Test for bandedness of high-dimensional covariance matrices and bandwidth estimation

Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance $\Sigma$, we propose a test for $\Sigma$ being banded with possible diverging bandwidth. The test is adaptive to the "large $p$, small $n$" situations without assuming a specific parametric distribution for the data. We also formulate a consistent estimator for the bandwidth of a banded high-dimensional covariance matrix. The properties of the test and the bandwidth estimator are investigated by theoretical evaluations and simulation studies, as well as an empirical analysis on a protein mass spectroscopy data.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1002 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fumihiko Maki and His Theory of Collective Form: A Study on Its Practical and Pedagogical Implications

This thesis seeks to reexamine Fumihiko Maki’s Investigations in Collective Form: 1964) from a historical and educational point of view, speculating the practical and pedagogical implications of Maki’s collective form theory. Firstly, to better understand the formation of both the writer himself and the book, the historical context in the 1950s and 1960s will be unfolded to reveal what Maki had encountered during his formative years that had contributed to his cross-cultural background and had inspired his thoughts in the book. Secondly, the three paradigms and the notion of linkage, as proposed in the book, will be analyzed through comparisons with other influential architectural theories and studies. The understanding of the collective form theory will be expanded through exploring parallel ideas and examining Maki’s practice. Moreover, past educational integrations of the design philosophies derived from collective form will be studied, which will include, but not limit to, the earliest urban design studios in School of Architecture at Washington University: WU) and the Graduate School of Design: GSD) at Harvard. Last but not least, contemporary application and development of collective form theory will be explored. Conclusions will be drawn upon the possibilities of how the inherited nature of collective form can further contribute to the future architectural practice and pedagogy

Algorithms to test open set condition for self-similar set related to P.V. numbers

Fix a P.V. number $\lambda ^{-1}>1.$ Given $\mathbf{p}=(p_{1},\cdots,p_{m})\in \mathbb{N}^{m}$, \mathbf{b}=(b_{1},\cdots,b_{m})\in \mathbb{Q^{m}, for the self-similar set $E_{\mathbf{p},\mathbf{b}}=\cup_{i=1}^{m}(\lambda ^{p_{i}}E_{\mathbf{p},\mathbf{b}}+b_{i})$ we find an efficient algorithm to test whether $E_{\mathbf{p},\mathbf{b}}$ satisfies the open set condition (strong separation condition) or not

Research on Combustion Chamber Structure Improvement and Ignition System of Missile Turbojet Engine for Diesel Fuel

To meet the conditions of diesel ignition, this paper presents several structural improvements of a small missile turbojet engine for diesel fuel. The engine starts motor-assisted, and its fuel is ignited by silicon nitride ceramic ignitor. Theoretical analysis is performed by establishing a mathematical model of the combustion model and combustion conditions. The feasibility of diesel used as a small turbojet fuel is analyzed by using numerical simulation software. Research is carried out based on the following points: the improvement of combustion chamber and evaporator, selection of ignitor position and sustainability of fire. This paper proposed the method of linking the engine-assisting startup system and selected the right type of ignitor, and on the advanced experimental platform several groups ignition tests were carried out