Cooperation between Top-Down and Bottom-Up Theorem Provers

Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are goal-oriented but often have weak calculi when their proof lengths are considered. In order to integrate both approaches, we try to achieve cooperation between a top-down and a bottom-up prover in two different ways: The first technique aims at supporting a bottom-up with a top-down prover. A top-down prover generates subgoal clauses, they are then processed by a bottom-up prover. The second technique deals with the use of bottom-up generated lemmas in a top-down prover. We apply our concept to the areas of model elimination and superposition. We discuss the ability of our techniques to shorten proofs as well as to reorder the search space in an appropriate manner. Furthermore, in order to identify subgoal clauses and lemmas which are actually relevant for the proof task, we develop methods for a relevancy-based filtering. Experiments with the provers SETHEO and SPASS performed in the problem library TPTP reveal the high potential of our cooperation approaches

Formal rigidity of the Witt and Virasoro Algebra

The formal rigidity of the Witt and Virasoro algebras was first established by the author in [4]. The proof was based on some earlier results of the author and Goncharowa, and was not presented there. In this paper we give an elementary proof of these facts.Comment: 5 page

Large amplitude spin waves in ultra-cold gases

We discuss the theory of spin waves in non-degenerate ultra-cold gases, and compare various methods which can be used to obtain appropriate kinetic equations. We then study non-hydrodynamic situations, where the amplitude of spin waves is sufficiently large to bring the system far from local equilibrium. In the first part of the article, we compare two general methods which can be used to derive a kinetic equation for a dilute gas of atoms (bosons or fermions) with two internal states (treated as a pseudo-spin 1/2). The collisional methods are in the spirit of Boltzmann's original derivation of his kinetic equation where, at each point of space, the effects of all sorts of possible binary collisions are added. We discuss two different versions of collisional methods, the Yvon-Snider approach and the S matrix approach. The second method uses the notion of mean field, which modifies the drift term of the kinetic equation, in the line of the Landau theory of transport in quantum liquids. For a dilute cold gas, it turns out that all these derivations lead to the same drift terms in the transport equation, but differ in the precise expression of the collision integral and in higher order gradient terms. In the second part of the article, the kinetic equation is applied to spin waves in trapped ultra-cold gases. Numerical simulations are used to illustrate the strongly non-hydrodynamic character of the spin waves recently observed with trapped Rb87 atoms. The decay of the phenomenon, which takes place when the system relaxes back towards equilibrium, is also discussed, with a short comment on decoherence.Comment: To appear in Eur. Phys. J.

Castaing's instability in a trapped ultra-cold gas

We consider a trapped ultra-cold gas of (non-condensed) bosons with two internal states (described by a pseudo spin) and study the stability of a longitudinal pseudo spin polarization gradient. For this purpose, we numerically solve a kinetic equation corresponding to a situation close to an experiment at JILA. It shows the presence of Castaing's instability of transverse spin polarization fluctuations at long wavelengths. This phenomenon could be used to create spontaneous transverse spin waves.Comment: 5 pages, 3 figures; equation (8) corrected; submitted to EPJ

Near-field coupling of gold plasmonic antennas for sub-100 nm magneto-thermal microscopy

The development of spintronic technology with increasingly dense, high-speed, and complex devices will be accelerated by accessible microscopy techniques capable of probing magnetic phenomena on picosecond time scales and at deeply sub-micron length scales. A recently developed time-resolved magneto-thermal microscope provides a path towards this goal if it is augmented with a picosecond, nanoscale heat source. We theoretically study adiabatic nanofocusing and near-field heat induction using conical gold plasmonic antennas to generate sub-100 nm thermal gradients for time-resolved magneto-thermal imaging. Finite element calculations of antenna-sample interactions reveal focused electromagnetic loss profiles that are either peaked directly under the antenna or are annular, depending on the sample's conductivity, the antenna's apex radius, and the tip-sample separation. We find that the thermal gradient is confined to 40 nm to 60 nm full width at half maximum for realistic ranges of sample conductivity and apex radius. To mitigate this variation, which is undesirable for microscopy, we investigate the use of a platinum capping layer on top of the sample as a thermal transduction layer to produce heat uniformly across different sample materials. After determining the optimal capping layer thickness, we simulate the evolution of the thermal gradient in the underlying sample layer, and find that the temporal width is below 10 ps. These results lay a theoretical foundation for nanoscale, time-resolved magneto-thermal imaging.Comment: 24 pages including Supporting Information, 6 figures in the main text, 4 supporting figure

On Lagrangian tangent sweeps and Lagrangian outer billiards

Given a Lagrangian submanifold in linear symplectic space, its tangent sweep is the union of its (affine) tangent spaces, and its tangent cluster is the result of parallel translating these spaces so that the foot point of each tangent space becomes the origin. This defines a multivalued map from the tangent sweep to the tangent cluster, and we show that this map is a local symplectomorphism (a well known fact, in dimension two). We define and study the outer billiard correspondence associated with a Lagrangian submanifold. Two points are in this correspondence if they belong to the same tangent space and are symmetric with respect to its foot pointe. We show that this outer billiard correspondence is symplectic and establish the existence of its periodic orbits. This generalizes the well studied outer billiard map in dimension two.Comment: revision as requested by the refere

Internet Surveillance after Snowden: A Critical Empirical Study of Computer Experts' Attitudes on Commercial and State Surveillance of the Internet and Social Media post-Edward Snowden

Acknowledgement: The research presented in this paper was conducted as part of the EU FP7 research project PACT (http://www.projectpact.eu), grant agreement number 285635