Francy 
Data visualization and interaction with large data sets is known to be essential and critical in many businesses today, and the same applies to research and teaching, in this case, when exploring large and complex mathematical objects. GAP is a computer algebra system for computational discrete algebra with an emphasis on computational group theory. The existing XGAP package for GAP works exclusively on the X Window System. It lacks abstraction between its mathematical and graphical cores, making it difficult to extend, maintain, or port. In this paper, we present Francy, a graphical semantics package for GAP. Francy is responsible for creating a representational structure that can be rendered using many GUI frameworks independent from any particular programming language or operating system. Building on this, we use state of the art web technologies that take advantage of an improved REPL environment, which is currently under development for GAP. The integration of this project with Jupyter provides a rich graphical environment full of features enhancing the usability and accessibility of GAP. …
Probabilistic Latent Semantic Analysis (PLSA)
We consider the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. This problem has appeared in the literature as probabilistic latent semantic analysis (pLSA), and has connections to non-negative matrix factorization. When the simplicity of the variable is measured through its cardinality, we show that a solution to this latent variable discovery problem can be used to distinguish direct causal relations from spurious correlations among almost all joint distributions on simple causal graphs with two observed variables. Conjecturing a similar identifiability result holds with Shannon entropy, we study a loss function that trades-off between entropy of the latent variable and the conditional mutual information of the observed variables. We then propose a latent variable discovery algorithm — LatentSearch — and show that its stationary points are the stationary points of our loss function. We experimentally show that LatentSearch can indeed be used to distinguish direct causal relations from spurious correlations.
Entropic Latent Variable Discovery …
Attention Gated Network
We propose a novel attention gate (AG) model for medical image analysis that automatically learns to focus on target structures of varying shapes and sizes. Models trained with AGs implicitly learn to suppress irrelevant regions in an input image while highlighting salient features useful for a specific task. This enables us to eliminate the necessity of using explicit external tissue/organ localisation modules when using convolutional neural networks (CNNs). AGs can be easily integrated into standard CNN models such as VGG or U-Net architectures with minimal computational overhead while increasing the model sensitivity and prediction accuracy. The proposed AG models are evaluated on a variety of tasks, including medical image classification and segmentation. For classification, we demonstrate the use case of AGs in scan plane detection for fetal ultrasound screening. We show that the proposed attention mechanism can provide efficient object localisation while improving the overall prediction performance by reducing false positives. For segmentation, the proposed architecture is evaluated on two large 3D CT abdominal datasets with manual annotations for multiple organs. Experimental results show that AG models consistently improve the prediction performance of the base architectures across different datasets and training sizes while preserving computational efficiency. Moreover, AGs guide the model activations to be focused around salient regions, which provides better insights into how model predictions are made. The source code for the proposed AG models is publicly available. …
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