A Deep Neural Network as Surrogate Model for Forward Simulation of Borehole Resistivity Measurements

Inverse problems appear in multiple industrial applications. Solving such inverse problems require the repeated solution of the forward problem. This is the most time-consuming stage when employing inversion techniques, and it constitutes a severe limitation when the inversion needs to be performed in real-time. In here, we focus on the real-time inversion of resistivity measurements for geosteering. We investigate the use of a deep neural network (DNN) to approximate the forward function arising from Maxwell's equations, which govern the electromagnetic wave propagation through a media. By doing so, the evaluation of the forward problems is performed offline, allowing for the online real-time evaluation (inversion) of the DNN

Solution of Some Integrable One-Dimensional Quantum Systems

In this paper, we investigate a family of one-dimensional multi-component quantum many-body systems. The interaction is an exchange interaction based on the familiar family of integrable systems which includes the inverse square potential. We show these systems to be integrable, and exploit this integrability to completely determine the spectrum including degeneracy, and thus the thermodynamics. The periodic inverse square case is worked out explicitly. Next, we show that in the limit of strong interaction the "spin" degrees of freedom decouple. Taking this limit for our example, we obtain a complete solution to a lattice system introduced recently by Shastry, and Haldane; our solution reproduces the numerical results. Finally, we emphasize the simple explanation for the high multiplicities found in this model

Conservation laws in the continuum 1/r21/r^2 systems

We study the conservation laws of both the classical and the quantum mechanical continuum $1/r^2$ type systems. For the classical case, we introduce new integrals of motion along the recent ideas of Shastry and Sutherland (SS), supplementing the usual integrals of motion constructed much earlier by Moser. We show by explicit construction that one set of integrals can be related algebraically to the other. The difference of these two sets of integrals then gives rise to yet another complete set of integrals of motion. For the quantum case, we first need to resum the integrals proposed by Calogero, Marchioro and Ragnisco. We give a diagrammatic construction scheme for these new integrals, which are the quantum analogues of the classical traces. Again we show that there is a relationship between these new integrals and the quantum integrals of SS by explicit construction.Comment: 19 RevTeX 3.0 pages with 2 PS-figures include

Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

MODELLING WITHIN-PLANT SPATIAL DEPENDENCIES OF COTTON YIELD

In field experiments during 1987-1990, cotton plants were grown under 8 different levels of nitrogen application to assess the impact of nitrogen fertilization on the fruiting and yield distribution of cotton within the plant (Boquet et al. 1993).lr.dividual boll weights and average seedcotton yield were determined at each fruiting site fur each main-stem node along the plant. Various models of dependence and independence are possible to explain and account for the dependencies of the yields among the sites and nodes of the plant. Here we investigate models of total yield per node and yield per node adjusted for the number of sites using several models for the spatial dependence among the nodes. Typical univariate models would either assume a simple homogeneous error structure or a compound symmetry error structure among the nodes, leading to the split-plot-type models. A multivariate unstructured approach ignores obvious spatial dependencies among the nodes. Spatial models and ante-dependence models permit a parsimonious summary of the error structure and are compared with the compound symmetry and multivariate models

Morphological Development Rates of Perennial Forage Grasses

The objective of this study was to determine the rate of change in the morphological development of switchgrass (Panicum virgatum L.) and big bluestem (Andropogon gerardii Vitman). Pure stands of each species were sampled at weekly intervals in 1990 and 1991 at Mead, NE, and morphologically classified as mean stage count (MSC) and mean stage weight (MSW). Linear day of the year equations accounted for 94% of the variation in switchgrass MSC and MSW. Switchgrass MSC and MSW increased at an average rate of 0.0204 and 0.0234 units per day, respectively. Linear day of the year equations accounted for 73 and 84% of the variation in big bluestem MSC and MSW, respectively. Big bluestem MSC and MSW increased at an average rate of 0.0147 and 0.0215 units per day, respectively. The morphological development of switchgrass and big bluestem can be reliably predicted for adapted cultivars in the central Great Plains using day of the year due to the determinate growth habit of these grasses and their strong response to photoperiod

Bohmian trajectories and Klein's paradox

We compute the Bohmian trajectories of the incoming scattering plane waves for Klein's potential step in explicit form. For finite norm incoming scattering solutions we derive their asymptotic space-time localization and we compute some Bohmian trajectories numerically. The paradox, which appears in the traditional treatments of the problem based on the outgoing scattering asymptotics, is absent.Comment: 14 pages, 3 figures; minor format change

Constructive counterexamples to additivity of minimum output R\'enyi entropy of quantum channels for all p>2

We present a constructive example of violation of additivity of minimum output R\'enyi entropy for each p>2. The example is provided by antisymmetric subspace of a suitable dimension. We discuss possibility of extension of the result to go beyond p>2 and obtain additivity for p=0 for a class of entanglement breaking channels.Comment: 4 pages; a reference adde