Automated Synthesis of Tableau Calculi

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.Comment: 32 page

Arithmetically Cohen-Macaulay Bundles on complete intersection varieties of sufficiently high multidegree

Recently it has been proved that any arithmetically Cohen-Macaulay (ACM) bundle of rank two on a general, smooth hypersurface of degree at least three and dimension at least four is a sum of line bundles. When the dimension of the hypersurface is three, a similar result is true provided the degree of the hypersurface is at least six. We extend these results to complete intersection subvarieties by proving that any ACM bundle of rank two on a general, smooth complete intersection subvariety of sufficiently high multi-degree and dimension at least four splits. We also obtain partial results in the case of threefolds.Comment: 15 page

Neurology

Contains reports on six research projects.United States Public Health Service (B-3055-4, B-3090-4, MH-06175-02)United States Navy, Office of Naval Research (Contract Nonr-1841(70))United States Air Force (AF49(638)-1313), administered by the Electronic Systems Laboratory, M. I. T

Neurology

Contains research objectives and reports on six research projects.National Science Foundation (Grant G-16526)National Institutes of Health (Grant MH-04737-03)U.S. Public Health Service (B-3055-3)U.S. Public Health Service (B-3090-3)U.S. Public Health Service (MH-06175-01A1)Office of Naval Research (Nonr-1841(70))Air Force (AFOSR 155-63)Army Chemical Corps (DA- 18-108-405-CML-942

A mechanistic model of tau amyloid aggregation based on direct observation of oligomers.

Protein aggregation plays a key role in neurodegenerative disease, giving rise to small oligomers that may become cytotoxic to cells. The fundamental microscopic reactions taking place during aggregation, and their rate constants, have been difficult to determine due to lack of suitable methods to identify and follow the low concentration of oligomers over time. Here we use single-molecule fluorescence to study the aggregation of the repeat domain of tau (K18), and two mutant forms linked with familial frontotemporal dementia, the deletion mutant ΔK280 and the point mutant P301L. Our kinetic analysis reveals that aggregation proceeds via monomeric assembly into small oligomers, and a subsequent slow structural conversion step before fibril formation. Using this approach, we have been able to quantitatively determine how these mutations alter the aggregation energy landscape.D.K. acknowledges funding from the Wellcome Trust (WT089703) and MRC. E.M. acknowledges funding from the Wellcome Trust (WT089703), DZNE and Max-Planck-Society. M.K. acknowledges fellowships from the Danish research council and the Lundbeck Foundation. N.S. and M.H.H acknowledge funding from the Augustus Newman foundation. G.A.G is funded by the Schiff Foundation. T.P.J.K acknowledges funding from the ERC, Augustus Newman Foundation and the BBSRC.This is the final version of the article. It first appeared from NPG via http://dx.doi.org/10.1038/ncomms802

Response of soil health indicators to dung, urine and mineral fertilizer application in temperate pastures

Healthy soils are key to sustainability and food security. In temperate grasslands, not many studies have focused on soil health comparisons between contrasting pasture systems under different management strategies and treatment applications (e.g. manures and inorganic fertilisers). The aim of this study was to assess the responses of soil health indicators to dung, urine and inorganic N fertiliser in three temperate swards: permanent pasture not ploughed for at least 20 years (PP), high sugar ryegrass with white clover targeted at 30% coverage reseeded in 2013 (WC), and high sugar ryegrass reseeded in 2014 (HG). This study was conducted on the North Wyke Farm Platform (UK) from April 2017 to October 2017. Soil health indicators including soil organic carbon (SOC, measured by loss of ignition and elemental analyser), dissolved organic carbon (DOC), total nitrogen (TN), C:N ratio, soil C and N bulk isotopes, pH, bulk density (BD), aggregate stability, ergosterol concentration (as a proxy for fungi biomass), and earthworms (abundance, mass and density) were measured and analysed before and after application of dung and N fertilizer, urine and N fertiliser, and only N fertiliser. The highest SOC, TN, DOC, ergosterol concentration and earthworms as well as the lowest BD were found in PP, likely due to the lack of ploughing. Differences among treatments were observed due to the application of dung, resulting in an improvement in chemical indicators of soil health after 50 days of its application. Ergosterol concentration was significantly higher before treatment applications than at the end of the experiment. No changes were detected in BD and aggregate stability after treatment applications. We conclude that not enough time had passed for the soil to recover after the ploughing and reseeding of the permanent pasture, independently of the sward composition (HG or WC). Our results highlight the strong influence of the soil management legacy in temperate pasture and the positive effects of dung application on soil health over the short term. In addition, we point out the relevance of using standardised methods to report soil health indicators and some methodological limitations

Stability of homogeneous bundles on P^3

We study the stability of some homogeneous bundles on P^3 by using their representations of the quiver associated to the homgeneous bundles on P^3. In particular we show that homogeneous bundles on P^3 whose support of the quiver representation is a parallelepiped are stable, for instance the bundles E whose minimal free resolution is of the kind 0 --> S^{l_1, l_2, l_3} V (t) --> S^{l_1 +s, l_2, l_3} V (t+s) --> E --> 0 are stable.Comment: to appear in Geometriae Dedicata http://www.springer.com/mathematics/geometry/journal/1071