Let (W, C) be an m-cycle system of order n and let Ω ⊂ W , |Ω| = v < n. We say that a path design (Ω,P) of order v and block size s (2 ≤ s ≤ m− 1) is embedded in (W, C) if for every p ∈ P there is an m-cycle c = (a1, a2, . . . , am) ∈ C such that: (1) p = [ak, ak+1, . . . , ak+s−1] for some k ∈ {1, 2, . . . ,m} (i.e. the (s− 1)-path p occurs in the m-cycle c); and (2) ak−1, ak+s ∈ Ω. Note that ...

A (v, K, A) packing design of order v, block size K, and index 1 is a collection of K-element subsets, called blocks, of a v-set V such that every 2-subset of V occurs in at most L blocks. The packing problem is to determine the maximum number of blocks in a packing design. Packing with 1= 2 is called bipacking. In this paper we solve the bipacking problem in the case K = 5 and v = 13 (mod 20).

There exists a balanced ternary design with block size 3 and index 2 on 2v P2 + 4 and 2v P2 + 1 elements with a hole of size v, for all positive integers v and P2, such that v ~ 2P2 + 1. As an application of this result, we determine the numbers of common triples in two simple balanced ternary designs with block size 3 and index 2, for P2 = 3 and 4.

Let V be a finite set of order v. A (v,k,A.) covering design of index A. and block size k is a collection of k-element subsets, called blocks, such that every 2-subset of V occurs in at least '}.. blocks. The covering problem is to determine the minimum number of blocks, a (v, k, A.), in a covering design. It is well known that a(v,k''}..)Lr~~=~'}..ll=(v,k,A.), where rxl is the smallest integer

A directed covering design, DC(v, k, λ), is a (v, k, 2λ) covering design in which the blocks are regarded as ordered k-tuples and in which each ordered pair of elements occurs in at least λ blocks. Let DE(v, k, λ) denote the minimum number of blocks in a DC(v, k, λ). In this paper the values of the function DE(v, 5, λ) are determined for all even integers v ≥ 5 and λ odd.

This article presents results on the cryptanalysis of a quasigroup block cipher, which was previously proposed. The quasigroup block cipher provides an attractive encryption system for resource constrained environments. Here, we identify the “odd-bit” and “identical-word” problems with the cipher and recommend configurations of the QGBC to counter these. Following this analysis, we propose an i...

Iowa Gambling Task (IGT) is one of the most widely used tools to assess economic decision-making. However, the research tradition on aging and the Iowa Gambling Task (IGT) has been mainly focused on the overall performance of older adults in relation to younger or clinical groups, remaining unclear whether older adults are capable of learning along the task. We conducted a meta-analysis to exam...

The statistical analysis of spatial data is usually done under Gaussian assumption for the underlying random field model. When this assumption is not satisfied, block bootstrap methods can be used to analyze spatial data. One of the crucial problems in this setting is specifying the block sizes. In this paper, we present asymptotic optimal block size for separate block bootstrap to estimate the...

The state-of-the-art video coding standard H.264/AVC achieves significant coding performance by adopting variable block sizes for motion estimation (ME) and mode decision. However, this technique brings out high computational complexity since the optimal mode is determined by exhaustively performing rate-distortion optimization (RDO) on each coding mode with different block sizes. In this paper...