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

Polymer and Fock representations for a Scalar field

In loop quantum gravity, matter fields can have support only on the `polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilbert spaces. Second, to make contact with low energy physics, one has to relate this `polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.Comment: 13 pages, no figure

Electrodynamics of balanced charges

In this work we modify the wave-corpuscle mechanics for elementary charges introduced by us recently. This modification is designed to better describe electromagnetic (EM) phenomena at atomic scales. It includes a modification of the concept of the classical EM field and a new model for the elementary charge which we call a balanced charge (b-charge). A b-charge does not interact with itself electromagnetically, and every b-charge possesses its own elementary EM field. The EM energy is naturally partitioned as the interaction energy between pairs of different b-charges. We construct EM theory of b-charges (BEM) based on a relativistic Lagrangian with the following properties: (i) b-charges interact only through their elementary EM potentials and fields; (ii) the field equations for the elementary EM fields are exactly the Maxwell equations with proper currents; (iii) a free charge moves uniformly preserving up to the Lorentz contraction its shape; (iv) the Newton equations with the Lorentz forces hold approximately when charges are well separated and move with non-relativistic velocities. The BEM theory can be characterized as neoclassical one which covers the macroscopic as well as the atomic spatial scales, it describes EM phenomena at atomic scale differently than the classical EM theory. It yields in macroscopic regimes the Newton equations with Lorentz forces for centers of well separated charges moving with nonrelativistic velocities. Applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the same for the Schrodinger model with any desired accuracy.Comment: Manuscript was edited to improve the exposition and to remove noticed typo

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

On the computation of black hole entropy in loop quantum gravity

We discuss some issues related to the computation of black hole entropy in loop quantum gravity from the novel point of view provided by the recent number-theoretical methods introduced by the authors and their collaborators. In particular we give exact expressions, in the form of integral transforms, for the black hole entropy in terms of the area. We do this by following several approaches based both on our combinatorial techniques and also on functional equations similar to those employed by Meissner in his pioneering work on this subject. To put our results in perspective we compare them with those of Meissner. We will show how our methods confirm some of his findings, extend the validity of others, and correct some mistakes. At the end of the paper we will discuss the delicate issue of the asymptotics of black hole entropy.Comment: 25 page

The variational Bayesian approach to fitting mixture models to circular wave direction data

The emerging variational Bayesian (VB) technique for approximate Bayesian statistical inference is a nonsimulation- based and time-efficient approach. It provides a useful, practical alternative to other Bayesian statistical approaches such as Markov chain Monte Carlo–based techniques, particularly for applications involving large datasets. This article reviews the increasingly popular VB statistical approach and illustrates how it can be used to fit Gaussian mixture models to circular wave direction data. This is done by taking the straightforward approach of padding the data; this method involves adding a repeat of a complete cycle of the data to the existing dataset to obtain a dataset on the real line. The padded dataset can then be analyzed using the standard VB technique. This results in a practical, efficient approach that is also appropriate for modeling other types of circular, or directional, data such as wind direction

DNA of free-living bodonids (Euglenozoa: Kinetoplastea) in bat ectoparasites: potential relevance to the evolution of parasitic trypanosomatids

Kinetoplastids are flagellated protozoa, including principally free-living bodonids and exclusively parasitic trypanosomatids. In the most species-rich genus, Trypanosoma, more than thirty species were found to infect bats worldwide. Bat trypanosomes are also known to have played a significant role in the evolution of T. cruzi, a species with high veterinary medical significance. Although preliminary data attested the occurrence of bat trypanosomes in Hungary, these were never sought for with molecular methods. Therefore, amplification of an approx. 900-bp fragment of the 18S rRNA gene of kinetoplastids was attempted from 307 ixodid and 299 argasid ticks collected from bats, and from 207 cimicid bugs collected from or near bats in Hungary and Romania. Three samples, one per each bat ectoparasite group, were PCR positive. Sequencing revealed the presence of DNA from free-living bodonids (Bodo saltans and neobodonids), but no trypanosomes were detected. The most likely source of bodonid DNA detected here in engorged bat ectoparasites is the blood of their bat hosts. However, how bodonids were acquired by bats, can only be speculated. Bats are known to drink from freshwater bodies, i.e. the natural habitats of B. saltans and related species, allowing bats to ingest bodonids. Consequently, these results suggest that at least the DNA of bodonids might pass through the alimentary mucosa of bats into their circulation. The above findings highlight the importance of studying bats and other mammals for the occurrence of bodonids in their blood and excreta, with potential relevance to the evolution of free-living kinetoplastids towards parasitism