Maximum Margin Classifiers with Specified False Positive and False Negative Error Rates

This paper addresses the problem of maximum margin classification given the moments of class conditional densities and the false positive and false negative error rates. Using Chebyshev inequalities, the problem can be posed as a second order cone programming problem. The dual of the formulation leads to a geometric optimization problem, that of computing the distance between two ellipsoids, which is solved by an iterative algorithm. The formulation is extended to non-linear classifiers using kernel methods. The resultant classifiers are applied to the case of classification of unbalanced datasets with asymmetric costs for misclassification. Experimental results on benchmark datasets show the efficacy of the proposed method.

A Fast Linear Separability Test by Projection of Positive Points on Subspaces

A geometric and non parametric procedure for testing if two finite set of points are linearly separable is proposed. The Linear Separability Test is equivalent to a test that determines if a strictly positive point h > 0 exists in the range of a matrix A (related to the points in the two finite sets). The algorithm proposed in the paper iteratively checks if a strictly positive point exists in a subspace by projecting a strictly positive vector with equal co-ordinates (p), on the subspace. At the end of each iteration, the subspace is reduced to a lower dimensional subspace. The test is completed within r ≤ min(n, d + 1) steps, for both linearly separable and non separable problems (r is the rank of A, n is the number of points and d is the dimension of the space containing the points). The worst case time complexity of the algorithm is O(nr3) and space complexity of the algorithm is O(nd). A small review of some of the prominent algorithms and their time complexities is included. The worst case computational complexity of our algorithm is lower than the worst case computational complexity of Simplex, Perceptron, Support Vector Machine and Convex Hull Algorithms, if d

Analytical Solution of Joule-Heating Equation for Metallic Single-Walled Carbon Nanotube Interconnects

In this paper, we address a closed-form analytical solution of the Joule-heating equation for metallic single-walled carbon nanotubes (SWCNTs). Temperature-dependent thermal conductivity kappa has been considered on the basis of second-order three-phonon Umklapp, mass difference, and boundary scattering phenomena. It is found that kappa, in case of pure SWCNT, leads to a low rising in the temperature profile along the via length. However, in an impure SWCNT, kappa reduces due to the presence of mass difference scattering, which significantly elevates the temperature. With an increase in impurity, there is a significant shift of the hot spot location toward the higher temperature end point contact. Our analytical model, as presented in this study, agrees well with the numerical solution and can be treated as a method for obtaining an accurate analysis of the temperature profile along the CNT-based interconnects.

Docking and free energy simulations to predict conformational domains involved in hCG-LH receptor interactions using recombinant antibodies

Single chain fragment variables (ScFvs) have been extensively employed in studying the protein-protein interactions. ScFvs derived from phage display libraries have an additional advantage of being generated against a native antigen, circumventing loss of information on conformational epitopes. In the present study, an attempt has been made to elucidate human chorionic gonadotropin (hCG)-luteinizing hormone (LH) receptor interactions by using a neutral and two inhibitory ScFvs against hCG. The objective was to dock a computationally derived model of these ScFvs onto the crystal structure of hCG and understand the differential roles of the mapped epitopes in hCG-LH receptor interactions. An anti-hCG ScFv, whose epitope was mapped previously using biochemical tools, served as the positive control for assessing the quality of docking analysis. To evaluate the role of specific side chains at the hCG-ScFv interface, binding free energy as well as residue interaction energies of complexes in solution were calculated using molecular mechanics Poisson-Boltzmann/surface area method after performing the molecular dynamic simulations on the selected hCG-ScFv models and validated using biochemical and SPR analysis. The robustness of these calculations was demonstrated by comparing the theoretically determined binding energies with the experimentally obtained kinetic parameters for hCG-ScFv complexes. Superimposition of hCG-ScFv model onto a model of hCG complexed with the 51-266 residues of LH receptor revealed importance of the residues previously thought to be unimportant for hormone binding and response. This analysis provides an alternate tool for understanding the structure-function analysis of ligand-receptor interactions. Proteins 2011;79:3108-3122. (C) 2011 Wiley-Liss, Inc.

