Variational approximation for mixtures of linear mixed models

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare different mixture models using penalized log-likelihood criteria such as BIC.We propose fitting MLMMs with variational methods which can perform parameter estimation and model selection simultaneously. A variational approximation is described where the variational lower bound and parameter updates are in closed form, allowing fast evaluation. A new variational greedy algorithm is developed for model selection and learning of the mixture components. This approach allows an automatic initialization of the algorithm and returns a plausible number of mixture components automatically. In cases of weak identifiability of certain model parameters, we use hierarchical centering to reparametrize the model and show empirically that there is a gain in efficiency by variational algorithms similar to that in MCMC algorithms. Related to this, we prove that the approximate rate of convergence of variational algorithms by Gaussian approximation is equal to that of the corresponding Gibbs sampler which suggests that reparametrizations can lead to improved convergence in variational algorithms as well.Comment: 36 pages, 5 figures, 2 tables, submitted to JCG

DNA Interaction with Palladium Chelates of Biogenic Polyamines Using Atomic Force Microscopy and Voltammetric Characterization

The interaction of double-stranded DNA with two polynuclear Pd(II) chelates with the biogenic polyamines spermidine (Spd) and spermine (Spm), Pd(II)-Spd and Pd(II)-Spm, as well as with the free ligands Spd and Spm, was studied using atomic force microscopy (AFM) at a highly oriented pyrolytic graphite (HOPG) surface, voltammetry at a glassy carbon (GC) electrode, and gel electrophoresis. The AFM and voltammetric results showed that the interaction of Spd and Spm with DNA occurred even for a low concentration of polyamines and caused no oxidative damage to DNA. The Pd(II)-Spd and Pd(II)-Spm complexes were found to induce greater morphological changes in the dsDNA conformation, when compared with their ligands. The interaction was specific, inducing distortion and local denaturation of the B-DNA structure with release of some guanine bases. The DNA strands partially opened give rise to palladium intra- and interstrand cross-links, leading to the formation of DNA adducts and aggregates, particularly in the case of the Pd(II)-Spd complex

Analytic Controllability of Time-Dependent Quantum Control Systems

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrodinger equation may be expressed globally in exponential form. The issue of controllability then naturally focuses on the ability to steer the quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert space -- and thus on analytic controllability. A relatively straightforward strategy allows the extension of Lie-algebraic conditions for strong analytic controllability derived earlier for the simpler, time-independent system in which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic time dependence. Enlarging the state space by one dimension corresponding to the time variable, we construct an augmented control system that can be treated as time-independent. Methods developed by Kunita can then be implemented to establish controllability conditions for the one-dimension-reduced system defined by the original time-dependent Schrodinger control problem. The applicability of the resulting theorem is illustrated with selected examples.Comment: 13 page

Some Aspects of Latent Structure Analysis

Latent structure models involve real, potentially observable variables and latent, unobservable variables. The framework includes various particular types of model, such as factor analysis, latent class analysis, latent trait analysis, latent profile models, mixtures of factor analysers, state-space models and others. The simplest scenario, of a single discrete latent variable, includes finite mixture models, hidden Markov chain models and hidden Markov random field models. The paper gives a brief tutorial of the application of maximum likelihood and Bayesian approaches to the estimation of parameters within these models, emphasising especially the fact that computational complexity varies greatly among the different scenarios. In the case of a single discrete latent variable, the issue of assessing its cardinality is discussed. Techniques such as the EM algorithm, Markov chain Monte Carlo methods and variational approximations are mentioned

Polynuclear palladium complexes with biogenic polyamines: AFM and voltammetric characterization

Polynuclear Pd(II) complexes with biogenic polyamines present great potential clinical importance, due to their antiproliferative and cytotoxic activity coupled to less severe side-effects. The adsorption process and the redox behaviour of two polynuclear palladium chelates with spermine (Spm) and spermidine (Spd), Pd(II)-Spm and Pd(II)-Spd, as well as of their ligands Spm and Spd, were studied using atomic force microscopy (AFM) and voltammetry at highly oriented pyrolytic graphite and glassy carbon electrodes. AFM revealed different adsorption patterns and degree of surface coverage, correlated with the chelate structure, concentration of the solution, applied potential and voltammetric behaviour of the Spm, Spd, Pd(II)-Spm and Pd(II)-Spd systems. The voltammetric study of Spm and Spd showed that these biogenic polyamines undergo an irreversible and pH-dependent oxidation. In acid medium the polyamines are fully protonated, rendering their oxidation more difficult. With increasing pH the oxidation potential for both Spm and Spd is shifted to less positive values, indicating a greater ease of oxidation in alkaline medium. The Pd(II)-Spm and Pd(II)-Spd complexes dissociate at high negative or high positive potentials. The application of a positive potential induced the oxidation of these Pd complexes and the formation of mixed layers of palladium oxides, Spm/Spd and Pd(II)-Spm/Pd(II)-Spd

DNA Interaction with Palladium Chelates of Biogenic Polyamines Using Atomic Force Microscopy and Voltammetric Characterization

The interaction of double-stranded DNA with two polynuclear Pd(II) chelates with the biogenic polyamines spermidine (Spd) and spermine (Spm), Pd(II)-Spd and Pd(II)-Spm, as well as with the free ligands Spd and Spm, was studied using atomic force microscopy (AFM) at a highly oriented pyrolytic graphite (HOPG) surface, voltammetry at a glassy carbon (GC) electrode, and gel electrophoresis. The AFM and voltammetric results showed that the interaction of Spd and Spm with DNA occurred even for a low concentration of polyamines and caused no oxidative damage to DNA. The Pd(II)-Spd and Pd(II)-Spm complexes were found to induce greater morphological changes in the dsDNA conformation, when compared with their ligands. The interaction was specific, inducing distortion and local denaturation of the B-DNA structure with release of some guanine bases. The DNA strands partially opened give rise to palladium intra- and interstrand cross-links, leading to the formation of DNA adducts and aggregates, particularly in the case of the Pd(II)-Spd complex