High-dimensional Sparse Inverse Covariance Estimation using Greedy Methods

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two novel greedy approaches to solving this problem. The first estimates the non-zero covariates of the overall inverse covariance matrix using a series of global forward and backward greedy steps. The second estimates the neighborhood of each node in the graph separately, again using greedy forward and backward steps, and combines the intermediate neighborhoods to form an overall estimate. The principal contribution of this paper is a rigorous analysis of the sparsistency, or consistency in recovering the sparsity pattern of the inverse covariance matrix. Surprisingly, we show that both the local and global greedy methods learn the full structure of the model with high probability given just $O(d\log(p))$ samples, which is a \emph{significant} improvement over state of the art $\ell_1$-regularized Gaussian MLE (Graphical Lasso) that requires $O(d^2\log(p))$ samples. Moreover, the restricted eigenvalue and smoothness conditions imposed by our greedy methods are much weaker than the strong irrepresentable conditions required by the $\ell_1$-regularization based methods. We corroborate our results with extensive simulations and examples, comparing our local and global greedy methods to the $\ell_1$-regularized Gaussian MLE as well as the Neighborhood Greedy method to that of nodewise $\ell_1$-regularized linear regression (Neighborhood Lasso).Comment: Accepted to AI STAT 2012 for Oral Presentatio

Tuning phase-stability and short-range order through Al-doping in (CoCrFeMn)100-xAlx high entropy alloys

For (CoCrFeMn)$_{100-x}$Al$_{x}$ high-entropy alloys, we investigate the phase evolution with increasing Al-content (0 $\le$ x $\le$ 20 at.%). From first-principles theory, the Al-doping drives the alloy structurally from FCC to BCC separated by a narrow two-phase region (FCC+BCC), which is well supported by our experiments. We highlight the effect of Al-doping on the formation enthalpy and electronic structure of (CoCrFeMn)$_{100-x}$Al$_{x}$ alloys. As chemical short-range order (SRO) in multicomponent alloys indicates the nascent local order (and entropy changes), as well as expected low-temperature ordering behavior, we use thermodynamic linear-response within density-functional theory to predict SRO and ordering transformation and temperatures inherent in (CoCrFeMn)$_{100-x}$Al$_{x}$. The predictions agree with our present experimental findings, and other reported ones.Comment: 27 pages, 9 figures, 1 tabl

Hybrid MOPA having narrowband oscillator and amplifier with integrated optical coupling.

This invention was disclosed in a FHOENICS Program Meeting on April 4, 2005. This invention utilizes the concepts of internal wavelength locking and gain switching to create high brightness optical pulses that range in pulse width from 20 picoseconds to 100s of picoseconds

Novel method for the fabrication of spatially variant structures

Spatially varying grating structures formed at the subwave-length scale behave as a layer with an artificial effective refractive index that is dependent on the local fill fraction. We describe a novel technique to pattern gratings with a spatially varying fill fraction using a simple two-step exposure process. The first exposure forms a partial latent image of a grating in the photoresist. The resist is then saturated by overlaying an exposure with an analog spatially varying intensity, generated by using a phase-only masking technique. The cumulative exposure dose from the two steps was designed so that the point of minimum intensity will still develop the photoresist through, in all the spaces in the grating. By varying the exposure window around the saturation dose, the fill fraction of the patterned gratings was modulated; thus, the size of the space cleared at any location in the grating is a scalable function of the local cumulative dose delivered. Constant feature height is achieved across the patterned area by keeping the second exposure dose below the resist threshold exposure value. The exposure process was modeled numerically to predict the relationship between the local dose and patterned fill fraction. This technique enables rapid, low-cost fabrication of apodized grating structures for applications in diffractive optics technology

Don't Thrash: How to Cache Your Hash on Flash

This paper presents new alternatives to the well-known Bloom filter data structure. The Bloom filter, a compact data structure supporting set insertion and membership queries, has found wide application in databases, storage systems, and networks. Because the Bloom filter performs frequent random reads and writes, it is used almost exclusively in RAM, limiting the size of the sets it can represent. This paper first describes the quotient filter, which supports the basic operations of the Bloom filter, achieving roughly comparable performance in terms of space and time, but with better data locality. Operations on the quotient filter require only a small number of contiguous accesses. The quotient filter has other advantages over the Bloom filter: it supports deletions, it can be dynamically resized, and two quotient filters can be efficiently merged. The paper then gives two data structures, the buffered quotient filter and the cascade filter, which exploit the quotient filter advantages and thus serve as SSD-optimized alternatives to the Bloom filter. The cascade filter has better asymptotic I/O performance than the buffered quotient filter, but the buffered quotient filter outperforms the cascade filter on small to medium data sets. Both data structures significantly outperform recently-proposed SSD-optimized Bloom filter variants, such as the elevator Bloom filter, buffered Bloom filter, and forest-structured Bloom filter. In experiments, the cascade filter and buffered quotient filter performed insertions 8.6-11 times faster than the fastest Bloom filter variant and performed lookups 0.94-2.56 times faster.Comment: VLDB201

Tuning phase-stability and short-range order through AI-doping in (CoCrFeMn)100-xAIx high entropy alloys

For (CoCrFeMn)100−xAlx high-entropy alloys, we investigate the phase evolution with increasing Al content (0≤x≤20 at.%). From first-principles theory, aluminum doping drives the alloy structurally from fcc to bcc separated by a narrow two-phase region (fcc+bcc), which is well supported by our experiments. Using KKR-CPA electronic-structure calculations, we highlight the effect of Al doping on the formation enthalpy (alloy stability) and electronic dispersion of (CoCrFeMn)100−xAlx alloys. As chemical short-range order indicates the nascent local order, and entropy changes, as well as expected low-temperature ordering behavior, we use KKR-CPA-based thermodynamic linear response to predict the chemical ordering behavior of arbitrary complex solid-solution alloys—an ideal approach for predictive design of high-entropy alloys. The predictions agree with our present experimental findings and other reported ones

Harnessing the expertise - analysis 2

This is the second Briefing Paper submitted to the School of Health and Society

Micro-optical spatial and spectral elements

Interference filters have a defect layer incorporated within a photonic crystal structure and generate a narrow transmission notch within a wide stop band. In this paper, we propose and demonstrate wavelength-tunable spatial filters by introducing diffractive optical elements in the defect layer. The spectral transmission through the device was a function of the local defect layer thickness under broadband illumination. For each wavelength, the spatial transmission followed the contours of equal defect layer optical thickness. The devices were implemented by depositing a one-dimensional photonic crystal with a centrally integrated defect layer on a silicon substrate using plasma-enhanced chemical vapor deposition. The defect layer was lithographically patterned with charge 2, 8-level vortex structures. The spectral transmission peak and linewidth was characterized by separately illuminating each zone of diffractive element using a tunable laser source and compared with model simulations. The spatial transmission through the device was imaged onto a CCD camera. Triangular wedge-shaped zones with wavelength-dependent orientations were observed. These novel devices with spectrally tunable spatial transmission have potential applications in pupil filtering, hyperspectral imaging, and engineered illumination systems