On the Topological Origin of Entanglement in Ising Spin Glasses

The origin of thermal and quantum entanglement in a class of three-dimensional spin models, at low momenta, is traced to purely topological reasons. The establishment of the result is facilitated by the gauge principle which, when used in conjunction with the duality mapping of the spin models, enables us to recast them as lattice Chern-Simons gauge theories. The thermal and quantum entanglement measures are expressed in terms of the expectation values of Wilson lines, loops, and their generalisations. For continuous spins, these are known to yield the topological invariants of knots and links. For Ising-like models, they are expressible in terms of the topological invariants of three-manifolds obtained from finite group cohomology -- the so-called Dijkgraaf-Witten invariants.Comment: RevTex4, 6 page

Monitoring-Oriented Programming: A Tool-Supported Methodology for Higher Quality Object-Oriented Software

This paper presents a tool-supported methodological paradigm for object-oriented software development, called monitoring-oriented programming and abbreviated MOP, in which runtime monitoring is a basic software design principle. The general idea underlying MOP is that software developers insert specifications in their code via annotations. Actual monitoring code is automatically synthesized from these annotations before compilation and integrated at appropriate places in the program, according to user-defined configuration attributes. This way, the specification is checked at runtime against the implementation. Moreover, violations and/or validations of specifications can trigger user-defined code at any points in the program, in particular recovery code, outputting or sending messages, or raising exceptions. The MOP paradigm does not promote or enforce any specific formalism to specify requirements: it allows the users to plug-in their favorite or domain-specific specification formalisms via logic plug-in modules. There are two major technical challenges that MOP supporting tools unavoidably face: monitor synthesis and monitor integration. The former is heavily dependent on the specification formalism and comes as part of the corresponding logic plug-in, while the latter is uniform for all specification formalisms and depends only on the target programming language. An experimental prototype tool, called Java-MOP, is also discussed, which currently supports most but not all of the desired MOP features. MOP aims at reducing the gap between formal specification and implementation, by integrating the two and allowing them together to form a system

Paley-Wiener theorems for the Dunkl transform

We conjecture a geometrical form of the Paley-Wiener theorem for the Dunkl transform and prove three instances thereof, one of which involves a limit transition from Opdam's results for the graded Hecke algebra. Furthermore, the connection between Dunkl operators and the Cartan motion group is established. It is shown how the algebra of radial parts of invariant differential operators can be described explicitly in terms of Dunkl operators, which implies that the generalized Bessel functions coincide with the spherical functions. In this context, the restriction of Dunkl's intertwining operator to the invariants can be interpreted in terms of the Abel transform. Using shift operators we also show that, for certain values of the multiplicities of the restricted roots, the Abel transform is essentially inverted by a differential operator.Comment: LaTeX, 26 pages, no figures. References updated and minor changes, mathematically identical to the first version. To appear in Trans. Amer. Math. So

A Quaternionic Wavelet Transform-based Approach for Object Recognition

Recognizing the objects in complex natural scenes is the challenging task as the object may be occluded, may vary in shape, position and in size. In this paper a method to recognize objects from different categories of images using quaternionic wavelet transform (QWT) is presented. This transform separates the information contained in the image better than a traditional Discrete wavelet transform and provides a multiscale image analysis whose coefficients are 2D analytic, with one near-shift invariant magnitude and three phases. The two phases encode local image shifts and the third one contains texture information. In the domain of object recognition, it is often to classify objects from images that make only limited part of the image. Hence to identify local features and certain region of images, patches are extracted over the interest points detected from the original image using Wavelet based interest point detector. Here QWT magnitude and phase features are computed for every patch. Then these features are trained, tested and classified using SVM classifier in order to have supervised learning model. In order to compare the performance of local feature with global feature, the transform is applied to the entire image and the global features are derived. The performance of QWT is compared with discrete wavelet transform (DWT) and dual tree discrete wavelet transform (DTDWT). Observations revealed that QWT outperforms the DWT and shift invariant DTDWT with lesser equal error rate. The experimental evaluation is done using the complex Graz databases.Defence Science Journal, Vol. 64, No. 4, July 2014, pp. 350-357, DOI:http://dx.doi.org/10.14429/dsj.64.450

Rashba Torque Driven Domain Wall Motion in Magnetic Helices

Manipulation of the domain wall propagation in magnetic wires is a key practical task for a number of devices including racetrack memory and magnetic logic. Recently, curvilinear effects emerged as an efficient mean to impact substantially the statics and dynamics of magnetic textures. Here, we demonstrate that the curvilinear form of the exchange interaction of a magnetic helix results in an effective anisotropy term and Dzyaloshinskii--Moriya interaction with a complete set of Lifshitz invariants for a one-dimensional system. In contrast to their planar counterparts, the geometrically induced modifications of the static magnetic texture of the domain walls in magnetic helices offer unconventional means to control the wall dynamics relying on spin-orbit Rashba torque. The chiral symmetry breaking due to the Dzyaloshinskii-Moriya interaction leads to the opposite directions of the domain wall motion in left- or right-handed helices. Furthermore, for the magnetic helices, the emergent effective anisotropy term and Dzyaloshinskii-Moriya interaction can be attributed to the clear geometrical parameters like curvature and torsion offering intuitive understanding of the complex curvilinear effects in magnetism

3d Modularity

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures include: mock modular forms, $SL(2,\mathbb{Z})$ Weil representations, quantum modular forms, non-semisimple modular tensor categories, and chiral algebras of logarithmic CFTs.Comment: 119 pages, 10 figures and 20 table