Applying parabolic Peterson: affine algebras and the quantum cohomology of the Grassmannian

The Peterson isomorphism relates the homology of the affine Grassmannian to the quantum cohomology of any flag variety. In the case of a partial flag, Peterson’s map is only a surjection, and one needs to quotient by a suitable ideal on the affine side to map isomorphically onto the quantum cohomology. We provide a detailed exposition of this parabolic Peterson isomorphism in the case of the Grassmannian of m-planes in complex n-space, including an explicit recipe for doing quantum Schubert calculus in terms of the appropriate subset of non-commutative k-Schur functions. As an application, we recast Postnikov’s affine approach to the quantum cohomology of the Grassmannian as a consequence of parabolic Peterson by showing that the affine nilTemperley–Lieb algebra arises naturally when forming the requisite quotient of the homology of the affine Grassmannian

Location and product bundling in the provision of WiFi networks

WiFi promises to revolutionise how and where we access the internet. As WiFi networks are rolled out around the globe, access to the internet will no longer be through fixed networks or unsatisfactory mobile phone connections. Instead access will be through low cost wireless networks at speeds of up to 11Mbps. It is hard not to be impressed by the enthusiasm with which WiFi has been embraced. GREEN, ROSENBUSH, CROKETT and HOLMES (2003) assert that WiFi is a disruptive technology akin to telephones in the 1920s and network computers in the 1990s. WiFi is seen as both an opportunity in its own right, as well as an enabler of opportunities for others. Computer manufacturers are hoping that WiFi will increases sales of their laptops, whilst Microsoft feels that WiFi will result in users upgrading their operating systems to Windows XP. This paper seeks to understand why three companies have sought to provide WiFi

Shape Generation using Spatially Partitioned Point Clouds

We propose a method to generate 3D shapes using point clouds. Given a point-cloud representation of a 3D shape, our method builds a kd-tree to spatially partition the points. This orders them consistently across all shapes, resulting in reasonably good correspondences across all shapes. We then use PCA analysis to derive a linear shape basis across the spatially partitioned points, and optimize the point ordering by iteratively minimizing the PCA reconstruction error. Even with the spatial sorting, the point clouds are inherently noisy and the resulting distribution over the shape coefficients can be highly multi-modal. We propose to use the expressive power of neural networks to learn a distribution over the shape coefficients in a generative-adversarial framework. Compared to 3D shape generative models trained on voxel-representations, our point-based method is considerably more light-weight and scalable, with little loss of quality. It also outperforms simpler linear factor models such as Probabilistic PCA, both qualitatively and quantitatively, on a number of categories from the ShapeNet dataset. Furthermore, our method can easily incorporate other point attributes such as normal and color information, an additional advantage over voxel-based representations.Comment: To appear at BMVC 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

Learning Grimaces by Watching TV

Differently from computer vision systems which require explicit supervision, humans can learn facial expressions by observing people in their environment. In this paper, we look at how similar capabilities could be developed in machine vision. As a starting point, we consider the problem of relating facial expressions to objectively measurable events occurring in videos. In particular, we consider a gameshow in which contestants play to win significant sums of money. We extract events affecting the game and corresponding facial expressions objectively and automatically from the videos, obtaining large quantities of labelled data for our study. We also develop, using benchmarks such as FER and SFEW 2.0, state-of-the-art deep neural networks for facial expression recognition, showing that pre-training on face verification data can be highly beneficial for this task. Then, we extend these models to use facial expressions to predict events in videos and learn nameable expressions from them. The dataset and emotion recognition models are available at http://www.robots.ox.ac.uk/~vgg/data/facevalueComment: British Machine Vision Conference (BMVC) 201