in conjunction with Euler’s formula, f1 = f0 + f2 − 2; see also [6, Sect. 10.3]. Moreover, the cone of flag vectors of 3-polytopes is also given by these two inequalities, together with the usual Dehn– Sommerville relations, such as f02 = 2f1 and f012 = 4f1. Here the extreme cases, polytopes whose f or flag vectors lie at the boundary of the cone, are given by the simplicial polytopes (for whic...

This paper develops a test for homogeneity in finite mixture models where the mixing proportions are known a priori (taken to be 0.5) and a common nuisance parameter is present. Statistical tests based on the notion of Projected Likelihood Contrasts (PLC) are considered. The PLC is a slight modification of the usual likelihood ratio statistic or the Wilk’s Λ and is similar in spirit to the Rao’...

We construct a class of projected SO~5! models where the Gutzwiller constraint of no-double-occupancy is implemented exactly. We introduce the concept of projected SO~5! symmetry where all static correlation functions are exactly SO~5! symmetric and discuss the signature of the projected SO~5! symmetry in dynamical correlation functions. We show that this class of projected SO~5! models can giv...

Model counting is the task of computing the number of assignments to variables V that satisfy a given propositional theory F . The model counting problem is denoted as #SAT. Model counting is an essential tool in probabilistic reasoning. In this paper, we introduce the problem of model counting projected on a subset of original variables that we call priority variables P ⊆ V. The task is to com...

Prediction of projected tree leaf area using allometric relationships with sapwood cross-sectional area is common in treeand stand-level production studies. Measuring sapwood is difficult and often requires destructive sampling. This study tested multiple leaf area prediction models across seven diverse conifer species in the Sierra Nevada of California. The best-fit whole tree leaf area predic...

A climate model that includes a coupled ocean biogeochemistry model is used to define large oceanic biomes in the North Pacific Ocean and describe their changes over the 21st century in response to the IPCC Special Report on Emission Scenario A2 future atmospheric CO2 emissions scenario. Driven by enhanced stratification and a northward shift in the mid-latitude westerlies under climate change,...

Climate influences forests directly and indirectly through disturbance. The interaction of climate change and increasing area burned has the potential to alter forest composition and community assembly. However, the overall forest response is likely to be influenced by species-specific responses to environmental change and the scale of change in overstory species cover. In this study, we sought...