Variational Message Passing and Local Constraint Manipulation in Factor Graphs

Accurate evaluation of Bayesian model evidence for a given data set is a fundamental problem in model development. Since evidence evaluations are usually intractable, in practice variational free energy (VFE) minimization provides an attractive alternative, as the VFE is an upper bound on negative model log-evidence (NLE). In order to improve tractability of the VFE, it is common to manipulate the constraints in the search space for the posterior distribution of the latent variables. Unfortunately, constraint manipulation may also lead to a less accurate estimate of the NLE. Thus, constraint manipulation implies an engineering trade-off between tractability and accuracy of model evidence estimation. In this paper, we develop a unifying account of constraint manipulation for variational inference in models that can be represented by a (Forney-style) factor graph, for which we identify the Bethe Free Energy as an approximation to the VFE. We derive well-known message passing algorithms from first principles, as the result of minimizing the constrained Bethe Free Energy (BFE). The proposed method supports evaluation of the BFE in factor graphs for model scoring and development of new message passing-based inference algorithms that potentially improve evidence estimation accuracy.     

Controlled thermoreversible transfer of poly(oxazoline) micelles between an ionic liquid and water

Poly(2-nonyl-2-oxazoline-block-2-ethyl-2-oxazoline) block copolymer micelles were investigated as an alternative system to the approach proposed by He and Lodge (Y. He and T. P. Lodge, J. Am. Chem. Soc., 2006, 128, 12666) for the thermoreversible transfer of micelles between a hydrophobic ionic liquid phase and an aqueous phase; this work describes the possibility of thermally triggering and controlling this process.     

Choline saccharinate and choline acesulfamate: ionic liquids with low toxicities

Choline saccharinate and choline acesulfamate are two examples of hydrophilic ionic liquids, which can be prepared from easily available starting materials (choline chloride and a non-nutritive sweetener). The (eco)toxicity of these ionic liquids in aqueous solution is very low in comparison to other types of ionic liquids. A general method for the synthesis and purification of hydrophilic ionic liquids is presented. The method consists of a silver-free metathesis reaction, followed by purification of the ionic liquid by ion-exchange chromatography. The crystal structures show a marked difference in hydrogen bonding between the two ionic liquids, although the saccharinate and the acesulfamate anions show structural similarities. The optimized structures, the energetics, and the charge distribution of cation-anion pairs in the ionic liquids were studied by density functional theory (DFT) and second-order (M?ller-Plesset) perturbation theory calculations. The occupation of the non-Lewis orbitals was considered to obtain a qualitative picture of the Lewis structures. The calculated interaction energies and the dipole moments for the ion pairs in the gas phase were discussed.     

Dynamically controlled dielectrophoresis using resonant tuning

Electrically polarizable micro- and nanoparticles and droplets can be trapped using the gradient electric field of electrodes. But the spatial profile of the resultant dielectrophoretic force is fixed once the electrode structure is defined. To change the force profile, entire complex lab-on-a-chip systems must be re-fabricated with modified electrode structures. To overcome this problem, we propose an approach for the dynamic control of the spatial profile of the dielectrophoretic force by interfacing the trap electrodes with a resistor and an inductor to form a resonant resistor–inductor–capacitor (RLC) circuit. Using a dielectrophoretically trapped water droplet suspended in silicone oil, we show that the resonator amplitude, detuning, and linewidth can be continuously varied by changing the supply voltage, supply frequency, and the circuit resistance to obtain the desired trap depth, range, and stiffness. We show that by proper tuning of the resonator, the trap range can be extended without increasing the supply voltage, thus preventing sensitive samples from exposure to high electric fields at the stable trapping position. Such unprecedented dynamic control of dielectrophoretic forces opens avenues for the tunable active manipulation of sensitive biological and biochemical specimen in droplet microfluidic devices used for single-cell and biochemical reaction analysis.     

Synthesis,characterization, and cross‐linking of a library of statistical copolymers based on 2‐“soy alkyl”‐2‐oxazoline and 2‐ethyl‐2‐oxazoline

The synthesis of statistical copolymers consisting of 2‐ethyl‐2‐oxazoline (EtOx) and 2‐“soy alkyl”‐2‐oxazoline (SoyOx) via a microwave‐assisted cationic ring‐opening polymerization procedure is described. The majority of the resulting copolymers revealed polydispersity indices below 1.30. The reactivity ratios (r_EtOx 1.4 ± 0.3; r_SoyOx = 1.7 ± 0.3) revealed a clustered monomer distribution throughout the polymer chains. The thermal and surface properties of the pEtOx‐stat‐SoyOx copolymers were analyzed before and after UV‐curing demonstrating the decreased chain mobility after cross‐linking. In addition, the cross‐linked materials showed shape‐persistent swelling upon absorption of water from the air, whereby as little as 5 mol % SoyOx was found to provide efficient cross‐linking. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5371,–5379, 2007