scholarly journals Optimal Multiplicative Generalized Linear Search Plan for a Discrete Random Walker

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Abd-Elmoneim Anwar Mohamed ◽  
Mohamed Abd Allah El-Hadidy
Keyword(s):  
Linear Search ◽  
Random Walker ◽  
Search Plan

scholarly journals Parabolic Spiral Search Plan for a Randomly Located Target in the Plane

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed Beltagy ◽  
Mohamed Abd Allah El-Hadidy
Keyword(s):  
Target Position ◽  
Expected Value ◽  
Dimensional Case ◽  
Linear Search ◽  
Search Technique ◽  
One Dimensional ◽  
Search Plan ◽  
Starting Point ◽  
Complete Revolution ◽  
The One

This paper addresses the problem of searching for a located target in the plane by using one searcher starting its motion from the point . The searcher moves along parabolic spiral curve. The position of the target has a known distribution. We show that the distance between the target position and the searcher starting point depends on the number of revolutions, where the complete revolution is done when . Furthermore, we study this technique in the one-dimensional case (i.e., when the searcher moves with linear search technique). It is desired to get the expected value of the time for detecting the target. Illustrative examples are given to demonstrate the applicability of this technique assuming circular normal distributed estimates of the target position.

Searching for a one-dimensional random walker

1974 ◽  
Vol 11 (01) ◽  
pp. 86-93 ◽  
Author(s):  
Bernard J. McCabe
Keyword(s):  
Random Walk ◽  
Wiener Process ◽  
One Dimensional ◽  
Random Walker ◽  
Search Plan ◽  
Crossing Time ◽  
Definition Of ◽  
First Crossing Time ◽  
Finite Moments ◽  
Bernoulli Random Walk

Let {xk } k ≧ − r be a simple Bernoulli random walk with x –r = 0. An integer valued threshold ϕ = {ϕ k } k≧1 is called a search plan if |ϕ k+1−ϕ k |≦1 for all k ≧ 1. If ϕ is a search plan let τϕ be the smallest integer k such that x and ϕ cross or touch at k. We show the existence of a search plan ϕ such that ϕ 1 = 0, the definition of ϕ does not depend on r, and the first crossing time τϕ has finite mean (and in fact finite moments of all orders). The analogous problem for the Wiener process is also solved.

Searching for a one-dimensional random walker

1974 ◽  
Vol 11 (1) ◽  
pp. 86-93 ◽  
Author(s):  
Bernard J. McCabe
Keyword(s):  
Random Walk ◽  
Wiener Process ◽  
One Dimensional ◽  
Random Walker ◽  
Search Plan ◽  
Crossing Time ◽  
Definition Of ◽  
First Crossing Time ◽  
Finite Moments ◽  
Bernoulli Random Walk

Let {xk}k ≧ − r be a simple Bernoulli random walk with x–r = 0. An integer valued threshold ϕ = {ϕk}k≧1 is called a search plan if |ϕk+1−ϕk|≦1 for all k ≧ 1. If ϕ is a search plan let τϕ be the smallest integer k such that x and ϕ cross or touch at k. We show the existence of a search plan ϕ such that ϕ1 = 0, the definition of ϕ does not depend on r, and the first crossing time τϕ has finite mean (and in fact finite moments of all orders). The analogous problem for the Wiener process is also solved.

Searching for the Random Walking microorganism cells

2019 ◽  
Vol 12 (06) ◽  
pp. 1950064 ◽  
Author(s):  
Mohamed Abd Allah El-Hadidy ◽  
Hamdy M. Abou-Gabal
Keyword(s):  
Expected Value ◽  
Random Walking ◽  
Search Technique ◽  
Cooperative Search ◽  
Search Plan ◽  
Unit Speed ◽  
Text Unit

In this paper, we present a complex cooperative search technique for finding the Random Walking microorganism cells on one of [Formula: see text]-intersect real lines at the origin. We have 2[Formula: see text] unit speed searchers starting together from the origin. Furthermore, proving the existence of a finite search plan, we are discussing the existence of optimality for this search plan which minimizes the expected value of the first meeting time between one of the searchers and the microorganism cells.

Sign in / Sign up

Export Citation Format

Share Document