CnC^n-almost periodic and almost periodic solutions for some nonlinear integral equations

In this paper, we investigate the existence of $C^n$-almost periodic solution for a class of nonlinear Fredholm integral equations, and the existence of almost periodic solution for a class of nonlinear functional integral equations. Our existence theorems extend some earlier results. Two examples are given to illustrate our results

Quenched lattice calculation of semileptonic heavy-light meson form factors

We calculate, in the continuum limit of quenched lattice QCD, the matrix elements of the heavy-heavy vector current between heavy-light pseudoscalar meson states. We present the form factors for different values of the initial and final meson masses at finite momentum transfer. In particular, we calculate the non-perturbative correction to the differential decay rate of the process B --> D l nu including the case of a non-vanishing lepton mass.Comment: 16 pages, 10 figures, version accepted for publication on JHE

Accretion and photodesorption of CO ice as a function of the incident angle of deposition

Non-thermal desorption of inter- and circum-stellar ice mantles on dust grains, in particular ultraviolet photon-induced desorption, has gained importance in recent years. These processes may account for the observed gas phase abundances of molecules like CO toward cold interstellar clouds. Ice mantle growth results from gas molecules impinging on the dust from all directions and incidence angles. Nevertheless, the effect of the incident angle for deposition on ice photo-desorption rate has not been studied. This work explores the impact on the accretion and photodesorption rates of the incidence angle of CO gas molecules with the cold surface during deposition of a CO ice layer. Infrared spectroscopy monitored CO ice upon deposition at different angles, ultraviolet-irradiation, and subsequent warm-up. Vacuum-ultraviolet spectroscopy and a Ni-mesh measured the emission of the ultraviolet lamp. Molecules ejected from the ice to the gas during irradiation or warm-up were characterized by a quadrupole mass spectrometer. The photodesorption rate of CO ice deposited at 11 K and different incident angles was rather stable between 0 and 45$^{\circ}$. A maximum in the CO photodesorption rate appeared around 70$^{\circ}$-incidence deposition angle. The same deposition angle leads to the maximum surface area of water ice. Although this study of the surface area could not be performed for CO ice, the similar angle dependence in the photodesorption and the ice surface area suggests that they are closely related. Further evidence for a dependence of CO ice morphology on deposition angle is provided by thermal desorption of CO ice experiments

Transonic Shocks In Multidimensional Divergent Nozzles

We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure. The proof is based on solving a free boundary problem for a system of partial differential equations consisting of an elliptic equation and a transport equation. In the process, we obtain unique solvability for a class of transport equations with velocity fields of weak regularity(non-Lipschitz), an infinite dimensional weak implicit mapping theorem which does not require continuous Frechet differentiability, and regularity theory for a class of elliptic partial differential equations with discontinuous oblique boundary conditions.Comment: 54 page

Experimental study of weak antilocalization effect in a high mobility InGaAs/InP quantum well

The magnetoresistance associated with quantum interference corrections in a high mobility, gated InGaAs/InP quantum well structure is studied as a function of temperature, gate voltage, and angle of the tilted magnetic field. Particular attention is paid to the experimental extraction of phase-breaking and spin-orbit scattering times when weak anti- localization effects are prominent. Compared with metals and low mobility semiconductors the characteristic magnetic field $B_{tr} = \hbar/4eD \tau$ in high mobility samples is very small and the experimental dependencies of the interference effects extend to fields several hundreds of times larger. Fitting experimental results under these conditions therefore requires theories valid for arbitrary magnetic field. It was found, however, that such a theory was unable to fit the experimental data without introducing an extra, empirical, scale factor of about 2. Measurements in tilted magnetic fields and as a function of temperature established that both the weak localization and the weak anti-localization effects have the same, orbital origin. Fits to the data confirmed that the width of the low field feature, whether a weak localization or a weak anti-localization peak, is determined by the phase-breaking time and also established that the universal (negative) magnetoresistance observed in the high field limit is associated with a temperature independent spin-orbit scattering time.Comment: 13 pages including 10 figure

Development and application of a data-driven reaction classification model : comparison of an electronic lab notebook and the medicinal chemistry literature

Reaction classification has often been considered an important task for many different applications, and has traditionally been accomplished using hand-coded rule-based approaches. However, the availability of large collections of reactions enables data-driven approaches to be developed. We present the development and validation of a 336-class machine learning-based classification model integrated within a Conformal Prediction (CP) framework in order to associate reaction class predictions with confidence estimations. We also propose a data-driven approach for 'dynamic' reaction fingerprinting to maximise the effectiveness of reaction encoding, as well as developing a novel reaction classification system that organises labels in four hierarchical levels (SHREC: Sheffield Hierarchical REaction Classification). We show that the performance of the CP augmented model can be improved by defining confidence thresholds to detect predictions that are less likely to be false. For example, the external validation of the model reports 95% of predictions as correct by filtering out less than 15% of the uncertain classifications. The application of the model is demonstrated by classifying two reaction datasets: one extracted from an industrial ELN and the other from the medicinal chemistry literature. We show how confidence estimations and class compositions across different levels of information can be used to gain immediate insights on the nature of reaction collections and hidden relationship between reaction classes

