The norm of polynomials in large random and deterministic matrices

Let X_N= (X_1^(N), ..., X_p^(N)) be a family of N-by-N independent, normalized random matrices from the Gaussian Unitary Ensemble. We state sufficient conditions on matrices Y_N =(Y_1^(N), ..., Y_q^(N)), possibly random but independent of X_N, for which the operator norm of P(X_N, Y_N, Y_N^*) converges almost surely for all polynomials P. Limits are described by operator norms of objects from free probability theory. Taking advantage of the choice of the matrices Y_N and of the polynomials P we get for a large class of matrices the "no eigenvalues outside a neighborhood of the limiting spectrum" phenomena. We give examples of diagonal matrices Y_N for which the convergence holds. Convergence of the operator norm is shown to hold for block matrices, even with rectangular Gaussian blocks, a situation including non-white Wishart matrices and some matrices encountered in MIMO systems.Comment: 41 pages, with an appendix by D. Shlyakhtenk

Business Cycle Persistence in Developing Countries: How Successful is a DSGE Model with a Vertical Production Chain and Sticky Prices?

It is well documented that business cycles of developed countries are characterised by persistent output fluctuations, and this has been the subject of much theoretical interest. However, the case for developing countries has been somewhat neglected in the literature. This paper addresses this imbalance, revealing that whilst both developed and developing countries exhibit persistent output fluctuations, there is a significant positive relationship between output persistence and level of economic development. This relationship was successfully modelled using a vertical production chain DSGE model (Huang and Liu, 2001). This model lends itself to such an analysis, as by altering the number of production stages (N) it is possible to represent economies at different levels of development. However, calibration of low input-output (γ) parameter values for the US and UK effectively inhibited the model from generating enough persistence to match that observed in these countries. Nonetheless, after abstracting from the US and UK results, there was found to be a strong significant positive relationship between the magnitude of output persistence generated by the model and economic development. A final very significant finding of this analysis is that the model overestimates output persistence in high inflation countries and underestimates output persistence in low inflation countries. This has important implications not only for this model, but also for any economist attempting to construct a business cycle model capable of replicating the observed patterns of output persistence.Output persistence, Vertical production chain, Staggered price contracts, Economic development, Inflation

Developing Country Business Cycles: Characterising the Cycle

Classical business cycles, following Burns and Mitchell (1946), can be defined as the sequential pattern of expansions and contractions in aggregate economic activity. Recently, Harding and Pagan (2002, 2006) have provided an econometric toolkit for the analysis of these cycles, and this has resulted in a recent surge in researchers using these methods to analyse developing country business cycles. However, the existing literature consists of diminutive samples and the majority fail to consider the statistical significance of the concordance statistics. To address this shortfall, this paper examines the business cycle characteristics and synchronicity for thirty-two developing countries. Furthermore, the US, the UK and Japan are included; this provides benchmarks upon which to compare the characteristics of the developing country cycles and also to examine the degree of synchronisation between developed and developing countries. Significantly, this research reveals that business cycles of developing countries are not, as previously believed, significantly shorter than those of the developed countries. However, the amplitude of both expansion and contraction phases tends to be greater in the developing countries. Furthermore a clear relationship between the timing of business cycle fluctuations and periods of significant regional crises, such as the Asian Financial Crisis, is exhibited. However, the more specific timing of the onset of these fluctuations appears to be determined by country-specific factors. Moreover, there are no clear patterns of concordance either within regions or between developed and developing country business cycles.Classical business cycle, Turning points, Synchronisation, Concordance, Contagion, Developing economies

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

Self-assembly of Escherichia coli phage shock protein A

The Phage shock protein (Psp) response is an extracytoplasmic stress response. The central component of this system is PspA, a protein that mediates the physiological response to membrane stress. PspA is also involved in regulating its own transcription and that of the psp operon, forming a positive feedback loop. PspA has been previously shown to oligomerise into higher-order species, including a 36-meric species with ring-like structure. In this study, we demonstrate that the ring-like PspA structures further self-assemble into rod-shaped complexes. These rod-like structures may play a scaffolding role in the maintenance of membrane integrity during phage shock protein response

The strong asymptotic freeness of Haar and deterministic matrices

In this paper, we are interested in sequences of q-tuple of N-by-N random matrices having a strong limiting distribution (i.e. given any non-commutative polynomial in the matrices and their conjugate transpose, its normalized trace and its norm converge). We start with such a sequence having this property, and we show that this property pertains if the q-tuple is enlarged with independent unitary Haar distributed random matrices. Besides, the limit of norms and traces in non-commutative polynomials in the enlarged family can be computed with reduced free product construction. This extends results of one author (C. M.) and of Haagerup and Thorbjornsen. We also show that a p-tuple of independent orthogonal and symplectic Haar matrices have a strong limiting distribution, extending a recent result of Schultz.Comment: 12 pages. Accepted for publication to Annales Scientifique de l'EN

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