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Register a new userMaking drawings speak through mathematical metrics
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Figurative drawing is a skill that takes time to learn, and evolves during different childhood phases that begin with scribbling and end with representational drawing. Between these phases, it is difficult to assess when and how children demonstrate intentions and representativeness in their drawings. The marks produced are increasingly goal-oriented and efficient as the childs skills progress from scribbles to figurative drawings. Pre-figurative activities provide an opportunity to focus on drawing processes. We applied fourteen metrics to two different datasets (N=65 and N=345) to better understand the intentional and representational processes behind drawing, and combined these metrics using principal component analysis (PCA) in different biologically significant dimensions. Three dimensions were identified: efficiency based on spatial metrics, diversity with colour metrics, and temporal sequentiality. The metrics at play in each dimension are similar for both datasets, and PCA explains 77% of the variance in both datasets. These analyses differentiate scribbles by children from those drawn by adults. The three dimensions highlighted by this study provide a better understanding of the emergence of intentions and representativeness in drawings. We have already discussed the perspectives of such findings in Comparative Psychology and Evolutionary Anthropology.
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Time series datasets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the systems under study. To better extract this information, we investigate the asymptotic statistical properties of coupling measures between continuous signals and point processes. We first introduce martingale stochastic integration theory as a mathematical model for a family of statistical quantities that include the Phase Locking Value, a classical coupling measure to characterize complex dynamics. Based on the martingale Central Limit Theorem, we can then derive the asymptotic Gaussian distribution of estimates of such coupling measure, that can be exploited for statistical testing. Second, based on multivariate extensions of this result and Random Matrix Theory, we establish a principled way to analyze the low rank coupling between a large number of point processes and continuous signals. For a null hypothesis of no coupling, we establish sufficient conditions for the empirical distribution of squared singular values of the matrix to converge, as the number of measured signals increases, to the well-known Marchenko-Pastur (MP) law, and the largest squared singular value converges to the upper end of the MPs support. This justifies a simple thresholding approach to assess the significance of multivariate coupling. Finally, we illustrate with simulations the relevance of our univariate and multivariate results in the context of neural time series, addressing how to reliably quantify the interplay between multi channel Local Field Potential signals and the spiking activity of a large population of neurons.
The hematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. Feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in hematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. Developing a proper experimental design for these studies is an extremely challenging task. To address this issue, we have developed a novel Bayesian framework for optimal design of perturbation experiments. We model the numbers of hematopoietic stem and progenitor cells in mice that are exposed to a low dose of radiation. We use a differential equations model that accounts for feedback and feedforward regulation. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. This model is embedded in a hierarchical framework with latent variables that capture unobserved cellular population levels. We select the optimum design based on the amount of information gain, measured by the Kullback-Leibler divergence between the probability distributions before and after observing the data. We evaluate our approach using synthetic and experimental data. We show that a proper design can lead to better estimates of model parameters even with relatively few subjects. Additionally, we demonstrate that the model parameters show a wide range of sensitivities to design options. Our method should allow scientists to find the optimal design by focusing on their specific parameters of interest and provide insight to hematopoiesis. Our approach can be extended to more complex models where latent components are used.
Treatment recommendations within Clinical Practice Guidelines (CPGs) are largely based on findings from clinical trials and case studies, referred to here as research studies, that are often based on highly selective clinical populations, referred to here as study cohorts. When medical practitioners apply CPG recommendations, they need to understand how well their patient population matches the characteristics of those in the study cohort, and thus are confronted with the challenges of locating the study cohort information and making an analytic comparison. To address these challenges, we develop an ontology-enabled prototype system, which exposes the population descriptions in research studies in a declarative manner, with the ultimate goal of allowing medical practitioners to better understand the applicability and generalizability of treatment recommendations. We build a Study Cohort Ontology (SCO) to encode the vocabulary of study population descriptions, that are often reported in the first table in the published work, thus they are often referred to as Table 1. We leverage the well-used Semanticscience Integrated Ontology (SIO) for defining property associations between classes. Further, we model the key components of Table 1s, i.e., collections of study subjects, subject characteristics, and statistical measures in RDF knowledge graphs. We design scenarios for medical practitioners to perform population analysis, and generate cohort similarity visualizations to determine the applicability of a study population to the clinical population of interest. Our semantic approach to make study populations visible, by standardized representations of Table 1s, allows users to quickly derive clinically relevant inferences about study populations.
The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem, due to the non-uniqueness of the solution, and many kinds of prior information have been used to constrain it. A combination of smoothness (L2 norm-based) and sparseness (L1 norm-based) constraints is a flexible approach that have been pursued by important examples such as the Elastic Net (ENET) and mixed-norm (MXN) models. The former is used to find solutions with a small number of smooth non-zero patches, while the latter imposes sparseness and smoothness simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using computationally intensive Monte Carlo/Expectation Maximization methods. In this work we attempt to solve the EEG IP using a Bayesian framework for models based on mixtures of L1/L2 norms penalization functions (Laplace/Normal priors) such as ENET and MXN. We propose a Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using simple but realistic simulations we found that our methods are able to recover complicated source setups more accurately and with a more robust variable selection than the ENET and LASSO solutions using classical algorithms. We also solve the EEG IP using data coming from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods, as compared with other known methods such as LORETA, ENET and LASSO FUSION using the classical regularization approach.
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to posterior densities on model parameters. In this note, we review the main variants of VL approaches, that follow from considering nonlinear models of continuous and/or categorical data. En passant, we also derive a few novel theoretical results that complete the portfolio of existing analyses of variational Bayesian approaches, including investigations of their asymptotic convergence. We also suggest practical ways of extending existing VL approaches to hierarchical generative models that include (e.g., precision) hyperparameters.
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