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

Tropical Forest Protection, Uncertainty, and the Environmental Integrity of Carbon Mitigation Policies

Tropical forests are estimated to release approximately 1.7 PgC per year as a result of deforestation. Avoiding tropical deforestation could potentially play a significant role in carbon mitigation over the next 50 years if not longer. Many policymakers and negotiators are skeptical of our ability to reduce deforestation effectively. They fear that if credits for avoided deforestation are allowed to replace fossil fuel emission reductions for compliance with Kyoto, the environment will suffer because the credits will not reflect truly additional carbon storage. This paper considers the nature of the uncertainties involved in estimating carbon stocks and predicting deforestation. We build an empirically based stochastic model that combines data from field ecology, geographical information system (GIS) data from satellite imagery, economic analysis and ecological process modeling to simulate the effects of these uncertainties on the environmental integrity of credits for avoided deforestation. We find that land use change, and hence additionality of carbon, is extremely hard to predict accurately and errors in the numbers of credits given for avoiding deforestation are likely to be very large. We also find that errors in estimation of carbon storage could be large and could have significant impacts. We find that in Costa Rica, nearly 42% of all the loss of environmental integrity that would arise from poor carbon estimates arises in one life zone, tropical wet. This suggests that research effort might be focused in this life zone.climate, economics, carbon sequestration, uncertainty, policy, tropics

Prospects for India's cereal supply and demand to 2020:

The possibility of an emerging cereal gap of serious proportions by the year 2020, is a useful illustration of the kind of constructive dialogue IFPRI hopes to encourage. It responds to several quite recent developments, notably the rapid expansion of India's industrial and service sectors since the 1991 structural reforms, the improved prospects for continued growth over the next few decades, and the likelihood of rising per capita incomes that could generate substantially increased demand for livestock products. As demand for livestock products grows, livestock production could increasingly depend on cereals for feed — perhaps as much as 50 million tons by 2020, according to G.S. Bhalla, Peter Hazell, and John Kerr, authors of this 2020 discussion paper on Prospects for Balancing Cereal Needs in India to 2020. These conclusions differ somewhat from other IFPRI studies, which have generally found that growth in demand for livestock products will be lower than the current study. This divergence of views is a useful signal to policymakers to pay careful attention to trends in demand for livestock products in India in the coming years. This study and the rest of IFPRI's 2020 research have consistently pointed to the vital link between agricultural policies and prospects for production growth in the next two decades. (from Forward by Per Pinstrup-Andersen)South Asia, South Asia and Central Asia, Grain Yields India., Food supply India Forecasting., Grain as feed India Forecasting., Consumption (Economics) India., Livestock India.,

Prospects for India's cereal supply and demand to 2020:

The possibility of an emerging cereal gap of serious proportions by the year 2020, is a useful illustration of the kind of constructive dialogue IFPRI hopes to encourage. It responds to several quite recent developments, notably the rapid expansion of India's industrial and service sectors since the 1991 structural reforms, the improved prospects for continued growth over the next few decades, and the likelihood of rising per capita incomes that could generate substantially increased demand for livestock products. As demand for livestock products grows, livestock production could increasingly depend on cereals for feed — perhaps as much as 50 million tons by 2020, according to G.S. Bhalla, Peter Hazell, and John Kerr, authors of this 2020 discussion paper on Prospects for Balancing Cereal Needs in India to 2020. These conclusions differ somewhat from other IFPRI studies, which have generally found that growth in demand for livestock products will be lower than the current study. This divergence of views is a useful signal to policymakers to pay careful attention to trends in demand for livestock products in India in the coming years. This study and the rest of IFPRI's 2020 research have consistently pointed to the vital link between agricultural policies and prospects for production growth in the next two decades. (from Forward by Per Pinstrup-Andersen)Grain Yields India., Food supply India Forecasting., Grain as feed India Forecasting., Consumption (Economics) India., Livestock India.,

A Dynamical Systems Approach to Schwarzschild Null Geodesics

The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential. We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions. All the null geodesics belong to one of four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L|>|L_c|, (1) the set that flow outward from the white hole, turn around, then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L|<|L_c|, (3) the set that flow outward from the white hole and continue to future null infinity, (4) the set that flow inward from past null infinity and into the black hole. The critical angular momentum Lc corresponds to the unstable circular orbit at r=3M, and the homoclinic orbits associated with it. There are two additional critical points of the flow at the singularity at r=0. Though the solutions of geodesic motion and Hamiltonian flow we describe here are well known, what we believe is a novel aspect of this work is the mapping between the two equivalent descriptions, and the different insights each approach can give to the problem. For example, the McGehee picture points to a particularly interesting limiting case of the class (1) that move from the white to black hole: in the limit as L goes to infinity, as described in Schwarzschild coordinates, these geodesics begin at r=0, flow along t=constant lines, turn around at r=2M, then continue to r=0. During this motion they circle in azimuth exactly once, and complete the journey in zero affine time.Comment: 14 pages, 3 Figure

Carbon Dynamics and Land-Use Choices: Building a Regional-Scale Multidisciplinary Model

