Математична модель контактного з’єднання метало-пластмасових циліндричних оболонок

We consider alpha scale spaces, a parameterized class (alpha is an element of (0, 1]) of scale space representations beyond the well-established Gaussian scale space, which are generated by the alpha-th power of the minus Laplace operator on a bounded domain using the Neumann boundary condition. The Neumann boundary condition ensures that there is no grey-value flux through the boundary. Thereby no artificial grey-values from outside the image affect the evolution proces, which is the case for the alpha scale spaces on an unbounded domain. Moreover, the connection between the a scale spaces which is not trivial in the unbounded domain case, becomes straightforward: The generator of the Gaussian semigroup extends to a compact, self-adjoint operator on the Hilbert space L-2(Omega) and therefore it has a complete countable set of eigen functions. Taking the alpha-th power of the Gaussian generator simply boils down to taking the alpha-th power of the corresponding eigenvalues. Consequently, all alpha scale spaces have exactly the same eigen-modes and can be implemented simultaneously as scale dependent Fourier series. The only difference between them is the (relative) contribution of each eigen-mode to the evolution proces. By introducing the notion of (non-dimensional) relative scale in each a scale space, we are able to compare the various alpha scale spaces. The case alpha = 0.5, where the generator equals the square root of the minus Laplace operator leads to Poisson scale space, which is at least as interesting as Gaussian scale space and can be extended to a (Clifford) analytic scale space

Separable time-causal and time-recursive spatio-temporal receptive fields

We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of non-enhancement of local extrema or scale invariance, these receptive fields are based on different scale-space axiomatics over time by ensuring non-creation of new local extrema or zero-crossings with increasing temporal scale. Specifically, extensions are presented about parameterizing the intermediate temporal scale levels, analysing the resulting temporal dynamics and transferring the theory to a discrete implementation in terms of recursive filters over time.Comment: 12 pages, 2 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1404.203

The Multiscale Morphology Filter: Identifying and Extracting Spatial Patterns in the Galaxy Distribution

We present here a new method, MMF, for automatically segmenting cosmic structure into its basic components: clusters, filaments, and walls. Importantly, the segmentation is scale independent, so all structures are identified without prejudice as to their size or shape. The method is ideally suited for extracting catalogues of clusters, walls, and filaments from samples of galaxies in redshift surveys or from particles in cosmological N-body simulations: it makes no prior assumptions about the scale or shape of the structures.}Comment: Replacement with higher resolution figures. 28 pages, 17 figures. For Full Resolution Version see: http://www.astro.rug.nl/~weygaert/tim1publication/miguelmmf.pd

Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table

Interpreting predictions of cognition from simulated versus empirical resting state functional connectivity

The relation between structure and function of the brain, and how behavior arises from it, is a central topic of interest in neuroscience. This problem can be formulated in terms of Structural Connectivity (SC) and Functional Connectivity (FC), respectively representing anatomical connections and functional interactions between regions in the brain. Recently, a study by Sarwar and colleagues has demonstrated individualized prediction of FC from SC using machine learning, additionally showing that variation in cognitive performance is explained by simulated FC (sFC) almost as well as by empirical FC (eFC). We investigated how decisions made to predict cognition differ between the models based on eFC and sFC. We predicted cognitive performance with Lasso regression in 100 cross-validation loops from both eFC and sFC separately, using FC between each of the 2278 pairs of regions in the 68-region Desikan-Killiany parcellation as features. We identified relevant predictors of cognition by inspecting permutation importance scores and keeping only features whose importance scores were consistently high across validation loops. 13 eFC features and 21 sFC features survived this procedure. Of these, only one feature overlapped between eFC and sFC. Analyzing overlap between regions corresponding to important features and functional systems known to support cognition revealed no patterns for either eFC or sFC features. In conclusion, we found that while cognition can be predicted from sFC almost as well as from eFC, different features are used in the models, and these features were not found to follow any structure in terms of functional systems. This shows that while machine learning models provide a theoretical upper bound on how accurately function can be predicted from structure, they do not necessarily produce output that can be interpreted in the same way as the data the models were trained on

Working memory performance is associated with functional connectivity between the right dlPFC and DMN in glioma patients

