212 research outputs found
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On the number of additive permutations and Skolem-type sequences
Cavenagh and Wanless recently proved that, for sufficiently large odd n, the number of transversals in the Latin square formed from the addition table for integers modulo n is greater than (3.246)n. We adapt their proof to show that for sufficiently large t the number of additive permutations on [-t,t] is greater than (3.246)2t+1 and we go on to derive some much improved lower bounds on the numbers of Skolem-type sequences. For example, it is shown that for sufficiently large t ≡ 0$ or 3 (mod 4), the number of split Skolem sequences of order n=7t+3 is greater than (3.246)6t+3. This compares with the previous best bound of 2⌊n/3⌋
On the number of transversals in a class of Latin squares
Denote by the Latin square of order formed by the Cayley table of the additive group , where is an odd prime and is a positive integer. It is shown that for each there exists such that for all sufficiently large , the number of transversals in exceeds
A Simple Approach to Constructing Quasi-Sudoku-based Sliced Space-Filling Designs
Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced
orthogonal array-based space-filling designs are useful experimental designs in
several contexts, including computer experiments with categorical in addition
to quantitative inputs and cross-validation. Here, we provide a straightforward
construction of doubly orthogonal quasi-Sudoku Latin squares which can be used
to generate sliced space-filling designs which achieve uniformity in one and
two-dimensional projections for both the full design and each slice. A
construction of quasi-sliced orthogonal arrays based on these constructed
doubly orthogonal quasi-Sudoku Latin squares is also provided and can, in turn,
be used to generate sliced space-filling designs which achieve uniformity in
one and two-dimensional projections for the full design and and uniformity in
two-dimensional projections for each slice. These constructions are very
practical to implement and yield a spectrum of design sizes and numbers of
factors not currently broadly available.Comment: 15 pages, 9 figure
Populations of models, Experimental Designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling
In this paper we have used simulations to make a conjecture about the
coverage of a dimensional subspace of a dimensional parameter space of
size when performing trials of Latin Hypercube sampling. This takes the
form . We suggest that this coverage formula is
independent of and this allows us to make connections between building
Populations of Models and Experimental Designs. We also show that Orthogonal
sampling is superior to Latin Hypercube sampling in terms of allowing a more
uniform coverage of the dimensional subspace at the sub-block size level.Comment: 9 pages, 5 figure
Function Before Form: Designing the Ideal Library Classroom
At Indiana University-Bloomington, the libraries house many rooms that are used for instructional purposes, but none represents the characteristics of an ideal learning environment. In order to address the growing instructional needs of the IUB libraries and the lack of appropriate space in which to provide IL instruction, the libraries created a committee that was charged with making recommendations for new library classrooms. The group started this task by conducting a literature review on the concepts of classroom design and best practices. Finding surprisingly little research or practical information published about classroom design with which to guide them, the committee devised their own approach for assessing needs, reviewing current practices, and developing a plan for implementation.
During this presentation, we will share our experiences and the knowledge we gained in designing our ideal classrooms in order to assist others who are faced with a similar task. In addition, we hope this presentation will fill what we believe to be a gap in the professional literature by providing a forum for discussion and innovation which we will document and share broadly. To achieve this, our presentation will include an interactive breakout session during which groups of attendees will work together to design space for various types of teaching models. We will give participants “kits” to build the space using graph paper and pre-cut shapes. We will use the results of this session to launch a best practices website that includes the designs created by attendees, a blog, photo sharing, in addition to other relevant resources.
Interactive Sessio
Difference Covering Arrays and Pseudo-Orthogonal Latin Squares
Difference arrays are used in applications such as software testing,
authentication codes and data compression. Pseudo-orthogonal Latin squares are
used in experimental designs. A special class of pseudo-orthogonal Latin
squares are the mutually nearly orthogonal Latin squares (MNOLS) first
discussed in 2002, with general constructions given in 2007. In this paper we
develop row complete MNOLS from difference covering arrays. We will use this
connection to settle the spectrum question for sets of 3 mutually
pseudo-orthogonal Latin squares of even order, for all but the order 146
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Embedding partial Latin squares in Latin squares with many mutually orthogonal mates
In this paper it is shown that any partial Latin square of order can be embedded in a Latin square of order at most which has at least mutually orthogonal mates. Further, for any , it is shown that a pair of orthogonal partial Latin squares of order can be embedded in a set of mutually orthogonal Latin squares (MOLS) of order a polynomial with respect to . A consequence of the constructions is that, if denotes the size of the largest set of MOLS of order , then . In particular, it follows that , improving the previously known lower bound
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