Informing the design of a multisensory learning environment for elementary mathematics learning

It is well known that primary school children may face difficulties in acquiring mathematical competence, possibly because teaching is generally based on formal lessons with little opportunity to exploit more multisensory-based activities within the classroom. To overcome such difficulties, we report here the exemplary design of a novel multisensory learning environment for teaching mathematical concepts based on meaningful inputs from elementary school teachers. First, we developed and administered a questionnaire to 101 teachers asking them to rate based on their experience the learning difficulty for specific arithmetical and geometrical concepts encountered by elementary school children. Additionally, the questionnaire investigated the feasibility to use multisensory information to teach mathematical concepts. Results show that challenging concepts differ depending on children school level, thus providing a guidance to improve teaching strategies and the design of new and emerging learning technologies accordingly. Second, we obtained specific and practical design inputs with workshops involving elementary school teachers and children. Altogether, these findings are used to inform the design of emerging multimodal technological applications, that take advantage not only of vision but also of other sensory modalities. In the present work, we describe in detail one exemplary multisensory environment design based on the questionnaire results and design ideas from the workshops: the Space Shapes game, which exploits visual and haptic/proprioceptive sensory information to support mental rotation, 2D–3D transformation and percentages. Corroborating research evidence in neuroscience and pedagogy, our work presents a functional approach to develop novel multimodal user interfaces to improve education in the classroom

The nonlinear Bernstein-Schr\"odinger equation in Economics

In this paper we relate the Equilibrium Assignment Problem (EAP), which is underlying in several economics models, to a system of nonlinear equations that we call the "nonlinear Bernstein-Schr\"odinger system", which is well-known in the linear case, but whose nonlinear extension does not seem to have been studied. We apply this connection to derive an existence result for the EAP, and an efficient computational method.Comment: 8 pages, submitted to Lecture Notes in Computer Scienc

Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (i.e., walking, sitting, running). However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Furthermore, interpreting the resulting clusters is difficult, especially when the data is high-dimensional. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through alternating minimization, using a variation of the expectation maximization (EM) algorithm. We derive closed-form solutions to efficiently solve the two resulting subproblems in a scalable way, through dynamic programming and the alternating direction method of multipliers (ADMM), respectively. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile sensor dataset how TICC can be used to learn interpretable clusters in real-world scenarios.Comment: This revised version fixes two small typos in the published versio

Fast Optimal Transport Averaging of Neuroimaging Data

Knowing how the Human brain is anatomically and functionally organized at the level of a group of healthy individuals or patients is the primary goal of neuroimaging research. Yet computing an average of brain imaging data defined over a voxel grid or a triangulation remains a challenge. Data are large, the geometry of the brain is complex and the between subjects variability leads to spatially or temporally non-overlapping effects of interest. To address the problem of variability, data are commonly smoothed before group linear averaging. In this work we build on ideas originally introduced by Kantorovich to propose a new algorithm that can average efficiently non-normalized data defined over arbitrary discrete domains using transportation metrics. We show how Kantorovich means can be linked to Wasserstein barycenters in order to take advantage of an entropic smoothing approach. It leads to a smooth convex optimization problem and an algorithm with strong convergence guarantees. We illustrate the versatility of this tool and its empirical behavior on functional neuroimaging data, functional MRI and magnetoencephalography (MEG) source estimates, defined on voxel grids and triangulations of the folded cortical surface.Comment: Information Processing in Medical Imaging (IPMI), Jun 2015, Isle of Skye, United Kingdom. Springer, 201

Yin Yang of immunoregulation in organ transplantation and cancer

The ‘Yin Yang of Immunoregulation: Cancer and Organ Transplantation’ meeting took place in Nantes, France on 2–3 December 2010 and was dedicated to the biology of myeloid and lymphoid immune cells in the context of cancer and transplantation. This meeting was organized by the Immunotherapy Research group of the Western France Cancer Network Cancéropole Grand-Ouest and the Immunomonitorage et Biothérapies network (IMBIO) research program, which is supported by the Région Pays de la Loire

WeDRAW: using multisensory serious games to explore concepts in primary mathematics

WeDRAW aims to mediate learning of primary school mathematical concepts, such as geometry and arithmetic, through the design, development and evaluation of multisensory serious games, using a combination of sensory interactive technologies. Working closely with schools, using participatory design techniques, the WeDRAW system will be embedded into the school curricula, and configurable by teachers. Besides application to typically developing children, a major goal is to examine this multisensory approach with visually impaired and dyslexic children

Parameter estimation for biochemical reaction networks using Wasserstein distances

We present a method for estimating parameters in stochastic models of biochemical reaction networks by fitting steady-state distributions using Wasserstein distances. We simulate a reaction network at different parameter settings and train a Gaussian process to learn the Wasserstein distance between observations and the simulator output for all parameters. We then use Bayesian optimization to find parameters minimizing this distance based on the trained Gaussian process. The effectiveness of our method is demonstrated on the three-stage model of gene expression and a genetic feedback loop for which moment-based methods are known to perform poorly. Our method is applicable to any simulator model of stochastic reaction networks, including Brownian Dynamics.Comment: 22 pages, 8 figures. Slight modifications/additions to the text; added new section (Section 4.4) and Appendi

Machine-learning of atomic-scale properties based on physical principles

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the Smooth Overlap of Atomic Positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalisations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels---applicable to comparing entire molecules or periodic systems---that go beyond an additive combination of local environments