Spin Wave Diffraction Control and Read-out with a Quantum Memory for Light

A scheme for control and read-out of diffracted spins waves to propagating light fields is presented. Diffraction is obtained via sinusoidally varying lights shifts and ideal one-to-one mapping to light is realized using a gradient echo quantum memory. We also show that dynamical control of the diffracted spin waves spatial orders can be implemented to realize a quantum pulse sequencer for temporal modes that have high time-bandwidth products. Full numerical solutions suggest that both co-propagating and couterpropagating light shift geometries can be used, making the proposal applicable to hot and cold atomic vapours as well as solid state systems with two-level atoms.Comment: 5 pages, 3 figure

The Cube Recurrence

We construct a combinatorial model that is described by the cube recurrence, a nonlinear recurrence relation introduced by Propp, which generates families of Laurent polynomials indexed by points in $\mathbb{Z}^3$. In the process, we prove several conjectures of Propp and of Fomin and Zelevinsky, and we obtain a combinatorial interpretation for the terms of Gale-Robinson sequences. We also indicate how the model might be used to obtain some interesting results about perfect matchings of certain bipartite planar graphs

Unsupervised Learning of Visual Structure using Predictive Generative Networks

The ability to predict future states of the environment is a central pillar of intelligence. At its core, effective prediction requires an internal model of the world and an understanding of the rules by which the world changes. Here, we explore the internal models developed by deep neural networks trained using a loss based on predicting future frames in synthetic video sequences, using a CNN-LSTM-deCNN framework. We first show that this architecture can achieve excellent performance in visual sequence prediction tasks, including state-of-the-art performance in a standard 'bouncing balls' dataset (Sutskever et al., 2009). Using a weighted mean-squared error and adversarial loss (Goodfellow et al., 2014), the same architecture successfully extrapolates out-of-the-plane rotations of computer-generated faces. Furthermore, despite being trained end-to-end to predict only pixel-level information, our Predictive Generative Networks learn a representation of the latent structure of the underlying three-dimensional objects themselves. Importantly, we find that this representation is naturally tolerant to object transformations, and generalizes well to new tasks, such as classification of static images. Similar models trained solely with a reconstruction loss fail to generalize as effectively. We argue that prediction can serve as a powerful unsupervised loss for learning rich internal representations of high-level object features.Comment: under review as conference paper at ICLR 201

A mathematical analysis of the GW0 method for computing electronic excited energies of molecules

This paper analyses the GW method for finite electronic systems. In a first step, we provide a mathematical framework for the usual one-body operators that appear naturally in many-body perturbation theory. We then discuss the GW equations which construct an approximation of the one-body Green's function, and give a rigorous mathematical formulation of these equations. Finally, we study the well-posedness of the GW0 equations, proving the existence of a unique solution to these equations in a perturbative regime

Access or Barrier? Tuition and Fee Legislation for Undocumented Students across the States

States have responded in a variety of ways to undocumented immigration and its implications for higher education. Some states have allowed undocumented students to seek an affordable college education while others have created barriers. This article highlights the piecemeal legislation that the states have passed in order to respond to the needs of undocumented students; namely, policies allowing undocumented students in-state resident tuition. It also considers the policy impacts on undocumented students and the institutions and faculty that serve them

Reconstruction of Residual Stress in a Welded Plate Using the Variational Eigenstrain Approach

We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or distortion. The variational formulation employed seeks to achieve the best agreement between the model prediction and some measured parameters in the sense of a minimum of a functional given by a sum over the entire set of measurements. The advantage of this approach lies in its flexibility: different sets of measurements and information about different components of the stress-strain state can be incorporated. We demonstrate the power of the technique by analysing experimental data for welds in thin sheet of a nickel superalloy aerospace material. Very good agreement can be achieved between the prediction and the measurement results without the necessity of using iterative solution. In practice complete characterisation of residual stress states is often very difficult, due to limitations of facility access, measurement time or specimen dimensions. Implications of the new technique for experimental analysis are all the more significant, since it allows the reconstruction of the entire stress state from incomplete sets of data.Comment: 16 pages, 17 figure