Activities in the spinel solid solution, phase equilibria and thermodynamic properties of ternary phases in the system Cu Fe O

A review of the structural and thermodynamic information and phase equilibria in the Cu-Fe-O system suggested that a consistent, quantitative description of the system is hampered by lack of data on activities in the spinel solid solution CuFe2O4-Fe3O4. Therefore the activity of Fe3O4 in this solid solution is derived from measurements of the oxygen potentials established at 1000°C by mixtures containing Fe2O3 and spinel solid solutions of known composition. The oxygen pressures were measured manometrically for solid solutions rich in CuFe2O4, while for Fe3O4-rich compositions the oxygen potentials were obtained by an emf technique. The activities show significant negative deviations from Raoult’s law. The compositions of the spinel solid solutions in equilibrium with CuO + CuFeO2 and Cu + CuFeO2 were obtained from chemical analysis of the solid solution after magnetic separation. The oxygen potential of the three-phase mixture Cu + CuFeO2 + Fe3O4(spinel s.s.) was determined by a solid oxide galvanic cell. From these measurements a complete phase diagram and consistent thermodynamic data on the ternary condensed phases, CuFeO2 and CuFeO2O4, were obtained. An analysis of the free energy of mixing of the spinel solid solution furnished information on the distribution of cations and their valencies between the tetrahedral and octahedral sites of the spinel lattice, which is consistent with X-ray diffraction, magnetic and Seebeck coefficient measurements.

Electrochemical determination of activities in Cr2O3 Al2O3 solid solutions

The activity of Cr20~ in Cr20~-A12Oa solid solution has been determined in the temperature range 800~176 from electromotive force measurements on the solid oxide galvanic cell Pt,Cr + Cr2OJY~O~-ThO2/Cr + Cr~A12-xO~,Pt The activities of Cr203 and A120~ in the solid solution show both positive and negative deviations from Raoult's law. The heat and entropy of mixing of the solid Solution obtained from the temperature dependence of the emf can be expressed as AH = XCr203XA1203 [31,700Xcrzo3 -}- 37,470XA1203] J mole -I hS = -- 1.8R [Xcr2o3 In Xcr2o3 + XA12o3 In XAaos]The entropy of mixing is 10% lower than that predicted by the Temkin model.The large positive heat of mixing in the Cr2Os-A12Oa solid solution, however, suggests that this apparent: entropy discrepancy originates with the clustering of positive ions on the cation sublattice. The asymmetric miscibility gap exhibited in the CrzOa-A12Oa system below 900~ is consistent with the thermodynamic data trends recorded at the more elevated temperatures.

Thermodynamic properties of Fe3O4 FeAl2O4 spinel solid solution

The Gibbs energy of mixing for the system Fe3O4-FeAl2O4 was determined at 1573 K using a gas-metal-oxide equilibration technique. Oxide solid solution samples were equilibrated with Pt foils under controlled CO+CO2 gas streams. The equilibrium iron concentration in the foil was determined by chemical analysis. The cation distribution between tetrahedral and octahedral sites in the spinel crystal can be calculated from site-preference energies and used as an alternate method of determining some thermodynamic properties, including the Gibbs energy of mixing. The solvus occurring at low temperatures in the system Fe3C4-FeAl2C4 was used to derive the effect of lattice distortion due to cation size difference on the enthalpy of mixing and to obtain a better approximation to the measured thermodynamic quantities.

Phase relations and activities in the Co Ni O system at 1373 K

The tie-lines delineating equilibria between CoO-NiO and Co-Ni solid solutions in the ternary Co-Ni-O system at 1373 K have been determined by electron microprobe andedax point count analysis of the oxide phase equilibrated with the alloy. The oxygen potentials corresponding to the tie-line compositions have been measured using a solid oxide galvanic cell with calcia-stabilized zirconia electrolyte and Ni + NiO reference electrode. Activities in the metallic and oxide solid solution have been derived using a new Gibbs-Duhem integration technique. Both phases exhibit small positive deviations from ideality; the values ofG E/X 1 X 2 are 2640 J mol−1 for the metallic phase and 2870 J mol−1 for the oxide solid solution.

Application of composition gradient solid electrolytes in sensors and thermodynamic measurements

New compos~tiong radient solid electrolytes are developed which have application in high temperature solid state galvanic sensors and provide a new tool for thermodynamic measurements. The electrolyte consists oi a solid solution between two ionic conductors with a common mobile ion and spatial variation in composition of otber coxup nents. Incorporation of the composite electrolyte in sensors permits the use oi dissimilar gas electrodes. It is demonsuated, both experimentall y and theoretically, that the composition gradient of the relativeiy immobile species does not give rise to a diffusion potential.The emi of a cell is determined by the activity of the mobile species at the two eiectrodes. The thermodynamic properties of solid solutions can be measured using the gradient solid electrolyte. The experimental stuay is based on model systems A?(COj)x(S04)l-x (A=Na,K),where S \.aria across the electrolyte. The functionally gradient solid electrolytes used for activity measurements consist of pure carbonate at one ena and the solid solution under stuav at the other. The identical vaiues of activity, obtained h m t hree different modes of operation of the ceil. indicate unit transport number for the ddi metal ion in the graciient electrolyte. Tlle activities in the solid solutions exhibit moderate positive deviations from Raoult 's law.

