Convergence Results for the EM Approach to Mixtures of Experts Architectures

The Expectation-Maximization (EM) algorithm is an iterative approach to maximum likelihood parameter estimation. Jordan and Jacobs (1993) recently proposed an EM algorithm for the mixture of experts architecture of Jacobs, Jordan, Nowlan and Hinton (1991) and the hierarchical mixture of experts architecture of Jordan and Jacobs (1992). They showed empirically that the EM algorithm for these architectures yields significantly faster convergence than gradient ascent. In the current paper we provide a theoretical analysis of this algorithm. We show that the algorithm can be regarded as a variable metric algorithm with its searching direction having a positive projection on the gradient of the log likelihood. We also analyze the convergence of the algorithm and provide an explicit expression for the convergence rate. In addition, we describe an acceleration technique that yields a significant speedup in simulation experiments.

Learning Fine Motion by Markov Mixtures of Experts

Compliant control is a standard method for performing fine manipulation tasks, like grasping and assembly, but it requires estimation of the state of contact between the robot arm and the objects involved. Here we present a method to learn a model of the movement from measured data. The method requires little or no prior knowledge and the resulting model explicitly estimates the state of contact. The current state of contact is viewed as the hidden state variable of a discrete HMM. The control dependent transition probabilities between states are modeled as parametrized functions of the measurement We show that their parameters can be estimated from measurements concurrently with the estimation of the parameters of the movement in each state of contact. The learning algorithm is a variant of the EM procedure. The E step is computed exactly; solving the M step exactly would require solving a set of coupled nonlinear algebraic equations in the parameters. Instead, gradient ascent is used to produce an increase in likelihood.

Rubisco small subunit, chlorophyll a/b-binding protein and sucrose : fructan-6-fructosyl transferase gene expression and sugar status in single barley leaf cells in situ. Cell type specificity and induction by light

Chungui Lu, Olga A. Koroleva, John F. Farrar, Joe Gallagher, Chris J. Pollock, and A. Deri Tomos (2002). Rubisco small subunit, chlorophyll a/b-binding protein and sucrose : fructan-6-fructosyl transferase gene expression and sugar status in single barley leaf cells in situ. Cell type specificity and induction by light. Plant Physiology, 130 (3) pp.1335-1348 Sponsorship: BBSRC RAE2008

Sugar matrices in stabilization of bioactives by dehydration

Development of functional foods with bioactive components requires component stability in foods and ingredients. Stabilization of sensitive bioactive components can be achieved by entrapment or encapsulation of these components in solid food matrices. Lactose or trehalose was used as the structure-forming material for the entrapment of hydrophilic ascorbic acid and thiamine hydrochloride or the encapsulation of oil particles containing hydrophobic α-tocopherol. In the delivery of hydrophobic components, milk protein isolate, soy protein isolate, or whey protein isolate were used as emulsifiers and, in some cases, applied in excess amount to form matrices together with sugars. Dehydrated amorphous structures with bioactives were produced by freezing and freeze-drying. Experimental results indicated that: (i) lactose and trehalose showed similar water sorption and glass transition but very different crystallization behavior as pure sugars; (ii) the glass transition of sugar-based systems was slightly affected by the presence of other components in anhydrous systems but followed closely that of sugar after water plasticization; (iii) sugar crystallization in mixture systems was composition-dependent; (iv) the stability of bioactives was better retained in the amorphous matrices, although small losses of stability were observed for hydrophilic components above glass transition and for hydrophobic components as a function of water activity; (v) sugar crystallization caused significant loss of hydrophilic bioactives as a result of the exclusion from the continuous crystalline phase; (vi) loss of hydrophobic bioactives upon sugar crystallization was a result of dramatic change of emulsion properties and the exclusion of oil particles from the protecting structure; (vii) the double layers at the hydrophilic-hydrophobic interfaces improved the stability of hydrophobic bioactives in dehydrated systems. The present study provides information on the physical and chemical stability of sugar-based dehydrated delivery systems, which could be helpful in designing foods and ingredients containing bioactive components with improved storage stability.

