High-dimensional Ising model selection using ℓ1{\ell_1}-regularized logistic regression

We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on $\ell_1$-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an $\ell_1$-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes $p$ and maximum neighborhood size $d$ are allowed to grow as a function of the number of observations $n$. Our main results provide sufficient conditions on the triple $(n,p,d)$ and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes $n=\Omega(d^3\log p)$ with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of $n=\Omega(d^2\log p)$ suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete Markov random fields.Comment: Published in at http://dx.doi.org/10.1214/09-AOS691 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Efficient Decoding of Topological Color Codes

Color codes are a class of topological quantum codes with a high error threshold and large set of transversal encoded gates, and are thus suitable for fault tolerant quantum computation in two-dimensional architectures. Recently, computationally efficient decoders for the color codes were proposed. We describe an alternate efficient iterative decoder for topological color codes, and apply it to the color code on hexagonal lattice embedded on a torus. In numerical simulations, we find an error threshold of 7.8% for independent dephasing and spin flip errors.Comment: 7 pages, LaTe

On Gorenstein Surfaces Dominated by P^2

In this paper we prove that a normal Gorenstein surface dominated by the projective plane P^2 is isomorphic to a quotient P^2/G, where G is a finite group of automorphisms of P^2 (except possibly for one surface V_8'). We can completely classify all such quotients. Some natural conjectures when the surface is not Gorenstein are also stated.Comment: Nagoya Mathematical Journal, to appea

Real-time edge tracking using a tactile sensor

Object recognition through the use of input from multiple sensors is an important aspect of an autonomous manipulation system. In tactile object recognition, it is necessary to determine the location and orientation of object edges and surfaces. A controller is proposed that utilizes a tactile sensor in the feedback loop of a manipulator to track along edges. In the control system, the data from the tactile sensor is first processed to find edges. The parameters of these edges are then used to generate a control signal to a hybrid controller. Theory is presented for tactile edge detection and an edge tracking controller. In addition, experimental verification of the edge tracking controller is presented

Studies on mechanical behavior of glass epoxy composites with induced defects and correlations with NDT characterization parameters

Degradation in mechanical properties (compression, flexural and ILS) of glass epoxy composite laminates with induced defects (simulating delaminations) was studied. The defects were characterized by using the A-scan ultrasonic pulse-echo technique. The two A-scan parameters, viz. the back wall echo amplitude and time of flight, were followed respectively, as functions of the defect size (diameter) and its location in the laminate thickness. The mechanical properties of laminates were evaluated destructively for different defect sizes and locations. An attempt has been made to express the mechanical properties in terms of the two NDT scan parameters characterizing the defects and empirical equations presente

Regioselective Reactions of Highly Substituted Arynes

The fully regioselective reactivity of four new highly substituted silyl aryl triflate aryne precursors in aryne acyl-alkylation, acyl-alkylation/condensation, and heteroannulation reactions is reported. The application of these more complex arynes provides access to diverse natural product scaffolds and obviates late-stage functionalization of aromatic rings