Efficiency versus Convergence of Boolean Kernels for On-Line Learning Algorithms

The paper studies machine learning problems where each example is described using a set of Boolean features and where hypotheses are represented by linear threshold elements. One method of increasing the expressiveness of learned hypotheses in this context is to expand the feature set to include conjunctions of basic features. This can be done explicitly or where possible by using a kernel function. Focusing on the well known Perceptron and Winnow algorithms, the paper demonstrates a tradeoff between the computational efficiency with which the algorithm can be run over the expanded feature space and the generalization ability of the corresponding learning algorithm. We first describe several kernel functions which capture either limited forms of conjunctions or all conjunctions. We show that these kernels can be used to efficiently run the Perceptron algorithm over a feature space of exponentially many conjunctions; however we also show that using such kernels, the Perceptron algorithm can provably make an exponential number of mistakes even when learning simple functions. We then consider the question of whether kernel functions can analogously be used to run the multiplicative-update Winnow algorithm over an expanded feature space of exponentially many conjunctions. Known upper bounds imply that the Winnow algorithm can learn Disjunctive Normal Form (DNF) formulae with a polynomial mistake bound in this setting. However, we prove that it is computationally hard to simulate Winnows behavior for learning DNF over such a feature set. This implies that the kernel functions which correspond to running Winnow for this problem are not efficiently computable, and that there is no general construction that can run Winnow with kernels

Giant Resonances based on Unitarily Transformed Two-Nucleon plus Phenomenological Three-Nucleon Interactions

We investigate giant resonances of spherical nuclei on the basis of the Argonne V18 potential after unitary transformation within the Similarity Renormalization Group or the Unitary Correlation Operator Method supplemented by a phenomenological three-body contact interaction. Such Hamiltonians can provide a good description of ground-state energies and radii within Hartree-Fock plus low-order many-body perturbation theory. The standard Random Phase Approximation is applied here to calculate the isoscalar monopole, isovector dipole, and isoscalar quadrupole excitation modes of the 40Ca, 90Zr, and 208Pb nuclei. Thanks to the inclusion of the three-nucleon interaction and despite the minimal optimization effort, a reasonable agreement with experimental centroid energies of all three modes has been achieved. The role and scope of the Hartree-Fock reference state in RPA methods are discussed.Comment: v2: 11 pages, incl. 3 figures; extended discussion and outlook; to appear in J.Phys.

Density functional theory for hard-sphere mixtures: the White-Bear version Mark II

In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.Comment: 16 pages, 3 figures; minor changes; J. Phys.: Condens. Matter, accepte

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed `wetting' film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a `bridging' transition as the wetting films join to form a fluid bridge. The potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a non-zero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.Comment: 28 pages, 8 figure

Characteristics of the NASA Lewis bumpy torus plasma generated with high positive or negative applied potentials

The toroidal ring of plasma contained in the NASA Lewis bumpy-torus superconducting magnet facility may be biased to positive or negative potentials approaching 50 kilovolts by applying direct-current voltages of the respective polarity to 12 or fewer of the midplane electrode rings. The electric fields which are responsible for heating the ions by E/B drift then point radially outward or inward. The low-frequency fluctuations below the ion cyclotron frequency appeared to be dominated by rotating spokes

Initial results from the NASA Lewis Bumpy Torus experiment

Initial results were obtained from low power operation of the NASA Lewis Bumpy Torus experiment, in which a steady-state ion heating method based on the modified Penning discharge is applied in a bumpy torus confinement geometry. The magnet facility consists of 12 superconducting coils, each 19 cm i.d. and capable of 3.0 T, equally spaced in a toroidal array 1.52 m in major diameter. A 18 cm i.d. anode ring is located at each of the 12 midplanes and is maintained at high positive potentials by a dc power supply. Initial observations indicate electron temperatures from 10 to 150 eV, and ion kinetic temperatures from 200 eV to 1200 eV. Two modes of operation were observed, which depend on background pressure, and have different radial density profiles. Steady state neutron production was observed. The ion heating process in the bumpy torus appears to parallel closely the mechanism observed when the modified Penning discharge was operated in a simple magnetic mirror field

Microscopic theory of solvent mediated long range forces: influence of wetting

We show that a general density functional approach for calculating the force between two big particles immersed in a solvent of smaller ones can describe systems that exhibit fluid-fluid phase separation: the theory captures effects of strong adsorption (wetting) and of critical fluctuations in the solvent. We illustrate the approach for the Gaussian core model, a simple model of a polymer mixture in solution and find extremely attractive, long ranged solvent mediated potentials between the big particles for state points lying close to the binodal, on the side where the solvent is poor in the species which is favoured by the big particles.Comment: 7 pages, 3 figures, submitted to Europhysics Letter

Characteristics of the NASA Lewis bumpy-torus plasma generated with positive applied potentials

Experimental observations were made during steady-state operation of a bumpy-torus plasma at input powers up to 150 kW in deuterium and helium gas and with positive potentials applied to the midplane electrodes. In this steady-state ion heating method a modified Penning discharge is operated such that the plasma is acted upon by a combination of strong electric and magnetic fields. Experimental investigation of a deuterium plasma revealed electron temperatures from 14 to 140 eV and ion kinetic temperatures from 160 to 1785 eV. At least two distinct modes of operation exist. Experimental data shows that the average ion residence time in the plasma is virtually independent of the magnetic field strength. Data was taken when all 12 anode rings were at high voltage, and in other symmetric configurations in which the toroidal plasma was generated by applying positive potentials to six anode rings, three anode rings, and a single anode ring

Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two- Plus Three-Nucleon Interactions

We formulate the In-Medium Similarity Renormalization Group (IM-SRG) for open-shell nuclei using a multi-reference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multi-reference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of even oxygen isotopes with chiral NN and 3N Hamiltonians, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the Importance-Truncated No-Core Shell Model and the Coupled Cluster method. The agreement between conceptually different many-body approaches and experiment highlights the predictive power of current chiral two- and three-nucleon interactions, and establishes the MR-IM-SRG as a promising new tool for ab initio calculations of medium-mass nuclei far from shell closures.Comment: 5 pages, 4 figures, v2 corresponding to published versio