Large negative magnetoresistance in a ferromagnetic shape memory alloy : Ni_{2+x}Mn_{1-x}Ga

5% negative magnetoresistance (MR) at room temperature has been observed in bulk Ni_{2+x}Mn_{1-x}Ga. This indicates the possibility of using Ni_{2+x}Mn_{1-x}Ga as magnetic sensors. We have measured MR in the ferromagnetic state for different compositions (x=0-0.2) in the austenitic, pre-martensitic and martensitic phases. MR is found to increase with x. While MR for x=0 varies almost linearly in the austenitic and pre-martensitic phases, in the martensitic phase it shows a cusp-like shape. This has been explained by the changes in twin and domain structures in the martensitic phase. In the austenitic phase, which does not have twin structure, MR agrees with theory based on s-d scattering model.Comment: 3 pages, 3 figures, Appl. Phys. Lett 86, 202508 (2005

Decomposition Methods for Large Scale LP Decoding

When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be used to decode error-correcting codes at bit-error-rates comparable to state-of-the-art belief propagation (BP) decoders, but with significantly stronger theoretical guarantees. However, LP decoding when implemented with standard LP solvers does not easily scale to the block lengths of modern error correcting codes. In this paper we draw on decomposition methods from optimization theory, specifically the Alternating Directions Method of Multipliers (ADMM), to develop efficient distributed algorithms for LP decoding. The key enabling technical result is a "two-slice" characterization of the geometry of the parity polytope, which is the convex hull of all codewords of a single parity check code. This new characterization simplifies the representation of points in the polytope. Using this simplification, we develop an efficient algorithm for Euclidean norm projection onto the parity polytope. This projection is required by ADMM and allows us to use LP decoding, with all its theoretical guarantees, to decode large-scale error correcting codes efficiently. We present numerical results for LDPC codes of lengths more than 1000. The waterfall region of LP decoding is seen to initiate at a slightly higher signal-to-noise ratio than for sum-product BP, however an error floor is not observed for LP decoding, which is not the case for BP. Our implementation of LP decoding using ADMM executes as fast as our baseline sum-product BP decoder, is fully parallelizable, and can be seen to implement a type of message-passing with a particularly simple schedule.Comment: 35 pages, 11 figures. An early version of this work appeared at the 49th Annual Allerton Conference, September 2011. This version to appear in IEEE Transactions on Information Theor

Premartensite to martensite transition and its implications on the origin of modulation in Ni2MnGa ferromagnetic shape memory alloy

We present here results of temperature dependent high resolution synchrotron x-ray powder diffraction study of sequence of phase transitions in Ni2MnGa. Our results show that the incommensurate martensite phase results from the incommensurate premartensite phase, and not from the austenite phase assumed in the adaptive phase model. The premartensite phase transforms to the martensite phase through a first order phase transition with coexistence of the two phases in a broad temperature interval (~40K), discontinuous change in the unit cell volume as also in the modulation wave vector across the transition temperature and considerable thermal hysteresis in the characteristic transition temperatures. The temperature variation of the modulation wave vector q shows smooth analytic behaviour with no evidence for any devilish plateau corresponding to an intermediate or ground state commensurate lock-in phases. The existence of the incommensurate 7M like modulated structure down to 5K suggests that the incommensurate 7M like modulation is the ground state of Ni2MnGa and not the Bain distorted tetragonal L10 phase or any other lock-in phase with a commensurate modulation. These findings can be explained within the framework of the soft phonon model

Revealing the nature of antiferro-quadrupolar ordering in Cerium Hexaboride: CeB6_6

