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

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

Using Top-Points as Interest Points for Image Matching

We consider the use of so-called top-points for object retrieval. These points are based on scale-space and catastrophe theory, and are invariant under gray value scaling and offset as well as scale-Euclidean transformations. The differential properties and noise characteristics of these points are mathematically well understood. It is possible to retrieve the exact location of a top-point from any coarse estimation through a closed-form vector equation which only depends on local derivatives in the estimated point. All these properties make top-points highly suitable as anchor points for invariant matching schemes. In a set of examples we show the excellent performance of top-points in an object retrievaltask

Measures for pathway analysis in brain white matter using diffusion tensor images

In this paper we discuss new measures for connectivity analysis of brain white matter, using MR diffusion tensor imaging. Our approach is based on Riemannian geometry, the viability of which has been demonstrated by various researchers in foregoing work. In the Riemannian framework bundles of axons are represented by geodesies on the manifold. Here we do not discuss methods to compute these geodesies, nor do we rely on the availability of geodesies. Instead we propose local measures which are directly computable from the local DTI data, and which enable us to preselect viable or exclude uninteresting seed points for the potentially time consuming extraction of geodesies. If geodesies are available, our measures can be readily applied to these as well. We consider two types of geodesic measures. One pertains to the connectivity saliency of a geodesic, the second to its stability with respect to local spatial perturbations. For the first type of measure we consider both differential as well as integral measures for characterizing a geodesic's saliency either locally or globally. (In the latter case one needs to be in possession of the geodesic curve, in the former case a single tangent vector suffices.) The second type of measure is intrinsically local, and turns out to be related to a well known tensor in Riemannian geometry.</p

Stability of Top-Points in Scale Space

Abstract. This paper presents an algorithm for computing stability of top-points in scale-space. The potential usefulness of top-points in scalespace has already been shown for a number of applications, such as image reconstruction and image retrieval. In order to improve results only reliable top-points should be used. The algorithm is based on perturbation theory and noise propagation

Image Reconstruction from Multiscale Critical Points

A minimal variance reconstruction scheme is derived using derivatives of the Gaussian as filters. A closed form mixed correlation matrix for reconstructions from multiscale points and their local derivatives up to the second order is presented. With the inverse of this mixed correlation matrix, a reconstruction of the image can be easily calculated.Some interesting results of reconstructions from multiscale critical points are presented. The influence of limited calculation precision is considered, using the condition number of the mixed correlation matrix