The Equivalence Postulate of Quantum Mechanics

The Equivalence Principle (EP), stating that all physical systems are connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories depend on the Planck length through hidden variables which arise as initial conditions. The formulation has manifest p-q duality, a consequence of the involutive nature of the Legendre transform and of its recently observed relation with second-order linear differential equations. This reflects in an intrinsic psi^D-psi duality between linearly independent solutions of the Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even for bound states. No use of any axiomatic interpretation of the wave-function is made. Tunnelling is a direct consequence of the quantum potential which differs from the usual one and plays the role of particle's self-energy. The QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of the extended real line. This is an important feature as the L^2 condition, which in the usual formulation is a consequence of the axiomatic interpretation of the wave-function, directly follows as a basic theorem which only uses the geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP. As a result, the EP itself implies a dynamical equation that does not require any further assumption and reproduces both tunnelling and energy quantization. Several features of the formulation show how the Copenhagen interpretation hides the underlying nature of QM. Finally, the non-stationary higher dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the action of SL(2,R) subgroups acting on the reduced action explicitly reveals that the wave-function describes only equivalence classes of Planck length deterministic physics. New derivation of the Schwarzian derivative from the cocycle condition. "Legendre brackets" introduced to further make "Legendre duality" manifest. Introduction now contains examples and provides a short pedagogical review. Clarifications, conclusions, ackn. and references adde

Symptom screening rules to identify active pulmonary tuberculosis: Findings from the Zambian South African Tuberculosis and HIV/AIDS Reduction (ZAMSTAR) trial prevalence surveys.

BACKGROUND: High tuberculosis (TB) burden countries should consider systematic screening among adults in the general population. We identified symptom screening rules to be used in addition to cough ≥2 weeks, in a context where X-ray screening is not feasible, aiming to increase the sensitivity of screening while achieving a specificity of ≥85%. METHODS: We used 2010 Zambia South Africa Tuberculosis and HIV/AIDS Reduction (ZAMSTAR) survey data: a South African (SA) training dataset, a SA testing dataset for internal validation and a Zambian dataset for external validation. Regression analyses investigated relationships between symptoms or combinations of symptoms and active disease. Sensitivity and specificity were calculated for candidate rules. RESULTS: Among all participants, the sensitivity of using only cough ≥2 weeks as a screening rule was less than 25% in both SA and Zambia. The addition of any three of six TB symptoms (cough <2 weeks, night sweats, weight loss, fever, chest pain, shortness of breath), or 2 or more of cough <2 weeks, night sweats, and weight loss, increased the sensitivity to ~38%, while reducing specificity from ~95% to ~85% in SA and ~97% to ~92% in Zambia. Among HIV-negative adults, findings were similar in SA, whereas in Zambia the increase in sensitivity was relatively small (15% to 22%). CONCLUSION: High TB burden countries should investigate cost-effective strategies for systematic screening: one such strategy could be to use our rule in addition to cough ≥2 weeks

Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof

In recent work, we formalized the theory of optimal-size sorting networks with the goal of extracting a verified checker for the large-scale computer-generated proof that 25 comparisons are optimal when sorting 9 inputs, which required more than a decade of CPU time and produced 27 GB of proof witnesses. The checker uses an untrusted oracle based on these witnesses and is able to verify the smaller case of 8 inputs within a couple of days, but it did not scale to the full proof for 9 inputs. In this paper, we describe several non-trivial optimizations of the algorithm in the checker, obtained by appropriately changing the formalization and capitalizing on the symbiosis with an adequate implementation of the oracle. We provide experimental evidence of orders of magnitude improvements to both runtime and memory footprint for 8 inputs, and actually manage to check the full proof for 9 inputs.Comment: IMADA-preprint-c

Topographic zonation and polycyclic pedogenesis in the northern atolls of the Chagos Archipelago, Indian Ocean

