A PCP Characterization of AM

We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP Theorem for NP. Similar characterizations have been given for higher levels of the Polynomial Hierarchy, and for PSPACE; however, we suggest that the result for AM might be of particular significance for attempts to derandomize this class. To test this notion, we pose some `Randomized Optimization Hypotheses' related to our stochastic CSPs that (in light of our result) would imply collapse results for AM. Unfortunately, the hypotheses appear over-strong, and we present evidence against them. In the process we show that, if some language in NP is hard-on-average against circuits of size 2^{Omega(n)}, then there exist hard-on-average optimization problems of a particularly elegant form. All our proofs use a powerful form of PCPs known as Probabilistically Checkable Proofs of Proximity, and demonstrate their versatility. We also use known results on randomness-efficient soundness- and hardness-amplification. In particular, we make essential use of the Impagliazzo-Wigderson generator; our analysis relies on a recent Chernoff-type theorem for expander walks.Comment: 18 page

Ureteroscopic treatment of larger renal calculi (\u3e2 cm).

OBJECTIVES: To evaluate the current status of ureteroscopic lithotripsy (UL) for treating renal calculi of \u3e2 cm, as advances in flexible ureteroscope design, accessory instrumentation and lithotrites have revolutionised the treatment of urinary calculi. While previously reserved for ureteric and small renal calculi, UL has gained an increasing role in the selective management of larger renal stone burdens. METHODS: We searched the available databases, including PubMed, Google Scholar, and Scopus, for relevant reports in English, and the article bibliographies to identify additional relevant articles. Keywords included ureteroscopy, lithotripsy, renal calculi, and calculi \u3e2 cm. Retrieved articles were reviewed to consider the number of patients, mean stone size, success rates, indications and complications. RESULTS: In all, nine studies (417 patients) were eligible for inclusion. After one, two or three procedures the mean (range) success rates were 68.2 (23-84)%, 87.1 (79-91)% and 94.4 (90.1-96.7)%, respectively. Overall, the success rate was \u3e90% with a mean of 1.2-2.3 procedures per patient. The overall complication rate was 10.3%, including six (1.4%) intraoperative and 37 (8.9%) postoperative complications, most of which were minor. The most common indications for UL were a failed previous treatment (46%), comorbidities (18.2%), and technical and anatomical factors (12.3%). CONCLUSIONS: UL is safe and effective for treating large renal calculi. While several procedures might be required for total stone clearance, UL should be considered a standard approach in the urologist\u27s options treating renal calculi of \u3e2 cm

Stress concentrations around voids in three dimensions : The roots of failure

Funding This work forms part of a NERC New Investigator award for DH (NE/I001743/1), which is gratefully acknowledged. Acknowledgments The authors would like to acknowledge the reviewers, Elizabeth Ritz and Phillip Resor. Their reviews were very constructive, both helping to improve the manuscripts consistency and highlighting a number of errors in the initial submission. The authors would also like to thank Lydia Jagger's keen eye and patience, she helped greatly in removing a number of grammatical errors from the initial draft.Peer reviewedPublisher PD

Pore geometry as a control on rock strength

This study was funded via RJW's University of Leicester start-up fund, as part of AAB's PhD project. We thank Don Swanson and Mike Poland at HVO, Hawai'i, for their help and advice during fieldwork planning and sample collection in the Koa'e fault system, and the National Park Service for granting a research permit to collect rock samples. Sergio Vinciguerra is thanked for access to the Rock Mechanics and Physics lab at the British Geological Survey and Audrey Ougier-Simonin is thanked for her help preparing samples and advice during testing. We thank Mike Heap (EOST Strasbourg) and an anonymous reviewer for their detailed and careful comments that greatly improved the manuscript.Peer reviewedPostprin

Aspects of management options for pasture-based dairy production stocked at two cows per hectare

End of project reportWhite clover in association with Rhizobium bacteria have the capacity to fix or convent atmospheric N into plant available N. This can make a considerable contribution to sward productivity. One of the objectives of this experiment was to determine the upper carrying capacity of grass-white clover swards receiving 90 kg fertilizer N/ha. A second objective was to examine the impact of grass-clover swards on mineral-N in the soil and losses of nitrate-N from soil to drainage water during the winter. This experiment was conducted at Solohead Research Farm. There were three treatments: (i) A grass-only treatment (FN) stocked at 2.0 cows per ha in 2003 and 2.2 cows per ha during 2004, 2005 and 2006. This treatment received an average of 226 kg per ha of fertilizer N per year during these years. (ii) A grass-clover treatment (WC) stocked at the same rates as FN and received an average of 90 kg per ha of fertilizer N per year during the experiment. (iii) A grass-only treatment (CC) that was gradually converted over to grass-clover during the experiment and stocked at 2.0 cows per ha throughout the experiment. Fertilizer N input was gradually lowered from 150 kg per ha in 2003 to a target of 90 kg per ha in 2005 and 2006

Squeezing out the last 1 nanometer of water: A detailed nanomechanical study

In this study, we present a detailed analysis of the squeeze-out dynamics of nanoconfined water confined between two hydrophilic surfaces measured by small-amplitude dynamic atomic force microscopy (AFM). Explicitly considering the instantaneous tip-surface separation during squeezeout, we confirm the existence of an adsorbed molecular water layer on mica and at least two hydration layers. We also confirm the previous observation of a sharp transition in the viscoelastic response of the nanoconfined water as the compression rate is increased beyond a critical value (previously determined to be about 0.8 nm/s). We find that below the critical value, the tip passes smoothly through the molecular layers of the film, while above the critical speed, the tip encounters "pinning" at separations where the film is able to temporarily order. Pre-ordering of the film is accompanied by increased force fluctuations, which lead to increased damping preceding a peak in the film stiffness once ordering is completed. We analyze the data using both Kelvin-Voigt and Maxwell viscoelastic models. This provides a complementary picture of the viscoelastic response of the confined water film

Directed polymers in random media under confining force

The scaling behavior of a directed polymer in a two-dimensional (2D) random potential under confining force is investigated. The energy of a polymer with configuration $\{y(x)\}$ is given by H\big(\{y(x)\}\big) = \sum_{x=1}^N \exyx + \epsilon \Wa^\alpha, where $\eta(x,y)$ is an uncorrelated random potential and \Wa is the width of the polymer. Using an energy argument, it is conjectured that the radius of gyration $R_g(N)$ and the energy fluctuation $\Delta E(N)$ of the polymer of length $N$ in the ground state increase as $R_g(N)\sim N^{\nu}$ and $\Delta E(N)\sim N^\omega$ respectively with $\nu = 1/(1+\alpha)$ and $\omega = (1+2\alpha)/(4+4\alpha)$ for $\alpha\ge 1/2$. A novel algorithm of finding the exact ground state, with the effective time complexity of \cO(N^3), is introduced and used to confirm the conjecture numerically.Comment: 9 pages, 7 figure