Local mirror symmetry and the sunset Feynman integral

We study the sunset Feynman integral defined as the scalar two-point self-energy at two-loop order in a two dimensional space-time. We firstly compute the Feynman integral, for arbitrary internal masses, in terms of the regulator of a class in the motivic cohomology of a 1-parameter family of open elliptic curves. Using an Hodge theoretic (B-model) approach, we show that the integral is given by a sum of elliptic dilogarithms evaluated at the divisors determined by the punctures. Secondly we associate to the sunset elliptic curve a local non-compact Calabi-Yau 3-fold, obtained as a limit of elliptically fibered compact Calabi-Yau 3-folds. By considering the limiting mixed Hodge structure of the Batyrev dual A-model, we arrive at an expression for the sunset Feynman integral in terms of the local Gromov-Witten prepotential of the del Pezzo surface of degree 6. This expression is obtained by proving a strong form of local mirror symmetry which identifies this prepotential with the second regulator period of the motivic cohomology class.Comment: 67 pages. v2: minor typos corrected and now per-section numbering of theorems, lemmas, propositions and remarks. v3: minor typos corrected. Version to appear in Advances in Theoretical and Mathematical Physic

Has the incidence of empyema in Scottish children continued to increase beyond 2005?

Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.Peer reviewedPostprin

A Feynman integral via higher normal functions

We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard-Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of K3 surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the K3 family. We prove a conjecture by David Broadhurst that at a special kinematical point the Feynman integral is given by a critical value of the Hasse-Weil L-function of the K3 surface. This result is shown to be a particular case of Deligne's conjectures relating values of L-functions inside the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications. Version to appear in Compositio Mathematic

Cosmic Sound in the Lyman Alpha Forest

Using the Baryon Oscillation Spectroscopic Survey (BOSS) from the Sloan Digital Sky Survey (SDSS), the authors attempt to detect the baryonic acoustic oscillations (BAOs) using the discrete wavelet transform. The wavelet transform is used to construct the power spectrum of intergalactic clouds of matter at large (Mpc) distance scales. It was found that the wavelet transform used here does not have high enough resolution to detect the BAOs. However, the techniques used in this study allow for future improvements in the transform that could potentially resolve the expected peak in the power spectrum and indicate the existence of BAOs

Trouble with Images in Computational Physics

Over 18 months of ethnographic fieldwork with a group of computational physicists, I encountered many negative assessments of the part that images should play in the accomplishment of good research. In this essay I explore the question of where these anxieties might come from and what they mean. Using Bachelard’s philosophy, I first point to the role that the image plays in conditioning the imagination and in training intuitive judgement. But to get to the bottom of the trouble with images we are led through Rheinberger and Stiegler to a view of scientific cognition that extends beyond the mind to prosthetic circuits of artefacts, including both images and written inscriptions. Rather than locating the problem as one of the relation between the image and what it represents, I argue for the importance of general cultural difficulties in managing and manipulating artefactual assemblages

Additional Sulfur Does Not Alleviate Cadmium Toxicity In Soybean

Cadmium (Cd) is non-essential and toxic. Sulfur (S) addition to contaminated soils reduces Cd toxicity in rice and corn. I aimed to determine the underlying mechanisms by which S reduces Cd toxicity in hydroponically- and soil-grown soybean. In the presence of Cd, plant biomass was reduced by ~20%, Cd accumulated up to 45 μg/g in roots and 15 μg/g shoots, and concentrations of Cd chelators increased by more than 10-fold. Addition of S to Cd- treated plants had no effect on plant biomass, concentrations of Cd in roots and shoots, or vacuolar Cd sequestration in the root cortex. While additional S visibly altered Cd localization in the roots, it had no effect on altering Cd concentration in root plaque. Additional S in the presence of Cd resulted in a 0- to 1.5-fold increase in Cd chelator concentrations; however, addition of S to alleviate Cd toxicity has no benefit in soybean

Reason and Representation in Scientific Simulation

This thesis is a study of scientific practice in computational physics. It is based on an 18 month period of ethnographic research at the Imperial College Applied Modelling and Computation Group. Using a theoretical framework drawn from practice theory, science studies, and historical epistemology, I study how simulations are developed and used in science. Emphasising modelling as a process, I explore how software provides a distinctive kind of material for doing science on computers and how images and writings of various kinds are folded into the research process. Through concrete examples the thesis charts how projects are devised and evolve and how they draw together materials and technologies into semi-stable configurations that crystallise around the objects of their concern, what Hans-Jorg Rheinberger dubbed “epistemic things”. The main pivot of the research, however, is the connection of practice-theoretical science studies with the philosophy of Gaston Bachelard, whose concept of “phenomenotechnique” facilitates a rationalist reading of scientific practice. Rather than treating reason as a singular logic or method, or as a faculty of the mind, Bachelard points us towards processes of change within actual scientific research, a dynamic reason immanent to processes of skilled engagement. Combining this study of reason with the more recent attention to things within research from materialist and semiotic traditions, I also revive a new sense for the term “representation”, tracing the multiple relationships and shifting identities and differences that are involved in representing. I thus develop a theory of simulation that implies a non-representationalist concept of representing and a non-teleological concept of reason

Sanpete County Agriculture Profile

This publication includes a report that gives agricultural facts and statistics pertaining to Sanpete County