Oracles and query lower bounds in generalised probabilistic theories

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying three natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle to be well-defined. The three principles are: causality (roughly, no signalling from the future), purification (each mixed state arises as the marginal of a pure state of a larger system), and strong symmetry existence of non-trivial reversible transformations). Sorkin has defined a hierarchy of conceivable interference behaviours, where the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. Given our oracle model, we show that if a classical computer requires at least n queries to solve a learning problem, then the corresponding lower bound in theories lying at the kth level of Sorkin's hierarchy is n/k. Hence, lower bounds on the number of queries to a quantum oracle needed to solve certain problems are not optimal in the space of all generalised probabilistic theories, although it is not yet known whether the optimal bounds are achievable in general. Hence searches for higher-order interference are not only foundationally motivated, but constitute a search for a computational resource beyond that offered by quantum computation.Comment: 17+7 pages. Comments Welcome. Published in special issue "Foundational Aspects of Quantum Information" in Foundations of Physic

CAN ONE REALLY STUDY CHAOS ANALYTICALLY?

One generally thinks that chaos can be studied only numerically by aid of the computer. It is however suggested by the theorem of Sharkovskii and Li and Yorke that in Id continuous maps analytical studies are possible. How one might achieve such a goal in one special map is described

Ruling out higher-order interference from purity principles

As first noted by Rafael Sorkin, there is a limit to quantum interference. The interference pattern formed in a multi-slit experiment is a function of the interference patterns formed between pairs of slits, there are no genuinely new features resulting from considering three slits instead of two. Sorkin has introduced a hierarchy of mathematically conceivable higher-order interference behaviours, where classical theory lies at the first level of this hierarchy and quantum theory theory at the second. Informally, the order in this hierarchy corresponds to the number of slits on which the interference pattern has an irreducible dependence. Many authors have wondered why quantum interference is limited to the second level of this hierarchy. Does the existence of higher-order interference violate some natural physical principle that we believe should be fundamental? In the current work we show that such principles can be found which limit interference behaviour to second-order, or "quantum-like", interference, but that do not restrict us to the entire quantum formalism. We work within the operational framework of generalised probabilistic theories, and prove that any theory satisfying Causality, Purity Preservation, Pure Sharpness, and Purification---four principles that formalise the fundamental character of purity in nature---exhibits at most second-order interference. Hence these theories are, at least conceptually, very "close" to quantum theory. Along the way we show that systems in such theories correspond to Euclidean Jordan algebras. Hence, they are self-dual and, moreover, multi-slit experiments in such theories are described by pure projectors.Comment: 18+8 pages. Comments welcome. v2: Minor correction to Lemma 5.1, main results are unchange

Persistence in the Voter model: continuum reaction-diffusion approach

We investigate the persistence probability in the Voter model for dimensions d\geq 2. This is achieved by mapping the Voter model onto a continuum reaction-diffusion system. Using path integral methods, we compute the persistence probability r(q,t), where q is the number of ``opinions'' in the original Voter model. We find r(q,t)\sim exp[-f_2(q)(ln t)^2] in d=2; r(q,t)\sim exp[-f_d(q)t^{(d-2)/2}] for 2<d<4; r(q,t)\sim exp[-f_4(q)t/ln t] in d=4; and r(q,t)\sim exp[-f_d(q)t] for d>4. The results of our analysis are checked by Monte Carlo simulations.Comment: 10 pages, 3 figures, Latex, submitted to J. Phys. A (letters

CRITICAL RELATIONSHIPS BETWEEN CONSTITUENTS OF THE ANTIGEN-ADJUVANT EMULSION AFFECTING EXPERIMENTAL ALLERGIC ENCEPHALOMYELITIS IN A COMPLETELY SUSCEPTIBLE MOUSE GENOTYPE

