Boundary value problems for the elliptic sine-Gordon equation in a semi-strip

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2 by 2 matrix Riemann-Hilbert problem whose \jump matrix" depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however a major difficulty for this problem is the existence of non-integrable singularities of the function q_y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann-Hilbert problem to an equivalent modified Riemann-Hilbert problem, we show that the solution can be expressed in terms of a 2 by 2 matrix Riemann-Hilbert problem whose jump matrix depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h. The determination of the function h remains open.

Inverse problems in neural field theory

We study inverse problems in neural field theory, i.e., the construction of synaptic weight kernels yielding a prescribed neural field dynamics. We address the issues of existence, uniqueness, and stability of solutions to the inverse problem for the Amari neural field equation as a special case, and prove that these problems are generally ill-posed. In order to construct solutions to the inverse problem, we first recast the Amari equation into a linear perceptron equation in an infinite-dimensional Banach or Hilbert space. In a second step, we construct sets of biorthogonal function systems allowing the approximation of synaptic weight kernels by a generalized Hebbian learning rule. Numerically, this construction is implemented by the Moore–Penrose pseudoinverse method. We demonstrate the instability of these solutions and use the Tikhonov regularization method for stabilization and to prevent numerical overfitting. We illustrate the stable construction of kernels by means of three instructive examples.

Specific detection and localization of microsporidian parasites in invertebrate hosts using in situ hybridization

We designed FISH-probes for two distinct microsporidian clades and demonstrated their application in detecting respectively Nosema/Vairimorpha and Dictyoceola species. We applied them to study the vertical transmission of two microsporidia infecting the amphipod Gammarus duebeni

A neurofuzzy classifier for two class problems

A neurofuzzy classifier identification algorithm is introduced for two class problems. The initial fuzzy base construction is based on fuzzy clustering utilizing a Gaussian mixture model (GMM) and the analysis of covariance (ANOVA) decomposition. The expectation maximization (EM) algorithm is applied to determine the parameters of the fuzzy membership functions. Then neurofuzzy model is identified via the supervised subspace orthogonal least square (OLS) algorithm. Finally a logistic regression model is applied to produce the class probability. The effectiveness of the proposed neurofuzzy classifier has been demonstrated using a real data set.

Localization of calcitonin receptor-like receptor (CLR) and receptor activity-modifying protein 1 (RAMP1) in human gastrointestinal tract

Calcitonin gene-related peptide (CGRP) exerts its diverse effects on vasodilation, nociception, secretion, and motor function through a heterodimeric receptor comprising of calcitonin receptor-like receptor (CLR) and receptor activity-modifying protein 1 (RAMP1). Despite the importance of CLR.RAMP1 in human disease, little is known about its distribution in the human gastrointestinal (GI) tract, where it participates in inflammation and pain. In this study, we determined that CLR and RAMP1 mRNAs are expressed in normal human stomach, ileum and colon by RT-PCR. We next characterized antibodies that we generated to rat CLR and RAMP1 in transfected HEK cells. Having characterized these antibodies in vitro, we then localized CLR-, RAMP1-, CGRP- and intermedin-immunoreactivity (IMD-IR) in various human GI segments. In the stomach, nerve bundles in the myenteric plexus and nerve fibers throughout the circular and longitudinal muscle had prominent CLR-IR. In the proximal colon and ileum, CLR was found in nerve varicosities of the myenteric plexus and surrounding submucosal neurons. Interestingly, CGRP expressing fibers did not co-localize, but were in close proximity to CLR. However, CLR and RAMP1, the two subunits of a functional CGRP receptor were clearly localized in myenteric plexus, where they may form functional cell-surface receptors. IMD, another member of calcitonin peptide family was also found in close proximity to CLR, and like CGRP, did not co-localize with either CLR or RAMP1 receptors. Thus, CGRP and IMD appear to be released locally, where they can mediate their effect on their receptors regulating diverse functions such as inflammation, pain and motility.

Localization of calcitonin receptor-like receptor and receptor activity modifying protein 1 in enteric neurons, dorsal root ganglia, and the spinal cord of the rat

Calcitonin receptor-like receptor (CLR) and receptor activity modifying protein 1 (RAMP1) comprise a receptor for calcitonin gene related peptide (CGRP) and intermedin. Although CGRP is widely expressed in the nervous system, less is known about the localization of CLR and RAMP1. To localize these proteins, we raised antibodies to CLR and RAMP1. Antibodies specifically interacted with CLR and RAMP1 in HEK cells coexpressing rat CLR and RAMP1, determined by Western blotting and immunofluorescence. Fluorescent CGRP specifically bound to the surface of these cells and CGRP, CLR, and RAMP1 internalized into the same endosomes. CLR was prominently localized in nerve fibers of the myenteric and submucosal plexuses, muscularis externa and lamina propria of the gastrointestinal tract, and in the dorsal horn of the spinal cord of rats. CLR was detected at low levels in the soma of enteric, dorsal root ganglia (DRG), and spinal neurons. RAMP1 was also localized to enteric and DRG neurons and the dorsal horn. CLR and RAMP1 were detected in perivascular nerves and arterial smooth muscle. Nerve fibers containing CGRP and intermedin were closely associated with CLR fibers in the gastrointestinal tract and dorsal horn, and CGRP and CLR colocalized in DRG neurons. Thus, CLR and RAMP1 may mediate the effects of CGRP and intermedin in the nervous system. However, mRNA encoding RAMP2 and RAMP3 was also detected in the gastrointestinal tract, DRG, and dorsal horn, suggesting that CLR may associate with other RAMPs in these tissues to form a receptor for additional peptides such as adrenomedullin.