Policy enabling tropical forests to approach their potential contribution to global-climate-change mitigation requires forecasts of land use and carbon storage on a large scale over long periods. In this paper, we present an integrated modeling methodology that addresses these needs. We model the dynamics of the human land-use system and of C pools contained in each ecosystem, as well as their interactions. The model is national scale, and is currently applied in a preliminary way to Costa Rica using data spanning a period of over fifty years. It combines an ecological process model, parameterized using field and other data, with an economic model, estimated using historical data to ensure a close link to actual behavior. These two models are linked so that ecological conditions affect land-use choices and vice versa. The integrated model predicts land use and its consequences for C storage for policy scenarios. These predictions can be used to create baselines, reward sequestration, and estimate the value in both environmental and economic terms of including C sequestration in tropical forests as part of the efforts to mitigate global climate change. The model can also be used to assess the benefits from costly activities to increase accuracy and thus reduce errors and their societal costs.carbon, sequestration, climate change, land use, modelling

Peculiar Spin Frequency and Radio Profile Evolution of PSR J1119−-6127 Following Magnetar-like X-ray Bursts

We present the spin frequency and profile evolution of the radio pulsar J1119$-$6127 following magnetar-like X-ray bursts from the system in 2016 July. Using data from the Parkes radio telescope, we observe a smooth and fast spin-down process subsequent to the X-ray bursts resulting in a net change in the pulsar rotational frequency of $\Delta\nu\approx-4\times10^{-4}$\,Hz. During the transition, a net spin-down rate increase of $\Delta\dot\nu\approx-1\times10^{-10}$\,Hz\,s$^{-1}$ is observed, followed by a return of $\dot{\nu}$ to its original value. In addition, the radio pulsations disappeared after the X-ray bursts and reappeared about two weeks later with the flux density at 1.4\,GHz increased by a factor of five. The flux density then decreased and undershot the normal flux density followed by a slow recovery back to normal. The pulsar's integrated profile underwent dramatic and short-term changes in total intensity, polarization and position angle. Despite the complex evolution, we observe correlations between the spin-down rate, pulse profile shape and radio flux density. Strong single pulses have been detected after the X-ray bursts with their energy distributions evolving with time. The peculiar but smooth spin frequency evolution of PSR~J1119$-$6127 accompanied by systematic pulse profile and flux density changes are most likely to be a result of either reconfiguration of the surface magnetic fields or particle winds triggered by the X-ray bursts. The recovery of spin-down rate and pulse profile to normal provides us the best case to study the connection between high magnetic-field pulsars and magnetars.Comment: Accepted for publication in MNRAS on 2018 July 2

X-Ray Observations of Black Widow Pulsars

We describe the first X-ray observations of five short orbital period ($P_B < 1$ day), $\gamma$-ray emitting, binary millisecond pulsars. Four of these, PSRs J0023+0923, J1124$-$3653, J1810+1744, and J2256$-$1024 are `black-widow' pulsars, with degenerate companions of mass $\ll0.1 M_{\odot}$, three of which exhibit radio eclipses. The fifth source, PSR J2215+5135, is an eclipsing `redback' with a near Roche-lobe filling $\sim$0.2 solar mass non-degenerate companion. Data were taken using the \textit{Chandra X-Ray Observatory} and covered a full binary orbit for each pulsar. Two pulsars, PSRs J2215+5135 and J2256$-$1024, show significant orbital variability while PSR J1124$-$3653 shows marginal orbital variability. The lightcurves for these three pulsars have X-ray flux minima coinciding with the phases of the radio eclipses. This phenomenon is consistent with an intrabinary shock emission interpretation for the X-rays. The other two pulsars, PSRs J0023+0923 and J1810+1744, are fainter and do not demonstrate variability at a level we can detect in these data. All five spectra are fit with three separate models: a power-law model, a blackbody model, and a combined model with both power-law and blackbody components. The preferred spectral fits yield power-law indices that range from 1.3 to 3.2 and blackbody temperatures in the hundreds of eV. The spectrum for PSR J2215+5135 shows a significant hard X-ray component, with a large number of counts above 2 keV, which is additional evidence for the presence of intrabinary shock emission and is similar to what has been detected in the low-mass X-ray binary to millisecond pulsar transition object PSR J1023+0038.Comment: 8 pages, 6 figures, 2 tables, submitted to Ap

Spectral Energy Distributions for Disk and Halo M--Dwarfs

We have obtained infrared (1 to 2.5 micron) spectroscopy for 42 halo and disk dwarfs with spectral type M1 to M6.5. These data are compared to synthetic spectra generated by the latest model atmospheres of Allard & Hauschildt. Photospheric parameters metallicity, effective temperature and radius are determined for the sample. We find good agreement between observation and theory except for known problems due to incomplete molecular data for metal hydrides and water. The metal-poor M subdwarfs are well matched by the models as oxide opacity sources are less important in this case. The derived effective temperatures for the sample range from 3600K to 2600K; at these temperatures grain formation and extinction are not significant in the photosphere. The derived metallicities range from solar to one-tenth solar. The radii and effective temperatures derived agree well with recent models of low mass stars.Comment: 24 pages including 13 figures, 4 Tables; accepted by Ap