Integrating a Global Induction Mechanism into a Sequent Calculus

Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof theoretic properties of the calculus. To the best of our knowledge, there are no such calculi which allow cut-elimination to a normal form with the subformula property, i.e. every formula occurring in the proof is a subformula of the end sequent. Proof schemata are a variant of LK-proofs able to simulate induction by linking proofs together. There exists a schematic normal form which has comparable proof theoretic behaviour to normal forms with the subformula property. However, a calculus for the construction of proof schemata does not exist. In this paper, we introduce a calculus for proof schemata and prove soundness and completeness with respect to a fragment of the inductive arguments formalizable in Peano arithmetic.Comment: 16 page

Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

The connection between the method of comparison equations (generalized WKB method) and the Ermakov-Pinney equation is established. A perturbative scheme of solution of the generalized Ermakov-Pinney equation is developed and is applied to the construction of perturbative series for second-order differential equations with and without turning points.Comment: The collective of the authors is enlarged and the calculations in Sec. 3 are correcte

Measurement of the Negative Muon Anomalous Magnetic Moment to 0.7 ppm

The anomalous magnetic moment of the negative muon has been measured to a precision of 0.7 parts per million (ppm) at the Brookhaven Alternating Gradient Synchrotron. This result is based on data collected in 2001, and is over an order of magnitude more precise than the previous measurement of the negative muon. The result a_mu= 11 659 214(8)(3) \times 10^{-10} (0.7 ppm), where the first uncertainty is statistical and the second is sytematic, is consistend with previous measurements of the anomaly for the positive and negative muon. The average for the muon anomaly a_{mu}(exp) = 11 659 208(6) \times 10^{-10} (0.5ppm).Comment: 4 pages, 4 figures, submitted to Physical Review Letters, revised to reflect referee comments. Text further revised to reflect additional referee comments and a corrected Fig. 3 replaces the older versio

Surveillance of testicular microlithiasis?: Results of an UK based national questionnaire survey

BACKGROUND: The association of testicular microlithiasis with testicular tumour and the need for follow-up remain largely unclear. METHODS: We conducted a national questionnaire survey involving consultant BAUS members (BAUS is the official national organisation (like the AUA in USA) of the practising urologists in the UK and Ireland), to provide a snapshot of current attitudes towards investigation and surveillance of patients with testicular microlithiasis. RESULTS: Of the 464 questionnaires sent to the BAUS membership, 263(57%) were returned. 251 returns (12 were incomplete) were analysed, of whom 173(69%) do and 78(31%) do not follow-up testicular microlithiasis. Of the 173 who do follow-up, 119(69%) follow-up all patients while 54(31%) follow-up only a selected group of patients. 172 of 173 use ultra sound scan while 27(16%) check tumour makers. 10(6%) arrange ultrasound scan every six months, 151(88%) annually while 10(6%) at longer intervals. 66(38%) intend to follow-up these patients for life while, 80(47%) until 55 years of age and 26(15%) for up to 5 years. 173(68.9%) believe testicular microlithiasis is associated with CIS in < 1%, 53(21%) think it is between 1&10% while 7(3%) believe it is > 10%. 109(43%) believe those patients who develop a tumour, will have survival benefit with follow-up while 142(57%) do not. Interestingly, 66(38%) who follow-up these patients do not think there is a survival benefit. CONCLUSION: There is significant variability in how patients with testicular microlithiasis are followed-up. However a majority of consultant urologists nationally, believe surveillance of this patient group confers no survival benefit. There is a clear need to clarify this issue in order to recommend a coherent surveillance policy

Properties of Graphene: A Theoretical Perspective

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic

BounceBack™ capsules for reduction of DOMS after eccentric exercise: a randomized, double-blind, placebo-controlled, crossover pilot study

