Minkowski Generalizations of Ward’s Method in Hierarchical Clustering

In this paper, we consider several generalizations of the popular Ward’s method for agglomerative hierarchical clustering. Our work was motivated by clustering software, such as the R function hclust, which accepts a distance matrix as input and applies Ward’s definition of inter-cluster distance to produce a clustering. The standard version of Ward’s method uses squared Euclidean distance to form the distance matrix. We explore the effect on the clustering of using other definitions of distance, such as the Minkowski distance.     

Microstructure-based multiphysics modeling for semiconductor integration and packaging

Semiconductor technology and packaging is advancing rapidly toward system integration where the packaging is co-designed and co-manufactured along with the wafer fabrication. However, materials issues, in par- ticular the mesoscale microstructure, have to date been excluded from the integrated product design cycle of electronic packaging due to the myriad of materials used and the complex nature of the material phenomena that require a multiphysics approach to describe. In the context of the materials genome initiative, we present an overview of a series of studies that aim to establish the linkages between the material microstructure and its responses by considering the multiple perspectives of the various mul- tiphysics fields. The microstructure was predicted using thermodynamic calculations, sharp interface kinetic models, phase field, and phase field crystal modeling techniques. Based on the predicted mesoscale microstruc- ture, linear elastic mechanical analyses and electromigra- tion simulations on the ultrafine interconnects were performed. The microstructural index extracted by a method based on singular value decomposition exhibits a monotonous decrease with an increase in the interconnect size. An artificial neural network-based fitting revealed a nonlinear relationship between the microstructure index and the average yon Mises stress in the ultrafine interconnects. Future work to address the randomness of microstructure and the resulting scatter in the reliability is discussed in this study.     

Variable effects of nitrogen additions on the stability and turnover of soil carbon

Soils contain the largest near-surface reservoir of terrestrial carbon and so knowledge of the factors controlling soil carbon storage and turnover is essential for understanding the changing global carbon cycle. The influence of climate on decomposition of soil carbon has been well documented, but there remains considerable uncertainty in the potential response of soil carbon dynamics to the rapid global increase in reactive nitrogen (coming largely from agricultural fertilizers and fossil fuel combustion). Here, using 14C, 13C and compound-specific analyses of soil carbon from long-term nitrogen fertilization plots, we show that nitrogen additions significantly accelerate decomposition of light soil carbon fractions (with decadal turnover times) while further stabilizing soil carbon compounds in heavier, mineral-associated fractions (with multidecadal to century lifetimes). Despite these changes in the dynamics of different soil pools, we observed no significant changes in bulk soil carbon, highlighting a limitation inherent to the still widely used single-pool approach to investigating soil carbon responses to changing environmental conditions. It remains to be seen if the effects observed here-caused by relatively high, short-term fertilizer additions-are similar to those arising from lower, long-term additions of nitrogen to natural ecosystems from atmospheric deposition, but our results suggest nonetheless that current models of terrestrial carbon cycling do not contain the mechanisms needed to capture the complex relationship between nitrogen availability and soil carbon storage.     

Discretionary databases in forecasting

Information for forecasting databases is often initially under the control of individuals who have no compelling reason to contribute, and who face various significant costs if they do. Such discretionary databases are subject to public goods problems, and are likely to be undersupplied, even when all participants agree that the overall benefits outweigh the overall costs. This paper explores the implications of this incentive structure for the existence, completeness and accuracy of forecasting databases. It also offers some hypotheses as to when the difficulties will be more and less severe, and outlines some directions for possible remedial strategies.     

Geminus and the concept of mean motion in Greco-Latin astronomy

Conclusion Geminus account of lunar motion in chapter 18 of hisIntroductio astronomiae is, in our view, an important contribution to Greco-Latin astronomy because, in attempting to reconstruct arithmetically (the parameters of) the Moon's motion in longitude, he undermines the task astronomers had hitherto set for themselves. This undermining of a commonly acknowledged view of the purpose of astronomy is articulated in a whole new set of questions concerning the nature and place of both observation and mathematical reasoning in the science of the heavens. Yet, one must not overlook the fact thatGeminus reconstruction also indicates resources for addressing these questions. Of these resources, the most powerful proved to be the idea that irregular motion could be quantified as a systematic departure from a mean motion, and the idea that observational data could be organized and structured by means of genetic arithmetical reconstructions.But, since we limit our attention to extant treatises and decline to speculate about works or parts of works that have not survived, we must say that it would takePtolemy to discern the new direction for astronomy thatGeminus opened up and to pursue it. In part, this involved straightening out the conflated conception of mean motion in chapter 18 — the qua arithmetic mean daily displacement can only be anapparent lunar motion in longitude and not one the Moonreally makes, but the same need not be true of the qua periodic mean daily displacement — and determining its proper relation to real and apparent planetary motion. Indeed,Ptolemy's genius lay, we think, in seeing that even though, in assimilating Babylonian astronomy, earlier and contemporary Greco-Latin writers betrayed a confused, inconsistent, and unsophisticated grasp of the proper role of arithmetic, geometry, and observation in astronomical argument [seeBowen 1994], the solution lay in a mathematical reconstruction of the observed celestial motions, in which mean motion played an essential role.     

Cool heliosheath plasma and deceleration of the upstream solar wind at the termination shock

The solar wind blows outward from the Sun and forms a bubble of solar material in the interstellar medium. The termination shock occurs where the solar wind changes from being supersonic (with respect to the surrounding interstellar medium) to being subsonic. The shock was crossed by Voyager 1 at a heliocentric radius of 94 au (1 au is the Earth-Sun distance) in December 2004 (refs 1-3). The Voyager 2 plasma experiment observed a decrease in solar wind speed commencing on about 9 June 2007, which culminated in several crossings of the termination shock between 30 August and 1 September 2007 (refs 4-7). Since then, Voyager 2 has remained in the heliosheath, the region of shocked solar wind. Here we report observations of plasma at and near the termination shock and in the heliosheath. The heliosphere is asymmetric, pushed inward in the Voyager 2 direction relative to the Voyager 1 direction. The termination shock is a weak, quasi-perpendicular shock that heats the thermal plasma very little. An unexpected finding is that the flow is still supersonic with respect to the thermal ions downstream of the termination shock. Most of the solar wind energy is transferred to the pickup ions or other energetic particles both upstream of and at the termination shock.