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Observation of Spin Relaxation in a Vanadate Chloride with Quasi-One-Dimensional Linear Chain
(2019)
A new cobalt(II) vanadate chloride, Pb2Co(OH)(V2O7)Cl, has been synthesized under mild hydrothermal conditions. It contains quasi-one-dimensional (1D) linear chains built by edge-sharing of (CoO6)-O-II octahedra. The cobalt(II) oxide chains are further interconnected by (V2O7)(4-) dimers into a three-dimensional (3D) anionic framework with Pb2+ and Cl- ions residing in Co4V8 12-member ring tunnels. The intrachain Co center dot center dot center dot Co distance is 3.041 angstrom, while the interchain distances are 8.742 and 9.256 angstrom. Magnetic measurements suggest the ferromagnetic intrachain and the antiferromagnetic interchain interactions with a specific value of J(intra)/J(inter) = 1.7 x 10(3). Zero-field heat capacity demonstrates the magnetic long-range ordering at 5.5 K. Alternating current (AC) magnetic susceptibility under zero external direct current (DC) fields displays two slow magnetic relaxations at low temperatures, giving characteristic relaxations (tau(0)) of 1.2(3) x 10(-12) and 1.9(4) x 10(-10) s with effective energy barriers (Delta(r)) of 76.1(2) and 48.4(5) K. The energy barrier between the spin up and spin-down states can be ascribed to the ferromagnetic spin chain and the Ising-like magnetic anisotropy in Pb2Co(OH)(V2O7)Cl.
We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve locality during the renormalisation procedure. Viewing renormalisation in the framework of Connes and Kreimer as the algebraic Birkhoff factorisation of characters on a Hopf algebra with values in a Rota-Baxter algebra, we build locality variants of these algebraic structures, leading to a locality variant of the algebraic Birkhoff factorisation. This provides an algebraic formulation of the conservation of locality while renormalising. As an application in the context of the Euler-Maclaurin formula on lattice cones, we renormalise the exponential generating function which sums over the lattice points in a lattice cone. As a consequence, for a suitable multivariate regularisation, renormalisation from the algebraic Birkhoff factorisation amounts to composition by a projection onto holomorphic multivariate germs.
Renormalisation and locality
(2020)
We equip the space of lattice cones with a coproduct which makes it a cograded, coaugmented, connnected coalgebra. The exponential generating sum and exponential generating integral on lattice cones can be viewed as linear maps on this space with values in the space of meromorphic germs with linear poles at zero. We investigate the subdivision properties-reminiscent of the inclusion-exclusion principle for the cardinal on finite sets-of such linear maps and show that these properties are compatible with the convolution quotient of maps on the coalgebra. Implementing the algebraic Birkhoff factorization procedure on the linear maps under consideration, we factorize the exponential generating sum as a convolution quotient of two maps, with each of the maps in the factorization satisfying a subdivision property. A direct computation shows that the polar decomposition of the exponential generating sum on a smooth lattice cone yields an Euler-Maclaurin formula. The compatibility with subdivisions of the convolution quotient arising in the algebraic Birkhoff factorization then yields the Euler-Maclaurin formula for any lattice cone. This provides a simple formula for the interpolating factor by means of a projection formula.
Superconductors are considered in view of applications to atom chip devices. The main features of magnetic traps based on superconducting wires in the Meissner and mixed states are discussed. The former state may mainly be interesting for improved atom optics, while in the latter, cold atoms may provide a probe of superconductor phenomena. The properties of a magnetic side guide based on a single superconducting strip wire placed in an external magnetic field are calculated analytically and numerically. In the mixed state of type II superconductors, inhomogeneous trapped magnetic flux, relaxation processes and noise caused by vortex motion are posing specific challenges for atom trapping.
The purpose of this paper is to build an algebraic framework suited to regularize branched structures emanating from rooted forests and which encodes the locality principle. This is achieved by means of the universal properties in the locality framework of properly decorated rooted forests. These universal properties are then applied to derive the multivariate regularization of integrals indexed by rooted forests. We study their renormalization, along the lines of Kreimer's toy model for Feynman integrals.
We introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision and closed cone subdivision relations respectively for conical zeta values. In order to achieve the closed cone subdivision relation, we also interpret linear relations among fractions as subdivisions of decorated closed cones. As a generalization of the double shuffle relation of multiple zeta values, we give the double subdivision relation of conical zeta values and formulate the extended double subdivision relation conjecture for conical zeta values.
A catalog of genetic loci associated with kidney function from analyses of a million individuals
(2019)
Chronic kidney disease (CKD) is responsible for a public health burden with multi-systemic complications. Through transancestry meta-analysis of genome-wide association studies of estimated glomerular filtration rate (eGFR) and independent replication (n = 1,046,070), we identified 264 associated loci (166 new). Of these,147 were likely to be relevant for kidney function on the basis of associations with the alternative kidney function marker blood urea nitrogen (n = 416,178). Pathway and enrichment analyses, including mouse models with renal phenotypes, support the kidney as the main target organ. A genetic risk score for lower eGFR was associated with clinically diagnosed CKD in 452,264 independent individuals. Colocalization analyses of associations with eGFR among 783,978 European-ancestry individuals and gene expression across 46 human tissues, including tubulo-interstitial and glomerular kidney compartments, identified 17 genes differentially expressed in kidney. Fine-mapping highlighted missense driver variants in 11 genes and kidney-specific regulatory variants. These results provide a comprehensive priority list of molecular targets for translational research.