Stable marker-particle method for the Voronoi diagram in a flow field

The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.     

Geometric separation and exact solutions for the parameterized independent set problem on disk graphs

We consider the parameterized problem, whether for a given set  of n disks (of bounded radius ratio) in the Euclidean plane there exists a set of k non-intersecting disks. For this problem, we expose an algorithm running in time that is—to our knowledge—the first algorithm with running time bounded by an exponential with a sublinear exponent. For λ-precision disk graphs of bounded radius ratio, we show that the problem is fixed parameter tractable with a running time  . The results are based on problem kernelization and a new “geometric ( -separator) theorem” which holds for all disk graphs of bounded radius ratio. The presented algorithm then performs, in a first step, a “geometric problem kernelization” and, in a second step, uses divide-and-conquer based on our new “geometric separator theorem.”     

Ab initio calculations of small hydrides including electron correlation

Five different structures of CH₅ ⁺ and one structure of CH₅ ^– are calculated using a gaussian basis both in the SCF approximation and with the inclusion of electron correlation in the independent electron pair approximation (IEPA). While on SCF level the C _sstructure of CH₅ ⁺ has to lowest energy, the energy difference between the C _sand C _2vstructures becomes negligible if correlation is included. In contrast to this the approach of a proton to CH₄ at large and intermediate distances is most favorable towards a corner of the CH₄ tetrahedron which means a structure. The decomposition of CH₅ ⁺ into CH₃ ⁺ and H₂ requires 20kcal/mol on SCF level and 40 kcal/mol if correlation is included.     

On the population monotonicity of independent set games

An independent set game is a cooperative game dealing with profit sharing in the maximum independent set problem. A population monotonic allocation scheme is a rule specifying how to share the profit of each coalition among its participants such that every participant is better off when the coalition expands. In this paper, we provide a necessary and sufficient characterization for independent set games admitting population monotonic allocation schemes. Moreover, our characterization can be verified efficiently.     

Dual-modality and dual-energy gamma ray densitometry of petroleum products using an artificial neural network

The prediction of volume fractions in order to measure the multiphase flow rate is a very important issue and is the key parameter of multi-phase flow meters (MPFMs). Currently, the gamma ray attenuation technique is known as one of the most precise methods for obtaining volume fractions. The gamma ray attenuation technique is based on the mass attenuation coefficient, which is sensitive to density changes; density is sensitive in turn to temperature and pressure fluctuations. Therefore, MPFM efficiency depends strongly on environmental conditions. The conventional solution to this problem is the periodical recalibration of MPFMs, which is a demanding task. In this study, a method based on dual-modality densitometry and artificial intelligence (AI) is presented, which offers the advantage of the measurement of the oil–gas–water volume fractions independent of density changes. For this purpose, several experiments were carried out and used to validate simulated dual modality densitometry results. The reference density point was established at a temperature of 20 °C and pressure of 1 bar. To cover the full range of likely density fluctuations, four additional density sets were defined (at changes of ±4% and ±8% from the reference point). An annular regime with different percentages of oil, gas and water at different densities was simulated. Four features were extracted from the transmission and scattered detectors and were applied to the artificial neural network (ANN) as inputs. The input parameters included the ²⁴¹Am full energy peak, ¹³⁷Cs Compton edge, ¹³⁷Cs full energy peak and total scattered count, and the outputs were the oil and air percentages. A multi-layer perceptron (MLP) neural network was used to predict the volume fraction independent of the oil and water density changes. The obtained results show that the proposed ANN model achieved good agreement with the real data, with an estimated root mean square error (RMSE) of less than 3.     

Membrane lipids are both the substrates and a mechanistically responsive environment of TMEM16 scramblase proteins

Recent discoveries about functional mechanisms of proteins in the TMEM16 family of phospholipid scramblases have illuminated the dual role of the membrane as both the substrate and a mechanistically responsive environment in the wide range of physiological processes and genetic disorders in which they are implicated. This is highlighted in the review of recent findings from our collaborative investigations of molecular mechanisms of TMEM16 scramblases that emerged from iterative functional, structural, and computational experimentation. In the context of this review, we present new MD simulations and trajectory analyses motivated by the fact that new structural information about the TMEM16 scramblases is emerging from cryo-EM determinations in lipid nanodiscs. Because the functional environment of these proteins in in vivo and in in vitro is closer to flat membranes, we studied comparatively the responses of the membrane to the TMEM16 proteins in flat membranes and nanodiscs. We find that bilayer shapes in the nanodiscs are very different from those observed in the flat membrane systems, but the function-related slanting of the membrane observed at the nhTMEM16 boundary with the protein is similar in the nanodiscs and in the flat bilayers. This changes, however, in the bilayer composed of longer-tail lipids, which is thicker near the phospholipid translocation pathway, which may reflect an enhanced tendency of the long tails to penetrate the pathway and create, as shown previously, a nonconductive environment. These findings support the correspondence between the mechanistic involvement of the lipid environment in the flat membranes, and the nanodiscs. © 2019 Wiley Periodicals, Inc.     

Algorithms with high order convergence speed for blind source extraction

A rigorous convergence analysis for the fixed point ICA algorithm of Hyvärinen and Oja is provided and a generalization of it involving cumulants of an arbitrary order is presented. We consider a specific optimization problem OP(p), p>3, integer, arising from a Blind Source Extraction problem (BSE) and prove that every local maximum of OP(p) is a solution of (BSE) in sense that it extracts one source signal from a linear mixture of unknown statistically independent signals. An algorithm for solving OP(p) is constructed, which has a rate of convergence p?1.     

On the convergence of a class of algorithms using linearly independent search directions

Powell has shown that the cyclic coordinate method with exact searches may not converge to a stationary point. In this note we consider a more general class of algorithms for unconstrained minimization, and establish their convergence under the assumption that the objective function has a unique minimum along any line.     

Tychonoff expansions by independent families

A method for Tychonoff expansions using independent families is introduced. Using this method we prove that every countable Tychonoff space which admits a partition into infinitely many open-hereditarily irresolvable dense subspaces has a Tychonoff expansion that is -resolvable but not strongly extraresolvable. We also show that, under Luzin's Hypothesis ( ), there exists an -resolvable Tychonoff space of size which is not maximally resolvable.

     

On the independence complex of square grids

The enumeration of independent sets of regular graphs is of interest in statistical mechanics, as it corresponds to the solution of hard-particle models. In 2004, it was conjectured by Fendley et al., that for some rectangular grids, with toric boundary conditions, the alternating number of independent sets is extremely simple. More precisely, under a coprimality condition on the sides of the rectangle, the number of independent sets of even and odd cardinality always differ by 1. In physics terms, this means looking at the hard-particle model on these grids at activity −1. This conjecture was recently proved by Jonsson. Here we produce other families of grid graphs, with open or cylindric boundary conditions, for which similar properties hold without any size restriction: the number of independent sets of even and odd cardinality always differ by 0, ±1, or, in the cylindric case, by some power of 2. We show that these results reflect a stronger property of the independence complexes of our graphs. We determine the homotopy type of these complexes using Forman’s discrete Morse theory. We find that these complexes are either contractible, or homotopic to a sphere, or, in the cylindric case, to a wedge of spheres. Finally, we use our enumerative results to determine the spectra of certain transfer matrices describing the hard-particle model on our graphs at activity −1. These results parallel certain conjectures of Fendley et al., proved by Jonsson in the toric case.