An Efficient Representation of Euclidean Gravity I

We explore how the topology of spacetime fabric is encoded into the local structure of Riemannian metrics using the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to prove that a general Einstein manifold arises as the sum of SU(2)_L Yang-Mills instantons and SU(2)_R anti-instantons where SU(2)_L and SU(2)_R are normal subgroups of the four-dimensional Lorentz group Spin(4) = SU(2)_L x SU(2)_R. Our proof relies only on the general properties in four dimensions: The Lorentz group Spin(4) is isomorphic to SU(2)_L x SU(2)_R and the six-dimensional vector space of two-forms splits canonically into the sum of three-dimensional vector spaces of self-dual and anti-self-dual two-forms. Consolidating these two, it turns out that the splitting of Spin(4) is deeply correlated with the decomposition of two-forms on four-manifold which occupies a central position in the theory of four-manifolds.Comment: 31 pages, 1 figur

Spatial-temporal rainfall simulation using generalized linear models

We consider the problem of simulating sequences of daily rainfall at a network of sites in such a way as to reproduce a variety of properties realistically over a range of spatial scales. The properties of interest will vary between applications but typically will include some measures of "extreme'' rainfall in addition to means, variances, proportions of wet days, and autocorrelation structure. Our approach is to fit a generalized linear model (GLM) to rain gauge data and, with appropriate incorporation of intersite dependence structure, to use the GLM to generate simulated sequences. We illustrate the methodology using a data set from southern England and show that the GLM is able to reproduce many properties at spatial scales ranging from a single site to 2000 km 2 ( the limit of the available data)

Comparing Results of Five Glomerular Filtration Rate-Estimating Equations in the Korean General Population. MDRD Study, Revised Lund-Malmö, and Three CKD-EPI Equations

Estimated glomerular filtration rate (eGFR) is a widely used index of kidney function. Recently, new formulas such as the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations or the Lund-Malmö equation were introduced for assessing eGFR. We compared them with the Modification of Diet in Renal Disease (MDRD) Study equation in the Korean adult population. METHODS: The study population comprised 1,482 individuals (median age 51 [42-59] yr, 48.9% males) who received annual physical check-ups during the year 2014. Serum creatinine (Cr) and cystatin C (CysC) were measured. We conducted a retrospective analysis using five GFR estimating equations (MDRD Study, revised Lund-Malmö, and Cr and/or CysC-based CKD-EPI equations). Reduced GFR was defined as eGFR <60 mL/min/1.73 m². RESULTS: For the GFR category distribution, large discrepancies were observed depending on the equation used; category G1 (≥90 mL/min/1.73 m²) ranged from 7.4-81.8%. Compared with the MDRD Study equation, the other four equations overestimated GFR, and CysC-based equations showed a greater difference (-31.3 for CKD-EPI(CysC) and -20.5 for CKD-EPI(Cr-CysC)). CysC-based equations decreased the prevalence of reduced GFR by one third (9.4% in the MDRD Study and 2.4% in CKD-EPI(CysC)). CONCLUSIONS: Our data shows that there are remarkable differences in eGFR assessment in the Korean population depending on the equation used, especially in normal or mildly decreased categories. Further prospective studies are necessary in various clinical settings

First report of Perkinsus honshuensis in the variegated carpet shell clam Ruditapes variegatus in Korea

The recent discovery of Perkinsus honshuensis, a new Perkinsus species infecting Manila clams Ruditapes philippinarum (Sowerby, 1852), in Japan, suggested that, based on proximity, P. honshuensis could also be in Korean waters, where to date, P. olseni was believed to be the only Perkinsus species present. Perkinsus sp. infections consistently occurred among Ruditapes variegatus clams on a pebble beach on Jeju Island, off the south coast of Korea. The typical \u27signet ring\u27 morphology of the parasite was observed in the connective tissue of the digestive gland, and infection intensity was comparatively low (3.3 x 10(3) +/- 1.2 x 10(4) to 1.3 x 10(4) +/- 6.1 x 10(4) cells g(-1) gill weight). Further DNA analyses of internal transcribed spacer (ITS-1, 5.8S and ITS-2) and non-transcribed spacer (NTS) regions of the parasite showed 98.9-99.8 and 98.5-99.5% similarity to those of P. honshuensis from Japan, respectively. Phylogenetic analyses using ITS and NTS sequences indicated that Perkinsus sp. from Jeju formed a highly supported clade with P. honshuensis. This is the first report of P. honshuensis infections in clams in Korean waters and the first report of R. variegatus as a host for that parasite