Localization and function of the Kv3.1b subunit in the rat medulla oblongata: focus on the nucleus tractus solitarii

The voltage-gated potassium channel subunit Kv3.1 confers fast firing characteristics to neurones. Kv3.1b subunit immunoreactivity (Kv3.1b-IR) was widespread throughout the medulla oblongata, with labelled neurones in the gracile, cuneate and spinal trigeminal nuclei. In the nucleus of the solitary tract (NTS), Kv3.1b-IR neurones were predominantly located close to the tractus solitarius (TS) and could be GABAergic or glutamatergic. Ultrastructurally, Kv3.1b-IR was detected in NTS terminals, some of which were vagal afferents. Whole-cell current-clamp recordings from neurones near the TS revealed electrophysiological characteristics consistent with the presence of Kv3.1b subunits: short duration action potentials (4.2 +/- 1.4 ms) and high firing frequencies (68.9 +/- 5.3 Hz), both sensitive to application of TEA (0.5 mm) and 4-aminopyridine (4-AP; 30 mum). Intracellular dialysis of an anti-Kv3.1b antibody mimicked and occluded the effects of TEA and 4-AP in NTS and dorsal column nuclei neurones, but not in dorsal vagal nucleus or cerebellar Purkinje cells (which express other Kv3 subunits, but not Kv3.1b). Voltage-clamp recordings from outside-out patches from NTS neurones revealed an outward K(+) current with the basic characteristics of that carried by Kv3 channels. In NTS neurones, electrical stimulation of the TS evoked EPSPs and IPSPs, and TEA and 4-AP increased the average amplitude and decreased the paired pulse ratio, consistent with a presynaptic site of action. Synaptic inputs evoked by stimulation of a region lacking Kv3.1b-IR neurones were not affected, correlating the presence of Kv3.1b in the TS with the pharmacological effects.

Emerging agricultural hydrology problems in post-conflict Libya

This paper develops a conceptual framework for analyzing emerging agricultural hydrology problems in post-conflict Libya. Libya is one of the most arid regions on the planet. Thus, as well as substantial political and social changes, post-conflict Libyan administrators are confronted with important hydrological issues in Libya’s emerging water-landuse complex. This paper presents a substantial background to the water-land-use problem in Libya; reviews previous work in Libya and elsewhere on water-land-use issues and water-land-use conflicts in the dry and arid zones; outlines a conceptual framework for fruitful research interventions; and details the results of a survey conducted on Libyan farmers’ water usage, perceptions of emerging water-land-use conflicts and the appropriate value one should place on agricultural-use hydrological resources in Libya. Extensions are discussed.

Standard cost model: three different paths and their common problems

Red tape is not desirable as it impedes business growth. Relief from the administrative burdens that businesses face due to legislation can benefit the whole economy, especially at times of recession. However, recent governmental initiatives aimed at reducing administrative burdens have encountered some success, but also failures. This article compares three national initiatives - in the Netherlands, UK and Italy - aimed at cutting red tape by using the Standard Cost Model. Findings highlight the factors affecting the outcomes of measurement and reduction plans and ways to improve the Standard Cost Model methodology.

Lessons from the private finance initiative in the UK: benefits, problems and critical success factors

Purpose – This paper summarises the main research findings from a detailed, qualitative set of structured interviews and case studies of private finance initiative (PFI) schemes in the UK, which involve the construction of built facilities. The research, which was funded by the Foundation for the Built Environment, examines the emergence of PFI in the UK. Benefits and problems in the PFI process are investigated. Best practice, the key critical factors for success, and lessons for the future are also analysed. Design/methodology/approach – The research is based around 11 semi-structured interviews conducted with stakeholders in key PFI projects in the UK. Findings – The research demonstrates that value for money and risk transfer are key success criteria. High procurement and transaction costs are a feature of PFI projects, and the large-scale nature of PFI projects frequently acts as barrier to entry. Research limitations/implications – The research is based on a limited number of in-depth case study interviews. The paper also shows that further research is needed to find better ways to measure these concepts empirically. Practical implications – The paper is important in highlighting four main areas of practical improvement in the PFI process: value for money assessment; establishing end-user needs; developing competitive markets and developing appropriate skills in the public sector. Originality/value – The paper examines the drivers, barriers and critical success factors for PFI in the UK for the first time in detail and will be of value to property investors, financiers, and others involved in the PFI process.

Current problems in four-dimensional data assimilation

The purpose of this lecture is to review recent development in data analysis, initialization and data assimilation. The development of 3-dimensional multivariate schemes has been very timely because of its suitability to handle the many different types of observations during FGGE. Great progress has taken place in the initialization of global models by the aid of non-linear normal mode technique. However, in spite of great progress, several fundamental problems are still unsatisfactorily solved. Of particular importance is the question of the initialization of the divergent wind fields in the Tropics and to find proper ways to initialize weather systems driven by non-adiabatic processes. The unsatisfactory ways in which such processes are being initialized are leading to excessively long spin-up times.