Dry mixing of spice powders - investigation of effect of powder properties on mixture quality of binary powder mixtures

Dry mixing of binary food powders was conducted in a 2L lab-scale paddle mixer. Different types of food powders such as paprika, oregano, black pepper, onion powder and salt were used for the studies. A novel method based on a digital colour imaging system (DCI) was developed to measure the mixture quality (MQ) of binary food powder mixtures. The salt conductivity method was also used as an alternative method to measure the MQ. In the first part of the study the DCI method was developed and it showed potential for assessing MQ of binary powder mixes provided there was huge colour difference between the powders. In the second and third part of the study the effect of composition, water content, particle size and bulk density on MQ was studied. Flowability of powders at various moisture contents was also investigated. The mixing behaviour was assessed using coefficient of variation. Results showed that water content and composition influence the mixing behavior of powders. Good mixing was observed up to size ratios of 4.45 and at higher ratios MQ disimproved. The bulk density had a larger influence on the MQ. In the final study the MQ evaluation of binary and ternary powder mixtures was compared by using two methods – salt conductivity method and DCI method. Two binary food and two quaternary food powder mixtures with different coloured ingredients were studied. Overall results showed that DCI method has a potential for use by industries and it can analyse powder mixtures with components that have differences in colour and that are not segregating in nature.

Understanding GPU programming for statistical computation: Studies in massively parallel massive mixtures

This article describes advances in statistical computation for large-scale data analysis in structured Bayesian mixture models via graphics processing unit (GPU) programming. The developments are partly motivated by computational challenges arising in fitting models of increasing heterogeneity to increasingly large datasets. An example context concerns common biological studies using high-throughput technologies generating many, very large datasets and requiring increasingly high-dimensional mixture models with large numbers of mixture components.We outline important strategies and processes for GPU computation in Bayesian simulation and optimization approaches, give examples of the benefits of GPU implementations in terms of processing speed and scale-up in ability to analyze large datasets, and provide a detailed, tutorial-style exposition that will benefit readers interested in developing GPU-based approaches in other statistical models. Novel, GPU-oriented approaches to modifying existing algorithms software design can lead to vast speed-up and, critically, enable statistical analyses that presently will not be performed due to compute time limitations in traditional computational environments. Supplementalmaterials are provided with all source code, example data, and details that will enable readers to implement and explore the GPU approach in this mixture modeling context. © 2010 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

THERMODYNMICS AND STRUCTURE OF POLY(ETHYLENE OXIDE) IN MIXTURES OF WATER AND ETHANOL

Poly(ethylene oxide) (PEO) is one of the most researched synthetic polymers due to the complex behavior which arises from the interplay of the hydrophilic and hydrophobic sites on the polymer chain. PEO in ethanol forms an opaque gel-like mixture with a partially crystalline structure. Addition of a small amount of water disrupts the gel: 5 wt % PEO in ethanol becomes a transparent solution with the addition of 4 vol % water. The phase behavior of PEO in mixed solvents have been studied using small-angle neutron scattering (SANS). PEO solutions (5 wt % PEO) which contain 4 vol % - 10 vol % (and higher) water behave as an athermal polymer solution and the phase behavior changes from UCST to LCST rapidly as the fraction of water is increased. 2 wt % PEO in water and 10 wt % PEO in ethanol/ water mixtures are examined to assess the role of hydration. The observed phase behavior is consistent with a hydration layer forming upon the addition of water as the system shifts from UCST to LCST behavior. At the molecular level, two or three water molecules can hydrate one PEO monomer (water molecules form a sheath around the PEO macromolecule) which is consistent with the suppression of crystallization and change in the mentioned phase behavior as observed by SANS. The clustering effect of aqueous PEO solution (M.W of PEO = 90,000 g/mol) is monitored as an excess scattering intensity at low-Q. Clustering intensity at Q = 0.004 Å^-1 is used for evaluating the clustering effect. The clustering intensity is proportional to the inverse temperature and levels off when the temperature is less than 50 ˚C. When the temperature is increased over 50 ˚C, the clustering intensity starts decreasing. The clustering of PEO is monitored in ethanol/ water mixtures. The clustering intensity increases as the fraction of water is increased. Based on the solvation intensity behavior, we confirmed that the ethanol/ water mixtures obey a random solvent mixing rule, whereby solvent mixtures are better at solvating the polymer that any of the two solvents. The solution behavior of PEO in ethanol was investigated in the presence of salt (CaCl2) using SANS. Binding of Ca2+ ions to the PEO oxygens transforms the neutral polymer to a weakly charged polyelectrolyte. We observed that the PEO/ethanol solution is better solvated at higher salt concentration due to the electrostatic repulsion of weakly charged monomers. The association of the Ca2+ ions with the PEO oxygen atoms transforms the neutral polymer to a weakly charged polyelectrolyte and gives rise to repulsive interactions between the PEO/Ca2+ complexes. Addition of salt disrupts the gel, which is consistent with better solvation as the salt concentration is increased. Moreover, SANS shows that the phase behavior of PEO/ethanol changes from UCST to LCST as the salt concentration is increased.