Thermodynamics and phase equilibria involving the spinel solid solution FexMg1-xCr2O4

Activities of FeCr2O4 in the spinel solid solutions Fe X Mg1−X Cr2O4 (0solution parameter Ω s =−2260 (±200) J/mol. The lattice parameter of the spinel solid solutions quenched from 1200 K was found to obey Vegard’s law. The phase relations in the FeO-MgO-Cr2O3 system have been deduced from the results obtained in this study together with other relevant thermodynamic data from the literature. The tie-lines between the solid solutions with rock salt and spinel structures represent the influence of intercrystalline ion exchange. The tie-lines are skewed toward the FeCr2O4 corner, primarily because of the higher stability of FeCr2O4 compared to MgCr2O4, with respect to their component binary oxides. The oxygen partial pressure corresponding to the two three-phase regions, Fe + Fe X Mg1−X Cr2O4 + Cr2O3 and Fe + Fe Y Mg1−Y O + Fe X Mg1−X Cr2O4, have been evaluated as a function of composition at 1200 K.

A thermodynamic study of liquid Cu-Cr alloys and metastable liquid immiscibility

he thermodynamic acitivity of chromium in liquid Cu-Cr alloys is measured in the temperature range from 1473 to 1873 K using the solid state cell: Pt, W, Cr + Cr2O3 |(Y2O3) ThO2|Cu - Cr + Cr2O3, Pt The activity of copper and the Gibbs energy of mixing of the liquid alloy are derived. Activities exhibit large positive deviations from Raoult's law. The mixing properties can be represented by a pseudo-subregular solution model in which the excess entropy has the same type of functional dependence on composition as the enthalpy of mixing: ΔGE = XCr(1 - XCr)[60880 - 18750 XCr)-- T(16.25 - 7.55 XCr)]J mol-1 Pure liquid Cu and Cr are taken as the reference states. The results predict a liquid-liquid metastable miscibility gap, with TC = 1787 (±3) K and XCr = 0.436 (±0.02), lying below the liquidus. The results obtained in this study are in general agreement with experimental information reported in the literature, but provide further refinement of the thermodynamic parameters.

Structure of the Pyridine-Chloranil Complex in Solution: A Surprise from Depolarized Hyper-Rayleigh Scattering Measurements

In this article, we report the structure of a 1:1 charge transfer complex between pyridine (PYR) and chloranil (CHL) in solution (CHCl(3)) from the measurement of hyperpolarizability (beta(HRS)) and linear and circular depolarization ratios, D and D', respectively, by the hyper-Rayleigh scattering technique and state-of-the-art quantum chemical calculations. Using linearly (electric field vector along X) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D = I(X,X)(2 omega)/I(X,Z)(2 omega) and D' = I(X,C)(2 omega)/I(Z,C)(2 omega) in the laboratory fixed XYZ frame by detecting the second harmonic (SH) scattered light in a polarization resolved fashion. The stabilization energy and the optical gap calculated through the MP2/cc-pVDZ method using Gaussian09 were not significantly different to distinguish between the cofacial and T-shape structures. Only when the experimentally obtained beta(HRS) and the depolarization ratios, D and D', were matched with the theoretically computed values from single and double configuration interaction (SDCI) calculations performed using the ZINDO-SCRF technique, we concluded that the room temperature equilibrium structure of the complex is cofacial. This is in sharp contrast to an earlier theoretical prediction of the T-shape structure of the complex.

Damping and synchronising torques contributed by a voltage regulator to a synchronous generator: a quantitative assessment

In the paper, the total damping and synchronising torques, which determine the dynamic stability of a synchronous generator in a power system, have been traced to their origin. The positive and negative components released or consumed by the voltage regulator, and by the various windings of the machine, have been isolated, with the object of making a quantitative assessment of the effects of various gains and time constants on the dynamic stability of a synchronous machine under different operating conditions. The analysis is based on the properties of quadratic invariance in tensor calculus. An alternative solution by network analysis has also been provided to establish the validity of the tensor approach.