Arbitrary Four String Scattering at High Energy and Fixed Angle

We calculate, using the group theoretic approach to string theory, the tree and one loop scattering of four open and closed arbitrary bosonic string states. In the limit of high energy, but fixed angle, the multi-string vertex at tree and one loop levels that we find takes a very simple form. We propose, and present arguments for, a form for the high energy multi-string vertex at all loops; in particular we give a path integral derivation of this vertex. Our results agree with those of Gross and Mende for tachyon scattering amplitudes, but those for any other string scattering are substantially different from that discussed in reference [5]. We also develop some of the technology used in the group theoretic method to compute loop corrections.Comment: Plain tex, 55 pages, 2 figures. A new section is added, giving a path integral derivation of four arbitrary string high energy scattering, in agreement with the results given earlier. Typos corrected, and some discussion in section 7 clarifie

Gauge fields and infinite chains of dualities

We show that the particle states of Maxwell's theory, in $D$ dimensions, can be represented in an infinite number of ways by using different gauge fields. Using this result we formulate the dynamics in terms of an infinite set of duality relations which are first order in space-time derivatives. We derive a similar result for the three form in eleven dimensions where such a possibility was first observed in the context of E11. We also give an action formulation for some of the gauge fields. In this paper we give a pedagogical account of the Lorentz and gauge covariant formulation of the irreducible representations of the Poincar\'e group, used previously in higher spin theories, as this plays a key role in our constructions. It is clear that our results can be generalised to any particle.Comment: 37 page

Quantum Computing with Continuous-Variable Clusters

Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.Comment: 17 pages, 5 figure

Generalizing Reduction-Based Algebraic Multigrid

Algebraic Multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their performance. Reduction-based AMG (AMGr) algorithms attempt to formalize these heuristics by providing two-level convergence bounds that depend concretely on properties of the partitioning of the given matrix into its fine- and coarse-grid degrees of freedom. MacLachlan and Saad (SISC 2007) proved that the AMGr method yields provably robust two-level convergence for symmetric and positive-definite matrices that are diagonally dominant, with a convergence factor bounded as a function of a coarsening parameter. However, when applying AMGr algorithms to matrices that are not diagonally dominant, not only do the convergence factor bounds not hold, but measured performance is notably degraded. Here, we present modifications to the classical AMGr algorithm that improve its performance on matrices that are not diagonally dominant, making use of strength of connection, sparse approximate inverse (SPAI) techniques, and interpolation truncation and rescaling, to improve robustness while maintaining control of the algorithmic costs. We present numerical results demonstrating the robustness of this approach for both classical isotropic diffusion problems and for non-diagonally dominant systems coming from anisotropic diffusion

Optimized Sparse Matrix Operations for Reverse Mode Automatic Differentiation

Sparse matrix representations are ubiquitous in computational science and machine learning, leading to significant reductions in compute time, in comparison to dense representation, for problems that have local connectivity. The adoption of sparse representation in leading ML frameworks such as PyTorch is incomplete, however, with support for both automatic differentiation and GPU acceleration missing. In this work, we present an implementation of a CSR-based sparse matrix wrapper for PyTorch with CUDA acceleration for basic matrix operations, as well as automatic differentiability. We also present several applications of the resulting sparse kernels to optimization problems, demonstrating ease of implementation and performance measurements versus their dense counterparts

Seasonal cues induce phenotypic plasticity of Drosophila suzukii to enhance winter survival

Additional file 7: Table S6. Table of differentially expressed genes in bodies of winter morphs of D. suzukii relative to those of summer morphs. Fold change represents the ratio of expression levels of winter to summer morphs

A note on spin-s duality

Duality is investigated for higher spin ($s \geq 2$), free, massless, bosonic gauge fields. We show how the dual formulations can be derived from a common "parent", first-order action. This goes beyond most of the previous treatments where higher-spin duality was investigated at the level of the equations of motion only. In D=4 spacetime dimensions, the dual theories turn out to be described by the same Pauli-Fierz (s=2) or Fronsdal ($s \geq 3$) action (as it is the case for spin 1). In the particular s=2 D=5 case, the Pauli-Fierz action and the Curtright action are shown to be related through duality. A crucial ingredient of the analysis is given by the first-order, gauge-like, reformulation of higher spin theories due to Vasiliev.Comment: Minor corrections, reference adde

The global energy balance of Titan

The global energy budget of planets and their moons is a critical factor to influence the climate change on these objects. Here we report the first measurement of the global emitted power of Titan. Long-term (2004–2010) observations conducted by the Composite Infrared Spectrometer (CIRS) onboard Cassini reveal that the total emitted power by Titan is (2.84 ± 0.01) × 10^(14) watts. Together with previous measurements of the global absorbed solar power of Titan, the CIRS measurements indicate that the global energy budget of Titan is in equilibrium within measurement error. The uncertainty in the absorbed solar energy places an upper limit on the energy imbalance of 6.0%

Metal-rich organic matter and hot continental passive margin: drivers for Devonian copper-cobalt-germanium mineralization in dolomitized reef-bearing carbonate platform

The abundance and types of reef-bearing carbonate platforms reflect the evolution of Devonian climate, with conspicuous microbial-algal reefs in the warm Early and Late Devonian and sponge-coral reefs in the cooler Middle Devonian. A dolomitized Wenlock-Lower Devonian microbial-algal reef-bearing carbonate platform hosts epigenetic copper-cobalt-germanium (Cu-Co-Ge) sulfide mineralization at Ruby Creek-Bornite in the Brooks Range, Alaska. Here, we present rhenium-osmium (Re-Os) radiometric ages and molybdenum and sulfur (δ(98/95)Mo = +2.04 to +5.48‰ and δ(34)S = −28.5 to −1.8‰) isotope variations for individual Cu-Co-Fe sulfide phases along the paragenetic sequence carrollite-bornite-pyrite. In the context of a hot, extensional passive margin, greenhouse conditions in the Early Devonian favored restriction of platform-top seawater circulation and episodic reflux of oxidized brines during growth of the carbonaceous carbonate platform. Molybdenum and sulfur isotope data signal the stepwise reduction of hot brines carrying Cu during latent reflux and geothermal circulation for at least ca. 15 million years from the Early Devonian until Cu-Co sulfide mineralization ca. 379–378 million years ago (Ma) in the Frasnian, Late Devonian (weighted mean of Re-Os model ages of carrollite at 379 ± 15 Ma [n = 4]; Re-Os isochron age of bornite at 378 ± 15 Ma [n = 6]). On the basis of petrographic relationships between sulfides and solid bitumen, and the Mo and S isotope data for sulfides, we imply that the endowment in critical metals (e.g., Co, Ge, Re) in the Ruby Creek-Bornite deposit is linked to the activity of primary producers that removed trace metals from the warm Early Devonian seawater and concentrated Co, Ge, and Re in algal-bacterial organic matter in carbonate sediments. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00126-022-01123-1