Pseudo-orthogonality for graph 1-Laplacian eigenvectors and applications to higher Cheeger constants and data clustering

The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data. This is an NP-hard problem that can be relaxed in the spectral graph theory, where the optimal cuts of a graph are related to the eigenvalues of graph 1-Laplacian. In this paper, we first give new notations to describe the paths, among critical eigenvectors of the graph 1-Laplacian, realizing sets with prescribed genus. We introduce the pseudo-orthogonality to characterize m₃(G), a special eigenvalue for the graph 1-Laplacian. Furthermore, we use it to give an upper bound for the third graph Cheeger constant h₃(G), that is, h₃(G) 6 m₃(G). This is a first step for proving that the k-th Cheeger constant is the minimum of the 1-Laplacian Raylegh quotient among vectors that are pseudo-orthogonal to the vectors realizing the previous k - 1 Cheeger constants. Eventually, we apply these results to give a method and a numerical algorithm to compute m₃(G), based on a generalized inverse power method.     

Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems

We consider quantum unbounded spin systems (lattice boson systems) in -dimensional lattice space Z. Under appropriate conditions on the interactions we prove that in a region of high temperatures the Gibbs state is unique, is translationally invariant, and has clustering properties. The main methods we use are the Wiener integral representation, the cluster expansions for zero boundary conditions and for general Gibbs state, and explicitly -dependent probability estimates. For one-dimensional systems we show the uniqueness of Gibbs states for any value of temperature by using the method of perturbed states. We also consider classical unbounded spin systems. We derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case.     

The measurement of high proton affinities for a variety of metallic compounds: a new approach by flame-ion mass spectrometry

A small amount (≤ 10⁻⁶ mol fraction) of four alkaline earth metals, tin and yttrium were introduced into five, premixed, fuel-rich, H₂–O₂–N₂ flames at atmospheric pressure in the temperature range 1820–2400 K. Aqueous salt solutions of the metals were sprayed into the premixed flame gas as an aerosol using an atomizer technique. Ions in a flame were observed by sampling flame gas through a nozzle into a mass spectrometer. The concentrations of the major neutral metallic species present in the flame were calculated from thermodynamic data currently available. The principal metallic ions observed were AOH⁺ (A = Mg, Ca, Sr, Ba, Sn) and A(OH)₂⁺ (A = Y), formed initially by proton transfer to AO and OAOH from H₃O⁺, a natural flame ion. Except for Mg, the ions were also produced by chemi-ionization processes. By adjusting the concentration(s) of the salt solution in the atomizer, it was found that a pair of ions could be brought into equilibrium within the time scale of the flame; the pairs included H₃O⁺ with a metal ion or two metallic ions. Because water is a major product of combustion, a very large difference in proton affinity PA⁰(AO) − PA⁰(H₂O) ≤ 490 kJ mol⁻¹ (117 kcal mol⁻¹) could be attempted for the proton transfer equilibrium. Using PA⁰(H₂O) = 691.0 kJ mol⁻¹ (165.2 kcal mol⁻¹) as a reference base to anchor the proton affinity scale, ion ratio measurements led to proton affinity PA⁰ values of 766, 912, 1004, 1184, 1201, and 1222 kJ mol⁻¹ (183, 218, 240, 283, 287, and 292 kcal mol⁻¹) corrected to 298 K for OYOH, SnO, MgO, CaO, SrO, and BaO, respectively; of these, only the value for OYOH has not been reported previously. If it is assumed that the neutral thermodynamic data are correct (although some appear to be in error), the uncertainties in the PA results reported here are ± 21 kJ mol⁻¹ (5 kcal mol⁻¹). The realization that these equilibria can be achieved in flames provides a new approach to consolidate and build the high end of the proton affinity ladder, primarily of metallic species which are not accessible at lower temperatures.     

Activation of trisacryl gels with chloroformates and their use for affinity chromatography and protein immobilization

In this study we describe the activation with chloroformates of Trisacryl-GF-2000, a new synthetic gel support that is stable, hydrophilic, and contains large amounts of hydroxyl groups available for activation. Of all the reagents tested, the activation withN-hydroxysuccinimide-chloroformate andp-nitrophenylchloroformate in organic solvents provides the best activation yield and subsequent coupling. When Trisacryl was activated in acetone with the chloroformates in the presence of 4-dimethylaminopyridine as base and catalyst, up to 30% of the hydroxyl groups, (i.e., 1/repeating unit) could be activated. Amino-containing ligands and proteins could be coupled to these carriers at pH 8 or higher. For better results in affinitychromatographic applications, spacers of ε-amino caproic acid or diaminohexane were introduced. The efficacy of these columns was demonstrated by purification of enzymes, antibodies, and antigens. The performance of these new columns were compared with that of Sepharose columns activated in various ways. In every case, the properties of the Trisacryl support proved superior with particular reference to the purity of the product obtained.     

