971 research outputs found
Blocked regular fractional factorial designs with minimum aberration
This paper considers the construction of minimum aberration (MA) blocked
factorial designs. Based on coding theory, the concept of minimum moment
aberration due to Xu [Statist. Sinica 13 (2003) 691--708] for unblocked designs
is extended to blocked designs. The coding theory approach studies designs in a
row-wise fashion and therefore links blocked designs with nonregular and
supersaturated designs. A lower bound on blocked wordlength pattern is
established. It is shown that a blocked design has MA if it originates from an
unblocked MA design and achieves the lower bound. It is also shown that a
regular design can be partitioned into maximal blocks if and only if it
contains a row without zeros. Sufficient conditions are given for constructing
MA blocked designs from unblocked MA designs. The theory is then applied to
construct MA blocked designs for all 32 runs, 64 runs up to 32 factors, and all
81 runs with respect to four combined wordlength patterns.Comment: Published at http://dx.doi.org/10.1214/009053606000000777 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Generalized resolution for orthogonal arrays
The generalized word length pattern of an orthogonal array allows a ranking
of orthogonal arrays in terms of the generalized minimum aberration criterion
(Xu and Wu [Ann. Statist. 29 (2001) 1066-1077]). We provide a statistical
interpretation for the number of shortest words of an orthogonal array in terms
of sums of values (based on orthogonal coding) or sums of squared
canonical correlations (based on arbitrary coding). Directly related to these
results, we derive two versions of generalized resolution for qualitative
factors, both of which are generalizations of the generalized resolution by
Deng and Tang [Statist. Sinica 9 (1999) 1071-1082] and Tang and Deng [Ann.
Statist. 27 (1999) 1914-1926]. We provide a sufficient condition for one of
these to attain its upper bound, and we provide explicit upper bounds for two
classes of symmetric designs. Factor-wise generalized resolution values provide
useful additional detail.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1205 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Quarter-fraction factorial designs constructed via quaternary codes
The research of developing a general methodology for the construction of good
nonregular designs has been very active in the last decade. Recent research by
Xu and Wong [Statist. Sinica 17 (2007) 1191--1213] suggested a new class of
nonregular designs constructed from quaternary codes. This paper explores the
properties and uses of quaternary codes toward the construction of
quarter-fraction nonregular designs. Some theoretical results are obtained
regarding the aliasing structure of such designs. Optimal designs are
constructed under the maximum resolution, minimum aberration and maximum
projectivity criteria. These designs often have larger generalized resolution
and larger projectivity than regular designs of the same size. It is further
shown that some of these designs have generalized minimum aberration and
maximum projectivity among all possible designs.Comment: Published in at http://dx.doi.org/10.1214/08-AOS656 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Construction of optimal multi-level supersaturated designs
A supersaturated design is a design whose run size is not large enough for
estimating all the main effects. The goodness of multi-level supersaturated
designs can be judged by the generalized minimum aberration criterion proposed
by Xu and Wu [Ann. Statist. 29 (2001) 1066--1077]. A new lower bound is derived
and general construction methods are proposed for multi-level supersaturated
designs. Inspired by the Addelman--Kempthorne construction of orthogonal
arrays, several classes of optimal multi-level supersaturated designs are given
in explicit form: Columns are labeled with linear or quadratic polynomials and
rows are points over a finite field. Additive characters are used to study the
properties of resulting designs. Some small optimal supersaturated designs of
3, 4 and 5 levels are listed with their properties.Comment: Published at http://dx.doi.org/10.1214/009053605000000688 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Minimum aberration designs for discrete choice experiments
A discrete choice experiment (DCE) is a survey method that givesinsight into individual preferences for particular attributes.Traditionally, methods for constructing DCEs focus on identifyingthe individual effect of each attribute (a main effect). However, aninteraction effect between two attributes (a two-factor interaction)better represents real-life trade-offs, and provides us a better understandingof subjects’ competing preferences. In practice it is oftenunknown which two-factor interactions are significant. To address theuncertainty, we propose the use of minimum aberration blockeddesigns to construct DCEs. Such designs maximize the number ofmodels with estimable two-factor interactions in a DCE with two-levelattributes. We further extend the minimum aberration criteria toDCEs with mixed-level attributes and develop some general theoreticalresults
FPGA-based Serial Port-controlled Frequency Adjustable Waveform Generator
This article explores the design, optimization, and applications of FPGA-based Direct Digital Synthesis (DDS) waveform generators. The DDS technology is widely used in signal generation and processing and is favored for its flexibility and precision. The paper discusses performance optimization strategies, focusing on enhancing frequency resolution, waveform quality, and phase accumulation speed. Suggestions include increasing phase accumulator’s bit width, optimizing the size of the phase lookup table, introducing frequency interpolation, and employing fast accumulation algorithms. Additionally, it delves into more applications such as high-precision testing, high-speed communication systems, multi-channel data synchronization, and multi-waveform outputs. The conclusion emphasizes the ongoing need for performance improvements and application advancements. Future directions include exploring higher-precision phase lookup table designs, sophisticated filtering, efficient accumulation algorithms, and leveraging advanced FPGA chips for broader application scope. Overall, FPGA-based DDS waveform generators exhibit significant potential across various domains, promising enhanced signal accuracy and adaptability
Mapping the Galaxy in 3D Using Observations of HII Region Absorption with the MWA
This thesis measures the distribution of the diffuse synchrotron emission in the Galactic Plane using data from the GaLactic and Extragalactic All-sky MWA survey (GLEAM) in the frequency range 72-231 MHz. It improves the method of calculating the synchrotron emissivity along sight lines intersecting HII regions, and increases the number of such measurements from tens to hundreds. A further 588 HII regions are identified using both their emission and absorption features in the GLEAM maps
Uniform fractional factorial designs
The minimum aberration criterion has been frequently used in the selection of
fractional factorial designs with nominal factors. For designs with
quantitative factors, however, level permutation of factors could alter their
geometrical structures and statistical properties. In this paper uniformity is
used to further distinguish fractional factorial designs, besides the minimum
aberration criterion. We show that minimum aberration designs have low
discrepancies on average. An efficient method for constructing uniform minimum
aberration designs is proposed and optimal designs with 27 and 81 runs are
obtained for practical use. These designs have good uniformity and are
effective for studying quantitative factors.Comment: Published in at http://dx.doi.org/10.1214/12-AOS987 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Model Augmented Deep Neural Networks for Medical Image Reconstruction Problems
Solving an ill-posed inverse problem is difficult because it doesn\u27t have a unique solution. In practice, for some important inverse problems, the conventional methods, e.g. ordinary least squares and iterative methods, cannot provide a good estimate. For example, for single image super-resolution and CT reconstruction, the results of these conventional methods cannot satisfy the requirements of these applications. While having more computational resources and high-quality data, researchers try to use machine-learning-based methods, especially deep learning to solve these ill-posed problems. In this dissertation, a model augmented recursive neural network is proposed as a general inverse problem method to solve these difficult problems. In the dissertation, experiments show the satisfactory performance of the proposed method for single image super-resolution, CT reconstruction, and metal artifact reduction
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