We conducted soil surveys on two islands in the Peros Banhos and Salomon atolls of the northern Chagos Archipelago, Indian Ocean. We found muted but consistent topographic and soil zonation from the ocean shores to the lagoons. The main elements of the zonation are: berms of coral boulders and rubble along the heads of the ocean-side beaches; rubble-strewn soils inland of the berm; and pale sands with shallower topsoils and few coral clasts on slight rises and declivities over the rest of the islands. The ocean-side rubbly soils have interstitial coarse sand and are the most fertile on the islands, with dense tangled stands of unmanaged coconuts, profuse litter, and deep humic topsoils. Topsoils are shallower and less humic in the pale sands inland. Sand size decreases from ocean to lagoon, but increases with depth in most profiles. Water tables are often <2 m deep, and many soils have faint pale brownish mottling in the lower subsoils. There is a low tabular outcrop of bare Holocene coral sandstone on one of the islands. It is incised by shallow grikes that are partly infilled with silty muck, as are some small depressions in the central parts of both islands. The pedogenic environment appears to be dynamic, with storm surges depositing fresh sand, eroding coastlines, and infilling inter-island channels. Some soils have buried humic topsoils, stone layers, sand size inversions, and slight changes in sand colour, which are attributed to polycyclic pedogenesis. Some topsoils have elevated levels of total Zn, which is thought to be derived from long distance volcanic ash. Our data indicate that the soils are of low nutrient fertility. Total N and available P do not attain the strikingly eutric levels found in some atoll soils. The low fertility is attributed to the predation of seabirds by inadvertently introduced black rats. This precludes soil enrichment with marine-derived nutrients by guano deposition

Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

Groundnut in intercropping systems

In the developing world, groundnuts are commonly grown in intercropping systems, especially by small farmers who use traditionalcombinations often involving up to 5-6 crops. Detailed statistics of farming practice are difficult to obtain, but it has been estimated that 95% of the groundnuts in Nigeria and 56% in Uganda are grown as mixtures with other crops (Okigbo and Greenland 1976). In the Northern Guinea Savanna Zone of Nigeria, Kassam (1976) reported that only about 16% of the total area under groundnut was in sole croppingwhile about 70% was in 2-4 crop mixtures

HST NIR Snapshot Survey of 3CR Radio Source Counterparts II: An Atlas and Inventory of the Host Galaxies, Mergers and Companions

We present the second part of an H-band (1.6 microns) atlas of z<0.3 3CR radio galaxies, using the Hubble Space Telescope Near Infrared Camera and Multi-Object Spectrometer (HST NICMOS2). We present new imaging for 21 recently acquired sources, and host galaxy modeling for the full sample of 101 (including 11 archival) -- an 87% completion rate. Two different modeling techniques are applied, following those adopted by the galaxy morphology and the quasar host galaxy communities. Results are compared, and found to be in excellent agreement, although the former breaks down in the case of strongly nucleated sources. Companion sources are tabulated, and the presence of mergers, tidal features, dust disks and jets are catalogued. The tables form a catalogue for those interested in the structural and morphological dust-free host galaxy properties of the 3CR sample, and for comparison with morphological studies of quiescent galaxies and quasar host galaxies. Host galaxy masses are estimated, and found to typically lie at around 2*10^11 solar masses. In general, the population is found to be consistent with the local population of quiescent elliptical galaxies, but with a longer tail to low Sersic index, mainly consisting of low-redshift (z<0.1) and low-radio-power (FR I) sources. A few unusually disky FR II host galaxies are picked out for further discussion. Nearby external sources are identified in the majority of our images, many of which we argue are likely to be companion galaxies or merger remnants. The reduced NICMOS data are now publicly available from our website (http://archive.stsci.edu/prepds/3cr/)Comment: ApJS, 177, 148: Final version; includes revised figures 1, 15b, and section 7.5 (and other minor changes from editing process. 65 pages, inc. 17 figure

Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime

In spacetimes admitting Yano tensors the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank two, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors.Comment: 1+32 pages, no figures. Accepted for publication on Classical and Quantum Gravity. New title and abstract. Some material has been moved to the Appendix. Concrete formulas for Yano tensors on some special holonomy manifolds have been provided. Some corrections included, bibliography enlarge