Intermittent search strategies

This review examines intermittent target search strategies, which combine phases of slow motion, allowing the searcher to detect the target, and phases of fast motion during which targets cannot be detected. We first show that intermittent search strategies are actually widely observed at various scales. At the macroscopic scale, this is for example the case of animals looking for food ; at the microscopic scale, intermittent transport patterns are involved in reaction pathway of DNA binding proteins as well as in intracellular transport. Second, we introduce generic stochastic models, which show that intermittent strategies are efficient strategies, which enable to minimize the search time. This suggests that the intrinsic efficiency of intermittent search strategies could justify their frequent observation in nature. Last, beyond these modeling aspects, we propose that intermittent strategies could be used also in a broader context to design and accelerate search processes.Comment: 72 pages, review articl

Optimal search in discrete locations:extensions and new findings

A hidden target needs to be found by a searcher in many real-life situations, some of which involve large costs and significant consequences with failure. Therefore, efficient search methods are paramount. In our search model, the target lies in one of several discrete locations according to some hiding distribution, and the searcher's goal is to discover the target in minimum expected time by making successive searches of individual locations. In Part I of the thesis, the searcher knows the hiding distribution. Here, if there is only one way to search each location, the solution to the search problem, discovered in the 1960s, is simple; search next any location with a maximal probability per unit time of detecting the target. An equivalent solution is derived by viewing the search problem as a multi-armed bandit and following a Gittins index policy. Motivated by modern search technology, we introduce two modes---fast and slow---to search each location. The fast mode takes less time, but the slow mode is more likely to find the target. An optimal policy is difficult to obtain in general, because it requires an optimal sequence of search modes for each location, in addition to a set of sequence-dependent Gittins indices for choosing between locations. For each mode, we identify a sufficient condition for a location to use only that search mode in an optimal policy. For locations meeting neither sufficient condition, an optimal choice of search mode is extremely complicated, depending both on the hiding distribution and the search parameters of the other locations. We propose several heuristic policies motivated by our analysis, and demonstrate their near-optimal performance in an extensive numerical study. In Part II of the thesis, the searcher has only one search mode per location, but does not know the hiding distribution, which is chosen by an intelligent hider who aims to maximise the expected time until the target is discovered. Such a search game, modelled via two-person, zero-sum game theory, is relevant if the target is a bomb, intruder, or, of increasing importance due to advances in technology, a computer hacker. By Part I, if the hiding distribution is known, an optimal counter strategy for the searcher is any corresponding Gittins index policy. To develop an optimal search strategy in the search game, the searcher must account for the hider’s motivation to choose an optimal hiding distribution, and consider the set of corresponding Gittins index policies. %It follows that an optimal search strategy in the search game must be some Gittins index policy if the hiding distribution is assumed to be chosen optimally by the hider. However, the searcher must choose carefully from this set of Gittins index policies to ensure the same expected time to discover the target regardless of where it is hidden by the hider. %It follows that an optimal search strategy in the search game must be a Gittins index policy applied to a hiding distribution which is optimal from the hider's perspective. However, to avoid giving the hider any advantage, the searcher must carefully choose such a Gittins index policy among the many available. As a result, finding an optimal search strategy, or even proving one exists, is difficult. We extend several results for special cases from the literature to the fully-general search game; in particular, we show an optimal search strategy exists and may take a simple form. Using a novel test, we investigate the frequency of the optimality of a particular hiding strategy that gives the searcher no preference over any location at the beginning of the search

Hide-and-seek and other search games

In the game of hide-and-seek played between two players, a Hider picks a hiding place and a Searcher tries to find him in the least possible time. Since Isaacs had the idea of formulating this mathematically as a zero-sum game almost fifty years ago in his book, Differential Games, the theory of search games has been studied and developed extensively. In the classic model of search games on networks, first formalised by Gal in 1979, a Hider strategy is a point on the network and a Searcher strategy is a constant speed path starting from a designated point of the network. The Searcher wishes to minimise the time to find the Hider (the payoff), and the Hider wishes to maximise it. Gal solved this game for certain classes of networks: that is, he found optimal strategies and the payoff assuming best play on both sides. Here we study new formulations of search games, starting with a model proposed by Alpern where the speed of the Searcher depends on which direction he is traveling. We give a solution of this game on a class of networks called trees, generalising Gal's work. We also show how the game relates to another new model of search studied by Baston and Kikuta, where the Searcher must pay extra search costs to search the network's nodes (or vertices). We go on to study another new model of search called expanding search, which models coal mining. We solve this game on trees and also study the related problem where the Hider's strategy is known to the Searcher. We extend the expanding search game to consider what happens if there are several hidden objects and solve this game for certain classes of networks. Finally we study a game in which a squirrel hides nuts from a pilferer

Stochastic models of intracellular transport

The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an over-damped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review we present a wide range of analytical methods and models of intracellular transport. In the case of diffusive transport, we consider narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion. In the case of active transport, we consider Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean field approximations. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self–organization of subcellular structures