Cerium-hexaboride (CeB$_6$) f-electron compound displays a rich array of low-temperature magnetic phenomena, including `magnetically hidden' order, identified as multipolar in origin via advanced x-ray scattering. From first-principles electronic-structure results, we find that the \emph{antiferro-quadrupolar} (AFQ) ordering in CeB$_{6}$ arises from crystal-field splitting and yields band structure in agreement with experiments. With interactions of $p$-electrons between Ce and B$_{6}$ being small, the electronic state of CeB$_{6}$ is suitably described as Ce(4$f^{1}$)$^{3+}$(e$^{-}$)(B$_{6}$)$^{2-}$. The AFQ state of orbital spins is caused by an exchange interaction induced through spin-orbit interaction, which also splits J=5/2 state into $\Gamma_{8}$ ground state and $\Gamma_{7}$ excited state. Within the smallest antiferromagnetic (111) configuration, an orbital-ordered AFQ state appears during charge self-consistency, and supports the appearance of `hidden' order. Hydrostatic pressure (either applied or chemically induced) stabilizes the AFM (AFQ) states over a ferromagnetic one, as observed at low temperatures.Comment: 6 pages, 4 figure

Influence of Ni doping on the electronic structure of Ni_2MnGa

The modifications in the electronic structure of Ni_{2+x}Mn_{1-x}Ga by Ni doping have been studied using full potential linearized augmented plane wave method and ultra-violet photoemission spectroscopy. Ni 3d related electron states appear due to formation of Ni clusters. We show the possibility of changing the minority-spin DOS with Ni doping, while the majority-spin DOS remains almost unchanged. The total magnetic moment decreases with excess Ni. The total energy calculations corroborate the experimentally reported changes in the Curie temperature and the martensitic transition temperature with x.Comment: 4 pages, 4 figures, accepted in Phys. Rev.

Privacy and Truthful Equilibrium Selection for Aggregative Games

We study a very general class of games --- multi-dimensional aggregative games --- which in particular generalize both anonymous games and weighted congestion games. For any such game that is also large, we solve the equilibrium selection problem in a strong sense. In particular, we give an efficient weak mediator: a mechanism which has only the power to listen to reported types and provide non-binding suggested actions, such that (a) it is an asymptotic Nash equilibrium for every player to truthfully report their type to the mediator, and then follow its suggested action; and (b) that when players do so, they end up coordinating on a particular asymptotic pure strategy Nash equilibrium of the induced complete information game. In fact, truthful reporting is an ex-post Nash equilibrium of the mediated game, so our solution applies even in settings of incomplete information, and even when player types are arbitrary or worst-case (i.e. not drawn from a common prior). We achieve this by giving an efficient differentially private algorithm for computing a Nash equilibrium in such games. The rates of convergence to equilibrium in all of our results are inverse polynomial in the number of players $n$. We also apply our main results to a multi-dimensional market game. Our results can be viewed as giving, for a rich class of games, a more robust version of the Revelation Principle, in that we work with weaker informational assumptions (no common prior), yet provide a stronger solution concept (ex-post Nash versus Bayes Nash equilibrium). In comparison to previous work, our main conceptual contribution is showing that weak mediators are a game theoretic object that exist in a wide variety of games -- previously, they were only known to exist in traffic routing games

Characterization of the hot Neptune GJ 436b with Spitzer and ground-based observations

We present Spitzer Space Telescope infrared photometry of a secondary eclipse of the hot Neptune GJ436b. The observations were obtained using the 8-micron band of the InfraRed Array Camera (IRAC). The data spanning the predicted time of secondary eclipse show a clear flux decrement with the expected shape and duration. The observed eclipse depth of 0.58 mmag allows us to estimate a blackbody brightness temperature of T_p = 717 +- 35 K at 8 microns. We compare this infrared flux measurement to a model of the planetary thermal emission, and show that this model reproduces properly the observed flux decrement. The timing of the secondary eclipse confirms the non-zero orbital eccentricity of the planet, while also increasing its precision (e = 0.14 +- 0.01). Additional new spectroscopic and photometric observations allow us to estimate the rotational period of the star and to assess the potential presence of another planet.Comment: Accepted for publication in A&A on 11/09/2007; 7 pages, 6 figure