Typing mineral deposits using their grades and tonnages in an artificial neural network

A test of the ability of a probabilistic neural network to classify deposits into types on the basis of deposit tonnage and average Cu, Mo, Ag, Au, Zn, and Pb grades is conducted. The purpose is to examine whether this type of system might serve as a basis for integrating geoscience information available in large mineral databases to classify sites by deposit type. Benefits of proper classification of many sites in large regions are relatively rapid identification of terranes permissive for deposit types and recognition of specific sites perhaps worthy of exploring further. Total tonnages and average grades of 1,137 well-explored deposits identified in published grade and tonnage models representing 13 deposit types were used to train and test the network. Tonnages were transformed by logarithms and grades by square roots to reduce effects of skewness. All values were scaled by subtracting the variable's mean and dividing by its standard deviation. Half of the deposits were selected randomly to be used in training the probabilistic neural network and the other half were used for independent testing. Tests were performed with a probabilistic neural network employing a Gaussian kernel and separate sigma weights for each class (type) and each variable (grade or tonnage). Deposit types were selected to challenge the neural network. For many types, tonnages or average grades are significantly different from other types, but individual deposits may plot in the grade and tonnage space of more than one type. Porphyry Cu, porphyry Cu-Au, and porphyry Cu-Mo types have similar tonnages and relatively small differences in grades. Redbed Cu deposits typically have tonnages that could be confused with porphyry Cu deposits, also contain Cu and, in some situations, Ag. Cyprus and kuroko massive sulfide types have about the same tonnages. Cu, Zn, Ag, and Au grades. Polymetallic vein, sedimentary exhalative Zn-Pb, and Zn-Pb skarn types contain many of the same metals. Sediment-hosted Au, Comstock Au-Ag, and low-sulfide Au-quartz vein types are principally Au deposits with differing amounts of Ag. Given the intent to test the neural network under the most difficult conditions, an overall 75% agreement between the experts and the neural network is considered excellent. Among the largestclassification errors are skarn Zn-Pb and Cyprus massive sulfide deposits classed by the neuralnetwork as kuroko massive sulfides—24 and 63% error respectively. Other large errors are the classification of 92% of porphyry Cu-Mo as porphyry Cu deposits. Most of the larger classification errors involve 25 or fewer training deposits, suggesting that some errors might be the result of small sample size. About 91% of the gold deposit types were classed properly and 98% of porphyry Cu deposits were classes as some type of porphyry Cu deposit. An experienced economic geologist would not make many of the classification errors that were made by the neural network because the geologic settings of deposits would be used to reduce errors. In a separate test, the probabilistic neural network correctly classed 93% of 336 deposits in eight deposit types when trained with presence or absence of 58 minerals and six generalized rock types. The overall success rate of the probabilistic neural network when trained on tonnage and average grades would probably be more than 90% with additional information on the presence of a few rock types.

Gaussian quantum operator representation for bosons

We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.

Orientation of biological cells using plane-polarized gaussian beam optical tweezers

Optical tweezers are widely used for the manipulation of cells and their internal structures. However, the degree of manipulation possible is limited by poor control over the orientation of the trapped cells. We show that it is possible to controllably align or rotate disc-shaped cells-chloroplasts of Spinacia oleracea-in a plane-polarized Gaussian beam trap, using optical torques resulting predominantly from circular polarization induced in the transmitted beam by the non-spherical shape of the cells.

Gaussian quantum Monte Carlo methods for fermions and bosons

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.

Nonclassicality of a photon-subtracted Gaussian field

We investigate the nonclassicality of a photon-subtracted Gaussian field, which was produced in a recent experiment, using negativity of the Wigner function and the nonexistence of well-behaved positive P function. We obtain the condition to see negativity of the Wigner function for the case including the mixed Gaussian incoming field, the threshold photodetection and the inefficient homodyne measurement. We show how similar the photon-subtracted state is to a superposition of coherent states.

Normalized Gaussian Networks with Mixed Feature Data

With mixed feature data, problems are induced in modeling the gating network of normalized Gaussian (NG) networks as the assumption of multivariate Gaussian becomes invalid. In this paper, we propose an independence model to handle mixed feature data within the framework of NG networks. The method is illustrated using a real example of breast cancer data.

Gaussian operator bases for correlated fermions

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus allows first-principles dynamical or equilibrium calculations in quantum many-body Fermi systems. We prove the completeness of the basis and derive differential forms for products with one- and two-body operators. Because the basis satisfies fermionic superselection rules, the resulting phase space involves only c-numbers, without requiring anticommuting Grassmann variables. Furthermore, because of the overcompleteness of the basis, the phase-space distribution can always be chosen positive. This has important consequences for the sign problem in fermion physics.

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multimode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behavior in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.

Palm kernel meal in broiler diets: effect on chicken performance and health

An increase in the production of palm kernel meal (PKM) coupled with the concern for continued availability of conventional feedstuffs in some parts of the world has led to research to establish the maximum inclusion level of palm kernel meal in broiler diets. The results suggested that palm kernel meal has no anti-nutritional properties and thus its inclusion is safe up to at least 40% in the diet, provided the diet is balanced in amino acids and metabolisable energy. Although feed digestibility is decreased due to high dietary fibre when PKM is included in the diet, the feed intake is increased. This makes total digestible nutrient intake relatively high. beta-mannan is the main component of palm kernel meal non-starch polysaccharide (NSP). Both mannose and manno-oligosaccharides have been reported to act as prebiotics. The inclusion of palm kernel meal in the diet improves the immune system of birds and reduces pathogenic bacteria and increases the population of nonpathogenic bacteria in the intestine. These two benefits should be considered as strong recommendations for using palm kernel meal in broiler diets, particularly in palm kernel meal producing countries, not only for increasing bird productivity but also to improve chicken health. Selective enzyme addition increases feed efficiency and digestibility as well as decreasing the moisture content of faeces.

A scalarization technique for computing the power and exponential moments of gaussian random matrices

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X=A+BWC for positive integer s and real t, where W is a standard normal random vector and A, B, C are appropriately dimensioned constant matrices. We solve the problems by a matrix product scalarization technique and interpret the solutions in system-theoretic terms. The results of the paper are applicable to Bayesian prediction in multivariate autoregressive time series and mean-reverting diffusion processes.

Kinetic energy conserving integrators for Gaussian thermostatted SLLOD

A new integration scheme is developed for nonequilibrium molecular dynamics simulations where the temperature is constrained by a Gaussian thermostat. The utility of the scheme is demonstrated by its application to the SLLOD algorithm which is the standard nonequilibrium molecular dynamics algorithm for studying shear flow. Unlike conventional integrators, the new integrators are constructed using operator-splitting techniques to ensure stability and that little or no drift in the kinetic energy occurs. Moreover, they require minimum computer memory and are straightforward to program. Numerical experiments show that the efficiency and stability of the new integrators compare favorably with conventional integrators such as the Runge-Kutta and Gear predictor-corrector methods. (C) 1999 American Institute of Physics. [S0021-9606(99)50125-6].