Experimental investigation on the deformation characteristics of granular materials under drained rotational shear

Rotational shear is the type of loading path where samples are subjected to cyclic rotation of principal stress directions while the magnitudes of principal stresses are maintained constant. This paper presents results from an experimental investigation on the drained deformation behaviour of saturated sand in rotational shear conducted in a hollow cylinder apparatus. Two types of granular materials, Leighton Buzzard sand and glass beads are tested. A range of influential factors are investigated including the material density, the deviatoric stress level, and the intermediate principal stress. It is observed that the volumetric strain during rotational shear is mainly contractive and most of strains are generated during the first 20 cycles. The mechanical behaviour of sand under rotational shear is generally non-coaxial, i.e., there is no coincidence between the principal axes of stress and incremental strain, and the variation of the non-coaxiality shows a periodic trend during the tests. The stress ratio has a significant effect on soil response in rotational shear. The larger the stress ratio, the more contractive behaviour and the lower degree of non-coaxiality are induced. The test also demonstrates that the effect of the intermediate principal stress, material density and particle shape on the results is pronounced

DEM and experimental study of bi-directional simple shear

Stress–strain responses of granular material under bi-directional simple shear are comprehensively studied experimentally and numerically. The variable direction dynamic cyclic simple shear apparatus is used to test glass beads under various loading paths, and the DEM is used to reproduce experimental results. These two methods are complementary to each other. The glass beads are subject to the first shearing until a specified shear strain is reached, followed by the second shearing until the failure of samples, and the two shears are at various angles. The experimental results are in good agreement with the numerical results. Both experimental and numerical studies indicate that the development of shear stresses is dependent on the angle between the two shears in the early stage, and they approach the same ultimate values at the failure. The lateral stress, principal stress and non-coaxiality are also studied in the DEM simulation. While the lateral stress and principal stress are dependent on the angle, the orientations of principal stresses and plastic strain rate almost reach the same value at the failure. The contact force network and material fabric are also investigated to provide insight into the micro-scale responses and macro–micro relations regarding bi-directional simple shear

Effects of the principal stress rotation in numerical simulations of geotechnical laboratory cyclic tests

Cyclic stress paths in geotechnical experiments can generate considerable principal stress rotation (PSR) in the saturated soil. The PSR without changes of principal stress magnitudes can generate additional excess pore water pressures and plastic strains, thus accelerating liquefactions in undrained conditions. This paper simulates a series of laboratory tests considering the PSR using two types of sand. The impact of PSR is taken into account by using an elastoplastic soil model developed on the basis of a kinematic hardening soil model with the bounding surface concept. The soil model considers the PSR by treating the stress rate generating the PSR independently. The capability of this soil model is verified by comparing the numerical predictions with and without PSR, as well as experimental results. The comparative results indicate that the simulation with the soil model considering the PSR can better reproduce the test results on the development of shear strain, reduction of effective confining pressure and liquefaction than the soil model without PSR. Therefore, it is important to consider PSR effects in simulations of geotechnical experiments under cyclic loadings

Gravity and compactified branes in matrix models

A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action, without invoking an Einstein-Hilbert-type term. The key requirements are compactified extra dimensions with extrinsic curvature M^4 x K \subset R^D and split noncommutativity, with a Poisson tensor \theta^{ab} linking the compact with the noncompact directions. The moduli of the compactification provide the dominant degrees of freedom for gravity, which are transmitted to the 4 noncompact directions via the Poisson tensor. The effective Newton constant is determined by the scale of noncommutativity and the compactification. This gravity theory is well suited for quantization, and argued to be perturbatively finite for the IKKT model. Since no compactification of the target space is needed, it might provide a way to avoid the landscape problem in string theory.Comment: 35 pages. V2: substantially revised and improved, conclusion weakened. V3: some clarifications, published version. V4: minor correctio