Enhancing reaction-based de novo design using a multi-label reaction class recommender

Reaction-based de novo design refers to the in-silico generation of novel chemical structures by combining reagents using structural transformations derived from known reactions. The driver for using reaction-based transformations is to increase the likelihood of the designed molecules being synthetically accessible. We have previously described a reaction-based de novo design method based on reaction vectors which are transformation rules that are encoded automatically from reaction databases. A limitation of reaction vectors is that they account for structural changes that occur at the core of a reaction only, and they do not consider the presence of competing functionalities that can compromise the reaction outcome. Here, we present the development of a Reaction Class Recommender to enhance the reaction vector framework. The recommender is intended to be used as a filter on the reaction vectors that are applied during de novo design to reduce the combinatorial explosion of in-silico molecules produced while limiting the generated structures to those which are most likely to be synthesisable. The recommender has been validated using an external data set extracted from the recent medicinal chemistry literature and in two simulated de novo design experiments. Results suggest that the use of the recommender drastically reduces the number of solutions explored by the algorithm while preserving the chance of finding relevant solutions and increasing the global synthetic accessibility of the designed molecules

Template coexistence in prebiotic vesicle models

The coexistence of distinct templates is a common feature of the diverse proposals advanced to resolve the information crisis of prebiotic evolution. However, achieving robust template coexistence turned out to be such a difficult demand that only a class of models, the so-called package models, seems to have met it so far. Here we apply Wright's Island formulation of group selection to study the conditions for the coexistence of two distinct template types confined in packages (vesicles) of finite capacity. In particular, we show how selection acting at the level of the vesicles can neutralize the pressures towards the fixation of any one of the template types (random drift) and of the type with higher replication rate (deterministic competition). We give emphasis to the role of the distinct generation times of templates and vesicles as yet another obstacle to coexistence.Comment: 7 pages, 8 figure

Multi-element bioimaging of Arabidopsis thaliana roots

Better understanding of root function is central for development of plants with more efficient nutrient uptake and translocation. We here present a method for multi-element bioimaging at the cellular level in roots of the genetic model system Arabidopsis thaliana. Using conventional protocols for microscopy we observed that diffusible ions such as potassium (K+) and sodium (Na+) were lost during sample dehydration. Thus, we developed a protocol which preserves ions in their native, cellular environment. Briefly, fresh roots are encapsulated in paraffin, then cryo-sectioned and freeze dried. Samples are finally analyzed by Laser Ablation-Inductively Coupled Plasma-Mass Spectrometry (LA-ICP-MS), utilizing a specially designed internal standard procedure. The method can be further developed to maintain the native composition of proteins, enzymes, RNA and DNA, making it attractive in combination with other omics techniques. To demonstrate the potential of the method we analyzed a mutant of A. thaliana unable to synthesize the metal chelator nicotianamine (NA). The mutant accumulated substantially more zinc (Zn) and manganese (Mn) than the wild type in the tissues surrounding the vascular cylinder. For iron (Fe) the images looked completely different, with Fe bound mainly in the epidermis of the WT plants, but confined to the cortical cell walls of the mutant. The method offers the power of ICP-MS to be fully employed, thereby providing a basis for detailed studies of ion transport in roots. Being applicable to A. thaliana, the molecular and genetic approaches available in this system can now be fully exploited in order to gain a better mechanistic understanding of these processes

Image-based measurement of alveoli volume expansion in an animal model of a diseased lung

Currently, there does not exist reliable MV treatment or protocols in critical care to treat acute respiratory diseases, and thus no proven way to optimise care to minimise the mortality, length of stay or cost. The overall approach of this research is to improve protocols by using appropriate computer models that take into account the essential lung mechanics. The aim of this research is to create an automated algorithm for tracking the boundary of individual or groups of alveoli, and to convert this into a pressure volume curve for three different types of alveoli. A technique called in vivo microscopy has been developed by Schiller et al which visualizes the inflation and deflation of individual alveoli in a surfactant deactivation model of lung injury in pigs. Three different types of alveoli were tracked using data from Schiller et al, type I, II and III. These types correspond to healthy alveoli, non-collapsing but partially diseased alveoli, and fully collapsing diseased alveoli respectively. The boundaries of all the alveoli that were tracked, compared well visually to the movies. Pressure versus Area curves were derived for both inflation and deflation, they captured the expected physiological behaviour, and were qualitatively similar to the quasi-static pressure area curves derived in Schiller et al, Quantitative differences are due to the dynamic effects of ventilation which were not investigated in Schiller et al