In this paper, we present algorithms and lower bounds for the Longest Increasing Subsequence (LIS) and Longest Common Subsequence (LCS) problems in the data streaming model. For the problem of deciding whether the LIS of a given stream of integers drawn from {1, . . . ,m} has length at least k, we discuss a one-pass streaming algorithm using O(k log m) space, with update time either O(log k) or...

A rollercoaster is a sequence of real numbers for which every maximal contiguous subsequence, that is increasing or decreasing, has length at least three. By translating this sequence to a set of points in the plane, a rollercoaster can be defined as a polygonal path for which every maximal sub-path, with positiveor negative-slope edges, has at least three points. Given a sequence of distinct r...

The longest increasing subsequence of a random walk with mean zero and finite variance is known to be n1/2+o(1). We show that this is not universal for symmetric random walks. In particular, the symmetric fat-tailed random walk has a longest increasing subsequence that is asymptotically at least n0.690 and at most n0.815. An exponent strictly greater than 1/2 is also shown for the symmetric sta...

Recently, many authors have considered the problem of simultaneous localisation and mapping (SLAM). The paper addresses a somewhat diierent problem, that of cooperative localisation and mapping (CLAM). Basically, CLAM involves two or more robots cooperating to build a map of the environment. This cooperation is not aimed at simply increasing the speed with which the map is constructed; rather, ...

We demonstrate that a local mapping f in a space of bisequences over {0, 1} which conserves the number of nonzero sites can be viewed as a deterministic particle system evolving according to a local mapping in a space of increasing bisequences over Z. We present an algorithm for determination of the local mapping in the space of particle coordinates corresponding to the local mapping f .

A new ultra-high-density mapping system (RhythmiaTM) is gaining increasing interest from the electrophyology community, especially for the mapping of organized complex tachycardias. The system uses the magnetic tracking of the mapping catheter. Whether this system is compatible with magnetic navigation is not known. We report the first case of combined ultra-high-density mapping and remote magn...

Teachers are required to be able apply digital tools and media every aspect of their professional duties. Teachers’ competence become important for teachers acquire. This research purpose is mapping the use technologies in teachers’ practice. Data was obtained through a survey analized with descriptive statistics analysis from 93 samples elementary, middle school, high vocational school teacher...

Background and Aim: Brain mapping is a study of the anatomy and function of the CNS (central nervous system). Brain mapping has many techniques and these techniques are permanently changing and updating. From the beginning, brain mapping was invasive and for brain mapping, electrical stimulation of the exposed brain was needed. However, nowadays brain mapping does not require electrical stimula...

Increasing access, even increasing supply, may not be sufficient to attract young teens who do not typically participate in youth programs. Several youth mapping projects in rural and urban communities have led to these conclusions: youth do not know what is available even in their own neighborhoods, young teens have a strong voice in how they spend their discretionary time, and we need to lear...