An Intuitionistic Formula Hierarchy Based on High-School Identities

We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal) propositional sequent calculi are formula (i.e. sequent) isomorphisms corresponding to the high-school identities, we show that one can obtain a more compact variant of a proof system, consisting of non-invertible proof rules only, and where the invertible proof rules have been replaced by a formula normalisation procedure. Moreover, for certain proof systems such as the G4ip sequent calculus of Vorob'ev, Hudelmaier, and Dyckhoff, it is even possible to see all of the non-invertible proof rules as strict inequalities between exponential polynomials; a careful combinatorial treatment is given in order to establish this fact. Finally, we extend the exponential polynomial analogy to the first-order quantifiers, showing that it gives rise to an intuitionistic hierarchy of formulas, resembling the classical arithmetical hierarchy, and the first one that classifies formulas while preserving isomorphism

Getting the best from pot trials with soil-borne Oomycetes

Soil-borne Oomycetes are important pathogens of nursery plants, agricultural and horticultural crops, and woody plants in natural ecosystems. They are most damaging when plants are overwatered or growing in poorly drained sites. Poor growth could result from root infection, root damage resulting from the anoxic conditions which develop in saturated soil, or both. This is essential information for devising appropriate management options, as these will differ depending on the primary cause of poor health. Pot experiments are often used to determine whether these soil-borne pathogens cause root infection which is assumed to be by zoospores produced in wet soil. Soil saturation followed by draining, is included as part of the experimental protocol to generate zoospores from the inoculum and facilitate their movement to, and infection of, plant roots. However, if soil saturation persists until the soil becomes anoxic, this may affect the host. In our opinion, this can muddle the interpretation of results, unless there are adequate controls which include root infection in unsaturated soil, and the effect of soil saturation on the host in the absence of the pathogen. Pot experiments are expensive in both time and equipment. They must be conducted to provide clear answers to the postulated hypotheses and ensure experiments are repeatable. We provide guidelines for conducting such pot experiments which will assist in clarifying the roles of these pathogens and soil saturation on plant growth, both separately and in combination

Rushforth's Latin Historical Inscriptions Latin Historical Inscriptions, by G. Mc N. Rushforth, M.A. Clarendon Press. 10s.

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Pomeron loops in zero transverse dimensions

We analyze a toy model which has a structure similar to that of the recently found QCD evolution equations, but without transverse dimensions. We develop two different but equivalent methods in order to compute the leading-order and next-to-leading order Pomeron loop diagrams. In addition to the leading-order result which has been derived from Mueller's toy model~\cite% {Mueller:1994gb}, we can also calculate the next-to-leading order contribution which provides the $(\alpha_{s}^{2}\alpha Y)$ correction. We interpret this result and discuss its possible implications for the four-dimensional QCD evolution.Comment: 11 pages, 4 figure

Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection

We consider the problem of distinguishing, with minimum probability of error, two optical beam-splitter channels with unequal complex-valued reflectivities using general quantum probe states entangled over M signal and M' idler mode pairs of which the signal modes are bounced off the beam splitter while the idler modes are retained losslessly. We obtain a lower bound on the output state fidelity valid for any pure input state. We define number-diagonal signal (NDS) states to be input states whose density operator in the signal modes is diagonal in the multimode number basis. For such input states, we derive series formulas for the optimal error probability, the output state fidelity, and the Chernoff-type upper bounds on the error probability. For the special cases of quantum reading of a classical digital memory and target detection (for which the reflectivities are real valued), we show that for a given input signal photon probability distribution, the fidelity is minimized by the NDS states with that distribution and that for a given average total signal energy N_s, the fidelity is minimized by any multimode Fock state with N_s total signal photons. For reading of an ideal memory, it is shown that Fock state inputs minimize the Chernoff bound. For target detection under high-loss conditions, a no-go result showing the lack of appreciable quantum advantage over coherent state transmitters is derived. A comparison of the error probability performance for quantum reading of number state and two-mode squeezed vacuum state (or EPR state) transmitters relative to coherent state transmitters is presented for various values of the reflectances. While the nonclassical states in general perform better than the coherent state, the quantitative performance gains differ depending on the values of the reflectances.Comment: 12 pages, 7 figures. This closely approximates the published version. The major change from v2 is that Section IV has been re-organized, with a no-go result for target detection under high loss conditions highlighted. The last sentence of the abstract has been deleted to conform to the arXiv word limit. Please see the PDF for the full abstrac

Simulation evaluation of a low-altitude helicopter flight guidance system adapted for a helmet-mounted display

A computer aiding concept for low-altitude helicopter flight was developed and evaluated in a real-time piloted simulation. The concept included an optimal control trajectory-generation algorithm based upon dynamic programming and a helmet-mounted display (HMD) presentation of a pathway-in-the-sky, a phantom aircraft, and flight-path vector/predictor guidance symbology. The trajectory-generation algorithm uses knowledge of the global mission requirements, a digital terrain map, aircraft performance capabilities, and advanced navigation information to determine a trajectory between mission way points that seeks valleys to minimize threat exposure. The pilot evaluation was conducted at NASA ARC moving base Vertical Motion Simulator (VMS) by pilots representing NASA, the U.S. Army, the Air Force, and the helicopter industry. The pilots manually tracked the trajectory generated by the algorithm utilizing the HMD symbology. The pilots were able to satisfactorily perform the tracking tasks while maintaining a high degree of awareness of the outside world

Patterns in Student Financial Aid at Rural Community Colleges

This article uses the 2005 Basic Classifications of the Carnegie Foundation for the Advancement of Teaching as a framing device through which to examine patterns of student financial aid at America\u27s rural community colleges, which represent 64% of all U.S. community colleges. Rural community colleges serve more first-time, full-time students than suburban and urban community colleges, and their 3.2 million students have different patterns of student financial aid. Rural small and medium colleges have the most aided students, receive more Pell Grants and institutional aid, and have more students incurring loan indebtedness than do other types of community colleges. The article offers recommendations for future research, as well as for policy development and practice

Enhancement and evaluation of Skylab photography for potential land use inventories, part 1

The author has identified the following significant results. Three sites were evaluated for land use inventory: Finger Lakes - Tompkins County, Lower Hudson Valley - Newburgh, and Suffolk County - Long Island. Special photo enhancement processes were developed to standardize the density range and contrast among S190A negatives. Enhanced black and white enlargements were converted to color by contact printing onto diazo film. A color prediction model related the density values on each spectral band for each category of land use to the spectral properties of the various diazo dyes. The S190A multispectral system proved to be almost as effective as the S190B high resolution camera for inventorying land use. Aggregate error for Level 1 averaged about 12% while Level 2 aggregate error averaged about 25%. The S190A system proved to be much superior to LANDSAT in inventorying land use, primarily because of increased resolution