Local Testing for Membership in Lattices

Motivated by the structural analogies between point lattices and linear error-correcting codes, and by the mature theory on locally testable codes, we initiate a systematic study of local testing for membership in lattices. Testing membership in lattices is also motivated in practice, by applications to integer programming, error detection in lattice-based communication, and cryptography. Apart from establishing the conceptual foundations of lattice testing, our results include the following: 1. We demonstrate upper and lower bounds on the query complexity of local testing for the well-known family of code formula lattices. Furthermore, we instantiate our results with code formula lattices constructed from Reed-Muller codes, and obtain nearly-tight bounds. 2. We show that in order to achieve low query complexity, it is sufficient to design one-sided non-adaptive canonical tests. This result is akin to, and based on an analogous result for error-correcting codes due to Ben-Sasson et al. (SIAM J. Computing 35(1) pp1-21)

Rectification of Confined Soft Vesicles Containing Active Particles

One of the most promising features of active systems is that they can extract energy from their environment and convert it to mechanical work. Self propelled particles enable rectification when in contact with rigid boundaries. They can rectify their own motion when confined in asymmetric channels and that of microgears. In this paper, we study the shape fluctuations of two dimensional flexible vesicles containing active Brownian particles. We show how these fluctuations not only are capable of easily squeezing a vesicle through narrow openings, but are also responsible for its rectification when placed within asymmetric confining channels (ratchetaxis). We detail the conditions under which this process can be optimized, and sort out the complex interplay between elastic and active forces responsible for the directed motion of the vesicle across these channels.Comment: 8 pages, 8 figure

MgB2 tunnel junctions with native or thermal oxide barriers

MgB2 tunnel junctions (MgB2/barrier/MgB2) were fabricated using a native oxide grown on the bottom MgB2 film as the tunnel barrier. Such barriers therefore survive the deposition of the second electrode at 300oC, even over junction areas of ~1 mm2. Studies of such junctions, and those of the type MgB2/native or thermal oxide/metal (Pb, Au, or Ag) show that tunnel barriers grown on MgB2 exhibit a wide range of barrier heights and widths.Comment: 9 pages, 3 figure

Effect of stoichiometry on oxygen incorporation in MgB2 thin films

The amount of oxygen incorporated into MgB2 thin films upon exposure to atmospheric gasses is found to depend strongly on the material's stoichiometry. Rutherford backscattering spectroscopy was used to monitor changes in oxygen incorporation resulting from exposure to: (a) ambient atmosphere, (b) humid atmospheres, (c) anneals in air and (d) anneals in oxygen. The study investigated thin-film samples with compositions that were systematically varied from Mg0.9B2 to Mg1.1B2. A significant surface oxygen contamination was observed in all of these films. The oxygen content in the bulk of the film, on the other hand, increased significantly only in Mg rich films and in films exposed to humid atmospheres.Comment: 10 pages, 6 figures, 1 tabl

The crumpling transition of active tethered membranes

We perform numerical simulations of active ideal and self-avoiding tethered membranes. Passive ideal membranes with bending interactions are known to exhibit a continuous crumpling transition between a low temperature flat phase and a high temperature crumpled phase. Conversely, self-avoiding membranes remain in an extended (flat) phase for all temperatures even in the absence of a bending energy. We find that the introduction of active fluctuations into the system produces a phase behavior that is overall consistent with that observed for passive membranes. The phases and the nature of the transition for ideal membranes is unchanged and active fluctuations can be remarkably accounted for by a simple rescaling of the temperature. For the self-avoiding membrane, we find that the extended phase is preserved even in the presence of very large active fluctuations.Comment: 9 pages, 7 figure

Rigidity transitions in zero-temperature polygons

We study geometrical clues of a rigidity transition due to the emergence of a system-spanning state of self stress in under-constrained systems of individual polygons and spring networks constructed from such polygons. When a polygon with harmonic bond edges and an area spring constraint is subject to an expansive strain, we observe that convexity of the polygon is a necessary condition for such a self stress. We prove that the cyclic configuration of the polygon is a sufficient condition for the self stress. This correspondence of geometry and rigidity is akin to the straightening of a one dimensional chain of springs to rigidify it. We predict the onset of the rigidity transition using a purely geometrical method. We also estimate the transition strain for a given initial configuration by approximating irregular polygons as regular polygons. These findings help determine the rigidity of an area-preserving polygon just by looking at it. Since two-dimensional spring networks can be considered as a network of polygons, we look for similar geometric features in under-constrained spring networks under isotropic expansive strain. In particular, we observe that all polygons attain convexity at the rigidity transition such that the fraction of convex, but not cyclic, polygons predicts the onset of the rigidity transition. Interestingly, acyclic polygons in the network correlate with larger tensions, thus, forming effective force chains.Comment: 12 pages, 10 figure

Spontaneous crumpling of active spherical shells

The existence of a crumpled phase for self-avoiding elastic surfaces was postulated more than three decades ago using simple Flory-like scaling arguments. Despite much effort, its stability in a microscopic environment has been the subject of much debate. In this Letter we show how a crumpled phase develops reliably and consistently upon subjecting a thin spherical shell to active fluctuations. We find a master curve describing how the relative volume of a shell changes with the strength of the active forces, that applies for every shell independent of size and elastic constants. Furthermore, we extract a general expression for the onset active force beyond which a shell begins to crumple. Finally, we calculate how the size exponent varies along the crumpling curve.Comment: 6 pages and 6 figures including the appendi

Protecting big data mining association rules using fuzzy system

Recently, big data is granted to be the solution to opening the subsequent large fluctuations of increase in fertility. Along with the growth, it is facing some of the challenges. One of the significant problems is data security. While people use data mining methods to identify valuable information following massive database, people further hold the necessary to maintain any knowledge so while not to be worked out, like delicate common itemsets, practices, taxonomy tree and the like Association rule mining can make a possible warning approaching the secrecy of information. So, association rule hiding methods are applied to evade the hazard of delicate information misuse. Various kinds of investigation already prepared on association rule protecting. However, maximum of them concentrate on introducing methods with a limited view outcome for inactive databases (with only existing information), while presently the researchers facing the problem with continuous information. Moreover, in the era of big data, this is essential to optimize current systems to be suited concerning the big data. This paper proposes the framework is achieving the data anonymization by using fuzzy logic by supporting big data mining. The fuzzy logic grouping the sensitivity of the association rules with a suitable association level. Moreover, parallelization methods which are inserted in the present framework will support fast data mining process