Detection of multivariate outliers in business survey data with incomplete information

Many different methods for statistical data editing can be found in the literature but only few of them are based on robust estimates (for example such as BACON-EEM, epidemic algorithms (EA) and transformed rank correlation (TRC) methods of Béguin and Hulliger). However, we can show that outlier detection is only reasonable if robust methods are applied, because the classical estimates are themselves influenced by the outliers. Nevertheless, data editing is essential to check the multivariate data for possible data problems and it is not deterministic like the traditional micro editing where all records are extensively edited manually using certain rules/constraints. The presence of missing values is more a rule than an exception in business surveys and poses additional severe challenges to the outlier detection. First we review the available multivariate outlier detection methods which can cope with incomplete data. In a simulation study, where a subset of the Austrian Structural Business Statistics is simulated, we compare several approaches. Robust methods based on the Minimum Covariance Determinant (MCD) estimator, S-estimators and OGK-estimator as well as BACON-BEM provide the best results in finding the outliers and in providing a low false discovery rate. Many of the discussed methods are implemented in the R package ${\tt{rrcovNA}}$ which is available from the Comprehensive R Archive Network (CRAN) at http://www.CRAN.R-project.org under the GNU General Public License.     

Analytical Linear Inequality Systems and Optimization

In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometrical information on the feasible set of these problems can be obtained directly from the given coefficient functions. One of these geometrical properties gives rise to a general purification scheme for linear semi-infinite programs equipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition class between polyhedral convex sets and closed convex sets in the Euclidean space of the unknowns.     

Motzkin predecomposable sets

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family.     

Electric light scattering from single-stranded DNA in linear polyacrylamide solutions

The electric light scattering (ELS) of ssDNA (calf thymus, 10 kbp, 55 micrograms/mL) in denaturing polyacrylamide (PAA) solutions was studied as a function of applied sinusoidal electric field and polymer concentration. Electric fields of strengths up to 300 V/cm and of frequencies between 100 and 5000 Hz were applied. It was found that the ELS effect increases with the field strength and decreases at high frequencies. The dependence of the ELS effect of ssDNA on polymer concentration passes through a maximum at 1% PAA. The relaxation times of decay of the ELS effect increase with increasing polymer concentrations. It was demonstrated that ELS is a useful method for investigation of ssDNA behavior in the course of pulse-field electrophoresis in polymer solutions.     

Energy isosbestic points in third-row transition metal alloys

The total electronic energies of the six electrons per atom (e per atom) alloys W, TaRe, HfOs, and YIr and the seven electrons per atom alloys Re, WOs, TaIr, HfPt, and YAu have been calculated in the local density approximation of density functional theory. When one considers common alloy structures such as atomically ordered variants of the body-centered cubic, face-centered cubic, or hexagonally closest packed structures and plots the total electronic energy as a function of the unit cell parameter, one finds for both the six and seven electrons per atom series energetic isosbestic points. An energetic isosbestic point corresponds to a critical value of the size parameter for which all members of the 6 or 7 e per atom series of compounds have nearly identical total electronic energy. Just as in spectroscopy, where the existence of such isosbestic points is the hallmark of two compounds present in the mixture, an energy isosbestic point implies there are just two separate energy curves. For both series it is found that the total electronic energy can be viewed as the weighted sum of a purely covalent term and a purely ionic term. Two semi-quantitative models are proposed to account for these two separate energies. In the first model the total energy is viewed as the sum of the elemental structural energy plus an ionic energy based on the Born-Mayer ionic model. In the second model one considers within the confines of mu2-Hückel theory the evolution of the total electronic energy as the Coulombic Hii integrals change in value.     

Influence of pH of the BSA solutions on velocity of the rising bubbles and stability of the thin liquid films and foams

Influence of pH of the BSA solutions on velocity of the rising bubbles, stability of foams, and properties of single foam and wetting films was studied. It was found that the solution pH affected significantly the BSA surface activity and properties of the protein adsorption layer under dynamic and static conditions. At pH close to the isoelectric point (pH_IEP=4.8) the BSA showed the highest surface activity. The equilibrium microscopic foam films of thicknesses of 64–80 nm, depending on the BSA concentration, were obtained at pH=5.8. Under dynamic conditions the bubble rising velocity was reduced in a highest degree and the foam formed were most stable at the solutions pH-5.8 and 4.8. Lowering the bubble velocity shows that the BSA adsorption layer was formed, which retarded fluidity of the bubble surface. When the solution pH was significantly lower (pH=3.9) or much higher (pH=10) than the pH_IEP then the BSA practically had no influence on the bubble velocity and the foam stability was drastically reduced. Moreover, the pH variations affected also the time of the three-phase contact (TPC) formation on mica surface covered by the BSA adsorption layers. These pH dependent changes in the BSA surface activity indicate that the BSA linear conformers, existing at pH far away from the pH_IEP, have much higher affinity to aqueous phase resulting from higher net electrical charge present over the extended BSA molecule conformers.     

Ligand-protein docking using a quantum stochastic tunneling optimization method

A novel hybrid optimization method called quantum stochastic tunneling has been recently introduced. Here, we report its implementation within a new docking program called EasyDock and a validation with the CCDC/Astex data set of ligand-protein complexes using the PLP score to represent the ligand-protein potential energy surface and ScreenScore to score the ligand-protein binding energies. When taking the top energy-ranked ligand binding mode pose, we were able to predict the correct crystallographic ligand binding mode in up to 75% of the cases. By using this novel optimization method run times for typical docking simulations are significantly shortened.     

QUASI: a novel method for simultaneous superposition of multiple flexible ligands and virtual screening using partial similarity

The structure of many receptors is unknown, and only information about diverse ligands binding to them is available. A new method is presented for the superposition of such ligands, derivation of putative receptor site models and utilization of the models for screening of compound databases. In order to generate a receptor model, the similarity of all ligands is optimized simultaneously taking into account conformational flexibility and also the possibility that the ligands can bind to different regions of the site and only partially overlap. Ligand similarity is defined with respect to a receptor site model serving as a common reference frame. The receptor model is dynamic and coevolves with the ligand alignment until an optimal self-consistent superposition is achieved. When ligand conformational flexibility is permitted, different superposition models are possible and consistent with the data. Clustering of the superposition solutions is used to obtain diverse models. When the models are used to screen a database of compounds, high enrichments are obtained, comparable to those obtained in docking studies.