By reviewing Longest Increasing Subsequence (LIS) and Longest Common Subsequence (LCS), the Longest Common Increasing Subsequence (LCIS) problem is explored for two non-random input cases in details. Specifically, we designed two algorithms, one solving the input sequence scenario with the case that one sequence is ordered and duplicate elements are allowed in each of sequences, and the second ...

We consider the problem of :nding the longest increasing subsequence in a sliding window over a given sequence (LISW). We propose an output-sensitive data structure that solves this problem in time O(n log log n+OUTPUT) for a sequence of n elements. This data structure substantially improves over the na?@ve generalization of the longest increasing subsequence algorithm and in fact produces an o...

In this paper we give parallel solutions to the problem of finding the Longest Increasing Subsequence of a given sequence of n integers. First, we show the existence of a simple dynamic programming solution. Its running time is Θ(n) and its space requirement is Θ(n). Then, we continue by showing that it is possible to develop two parallel solutions based on optical bus system of n processors, o...

We study the fluctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation. §.

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has always been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium...

This study aimed to provide basic materials for resolving the problems of baby boomers, emerging as a social issue by identifying the effect of baby boomers' participation motivation in leisure sports activities on recovery resilience and life satisfaction empirically. Using the convenience sampling method, the subjects were conducted by baby boomer's 323 person lived in Seoul and Gyeong-in, 20...

BACKGROUND Patient participation on both the individual and the collective level attracts broad attention from policy makers and researchers. Participation is expected to make decision making more democratic and increase the quality of decisions, but empirical evidence for this remains wanting. OBJECTIVE To study why problems arise in participation practice and to think critically about the c...

We review past studies on how scientists view the public, the goals of communication, the performance and impacts of the media, and the role of the public in policy decision-making. We add to these past findings by analyzing two recent large-scale surveys of scientists in the UK and US. These analyses show that scientists believe the public is uninformed about science and therefore prone to err...

We consider the concentration of measure for n iid, two-dimensional random variables, under the conditioning that they form a record. Under mild conditions, we show that all random variables tend to concentrate, as n ! 1, around limiting curves, which are the solutions of an appropriate variational problem. We also show that the same phenomenum occurs, without the records conditioning, for the ...