Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra

Let $\Gamma$ denote a distance-regular graph with diameter $D\geq 3$ and Bose-Mesner algebra $M$. For $\theta\in C\cup \infty$ we define a 1 dimensional subspace of $M$ which we call $M(\theta)$. If $\theta\in C$ then $M(\theta)$ consists of those $Y$ in $M$ such that $(A-\theta I)Y\in C A_D$, where $A$ (resp. $A_D$) is the adjacency matrix (resp. $D$th distance matrix) of $\Gamma.$ If $\theta = \infty$ then $M(\theta)= C A_D$. By a {\it pseudo primitive idempotent} for $\theta$ we mean a nonzero element of $M(\theta)$. We use pseudo primitive idempotents to describe the irreducible modules for the Terwilliger algebra, that are thin with endpoint one.Comment: 17 page

Earnings Returns to the British Education Expansion

We study the effects of the large expansion in British educational attainment that took place for cohorts born between 1970 and 1975. Using the Quarterly Labour Force Survey, we find that the expansion caused men to increase education by about a year on average and gain about 8% higher wages; women obtained a slightly greater increase in education and a similar increase in wages. Clearly, there was a sizeable gain from being born late enough to take advantage of the greater educational opportunities offered by the expansion. Treating the expansion as an exogenous increase in educational attainment, we obtain instrumental variables estimates of returns to schooling of about 6% for both men and women.return to education; higher education expansion

Simulation α of EEG using brain network model

In this paper, we developed a large-scale brain network model comprising of four cerebral areas in the left hemisphere, and each area is modelled as an oscillator Jansen and Rit (JR) model. Our model is based on the structural connectivity of human connectome (SC) which was a hybrid from CoCoMac neuroinformatics database and diffusion spectrum imaging (DSI.) This brain network model was designed and implemented on the neuroinformatics platform using The Virtual Brain (TVB v1.5.3). The results demonstrated that incorporating the large-scale connectivity of brain regions and neural mass of JR model can generate signals similar to the α oscillation in frequency range of (7-12HZ) of EEG