Linearized gravity as a gauge theory

We discuss linearized gravity from the point of view of a gauge theory. In (3+1)-dimensions our analysis allows to consider linearized gravity in the context of the MacDowell-Mansouri formalism. Our observations may be of particular interest in the strong-weak coupling duality for linearized gravity, in Randall-Sundrum brane world scenario and in Ashtekar formalism.Comment: Latex, 13 page

The leader operators of the (d+1)(d+1)-dimensional relativistic rotating oscillators

The main pairs of leader operators of the quantum models of relativistic rotating oscillators in arbitrary dimensions are derived. To this end one exploits the fact that these models generate P\"{o}schl-Teller radial problems with remarkable properties of supersymmetry and shape invariance.Comment: 11 page

Heisenberg-invariant Kummer surfaces

We study the geometry of Nieto's quintic threefold (Barth & Nieto, J. Alg. Geom. 3, 1994) and the Kummer and abelian surfaces that correspond to special loci.Comment: Plain TeX, 17 pages. Final version, with minor corrections, to appear in Proc. Edinburgh Math. So

On fractional derivatives and primitives of periodic functions

In this paper we prove that the fractional derivative or the fractional primitive of a $T$-periodic function cannot be a $\tilde{T}$-periodic function, for any period $\tilde{T}$, with the exception of the zero function.Comment: 12 page

From Pixels to Sentiment: Fine-tuning CNNs for Visual Sentiment Prediction

Visual multimedia have become an inseparable part of our digital social lives, and they often capture moments tied with deep affections. Automated visual sentiment analysis tools can provide a means of extracting the rich feelings and latent dispositions embedded in these media. In this work, we explore how Convolutional Neural Networks (CNNs), a now de facto computational machine learning tool particularly in the area of Computer Vision, can be specifically applied to the task of visual sentiment prediction. We accomplish this through fine-tuning experiments using a state-of-the-art CNN and via rigorous architecture analysis, we present several modifications that lead to accuracy improvements over prior art on a dataset of images from a popular social media platform. We additionally present visualizations of local patterns that the network learned to associate with image sentiment for insight into how visual positivity (or negativity) is perceived by the model.Comment: Accepted for publication in Image and Vision Computing. Models and source code available at https://github.com/imatge-upc/sentiment-201

Comparing Fixed and Adaptive Computation Time for Recurrent Neural Networks

Adaptive Computation Time for Recurrent Neural Networks (ACT) is one of the most promising architectures for variable computation. ACT adapts to the input sequence by being able to look at each sample more than once, and learn how many times it should do it. In this paper, we compare ACT to Repeat-RNN, a novel architecture based on repeating each sample a fixed number of times. We found surprising results, where Repeat-RNN performs as good as ACT in the selected tasks. Source code in TensorFlow and PyTorch is publicly available at https://imatge-upc.github.io/danifojo-2018-repeatrnn/Comment: Accepted as workshop paper at ICLR 201

Simple vs complex temporal recurrences for video saliency prediction

This paper investigates modifying an existing neural network architecture for static saliency prediction using two types of recurrences that integrate information from the temporal domain. The first modification is the addition of a ConvLSTM within the architecture, while the second is a conceptually simple exponential moving average of an internal convolutional state. We use weights pre-trained on the SALICON dataset and fine-tune our model on DHF1K. Our results show that both modifications achieve state-of-the-art results and produce similar saliency maps. Source code is available at https://git.io/fjPiB