro-scale diffusion. Our research builds upon the latest advances in visualization, high-performance computing, medical imaging, and human perception. We validate our research using the driving applications of nano-assembly and diffusion kurtosis imaging (DKI). In both of these applications, diffusion plays a central role. In the former it mediates the process of transporting micron-sized particles through moving lasers, and in the latter it conveys brain micro-geometry.
Nanocomponent-based devices, such as bio-sensors, electronic components, photonic devices, solar cells, and batteries, are expected to revolutionize health care, energy, communications, and the computing industry. However, in order to build such useful devices, nanoscale components need to be properly assembled together. We have developed a hybrid CPU/GPU-based computing tool to understand complex interactions between lasers, optical beads, and the suspension medium. We demonstrate how a high-performance visual computing tool can be used to accelerate an optical tweezers simulation to compute the force applied by a laser onto micro particles and study shadowing (refraction) behavior. This represents the first steps toward building a real-time nano-assembly planning system. A challenge in building such a system, however, is that optical tweezers systems typically lack stereo depth cues. We have developed a visual tool to provide an enhanced perception of a scene's 3D structure using the kinetic depth effect. The design of our tool has been informed by user studies of stereo perception using the kinetic-depth effect on monocular displays.
Diffusion kurtosis imaging is gaining rapid adoption in the medical imaging community due to its ability to measure the non-Gaussian property of water diffusion in biological tissues. Compared with the traditional diffusion tensor imaging (DTI), DKI can provide additional details about the underlying microstructural characteristics of neural tissues. It has shown promising results in studies on changes in gray matter and mild traumatic brain injuries, where DTI is often found to be inadequate. However, the highly detailed spatio-angular fields in DKI datasets present a special challenge for visualization. Traditional techniques that use glyphs are often inadequate for expressing subtle changes in the DKI fields. In this dissertation, we outline a systematic way to manage, analyze, and visualize spatio-angular fields using spherical harmonics lighting functions to facilitate insights into the micro-structural properties of the brain
Parametric temporal alignment for the detection of facial action temporal segments
In this paper we propose the very first weakly supervised approach for detecting facial action unit temporal segments. This is achieved by means of behaviour similarity matching, where no training of dedicated classifiers is needed and the input facial behaviour episode is compared to a template. The inferred temporal segment boundaries of the test sequence are those transferred from the template sequence. To this end, a parametric temporal alignment algorithm is proposed to align a single exemplar sequence to the test sequence. The proposed strategy can accommodate flexible time warp functions, does not need to exhaustively align all frames in both sequences, and the optimal warp parameters can be found by an efficient Gauss-Newton gradient descent search. We show that our approach produces the best results to date for the problem at hand, and provides a promising opportunity to studying facial actions from a new perspective
Pozostałości pików oddechowych w widmie zmienności rytmu serca dorosłego człowieka z szybkim rytmem oddechowym i wolnym rytmem serca
Wstęp: Analiza zmienności rytmu serca (HRV) w dziedzinie częstotliwości
jest użytecznym narzędziem do badania fluktuacji rytmu zatokowego powodowanych
przez autonomiczny układ nerwowy. Jednakże, nie jest jasne, jaka jest górna
granica częstotliwości, która może być analizowana w widmie HRV.
Materiał i metody: Badamy widma HRV dorosłego ochotnika z szybkim rytmem
oddechowym, gdy jego rytm serca jest zwalniany bądź przyspieszany. Stosując
szybką transformatę Fouriera (FFT), analizujemy serie odstępów między uderzeniami
serca w dziedzinie częstotliwości. Przeprowadzamy również komputerowe symulacje
mierzonych sygnałów i porównujemy otrzymane widma z widmami ochotnika.
Wyniki: Jeżeli częstość oddechów przekracza połowę średniej częstości
uderzeń serca, w widmie HRV są obecne dwa piki reprezentujące ten sam sygnał
oddechowy. Jeden z pików jest wynikiem zjawiska aliasingu, natomiast drugi jest
pozostałością prawdziwego piku oddechowego, jako efekt właściwości symetrii
FFT. Żaden z nich nie przynosi rzetelnej, ilościowej informacji o fali oddechowej
w widmie HRV.
Wnioski: Górna granica częstotliwości w widmie HRV jest zdeterminowana
przez połowęśredniej częstotliwości serca. Przed obliczaniem widma należy więc
określić górny możliwy do analizy limit częstotliwości, by uniknąć sytuacji,
w której analizowane zakresy lokalizują się poza tą granicą. Sytuacja taka jest
wielce prawdopodobna w przypadku, gdy pacjent wykazuje wolną akcję serca