Componentwise adaptation for high dimensional MCMC

Summary  We introduce a new adaptive MCMC algorithm, based on the traditional single component Metropolis-Hastings algorithm and on our earlier adaptive Metropolis algorithm (AM). In the new algorithm the adaption is performed component by component. The chain is no more Markovian, but it remains ergodic. The algorithm is demonstrated to work well in varying test cases up to 1000 dimensions.     

The contents of adp systems work in administrative ADP applications

An outline of the different phases in ADP work is presented. A detailed account is given of the purpose, contents, and results of each phase, and all inter-relations are illustrated in a flow chart.     

Asymptotic Lipschitz Regularity for Tug-of-War Games with Varying Probabilities

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in Ω ? ?ⁿ. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in Ω ×Ω via couplings.

     

Compact and Weakly Compact Composition Operators on BMOA

Any analytic map φ of the unit disc ${\mathbb{D}}$ into itself induces a composition operator C _φ on BMOA, mapping ${f \mapsto f \circ \varphi}$ , where BMOA is the Banach space of analytic functions ${f\colon \mathbb{D} \to \mathbb{C}}$ whose boundary values have bounded mean oscillation on the unit circle. We show that C _φ is weakly compact on BMOA precisely when it is compact on BMOA, thus solving a question initially posed by Tjani and by Bourdon, Cima and Matheson in the special case of VMOA. As a crucial step of our argument we simplify the compactness criterion due to Smith for C _φ on BMOA and show that his condition on the Nevanlinna counting function alone characterizes compactness. Additional equivalent compactness criteria are established. Furthermore, we prove the unexpected result that compactness of C _φ on VMOA implies compactness even from the Bloch space into VMOA.     

A Family of Graded Modules Associated to a Module

In this article we introduce a certain family of graded modules associated to a given module. These modules provide a natural extension of the notion of the associated graded ring of an ideal. We will investigate their properties. In particular, we will try to extend Ree' theorem on the associated graded ring of an ideal generated by a regular sequence to this context.     

Rigidity of commutators and elementary operators on Calkin algebras

LetA=(A ₁,...,A _n ),B=(B ₁,...,B _n )εL(ℓ ^p ) ⁿ be arbitraryn-tuples of bounded linear operators on (ℓ ^p ), with 1<p<∞. The paper establishes strong rigidity properties of the corresponding elementary operators ε _a,b on the Calkin algebraC(ℓ ^p )≡L(ℓ ^p )/K(ℓ ^p ); , where quotient elements are denoted bys=S+K(ℓ ^p ) forSεL(ℓ ^p ). It is shown among other results that the kernel Ker(ε _a,b ) is a non-separable subspace ofC(ℓ ^p ) whenever ε _a,b fails to be one-one, while the quotient is non-separable whenever ε _a,b fails to be onto. These results extend earlier ones in several directions: neither of the subsets {A ₁,...,A _n }, {B ₁,...,B _n } needs to consist of commuting operators, and the results apply to other spaces apart from Hilbert spaces. Supported by the Academy of Finland, Project 32837.     

Cellulose nanocrystal submonolayers by spin coating

Dilute concentrations of cellulose nanocrystal solutions were spin coated onto different substrates to investigate the effect of the substrate on the nanocrystal submonolayers. Three substrates were probed: silica, titania, and amorphous cellulose. According to atomic force microscopy (AFM) images, anionic cellulose nanocrystals formed small aggregates on the anionic silica substrate, whereas a uniform two-dimensional distribution of nanocrystals was achieved on the cationic titania substrate. The uniform distribution of cellulose nanocrystal submonolayers on titania is an important factor when dimensional analysis of the nanocrystals is desired. Furthermore, the amount of nanocrystals deposited on titania was multifold in comparison to the amounts on silica, as revealed by AFM image analysis and X-ray photoelectron spectroscopy. Amorphous cellulose, the third substrate, resulted in a somewhat homogeneous distribution of the nanocrystal submonolayers, but the amounts were as low as those on the silica substrate. These differences in the cellulose nanocrystal deposition were attributed to electrostatic effects: anionic cellulose nanocrystals are adsorbed on cationic titania in addition to the normal spin coating deposition. The anionic silica surface, on the other hand, causes aggregation of the weakly anionic cellulose nanocrystals which are forced on the repulsive substrate by spin coating. The electrostatically driven adsorption also influences the film thickness of continuous ultrathin films of cellulose nanocrystals. The thicker films of charged nanocrystals on a substrate of opposite charge means that the film thickness is not independent of the substrate when spin coating cellulose nanocrystals in the ultrathin regime (<100 nm).     

Indirect evidence of supramolecular changes within cellulose microfibrils of chemical pulp fibers upon drying

Dried and never-dried chemical pulps were subjected to strong sulfuric acid hydrolysis and the dimensions of the resulting cellulose nanocrystals (CNCs) were characterized by AFM image analysis. Although the average length of CNCs was fairly similar in all samples (55–65 nm), the length distribution histograms revealed that a higher number of longer crystals and a lower number of shorter crystals were present in the CNC suspensions prepared from never-dried pulps. The distinction was hypothetically ascribed to tensions building in individual cellulose microfibrils upon drying, resulting in irreversible supramolecular changes in the amorphous regions. The amorphous regions shaped by tensions were deemed as more susceptible to acid hydrolysis.     

Carboxymethyl cellulose on a fiber substrate: the interactions with cationic polyelectrolytes

High and low molecular weight (M_w) carboxymethyl celluloses (CMC) were adsorbed on a well-characterized fiber substrate (long fibers of a commercial bleached birch kraft pulp with the carboxylic acid groups in Na-form) to increase the charge of the fibers in a controlled fashion. The M_w played a role in the utilization of CMCs as a strength additive in paper sheets nearly doubling the tensile strength with the high M_w CMC. Swelling properties of the CMC treated fibers were measured with water retention value (WRV). The WRV increased more with the high M_w CMC. The swelling was further tuned by two highly cationic polyelectrolytes; high M_w poly(diallyldimethyl ammonium chloride) (PDADMAC) and low M_w polybrene (hexadimethrine bromide, [3,6]-ionene). They were chosen because of their known ability to neutralize the anionic charge either exclusively on the surface or in the whole fiber, respectively. Adsorption of PDADMAC could reduce WRV of the CMC pre-treated fibers to the level of the untreated reference, while polybrene adsorbed pulps with 3–10 times more cationic polyelectrolyte deswelled the fibers only slightly more than the surface neutralized fibers. These results indicated surface conformation differences with low and high M_w CMCs. While the conformation did play a role after physical alteration (drying and rewetting) of the fibers, the paper sheets produced from these fibers showed remarkable differences. In extreme cases, the strength of the paper could be retained after drying (low M_w CMC + PDADMAC) or paper, resistant to disintegration, could be achieved (CMC + polybrene).