Bayesian Search Under Dynamic Disaster Scenarios

Search and Rescue (SAR) is a hard decision making context where there is available a limited amount of resources that should be strategically allocated over the search region in order to find missing people opportunely. In this thesis, we consider those SAR scenarios where the search region is being affected by some type of dynamic threat such as a wilder or a hurricane. In spite of the large amount of SAR missions that consistently take place under these circumstances, and being Search Theory a research area dating back from more than a half century, to the best of our knowledge, this kind of search problem has not being considered in any previous research. Here we propose a bi-objective mathematical optimization model and three solution methods for the problem: (1) Epsilon-constraint; (2) Lexicographic; and (3) Ant Colony based heuristic. One of the objectives of our model pursues the allocation of resources in riskiest zones. This objective attempts to find victims located at the closest regions to the threat, presenting a high risk of being reached by the disaster. In contrast, the second objective is oriented to allocate resources in regions where it is more likely to find the victim. Furthermore, we implemented a receding horizon approach oriented to provide our planning methodology with the ability to adapt to disaster's behavior based on updated information gathered during the mission. All our products were validated through computational experiments.MaestríaMagister en Ingeniería Industria

Distributed Systems and Mobile Computing

The book is about Distributed Systems and Mobile Computing. This is a branch of Computer Science devoted to the study of systems whose components are in different physical locations and have limited communication capabilities. Such components may be static, often organized in a network, or may be able to move in a discrete or continuous environment. The theoretical study of such systems has applications ranging from swarms of mobile robots (e.g., drones) to sensor networks, autonomous intelligent vehicles, the Internet of Things, and crawlers on the Web. The book includes five articles. Two of them are about networks: the first one studies the formation of networks by agents that interact randomly and have the ability to form connections; the second one is a study of clustering models and algorithms. The three remaining articles are concerned with autonomous mobile robots operating in continuous space. One article studies the classical gathering problem, where all robots have to reach a common location, and proposes a fast algorithm for robots that are endowed with a compass but have limited visibility. The last two articles deal with the evacuations problem, where two robots have to locate an exit point and evacuate a region in the shortest possible time

Navigation problems for autonomous robots in distributed environments

This thesis studies algorithms for Distributed Computing. More specifically however the project aimed to carry out research on the performance analysis of mobile robots in a variety of different settings. In a range of different network and geometric settings we investigate efficient algorithms for the robots to perform given tasks. We looked at a variety of different models when completing this work but focused mainly on cases where the robots have limited communication mechanisms. Within this framework we investigated cases where the robots were numerous to cases where they were few in number. Also we looked at scenarios where the robots involved had different limitations on the maximal speeds they could travel. When conducting this work we explored two main tasks carried out by the robots that became the primary theme of the study. These two main tasks are Robot Location Discovery and Robot Evacuation. To accomplish these tasks we constructed algorithms that made use of both randomised and deterministic approaches in their solutions

Search efficiency of discrete fractional Brownian motion in a random distribution of targets

Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of Lévy walks, a specific range of optimal efficiencies was suggested under variation of search intrinsic and extrinsic environmental parameters. In this paper, we study fractional Brownian motion as a search process, which under parameter variation generates all three basic types of diffusion, from sub- to normal to superdiffusion. In contrast to Lévy walks, fractional Brownian motion defines a Gaussian stochastic process with power-law memory yielding antipersistent, respectively persistent motion. Computer simulations of search by time-discrete fractional Brownian motion in a uniformly random distribution of targets show that maximising search efficiencies sensitively depends on the definition of efficiency, the variation of both intrinsic and extrinsic parameters, the perception of targets, the type of targets, whether to detect only one or many of them, and the choice of boundary conditions. In our simulations, we find that different search scenarios favor different modes of motion for optimising search success, defying a universality across all search situations. Some of our numerical results are explained by a simple analytical model. Having demonstrated that search by fractional Brownian motion is a truly complex process, we propose an overarching conceptual framework based on classifying different search scenarios. This approach incorporates search optimization by Lévy walks as a special case

Coverage & cooperation: Completing complex tasks as quickly as possible using teams of robots

As the robotics industry grows and robots enter our homes and public spaces, they are increasingly expected to work in cooperation with each other. My thesis focuses on multirobot planning, specifically in the context of coverage robots, such as robotic lawnmowers and vacuum cleaners. Two problems unique to multirobot teams are task allocation and search. I present a task allocation algorithm which balances the workload amongst all robots in the team with the objective of minimizing the overall mission time. I also present a search algorithm which robots can use to find lost teammates. It uses a probabilistic belief of a target robot’s position to create a planning tree and then searches by following the best path in the tree. For robust multirobot coverage, I use both the task allocation and search algorithms. First the coverage region is divided into a set of small coverage tasks which minimize the number of turns the robots will need to take. These tasks are then allocated to individual robots. During the mission, robots replan with nearby robots to rebalance the workload and, once a robot has finished its tasks, it searches for teammates to help them finish their tasks faster