Stochastic models (cooperative and non-cooperative) for NMR analysis of the hetero-association of aromatic molecules in aqueous solution

Stochastic cooperative (STOCH-C) and non-cooperative (STOCH-NC) models have been developed for NMR analysis of the hetero-association of aromatic compounds in solution, in order to take into account all physically meaningful association reactions of molecules in which there are no limitations on the lengths of the aggregates and complexes. These algorithmical approaches are compared with previously published basic (BASE) and generalized (GEN) analytical statistical thermodynamical models of hetero-association of biologically active aromatic molecules using the same sets of published NMR data measured under the same solution conditions (0.1 M phosphate buffer, pD = 7.1, T = 298 K). It is shown that, within experimental errors, the BASE analytical model may be used to describe molecular systems characterized by relatively small contributions of hetero-association reactions, whereas the GEN model may be applied to hetero-association reactions of any aromatic compound with different self-association properties. The STOCH-C computational algorithm enabled the effect on hetero-association of the interactions of molecules with different cooperativity parameters of self-association to be estimated for the first time and it is proposed that the algorithm for the stochastic models has great potential for detailed investigation and understanding of the interactions of aromatic molecules in solution

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H>1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the classical Ito stochastic calculus. The existence result is based on the Yamada-Watanabe theorem.Comment: 21 page

The shape and behaviour of a granular bed in a rotating drum using Eulerian flow fields obtained from PEPT

Non-invasive single-particle tracking techniques, such as positron emission particle tracking (PEPT), provide useful information about the behaviour of a representative particle moving in a bulk of similar particles in a rotating drum. The Lagrangian trajectories that they yield can be used to study, for example, particulate diff usion or granular interaction. However, often the Eulerian flow fi elds of the entire granular bed are more useful-- they can be used to study segregation, for instance, or the evolution of the free surface of the bed. In this work, we present a technique for converting Lagrangian trajectories to Eulerian flow fields via a time-weighted residence time distribution (RTD) of the tracked particle. We then perform PEPT experiments on a mono-disperse bed of spherical particles in a cylindrical drum, rotated at various rates, and use the RTD procedure to obtain flow fi elds of the bed. We use these flow fi elds to investigate the e ffect of drum rotational speed on the shape and behaviour of a granular bed in a rotating drum, and the insights gained thereby to defi ne a comprehensive set of surfaces{ such as the bulk free surface{ to divide the bed into regions of distinct granular behaviour. We further defi ne scalar bed features-- such as the centre of circulation of the bed-- that can be used to quantitatively compare the behaviour of granular beds in rotating drums operated under various conditions

Learning the Smart Way: Lessons Learned by the Reaching Agents of Change Project.

The Reaching Agents of Change (RAC) project was a pilot that advocated for increased investment in orange-fleshed sweetpotato to combat vitamin A deficiency among young children and women of reproductive age. It was implemented by the International Potato Center and Helen Keller International primarily in Nigeria, Mozambique, Tanzania and to a lesser extent in Ghana and Burkina Faso between 2011 and 2014. The project had multiple deliverables in advocacy for raising of new investment, policy change and strengthening of institutional and individual capacities in the project countries. RAC incorporated a systematic and comprehensive results-based monitoring and evaluation system and continuously documented the implementation process over the project period. This booklet shares the learning process that RAC adopted and highlights some useful and replicable lessons learned

The composition of serous fluid after axillary dissection

Objective: To analyse the composition of the serous fluid formed after axillary dissection Design: Descriptive study Setting: University hospital and teaching hospital, The Netherlands Subjects: 16 patients whose axillas were dissected as part of a modified radical mastectomy for stage I or II breast cancer. Main outcome measures: Chemical and cellular composition of axillary drainage fluid on the first, fifth, and tenth postoperative days compared with the same constituents in blood and with reported data on the composition of peripheral lymph. Results and conclusion: On the first postoperative day the drainage fluid contained blood contents and a high concentration of creatine phosphokinase (CPK). After day one it changed to a peripheral lymph-like fluid but containing different cells, more protein, and no fibrinogen, making coagulation impossible. The reduction in the fluid production must be caused by other wound healing processes, such as formation of scars and connective tissue

Entropy and the variational principle for actions of sofic groups

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants, and we establish the variational principle in this context. In the case of residually finite groups we use the variational principle to compute the topological entropy of principal algebraic actions whose defining group ring element is invertible in the full group C*-algebra.Comment: 44 pages; minor changes; to appear in Invent. Mat

Gaussian multiplicative Chaos for symmetric isotropic matrices

Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985

Alkali incorporation into solution processed CIGS precursor layers

Solution based ion-exchange reactions offer a simple, non-vacuum route for adding Cu into In- Ga-Se precursor layers as a step in a low-cost process for the preparation of Cu(In, Ga)Se2 (CIGS) solar cells. The chemically treated precursor layers may be converted into CIGS by annealing with Se vapour. Structural and compositional characterisation has shown that the converted layers have good composition, microstructure and crystalline phase content. Nevertheless, photovoltaic cells processed from these layers have failed to produce energy conversion efficiencies greater than ~4% under standard test conditions. The chemical bath used for the incorporation of Cu into the precursor layers includes a complexant for stability and this complexant contains alkali atoms, which are known to strongly influence the properties of CIGS. Low alkali content is highly desirable in CIGS layers but excessive inclusion may be detrimental. This paper reports the results of an investigation into the potential incorporation of excess alkali atoms from the solution into the precursor layers. Whilst no evidence of alkali incorporation is detected by energy dispersive X-ray analysis, clear evidence is seen in time-of-flight secondary ion mass spectrometry measurements. The implications of this are discussed in terms of reported effects on device performance

On finite-difference approximations for normalized Bellman equations

A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of convergence of finite difference approximations for the optimal reward functions.Comment: 36 pages, ArXiv version updated to the version accepted in Appl. Math. Opti