Aqueous-phase ion solvation and the selectivity of anion exchange resins for monovalent ions

This research examines and quantifies the influence of ion solvation parameters on the affinity of monovalent anions for strong-base anion resins. A data set comprising resin selectivity coefficients and solvation parameters from the literature is statistically analyzed using correlation and multiple regression techniques. The affinity of monovalent anions for the resin phase correlated well to ionic radii. Solvation parameters such as the hydration number, and entropy, enthalpy and free energy of hydration are also strongly correlated to selectivity. Using the stepwise regression procedure on subsets of independent variables, the entropy of hydration, which characterizes the structure-influencing nature of ions in solution, is incorporated as the sole parameter in the predictive model for resin selectivity. The data are best correlated by the exponential form of the regression equation, and the physical meaning of the correlation is shown to be reasonable. A simple rule for categorizing ions as structure-makers and structure-breakers is proposed, and the results are consistent with conventional classifications.     

Dye-ligand chromatography for the resolution and purification of restriction endonucleases

The resolution of restriction endonucleases from the same microorganism is conventionally achieved by lengthy fractionation protocols. We now report effective single-step procedures that exploit dye-ligand chromatography for the resolution and purification of restriction enzymes. After suitable initial screening, we demonstrated that resolution of two restriction activites can be achieved in one chromatographic step, and further purification can subsequently be effected using selected dye-adsorbents. Accordingly, we resolved in one step, Hpa I from Hpa II, Hind II from Hind III, and Sac I from Sac II. Furthermore, a three-step Chromatographic procedure has been developed to purify EcoRV suitable for commercial exploitation, as judged by the “overdigestion” and “cut-ligate-recut” quality control tests.     

8-羟基喹啉-硅胶介质的合成及其在海水中痕量铅检测的应用

详细研究了以大孔硅胶为基质,一步合成8羟-基喹啉(8-HQ)型金属螯合色谱填料的方法,采用正交试验对合成方法进行了优化。与传统合成方法所得的填料进行了比较,从理化指标等方面来看,新的合成方法为佳。将该法用作微柱流动注射(FIA)在线分离、富集和电感耦合等离子体质谱(ICP-MS)分析流程中的固定相,对大洋海水中的痕量铅进行了在线分析,得到了较满意的结果。     

The configurational dependence of binding free energies: A Poisson–Boltzmann study of Neuraminidase inhibitors

The linear finite difference Poisson-Boltzmann (FDPB) equation is applied to the calculation of the electrostatic binding free energies of a group of inhibitors to the Neuraminidase enzyme. An ensemble of enzyme-inhibitor complex conformations was generated using Monte Carlo simulations and the electrostatic binding free energies of subtly different configurations of the enzyme-inhibitor complexes were calculated. It was seen that the binding free energies calculated using FDPB depend strongly on the configuration of the complex taken from the ensemble. This configurational dependence was investigated in detail in the electrostatic hydration free energies of the inhibitors. Differences in hydration energies of up to 7 kcal mol^–1 were obtained for root mean square (RMS) structural deviations of only 0.5 Å. To verify the result, the grid size and parameter dependence of the calculated hydration free energies were systematically investigated. This showed that the absolute hydration free energies calculated using the FDPB equation were very sensitive to the values of key parameters, but that the configurational dependence of the free energies was independent of the parameters chosen. Thus just as molecular mechanics energies are very sensitive to configuration, and single-structure values are not typically used to score binding free energies, single FDPB energies should be treated with the same caution.     

Cooperative Competition Clustering for Gene Selection

Clustering analysis of data from DNA microarray hybridization studies is an essential task for identifying biologically relevant groups of genes. Attribute cluster algorithm (ACA) has provided an attractive way to group and select meaningful genes. However, ACA needs much prior knowledge about the genes to set the number of clusters. In practical applications, if the number of clusters is misspecified, the performance of the ACA will deteriorate rapidly. We propose the Cooperative Competition Cluster Algorithm (CCCA) in this paper. In the algorithm, we assume that both cooperation and competition exist simultaneously between clusters in the process of clustering. By using this principle of Cooperative Competition, the number of clusters can be found in the process of clustering. Experimental results on a synthetic and gene expression data are demonstrated. The results show that CCCA can choose the number of clusters automatically and get excellent performance with respect to other competing methods.     

On the theoretical determination of the electron affinity of ozone

Summary Multiconfigurational electron correlation methods have been analyzed in order to theoretically compute the electron affinity (EA) of ozone. The near-degeneracy correlation effects, which are so important in O₃ and O ₃ ^– , have been described using complete active space (CAS) SCF wave functions. Remaining dynamic correlation effects are computed using second-order perturbation theory (the CASPT2 method). The best calculated adiabatic value (including zero-point energy corrections), 2.19 eV, is about 0.09 eV larger than the experimental value. Comparative studies using size-consistent coupled pair functional approaches (CPF and ACPF) have also been performed. The harmonic frequencies in O ₃ ^– have been determined to be: ₁=992, ₂=572, and ₃=879 cm^–1, which gives a zero-point energy of 0.151 eV.