The Breadth-one DD-invariant Polynomial Subspace

We demonstrate the equivalence of two classes of $D$-invariant polynomial subspaces introduced in [8] and [9], i.e., these two classes of subspaces are different representations of the breadth-one $D$-invariant subspace. Moreover, we solve the discrete approximation problem in ideal interpolation for the breadth-one $D$-invariant subspace. Namely, we find the points, such that the limiting space of the evaluation functionals at these points is the functional space induced by the given $D$-invariant subspace, as the evaluation points all coalesce at one point

Spectral distributions of adjacency and Laplacian matrices of random graphs

In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest eigenvalues of the adjacency and the Laplacian matrices; (ii) under some further independent conditions, the normalized largest eigenvalues of the Laplacian matrices are dense in a compact interval almost surely; (iii) the empirical distributions of the eigenvalues of the Laplacian matrices converge weakly to the free convolution of the standard Gaussian distribution and the Wigner's semi-circular law; (iv) the empirical distributions of the eigenvalues of the adjacency matrices converge weakly to the Wigner's semi-circular law.Comment: Published in at http://dx.doi.org/10.1214/10-AAP677 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Demographic Dividends, Human Capital, and Saving.

The objective of this paper is to provide new evidence about the development effects of changes in population age structure and human and physical capital. This extends our previous work by developing and employing a more comprehensive model of demographic dividends. In addition, we extend earlier analysis about the quantity-quality tradeoff using newly available NTA data for 39 countries, in contrast to the nineteen with the necessary data in our 2010 study. This permits a more detailed analysis, treating public expenditures and private expenditures separately, and considering the role of per capita income as well as fertility and child dependency in relation to human capital spending. The analysis is used in a simulation with realistic demography to show how human capital investment has varied in relation to the changing demography from 1950 to the present, and how it might be expected to change over the rest of this century. These new estimates are then used in a more comprehensive model that incorporates both human and physical capital. The analysis provides estimates of the first and second demographic dividends and how they are affected by speed of fertility decline. The timing of the effects is documented and the relative importance of investment in physical and human capital is assessed. This improves our understanding of the economic implications of the demographic dividend and particularly the “second demographic dividend”

Increment entropy as a measure of complexity for time series

Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters, one letter corresponding to direction and the other corresponding to magnitude. The Shannon entropy of the words is termed as increment entropy (IncrEn). Simulations on synthetic data and tests on epileptic EEG signals have demonstrated its ability of detecting the abrupt change, regardless of energetic (e.g. spikes or bursts) or structural changes. The computation of IncrEn does not make any assumption on time series and it can be applicable to arbitrary real-world data.Comment: 12pages,7figure,2 table