Stochastic groundwater flow analysis in the presence of trends in heterogeneous hydraulic conductivity fields

Due to changes in lithostatic pressure, differential fracturing across bedding planes and irregularities in depositional environments, hydraulic conductivity exhibits heterogeneities and trends at various spatial scales. Using spectral theory, we have examined the effect of trends in hydraulic conductivity on (1) the solution of the mean equation for hydraulic head, (2) the covariance of hydraulic head, (3) the cross-covariances of hydraulic head and log-hydraulic conductivity perturbations and their gradients, and (4) the effective hydraulic conductivity. It is shown that the field of hydraulic head is sensitive to the presence of trends in ways that cannot be predicted by the classical analysis based on stationary hydraulic conductivity fields. The controlling variables for the second moments of hydraulic head are the mean hydraulic gradient, the correlation scale of log-hydraulic conductivity and its variance, and the slope of the trend in log-hydraulic conductivity. The mean hydraulic gradient introduces complications in the analysis since it is, in general, spatially variable. In this respect, our results are approximate, yet indicative of the true role of spatially variable patterns of log-hydraulic conductivity on groundwater flow systems. © 1993 International Association for Mathematical Geology

Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant

We show that the ABJM theory, which is an N=6 superconformal U(N)*U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy, and confirm the N^{3/2} scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models.Comment: 35 pages, 20 figures; reference added. The simulation code is available upon request to [email protected]

Momento Económico (50)

En este número: Historia y Modernización. El Programa de Ciencia y Modernización Tecnológica, 1990-1994. Algunos comentarios generales al Programa de Ciencia y Modernización Tecnológica 1990-1994. Los objetivos del Programa Nacional de Población 1989-1994. La movilidad urbana en la Ciudad de México. Importación de leche en polvo en México: la utopía de la autosuficiencia lechera. América Latina: aspectos de la década perdida. Notas sobre la modernización agroindustrial. ¿Qué es el Estado ex-socialista ?. La investigación nacional y el Congreso Universitario. Temas de hoy

Probing AdS4/CFT3 proposals beyond chiral rings

We calculate the superconformal Witten index for the Chern-Simons-matter theory which was proposed to describe multiple M2-branes on $C^2 X C^2/Z_k$. We consider a variant of this model, which exhibits explicit N=3 supersymmetry and has the advantage of not having an exotic branch of the moduli space. At $k=1$, we compare the index with that from the proposed gravity dual and find a disagreement.Comment: references added; introduction modifie

Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors

Three-dimensional conformal field theories (CFTs) of deconfined gauge fields coupled to gapless flavors of fermionic and bosonic matter describe quantum critical points of condensed matter systems in two spatial dimensions. An important characteristic of these CFTs is the finite part of the entanglement entropy across a circle. The negative of this quantity is equal to the finite part of the free energy of the Euclidean CFT on the three-sphere, and it has been proposed to satisfy the so called F-theorem, which states that it decreases under RG flow and is stationary at RG fixed points. We calculate the three-sphere free energy of non-supersymmetric gauge theory with a large number N_F of bosonic and/or fermionic flavors to the first subleading order in 1/N_F. We also calculate the exact free energies of the analogous chiral and non-chiral {\cal N} = 2 supersymmetric theories using localization, and find agreement with the 1/N_F expansion. We analyze some RG flows of supersymmetric theories, providing further evidence for the F-theorem.Comment: 31 pages, 2 figures; v2 refs added, minor change

A quantitative performance study of two automatic methods for the diagnosis of ovarian cancer.

We present a quantitative study of the performance of two automatic methods for the early detection of ovarian cancer that can exploit longitudinal measurements of multiple biomarkers. The study is carried out for a subset of the data collected in the UK Collaborative Trial of Ovarian Cancer Screening (UKCTOCS). We use statistical analysis techniques, such as the area under the Receiver Operating Characteristic (ROC) curve, for evaluating the performance of two techniques that aim at the classification of subjects as either healthy or suffering from the disease using time-series of multiple biomarkers as inputs. The first method relies on a Bayesian hierarchical model that establishes connections within a set of clinically interpretable parameters. The second technique is a purely discriminative method that employs a recurrent neural network (RNN) for the binary classification of the inputs. For the available dataset, the performance of the two detection schemes is similar (the area under ROC curve is 0.98 for the combination of three biomarkers) and the Bayesian approach has the advantage that its outputs (parameters estimates and their uncertainty) can be further analysed by a clinical expert.This research was funded by Cancer Research UK and the Eve Appeal Gynaecological Cancer Research Fund (grant ref. A12677) and was supported by the National Institute for Health Research (NIHR) University College London Hospitals (UCLH) Biomedical Research Centre. UKCTOCS was core funded by the Medical Research Council, Cancer Research UK, and the Department of Health with additional support from the Eve Appeal, Special Trustees of Bart's and the London, and Special Trustees of UCLH. We also acknowledge support by the grant of the Ministry of Education and Science of the Russian Federation Agreement No. 074-02-2018-330. I.P.M. and M.A.V. acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness (projects TEC2015-69868-C2-1-R and TEC2017-86921-C2-1-R)

Partition Functions of Holographic Minimal Models

The partition function of the W_N minimal model CFT is computed in the large N 't Hooft limit and compared to the spectrum of the proposed holographic dual, a 3d higher spin gravity theory coupled to massive scalar fields. At finite N, the CFT contains additional light states that are not visible in the perturbative gravity theory. We carefully define the large N limit, and give evidence that, at N = infinity, the additional states become null and decouple from all correlation functions. The surviving states are shown to match precisely (for all values of the 't Hooft coupling) with the spectrum of the higher spin gravity theory. The agreement between bulk and boundary is partially explained by symmetry considerations involving the conjectured equivalence between the W_N algebra in the large N limit and the higher spin algebra of the Vasiliev theory.Comment: 56 page