SmartMirror: A Glance into the Future

In todays society, information is available to us at a glance through our phones, our laptops, our desktops, and more. But an extra level of interaction is required in order to access the information. As technology grows, technology should grow further and further away from the traditional style of interaction with devices. In the past, information was relayed through paper, then through computers, and in todays day and age, through our phones and multiple other mediums. Technology should become more integrated into our lives - more seamless and more invisible. We hope to push the envelope further, into the future. We propose a new simple way of connecting with your morning newspaper. We present our idea, the SmartMirror, information at a glance. Our system aims to deliver your information quickly and comfortably, with a new modern aesthetic. While modern appliances require input through modules such as keyboards or touch screen, we hope to follow a model that can function purely on voice and gesture. We seek to deliver your information during your morning routine and throughout the day, when taking out your phone is not always possible. This will cater to a larger audience base, as the average consumer nowadays hopes to accomplish tasks with minimal active interaction with their adopted technology. This idea has many future applications, such as integration with new virtual or augmented reality devices, or simplifying consumer personal media sources

Stochastic Blockmodeling for Online Advertising

Online advertising is an important and huge industry. Having knowledge of the website attributes can contribute greatly to business strategies for ad-targeting, content display, inventory purchase or revenue prediction. Classical inferences on users and sites impose challenge, because the data is voluminous, sparse, high-dimensional and noisy. In this paper, we introduce a stochastic blockmodeling for the website relations induced by the event of online user visitation. We propose two clustering algorithms to discover the instrinsic structures of websites, and compare the performance with a goodness-of-fit method and a deterministic graph partitioning method. We demonstrate the effectiveness of our algorithms on both simulation and AOL website dataset

Exploring Lattice Methods for Cold Fermionic Atoms

There has been a surge of experimental effort recently in cooling trapped fermionic atoms to quantum degeneracy. By varying an external magnetic field, interactions between atoms can be made arbitrarily strong. When the S wave scattering length becomes comparable to and larger than the interparticle spacing, standard mean field analysis breaks down. In this case the system exhibits a type of universality, and J-W. Chen and D. B. Kaplan recently showed how this system can be studied from first principles using lattice field theory. This poster presents the first results of exploratory simulations. The existence of a continuum limit is checked and the pairing condensate is studied as a function of the external source strength over a range of temperatures. Preliminary results show simulations can locate the critical temperature.Comment: Poster presented at Lattice2004(non-zero), Fermilab, 21-26 June 2004. 3 page

Stability of Steady Multi-Wave Configurations for the Full Euler Equations of Compressible Fluid Flow

We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the Riemann problem in the flow direction, consisting of two shocks, one vortex sheet, and one entropy wave, which is one of the core multi-wave configurations for the two-dimensional Euler equations. It is proved that such steady four-wave configurations in supersonic flow are stable in structure globally, even under the BV perturbation of the incoming flow in the flow direction. In order to achieve this, we first formulate the problem as the Cauchy problem (initial value problem) in the flow direction, and then develop a modified Glimm difference scheme and identify a Glimm-type functional to obtain the required BV estimates by tracing the interactions not only between the strong shocks and weak waves, but also between the strong vortex sheet/entropy wave and weak waves. The key feature of the Euler equations is that the reflection coefficient is always less than 1, when a weak wave of different family interacts with the strong vortex sheet/entropy wave or the shock wave, which is crucial to guarantee that the Glimm functional is decreasing. Then these estimates are employed to establish the convergence of the approximate solutions to a global entropy solution, close to the background solution of steady four-wave configuration.Comment: 9 figures

Generic Expression Hardness Results for Primitive Positive Formula Comparison

We study the expression complexity of two basic problems involving the comparison of primitive positive formulas: equivalence and containment. In particular, we study the complexity of these problems relative to finite relational structures. We present two generic hardness results for the studied problems, and discuss evidence that they are optimal and yield, for each of the problems, a complexity trichotomy

A Nonparametric Bayesian Approach to Uncovering Rat Hippocampal Population Codes During Spatial Navigation

Rodent hippocampal population codes represent important spatial information about the environment during navigation. Several computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. Here we extend our previous work and propose a nonparametric Bayesian approach to infer rat hippocampal population codes during spatial navigation. To tackle the model selection problem, we leverage a nonparametric Bayesian model. Specifically, to analyze rat hippocampal ensemble spiking activity, we apply a hierarchical Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference methods, one based on Markov chain Monte Carlo (MCMC) and the other based on variational Bayes (VB). We demonstrate the effectiveness of our Bayesian approaches on recordings from a freely-behaving rat navigating in an open field environment. We find that MCMC-based inference with Hamiltonian Monte Carlo (HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and MCMC approaches with hyperparameters set by empirical Bayes

Hypergeometric Functions of Matrix Arguments and Linear Statistics of Multi-Spiked Hermitian Matrix Models

This paper derives central limit theorems (CLTs) for general linear spectral statistics (LSS) of three important multi-spiked Hermitian random matrix ensembles. The first is the most common spiked scenario, proposed by Johnstone, which is a central Wishart ensemble with fixed-rank perturbation of the identity matrix, the second is a non-central Wishart ensemble with fixed-rank noncentrality parameter, and the third is a similarly defined non-central $F$ ensemble. These CLT results generalize our recent work to account for multiple spikes, which is the most common scenario met in practice. The generalization is non-trivial, as it now requires dealing with hypergeometric functions of matrix arguments. To facilitate our analysis, for a broad class of such functions, we first generalize a recent result of Onatski to present new contour integral representations, which are particularly suitable for computing large-dimensional properties of spiked matrix ensembles. Armed with such representations, our CLT formulas are derived for each of the three spiked models of interest by employing the Coulomb fluid method from random matrix theory along with saddlepoint techniques. We find that for each matrix model, and for general LSS, the individual spikes contribute additively to yield a $O(1)$ correction term to the asymptotic mean of the linear statistic, which we specify explicitly, whilst having no effect on the leading order terms of the mean or variance