<p>Abstract</p> <p>Background</p> <p>Delayed onset muscle soreness (DOMS) is muscle pain and discomfort experienced approximately one to three days after exercise. DOMS is thought to be a result of microscopic muscle fiber tears that occur more commonly after eccentric exercise rather than concentric exercise. This study sought to test the efficacy of a proprietary dietary supplement, BounceBack™, to alleviate the severity of DOMS after standardized eccentric exercise.</p> <p>Methods</p> <p>The study was a randomized, double-blind, placebo-controlled, crossover study. Ten healthy community-dwelling untrained subjects, ranging in age from 18–45 years, were enrolled. Mean differences within and between groups were assessed inferentially at each data collection time-point using t-tests for all outcome measures.</p> <p>Results</p> <p>In this controlled pilot study, intake of BounceBack™ capsules for 30 days resulted in a significant reduction in standardized measures of pain and tenderness post-eccentric exercise compared to the placebo group. There were trends towards reductions in plasma indicators of inflammation (high sensitivity C-reactive protein) and muscle damage (creatine phosphokinase and myoglobin).</p> <p>Conclusion</p> <p>BounceBack™ capsules were able to significantly reduce standardized measures of pain and tenderness at several post-eccentric exercise time points in comparison to placebo. The differences in the serological markers of DOMS, while not statistically significant, appear to support the clinical findings. The product appears to have a good safety profile and further study with a larger sample size is warranted based on the current results.</p

Glutathione Transferase from Trichoderma virens Enhances Cadmium Tolerance without Enhancing Its Accumulation in Transgenic Nicotiana tabacum

BACKGROUND: Cadmium (Cd) is a major heavy metal pollutant which is highly toxic to plants and animals. Vast agricultural areas worldwide are contaminated with Cd. Plants take up Cd and through the food chain it reaches humans and causes toxicity. It is ideal to develop plants tolerant to Cd, without enhanced accumulation in the edible parts for human consumption. Glutathione transferases (GST) are a family of multifunctional enzymes known to have important roles in combating oxidative stresses induced by various heavy metals including Cd. Some GSTs are also known to function as glutathione peroxidases. Overexpression/heterologous expression of GSTs is expected to result in plants tolerant to heavy metals such as Cd. RESULTS: Here, we report cloning of a glutathione transferase gene from Trichoderma virens, a biocontrol fungus and introducing it into Nicotiana tabacum plants by Agrobacterium-mediated gene transfer. Transgenic nature of the plants was confirmed by Southern blot hybridization and expression by reverse transcription PCR. Transgene (TvGST) showed single gene Mendelian inheritance. When transgenic plants expressing TvGST gene were exposed to different concentrations of Cd, they were found to be more tolerant compared to wild type plants, with transgenic plants showing lower levels of lipid peroxidation. Levels of different antioxidant enzymes such as glutathione transferase, superoxide dismutase, ascorbate peroxidase, guiacol peroxidase and catalase showed enhanced levels in transgenic plants expressing TvGST compared to control plants, when exposed to Cd. Cadmium accumulation in the plant biomass in transgenic plants were similar or lower than wild-type plants. CONCLUSION: The results of the present study suggest that transgenic tobacco plants expressing a Trichoderma virens GST are more tolerant to Cd, without enhancing its accumulation in the plant biomass. It should be possible to extend the present results to crop plants for developing Cd tolerance and in limiting Cd availability in the food chain

AI-Driven Assessment of Students: Current Uses and Research Trends

During the last decade, the use of AIs is being incorporated into the educational field whether to support the analysis of human behavior in teachinglearning contexts, as didactic resource combined with other technologies or as a tool for the assessment of the students. This proposal presents a Systematic Literature Review and mapping study on the use of AIs for the assessment of students that aims to provide a general overview of the state of the art and identify the current areas of research by answering 6 research questions related with the evolution of the field, and the geographic and thematic distribution of the studies. As a result of the selection process this study identified 20 papers focused on the research topic in the repositories SCOPUS and Web of Science from an initial amount of 129. The analysis of the papers allowed the identification of three main thematic categories: assessment of student behaviors, assessment of student sentiments and assessment of student achievement as well as several gaps in the literature and future research lines addressed in the discussion