The production of EAE in the fully susceptible BSVS mouse genotype has been found to be dependent on the ratio of proteolipid antigen and adjuvant mycobacterial concentration as used in the emulsion, of the Freund type. Disturbance of this ratio, by manipulation of either component, by diminution or increase, results in a decrease in the frequency by which EAE is produced. Simultaneous reduction of antigen and mycobacteria, so that the ratio remains unchanged, retains the full EAE-producing power of the emulsion. The limit of this has not been ascertained. Emulsifying agents have been found to restrict further the permissible limits of the antigen-mycobacterial ratio for full EAE production. Such effects of the emulsifier have been found to vary with the qualitative nature of the emulsifier. Aquaphor has been found to be less restrictive than falba. These phenomena, systematically analyzed here for the mouse, may have an application for other antigen-adjuvant systems and for other hosts

Correlation between microstructure and magnetotransport in organic semiconductor spin valve structures

We have studied magnetotransport in organic-inorganic hybrid multilayer junctions. In these devices, the organic semiconductor (OSC) Alq$_3$ (tris(8-hydroxyquinoline) aluminum) formed a spacer layer between ferromagnetic (FM) Co and Fe layers. The thickness of the Alq$_3$ layer was in the range of 50-150 nm. Positive magnetoresistance (MR) was observed at 4.2 K in a current perpendicular to plane geometry, and these effects persisted up to room temperature. The devices' microstructure was studied by X-ray reflectometry, Auger electron spectroscopy and polarized neutron reflectometry (PNR). The films show well-defined layers with modest average chemical roughness (3-5 nm) at the interface between the Alq$_3$ and the surrounding FM layers. Reflectometry shows that larger MR effects are associated with smaller FM/Alq$_3$ interface width (both chemical and magnetic) and a magnetically dead layer at the Alq$_3$/Fe interface. The PNR data also show that the Co layer, which was deposited on top of the Alq$_3$, adopts a multi-domain magnetic structure at low field and a perfect anti-parallel state is not obtained. The origins of the observed MR are discussed and attributed to spin coherent transport. A lower bound for the spin diffusion length in Alq$_3$ was estimated as $43 \pm 5$ nm at 80 K. However, the subtle correlations between microstructure and magnetotransport indicate the importance of interfacial effects in these systems.Comment: 21 pages, 11 figures and 2 table

The Reaction-Diffusion Front for A+B→∅A+B \to\emptyset in One Dimension

We study theoretically and numerically the steady state diffusion controlled reaction $A+B\rightarrow\emptyset$, where currents $J$ of $A$ and $B$ particles are applied at opposite boundaries. For a reaction rate $\lambda$, and equal diffusion constants $D$, we find that when $\lambda J^{-1/2} D^{-1/2}\ll 1$ the reaction front is well described by mean field theory. However, for $\lambda J^{-1/2} D^{-1/2}\gg 1$, the front acquires a Gaussian profile - a result of noise induced wandering of the reaction front center. We make a theoretical prediction for this profile which is in good agreement with simulation. Finally, we investigate the intrinsic (non-wandering) front width and find results consistent with scaling and field theoretic predictions.Comment: 11 pages, revtex, 4 separate PostScript figure

Localized Coating Removal Using Plastic Media Blasting

USBI, a Division of United Technologies/ is responsible for the assembly, checkout and refurbishment of the structural, guidance and recovery components of the Solid Rocket Booster (SRB) as part of the NASA Space Transportation system/ Space Shuttle. The work is performed at Kennedy Space Center/ Florida and the contract is administered by Marshall Space Flight Center (MSFC) in Huntsville/ Alabama. Figure 1 shows the SRB and associated hardware that USBI is responsible for. Recently/ a considerable effort was made to qualify the use of Plastic Media Blasting (PMB) for safely and effectively removing paint and other coatings from SRB aluminum structures. As a result of the effort an improvement was made in the design of surface finishing equipment for processing flight hardware/ in addition to a potentially patentable idea on improved plastic media composition

A diverse portfolio of novel drug discovery efforts for Alzheimer's disease: Meeting report from the 11th International Conference on Alzheimer's Drug Discovery, 27-28 September 2010, Jersey City, NJ, USA

While Alzheimer's disease researchers continue to debate the underlying cause(s) of the disease, most agree that a diverse, multi-target approach to treatment will be necessary. To this end, the Alzheimer's Drug Discovery Foundation (ADDF) recently hosted the 11th International Conference on Alzheimer's Drug Discovery to highlight the array of exciting efforts from the ADDF's funded investigators