A computational model of coupled heat and moisture transfer with phase change in granular sugar during varying environmental conditions

As part of a comprehensive effort to predict the development of caking in granular materials, a mathematical model is introduced to model simultaneous heat and moisture transfer with phase change in porous media when undergoing temperature oscillations/cycling. The resulting model partial differential equations were solved using finite-volume procedures in the context of the PHYSICA framework and then applied to the analysis of sugar in storage. The influence of temperature on absorption/desorption and diffusion coefficients is coupled into the transport equations. The temperature profile, the depth of penetration of the temperature oscillation into the bulk solid, and the solids moisture content distribution were first calculated, and these proved to be in good agreement with experimental data. Then, the influence of temperature oscillation on absolute humidity, moisture concentration, and moisture migration for different parameters and boundary conditions was examined. As expected, the results show that moisture near boundary regions responds faster than farther away from them with surface temperature changes. The moisture absorption and desorption in materials occurs mainly near boundary regions (where interactions with the environment are more pronounced). Small amounts of solids moisture content, driven by both temperature and vapour concentration gradients, migrate between boundary and center with oscillating temperature.

Analysis and modeling of heaping behavior of granular mixtures within a computational mechanics framework

This paper presents a continuum model of the flow of granular material during filling of a silo, using a viscoplastic constitutive relation based on the Drucker-Prager plasticity yield function. The performed simulations demonstrate the ability of the model to realistically represent complex features of granular flows during filling processes, such as heap formation and non-zero inclination angle of the bulk material-air interface. In addition, micro-mechanical parametrizations which account for particle size segregation are incorporated into the model. It is found that numerical predictions of segregation phenomena during filling of a binary granular mixture agree well with experimental results. Further numerical tests indicate the capability of the model to cope successfully with complex operations involving granular mixtures.

On the continuum modelling of segregation of granular mixtures during hopper emptying in core flow mode

In this paper, the application of a continuum model is presented, which deals with the discharge of multi-component granular mixtures in core flow mode. The full model description is given (including the constitutive models for the segregation mechanism) and the interactions between particles at the microscopic level are parametrised in order to predict the development of stagnant zone boundaries during core flow discharges. Finally, the model is applied to a real industrial problem and predictions are made for the segregation patterns developed during mixture discharge in core flow mode.

Spectroscopic studies of oligomers containing 2,5-trans furanoid sugar amino acids

Sugar amino acids and their oligomers, known as carbopeptoids, are commonly studied as foldamers. However, study of their conformational preference is often challenging when the adopted conformations are extended and/or disordered. This study is the first to explore the disordered nature of such carbopeptoids by utilizing a family of 2,5-trans carbopeptoids. An array of spectroscopic techniques has been used to investigate the conformational preference of these carbopeptoids. However, using this data alone it has not been possible to assign conformational preference as an ordered extended conformation or as a disordered family of closely related conformations. Computational methods need to be employed to achieve reliable interpretation of the spectroscopic data. Chirality, 2008. © 2008 Wiley-Liss, Inc.