Rough index theory on spaces of polynomial growth and contractibility

We will show that for a polynomially contractible manifold of bounded geometry and of polynomial volume growth every coarse and rough cohomology class pairs continuously with the K-theory of the uniform Roe algebra. As an application we will discuss non-vanishing of rough index classes of Dirac operators over such manifolds, and we will furthermore get higher-codimensional index obstructions to metrics of positive scalar curvature on closed manifolds with virtually nilpotent fundamental groups. We will give a computation of the homology of (a dense, smooth subalgebra of) the uniform Roe algebra of manifolds of polynomial volume growth.Comment: v4: final version, to appear in J. Noncommut. Geom. v3: added a computation of the homology of (a smooth subalgebra of) the uniform Roe algebra. v2: added as corollaries to the main theorem the multi-partitioned manifold index theorem and the higher-codimensional index obstructions against psc-metrics, added a proof of the strong Novikov conjecture for virtually nilpotent groups, changed the titl

Those wonderful elastic waves

We consider in a simple and general way elastic waves in isotropic and anisotropic media, their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. Reflection of quasi transverse waves in anisotropic media from a free surface is shown to be characterized by three critical angles.Comment: 11 Figures 26 page

Umbral Vade Mecum

In recent years the umbral calculus has emerged from the shadows to provide an elegant correspondence framework that automatically gives systematic solutions of ubiquitous difference equations --- discretized versions of the differential cornerstones appearing in most areas of physics and engineering --- as maps of well-known continuous functions. This correspondence deftly sidesteps the use of more traditional methods to solve these difference equations. The umbral framework is discussed and illustrated here, with special attention given to umbral counterparts of the Airy, Kummer, and Whittaker equations, and to umbral maps of solitons for the Sine-Gordon, Korteweg--de Vries, and Toda systems.Comment: arXiv admin note: text overlap with arXiv:0710.230

POSTER: Privacy-preserving Indoor Localization

Upcoming WiFi-based localization systems for indoor environments face a conflict of privacy interests: Server-side localization violates location privacy of the users, while localization on the user's device forces the localization provider to disclose the details of the system, e.g., sophisticated classification models. We show how Secure Two-Party Computation can be used to reconcile privacy interests in a state-of-the-art localization system. Our approach provides strong privacy guarantees for all involved parties, while achieving room-level localization accuracy at reasonable overheads.Comment: Poster Session of the 7th ACM Conference on Security & Privacy in Wireless and Mobile Networks (WiSec'14

Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta

A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main result it is shown with the example of a quadratically ultraviolet divergent graph in $\phi^4$ theory that nonzero minimal uncertainties in positions do have the power to regularise. These studies are motivated with the ansatz that nonzero minimal uncertainties in positions and in momenta arise from gravity. Algebraic techniques are used that have been developed in the field of quantum groups.Comment: 52 pages LATEX, DAMTP/93-33. Revised version now includes a chapter on the Poincare algebra and curvature as noncommutativity of momentum spac

Formal Verification of an Iterative Low-Power x86 Floating-Point Multiplier with Redundant Feedback

We present the formal verification of a low-power x86 floating-point multiplier. The multiplier operates iteratively and feeds back intermediate results in redundant representation. It supports x87 and SSE instructions in various precisions and can block the issuing of new instructions. The design has been optimized for low-power operation and has not been constrained by the formal verification effort. Additional improvements for the implementation were identified through formal verification. The formal verification of the design also incorporates the implementation of clock-gating and control logic. The core of the verification effort was based on ACL2 theorem proving. Additionally, model checking has been used to verify some properties of the floating-point scheduler that are relevant for the correct operation of the unit.Comment: In Proceedings ACL2 2011, arXiv:1110.447