Patients with primary brain tumors frequently suffer from cognitive impairments in multiple domains, leading to serious consequences for socio-professional functioning and quality of life. The functional-anatomical basis of these impairments is still poorly understood.The study of correlated BOLD activity in the brain (i.e. functional connectivity) has greatly contributed to our understanding of how brain activity supports cognitive function. In particular, activity observed during the execution of specific tasks can be related to various distributed functional networks, stressing the importance of interactions between remote brain regions. Among these networks, the Default Mode Network (DMN) and the Fronto-Parietal Network (FPN) have consistently been associated with working memory performance.Recently, using task-fMRI in glioma patients, poor performance in a working memory task was associated with less deactivation of the DMN during this task and to a lack of task-evoked changes in the DMN-FPN structure. In this study, we investigated whether these effects are reflected in the resting-state (RS) functional connectivity of the same patient group, i.e. when no task was performed during fMRI. We additionally zoomed in on the part of the FPN located in the dorsolateral Prefrontal Cortex (dlPFC), since this region is believed to be mainly responsible for DMN deactivation.Resting-state functional MRI data were acquired pre-operatively from 45 brain tumor patients (20 low- and 25 high-grade glioma patients). Results of a pre-operative in-scanner N-back working memory fMRI task were used to assess working memory performance.Patient brains were parcellated into ROIs using both the Gordon and Yeo atlas, which have the FPN and DMN network identities readily available. The dlPFC was defined based on masks retrieved from NeuroSynth.To measure DMN-FPN functional connectivity the average Pearson correlation between the activation time series in the regions belonging to the FPN and the DMN was calculated. Functional connectivity between the DMN and the dlPFC was calculated in a similar way.The average correlation between the resting-state fMRI activity in the right dlPFC and in the DMN was negatively associated with working memory performance for both the Gordon atlas (p \\< 0.003) and Yeo atlas (p \\< 0.007). No association was found for the correlation between activity in the left dlPFC and the DMN, nor for the correlation between the activity in the whole FPN and the DMN.Our findings show that working memory performance of glioma patients is related to interactions between networks that can be measured with resting-state fMRI. Furthermore, the results provide further evidence that not only specific brain regions are important for cognitive performance, but that also the interactions between large-scale networks should be considered

Evolution equations on Gabor transforms and their applications

We introduce a systematic approach to the design, implementation and analysis of left-invariant evolution schemes acting on Gabor transform, primarily for applications in signal and image analysis. Within this approach we relate operators on signals to operators on Gabor transforms. In order to obtain a translation and modulation invariant operator on the space of signals, the corresponding operator on the reproducing kernel space of Gabor transforms must be left invariant, i.e. it should commute with the left regular action of the reduced Heisenberg group H_r. By using the left-invariant vector fields on H_r in the generators of our evolution equations on Gabor transforms, we naturally employ the essential group structure on the domain of a Gabor transform. Here we distinguish between two tasks. Firstly, we consider non-linear adaptive left-invariant convection (reassignment) to sharpen Gabor transforms, while maintaining the original signal. Secondly, we consider signal enhancement via left-invariant diffusion on the corresponding Gabor transform. We provide numerical experiments and analytical evidence for our methods and we consider an explicit medical imaging application

Cardiac motion estimation using covariant derivatives and Helmholtz decomposition

The investigation and quantification of cardiac movement is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider new aperture problem-free methods to track cardiac motion from 2-dimensional MR tagged images and corresponding sine-phase images. Tracking is achieved by following the movement of scale-space maxima, yielding a sparse set of linear features of the unknown optic flow vector field. Interpolation/reconstruction of the velocity field is then carried out by minimizing an energy functional which is a Sobolev-norm expressed in covariant derivatives (rather than standard derivatives). These covariant derivatives are used to express prior knowledge about the velocity field in the variational framework employed. They are defined on a fiber bundle where sections coincide with vector fields. Furthermore, the optic flow vector field is decomposed in a divergence free and a rotation free part, using our multi-scale Helmholtz decomposition algorithm that combines diffusion and Helmholtz decomposition in a single non-singular analytic kernel operator. Finally, we combine this multi-scale Helmholtz decomposition with vector field reconstruction (based on covariant derivatives) in a single algorithm and present some experiments of cardiac motion estimation. Further experiments on phantom data with ground truth show that both the inclusion of covariant derivatives and the inclusion of the multi-scale Helmholtz decomposition improves the optic flow reconstruction