ABSTRACT We present a novel hierarchical formulation of the fourth-order forward symplectic integrator and its numerical implementation in GPU-accelerated direct-summation N-body code frost. The new is especially suitable for simulations with large dynamical range due to nature. strictly positive sub-steps are made possible by computing an additional gradient term addition Newtonian acceleratio...

How do students’ conceptualize the causes of their own academic successes and failures? Taking a phenomenological approach, students identified the causes of their performance immediately following return of a graded examination. We then used factor and item analyses to organize causes that were identified by a substantial number of students into meaningful conceptual clusters, and confirmed th...

In both the design and use of large-scale mathematical programming systems, a substantial portion of the effort has no direct relation to the variables and constraints, but is instead concerned with the description, manipulation and display of data. Established principles of database design do not apply directly to mathematical programming, however, because there are significant differences of ...

Alexandria is an implementation of the hierarchical verii-cation methodology for the Higher-Order Logic (HOL) theorem prover. The main contribution of Alexandria is the reduction of eeort required by the user to create and use hierarchical hardware proofs in HOL. We discuss the implementation and use of Alexandria with an example and outline our future work.

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect matching as a subroutine in order to efficiently explore the space of planar partitions. We apply our algorithm to the problem of hierarchical image segmentat...

In linear models with hierarchical interaction structures product type designs are shown to be D{optimal simultaneously for the whole parameter vector and for testing against any hierarchical submodel. Moreover, product type designs are also q {optimal for the highest order interactions.

This paper studies the hierarchical broadcast networks, which are deened as broadcast networks whose every connected induced subgraph is also a broadcast network. We show that the minimum number of edges of a hierarchical broadcast network of order n is d n(n?2) 2 e for any n 4.

We study closures of hierarchical models which are exponential families associated with hypergraphs by decomposing the corresponding interaction spaces in a natural and transparent way. Here, we apply general results on closures of exponential families. Index Terms – Closure of exponential family, graphical model, hierarchical model, interaction order.