Uniform regular weighted graphs with large degree: Wigner's law, asymptotic freeness and graphons limit

For each $N\geq 1$, let $G_N$ be a simple random graph on the set of vertices $[N]=\{1,2, ..., N\}$, which is invariant by relabeling of the vertices. The asymptotic behavior as $N$ goes to infinity of correlation functions: $$\mathfrak C_N(T)= \mathbb E\bigg[ \prod_{(i,j) \in T} \Big(\mathbf 1_{\big(\{i,j\} \in G_N \big)} - \mathbb P(\{i,j\} \in G_N) \Big)\bigg], \ T \subset [N]^2 \textrm{finite}$$ furnishes informations on the asymptotic spectral properties of the adjacency matrix $A_N$ of $G_N$. Denote by $d_N = N\times \mathbb P(\{i,j\} \in G_N)$ and assume $d_N, N-d_N\underset{N \rightarrow \infty}{\longrightarrow} \infty$. If $\mathfrak C_N(T) =\big(\frac{d_N}N\big)^{|T|} \times O\big(d_N^{-\frac {|T|}2}\big)$ for any $T$, the standardized empirical eigenvalue distribution of $A_N$ converges in expectation to the semicircular law and the matrix satisfies asymptotic freeness properties in the sense of free probability theory. We provide such estimates for uniform $d_N$-regular graphs $G_{N,d_N}$, under the additional assumption that $|\frac N 2 - d_N- \eta \sqrt{d_N}| \underset{N \rightarrow \infty}{\longrightarrow} \infty$ for some $\eta>0$. Our method applies also for simple graphs whose edges are labelled by i.i.d. random variables.Comment: 21 pages, 7 figure

Defining the intelligent public sector construction client

Recent efforts and aspirations to transform the delivery of major capital programmes and projects in UK public sector construction by focussing on achievement of value for money, whole life asset management and sustainable procurement have led to the adoption of integrated procurement routes characterised by multiplicity of stakeholders with a diversity of differing and often competing requirements. A study of the challenges faced by the public sector to deliver present and future major capital programmes and projects gravitates to the role of the intelligent client, and concomitant skills and capabilities. The results of the multiple case studies research show that the challenges of this role are especially evident at the interface between the internal organisation and the external suppliers and advisors from the private sector. The research concludes that the intelligent client role requires an individual champion with a unique set of skills working in an environment of a supporting team and capable organisation

Taking forward public procurement reforms in Ghana

The construction industry in Ghana, like many others worldwide, has had its fair share of damning independent reviews. Huge and unsustainable foreign debt, excessive budget deficits, huge contractual payment arrears, poor construction performance, corruption and pressure from international financial institutions, forced the government to commit to a reform of public procurement, which culminated in the passing of the Public Procurement Act, 2003 (Act 663). The paper outlines the events leading to, and features of, the public procurement reform in Ghana and analyses its potential impact and the unique challenges it presents. Comparisons are also drawn from relevant scenarios in other countries. The paper concludes that while the Procurement Act sets out the legal, institutional and regulatory framework to secure fiscal transparency and public accountability, the sole reliance on traditional contracting and price-based selection limits the scope for the value for money achievable. Expanding the reforms to cover procurement and project delivery methods and strategies, with a focus on ‘best value’, will increase the potential and likelihood of achieving value for money in public construction in Ghana

Teaching staff knowledge, attributions and confidence in relation to working with children with an intellectual disability and challenging behaviour

The present study examined Scottish teaching staff knowledge about the definition and management of challenging behaviour displayed by children with an intellectual disability. Knowledge levels were relatively low, and participants were most likely to define challenging behaviour by function or topography. Teaching staff were largely unaware of positive programming strategies, suggesting that they may not be properly equipped to manage challenging behaviour effectively in the longer term. The teaching staff were found to hold attributions which research suggests are associated with reduced helping behaviour and increased anger. This indicates a continuing need to identify effective ways of promoting more accurate knowledge and positive attributions in teaching staff

Electrochemical titrations and reaction time courses monitored in situ by magnetic circular dichroism spectroscopy

Magnetic circular dichroism (MCD) spectra, at ultraviolet–visible or near-infrared wavelengths (185–2000 nm), contain the same transitions observed in conventional absorbance spectroscopy, but their bisignate nature and more stringent selection rules provide greatly enhanced resolution. Thus, they have proved to be invaluable in the study of many transition metal-containing proteins. For mainly technical reasons, MCD has been limited almost exclusively to the measurement of static samples. But the ability to employ the resolving power of MCD to follow changes at transition metal sites would be a potentially significant advance. We describe here the development of a cuvette holder that allows reagent injection and sample mixing within the 50-mm-diameter ambient temperature bore of an energized superconducting solenoid. This has allowed us, for the first time, to monitor time-resolved MCD resulting from in situ chemical manipulation of a metalloprotein sample. Furthermore, we report the parallel development of an electrochemical cell using a three-electrode configuration with physically separated working and counter electrodes, allowing true potentiometric titration to be performed within the bore of the MCD solenoid