A Grassmann algebra for matroids

We introduce an idempotent analogue of the exterior algebra for which the theory of tropical linear spaces (and valuated matroids) can be seen in close analogy with the classical Grassmann algebra formalism for linear spaces. The top wedge power of a tropical linear space is its Plucker vector, which we view as a tensor, and a tropical linear space is recovered from its Plucker vector as the kernel of the corresponding wedge multiplication map. We prove that an arbitrary d-tensor satisfies the tropical Plucker relations (valuated exchange axiom) if and only if the d-th wedge power of the kernel of wedge-multiplication is free of rank one. This provides a new cryptomorphism for valuated matroids, including ordinary matroids as a special case

Measurement of Magnetic Exchange in Asymmetric Lanthanide Dimetallics: Toward a Transferable Theoretical Framework

Magnetic exchange interactions within the asymmetric dimetallic compounds [hqH2][Ln2(hq)4(NO3)3]∙MeOH, (Ln = Er(III) and Yb(III), hqH = 8-hydroxyquinoline) have been directly probed with EPR spectroscopy and accurately modelled by spin Hamiltonian techniques. Exploitation of site selectivity via doping experiments in Y(III) and Lu(III) matrices yields simple EPR spectra corresponding to isolated Kramers doublets, allowing determination of the local magnetic properties of the individual sites within the dimetallic compounds. CASSCF-SO calculations, INS and far-IR measurements are all employed to further support the identification and modelling of the local electronic structure for each site. EPR spectra of the pure dimetallic compounds are highly featured and correspond to transitions within the lowest-lying exchange-coupled manifold, permitting determination of the highly anisotropic magnetic exchange between the lanthanide ions. We find a unique orientation for the exchange interaction, corresponding to a common elongated oxygen bridge for both isostructural analogs. This suggests a microscopic physical connection to the magnetic superexchange. These results are of fundamental importance for building and validating model microscopic Hamiltonians to understand the origins of magnetic interactions between lanthanides and how they may be controlled with chemistr

The Compact Linear Collider (CLIC) - 2018 Summary Report

The Compact Linear Collider (CLIC) is a TeV-scale high-luminosity linear $e^+e^-$ collider under development at CERN. Following the CLIC conceptual design published in 2012, this report provides an overview of the CLIC project, its current status, and future developments. It presents the CLIC physics potential and reports on design, technology, and implementation aspects of the accelerator and the detector. CLIC is foreseen to be built and operated in stages, at centre-of-mass energies of 380 GeV, 1.5 TeV and 3 TeV, respectively. CLIC uses a two-beam acceleration scheme, in which 12 GHz accelerating structures are powered via a high-current drive beam. For the first stage, an alternative with X-band klystron powering is also considered. CLIC accelerator optimisation, technical developments and system tests have resulted in an increased energy efficiency (power around 170 MW) for the 380 GeV stage, together with a reduced cost estimate at the level of 6 billion CHF. The detector concept has been refined using improved software tools. Significant progress has been made on detector technology developments for the tracking and calorimetry systems. A wide range of CLIC physics studies has been conducted, both through full detector simulations and parametric studies, together providing a broad overview of the CLIC physics potential. Each of the three energy stages adds cornerstones of the full CLIC physics programme, such as Higgs width and couplings, top-quark properties, Higgs self-coupling, direct searches, and many precision electroweak measurements. The interpretation of the combined results gives crucial and accurate insight into new physics, largely complementary to LHC and HL-LHC. The construction of the first CLIC energy stage could start by 2026. First beams would be available by 2035, marking the beginning of a broad CLIC physics programme spanning 25-30 years

Cyclic operad formality for compactified moduli spaces of genus zero surfaces

The framed little 2-discs operad is homotopy equivalent to the Kimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stable curves with tangent rays at the marked points and nodes. We show that this cyclic operad is formal, meaning that its chains and its homology (the Batalin-Vilkovisky operad) are quasi-isomorphic cyclic operads. To prove this we introduce a new complex of graphs in which the differential is a combination of edge deletion and contraction, and we show that this complex resolves BV as a cyclic operad