6,391 research outputs found
Decomposition tables for experiments I. A chain of randomizations
One aspect of evaluating the design for an experiment is the discovery of the
relationships between subspaces of the data space. Initially we establish the
notation and methods for evaluating an experiment with a single randomization.
Starting with two structures, or orthogonal decompositions of the data space,
we describe how to combine them to form the overall decomposition for a
single-randomization experiment that is ``structure balanced.'' The
relationships between the two structures are characterized using efficiency
factors. The decomposition is encapsulated in a decomposition table. Then, for
experiments that involve multiple randomizations forming a chain, we take
several structures that pairwise are structure balanced and combine them to
establish the form of the orthogonal decomposition for the experiment. In
particular, it is proven that the properties of the design for such an
experiment are derived in a straightforward manner from those of the individual
designs. We show how to formulate an extended decomposition table giving the
sources of variation, their relationships and their degrees of freedom, so that
competing designs can be evaluated.Comment: Published in at http://dx.doi.org/10.1214/09-AOS717 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Intersection numbers for subspace designs
Intersection numbers for subspace designs are introduced and -analogs of
the Mendelsohn and K\"ohler equations are given. As an application, we are able
to determine the intersection structure of a putative -analog of the Fano
plane for any prime power . It is shown that its existence implies the
existence of a - subspace design. Furthermore, several
simplified or alternative proofs concerning intersection numbers of ordinary
block designs are discussed
Decomposition tables for experiments. II. Two--one randomizations
We investigate structure for pairs of randomizations that do not follow each
other in a chain. These are unrandomized-inclusive, independent, coincident or
double randomizations. This involves taking several structures that satisfy
particular relations and combining them to form the appropriate orthogonal
decomposition of the data space for the experiment. We show how to establish
the decomposition table giving the sources of variation, their relationships
and their degrees of freedom, so that competing designs can be evaluated. This
leads to recommendations for when the different types of multiple randomization
should be used.Comment: Published in at http://dx.doi.org/10.1214/09-AOS785 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
An Algorithmic Framework for Efficient Large-Scale Circuit Simulation Using Exponential Integrators
We propose an efficient algorithmic framework for time domain circuit
simulation using exponential integrator. This work addresses several critical
issues exposed by previous matrix exponential based circuit simulation
research, and makes it capable of simulating stiff nonlinear circuit system at
a large scale. In this framework, the system's nonlinearity is treated with
exponential Rosenbrock-Euler formulation. The matrix exponential and vector
product is computed using invert Krylov subspace method. Our proposed method
has several distinguished advantages over conventional formulations (e.g., the
well-known backward Euler with Newton-Raphson method). The matrix factorization
is performed only for the conductance/resistance matrix G, without being
performed for the combinations of the capacitance/inductance matrix C and
matrix G, which are used in traditional implicit formulations. Furthermore, due
to the explicit nature of our formulation, we do not need to repeat LU
decompositions when adjusting the length of time steps for error controls. Our
algorithm is better suited to solving tightly coupled post-layout circuits in
the pursuit for full-chip simulation. Our experimental results validate the
advantages of our framework.Comment: 6 pages; ACM/IEEE DAC 201
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