Efficient Orthogonalizing the Eigenvectors of the Laplacian Matrix to Estimate Social Network Structure

It is inherent difficult to directly quantify the structure of the social networks that describe human relations. The network resonance method was proposed to elucidate the unknown Laplacian matrix representing social network structure. This method gives information on the eigenvalues and eigenvectors of the Laplacian matrix from observations of the dynamics of a social network. If all the eigenvalues and eigenvectors are known, the original Laplacian matrix can be determined. One problem with the network resonance method is that only limited information about eigenvectors can be acquired, and only the absolute values of the vector elements are available. Therefore, to determine the Laplacian matrix, it is necessary to determine the signs of each element of the eigenvectors; this task has order of O(2^n) given the combinations of n users for every eigenvector. This paper proposes a method that determines eigenvector element signs efficiently by running a sign determination algorithm in parallel and uses only those with fewer calculation amount. The proposal executes sign determination in polynomial time. We also reduce the calculation overhead by applying compressed sensing; the computational complexity of sign determination is reduced to almost O(n^2)

Machine Learning towards General Medical Image Segmentation

The quality of patient care associated with diagnostic radiology is proportionate to a physician\u27s workload. Segmentation is a fundamental limiting precursor to diagnostic and therapeutic procedures. Advances in machine learning aims to increase diagnostic efficiency to replace single applications with generalized algorithms. We approached segmentation as a multitask shape regression problem, simultaneously predicting coordinates on an object\u27s contour while jointly capturing global shape information. Shape regression models inherent point correlations to recover ambiguous boundaries not supported by clear edges and region homogeneity. Its capabilities was investigated using multi-output support vector regression (MSVR) on head and neck (HaN) CT images. Subsequently, we incorporated multiplane and multimodality spinal images and presented the first deep learning multiapplication framework for shape regression, the holistic multitask regression network (HMR-Net). MSVR and HMR-Net\u27s performance were comparable or superior to state-of-the-art algorithms. Multiapplication frameworks bridges any technical knowledge gaps and increases workflow efficiency

Interpretable statistics for complex modelling: quantile and topological learning

As the complexity of our data increased exponentially in the last decades, so has our need for interpretable features. This thesis revolves around two paradigms to approach this quest for insights. In the first part we focus on parametric models, where the problem of interpretability can be seen as a “parametrization selection”. We introduce a quantile-centric parametrization and we show the advantages of our proposal in the context of regression, where it allows to bridge the gap between classical generalized linear (mixed) models and increasingly popular quantile methods. The second part of the thesis, concerned with topological learning, tackles the problem from a non-parametric perspective. As topology can be thought of as a way of characterizing data in terms of their connectivity structure, it allows to represent complex and possibly high dimensional through few features, such as the number of connected components, loops and voids. We illustrate how the emerging branch of statistics devoted to recovering topological structures in the data, Topological Data Analysis, can be exploited both for exploratory and inferential purposes with a special emphasis on kernels that preserve the topological information in the data. Finally, we show with an application how these two approaches can borrow strength from one another in the identification and description of brain activity through fMRI data from the ABIDE project

Dynamic brain networks explored by structure-revealing methods

The human brain is a complex system able to continuously adapt. How and where brain activity is modulated by behavior can be studied with functional magnetic resonance imaging (fMRI), a non-invasive neuroimaging technique with excellent spatial resolution and whole-brain coverage. FMRI scans of healthy adults completing a variety of behavioral tasks have greatly contributed to our understanding of the functional role of individual brain regions. However, by statistically analyzing each region independently, these studies ignore that brain regions act in concert rather than in unison. Thus, many studies since have instead examined how brain regions interact. Surprisingly, structured interactions between distinct brain regions not only occur during behavioral tasks but also while a subject rests quietly in the MRI scanner. Multiple groups of regions interact very strongly with each other and not only do these groups bear a striking resemblance to the sets of regions co-activated in tasks, but many of these interactions are also progressively disrupted in neurological diseases. This suggests that spontaneous fluctuations in activity can provide novel insights into fundamental organizing principles of the human brain in health and disease. Many techniques to date have segregated regions into spatially distinct networks, which ignores that any brain region can take part in multiple networks across time. A more natural view is to estimate dynamic brain networks that allow flexible functional interactions (or connectivity) over time. The estimation and analysis of such dynamic functional interactions is the subject of this dissertation. We take the perspective that dynamic brain networks evolve in a low-dimensional space and can be described by a small number of characteristic spatiotemporal patterns. Our proposed approaches are based on well-established statistical methods, such as principal component analysis (PCA), sparse matrix decompositions, temporal clustering, as well as a multiscale analysis by novel graph wavelet designs. We adapt and extend these methods to the analysis of dynamic brain networks. We show that PCA and its higher-order equivalent can identify co-varying functional interactions, which reveal disturbed dynamic properties in multiple sclerosis and which are related to the timing of stimuli for task studies, respectively. Further we show that sparse matrix decompositions provide a valid alternative approach to PCA and improve interpretability of the identified patterns. Finally, assuming an even simpler low-dimensional space and the exclusive temporal expression of individual patterns, we show that specific transient interactions of the medial prefrontal cortex are disturbed in aging and relate to impaired memory

Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewedThe authors would like to acknowledge support from the Spanish Ministry of Economy and Competitiveness through grants BIO2013-44647-R and BIO2016-76400-R (AEI/ FEDER, UE), Comunidad Autonoma de Madrid through grant S2017/BMD-3817, Instituto de Salud Carlos III through grants PT13 /0001/0009 and PT17/0009/0010,the European Union (EU) and Horizon 2020 through West-Life (EINFRA- 2015-1, Proposal 675858), CORBEL (INFRADEV-1-2014-1, Proposal 654248), ELIXIR–EXCELERATE (INFRADEV-3- 2015, Proposal 676559), iNEXT (INFRAIA-1-2014-2015, Proposal 653706), EOSCpilot (INFRADEV-04-2016, Proposal 739563) and the National Institutes of Health (P41 GM 103712) (IB

Diffusion-based spatial priors for imaging.

We describe a Bayesian scheme to analyze images, which uses spatial priors encoded by a diffusion kernel, based on a weighted graph Laplacian. This provides a general framework to formulate a spatial model, whose parameters can be optimised. The standard practice using the software statistical parametric mapping (SPM) is to smooth imaging data using a fixed Gaussian kernel as a pre-processing step before applying a mass-univariate statistical model (e.g., a general linear model) to provide images of parameter estimates (Friston et al., 2006). This entails the strong assumption that data are generated smoothly throughout the brain. An alternative is to include smoothness in a multivariate statistical model (Penny et al., 2005). The advantage of the latter is that each parameter field is smoothed automatically, according to a measure of uncertainty, given the data. Explicit spatial priors enable formal model comparison of different prior assumptions, e.g. that data are generated from a stationary (i.e. fixed throughout the brain) or non-stationary spatial process. We describe the motivation, background material and theory used to formulate diffusion-based spatial priors for fMRI data and apply it to three different datasets, which include standard and high-resolution data. We compare mass-univariate ordinary least squares estimates of smoothed data and three Bayesian models spatially independent, stationary and non-stationary spatial models of non-smoothed data. The latter of which can be used to preserve boundaries between functionally selective regional responses of the brain, thereby increasing the spatial detail of inferences about cortical responses to experimental input

Random Matrix Theories in Quantum Physics: Common Concepts

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.Comment: 178 pages, Revtex, 45 figures, submitted to Physics Report