Eugene Kagan

Turing Systems, Entropy, and Kinetic Models for Self-Healing Surfaces

The paper addresses the methods of description of friction-induced self-healing at the interface between two solid bodies. A macroscopic description of self-healing is based on a Turing system for the transfer of matter that leads to self-organization at the interface in the case of an unstable state. A microscopic description deals with a kinetic model of the process and entropy production during self-organization. The paper provides a brief overview of the Turing system approach and statistical kinetic models. The relation between these methods and the description of the self-healing surfaces is discussed, as well as results of their application. The analytical considerations are illustrated by numerical simulations.

An Informational Search for a Moving Target

We consider the problem of search for a randomly moving target in a discrete domain. The action available to the searcher is checking a sub-domain to detect whether the target is somewhere in this sub-domain or not. The procedure terminates if the searcher finds the target in a sub-domain that contains only one point. Starting from the Korf and Ishida-Korf algorithms, we suggest the informational learning real-time algorithm and the informational moving target search algorithm running on a states space with informational metric. We describe the properties of these algorithms and compare them with the known Zimmerman search procedure, with the generalized optimal testing algorithm, designed by Hartmann et al, and with the Pollock model of search. To illustrate the work of the informational moving target search algorithm, we present the results of simulative trials in comparison with the greedy probabilistic search procedure.

Moving Target Search Algorithm with Informational Distance Measures

We consider an Ishida and Korf Moving Target Search (MTS) algorithm with informational distance measures. Similarly to the previously defined Informational Learning Real-Time A* algorithm, the suggested algorithm acts on the set of partitions of the sample space, on which the probability mass function is defined. The information-based Rokhlin metric and its lower bound - Ornstein metric, give the necessary distance measures. We prove that similarly to the Ishida and Korf MTS algorithm, the proposed Informational MTS (IMTS) algorithm always terminates and finds the target. The comparison of the IMTS algorithm with known models shows that it outperforms known Markov decision process model of search with probabilistic and informational decision criteria. These findings help to construct a unified framework of search after both static and moving targets, and to bridge the gap between different search procedures that are related to both artificial intelligence and information theory.

Probabilistic double-distance algorithm of search after static or moving target by autonomous mobile agent

We propose a real-time algorithm of search and path planning after a static or a moving target in a discrete probability space. The search is conducted by an autonomous mobile agent that is given an initial probability distribution of the targets location, and at each search step obtains information regarding targets location in the agents local neighborhood. The suggested algorithm implements a decision-making procedure of a probabilistic version of local search with estimated global distances and results in agents path over the domain. The suggested algorithm finds efficiently both static and moving targets, as well as targets that change their movement patterns during the search. Additional information regarding the target locations, which is unknown at the beginning of the search, can be integrated in the search in real-time, as well. It is found that for the search after a static target, the algorithm actions depend on the global estimation at all stages of the search, while for the search after a moving target the global estimations mostly affect the initial search steps. Preliminary analysis shows that for the search after a static target the obtained average number of steps is close to optimal, while for the Markovian target the average number of steps is at least in the bounds that are provided by known search methods.

Fuzzy model of control for quantum-controlled mobile robots

In this work we consider a navigation of quantum-controlled mobile robot by the use of fuzzy methods. A fuzzy model of the robot behavior is obtained by transformation of the robots states (that appear in a form of qubits) into the pairs of membership functions. For a full description of the robots turns, we define a reverse fuzzy Hadamard operator that completes the known Hannachi, Hatakeyama and Hirota model. The suggested transformations and methods were comparatively studied by field trials using small mobile robots and by numerical simulations that model the robots behavior in the presence of noise.

Probabilistic Search for Tracking Targets: Theory and Modern Applications

Presents a probabilistic and information-theoretic framework for a search for static or moving targets in discrete time and space.Probabilistic Search for Tracking Targets uses an information-theoretic scheme to present a unified approach for known search methods to allow the development of new algorithms of search. The book addresses search methods under different constraints and assumptions, such as search uncertainty under incomplete information, probabilistic search scheme, observation errors, group testing, search games, distribution of search efforts, single and multiple targets and search agents, as well as online or offline search schemes. The proposed approach is associated with path planning techniques, optimal search algorithms, Markov decision models, decision trees, stochastic local search, artificial intelligence and heuristic information-seeking methods. Furthermore, this book presents novel methods of search for static and moving targets along with practical algorithms of partitioning and search and screening.Probabilistic Search for Tracking Targets includes complete material for undergraduate and graduate courses in modern applications of probabilistic search, decision-making and group testing, and provides several directions for further research in the search theory.The authors:Provide a generalized information-theoretic approach to the problem of real-time search for both static and moving targets over a discrete space.Present a theoretical framework, which covers known information-theoretic algorithms of search, and forms a basis for development and analysis of different algorithms of search over probabilistic space.Use numerous examples of group testing, search and path planning algorithms to illustrate direct implementation in the form of running routines.Consider a relation of the suggested approach with known search theories and methods such as search and screening theory, search games, Markov decision process models of search, data mining methods, coding theory and decision trees.Discuss relevant search applications, such as quality-control search for nonconforming units in a batch or a military search for a hidden target.Provide an accompanying website featuring the algorithms discussed throughout the book, along with practical implementations procedures.

Navigation of Quantum-Controlled Mobile Robots

The actions of autonomous mobile robots in stochastic medium imply certain intellectual behavior, which allows fulfilling the mission in spite of the environmental uncertainty and the robot’s influence on the characteristics of the medium. To provide such a behavior, the controllers of the robots are considered as probabilistic automata with decision-making and, in some cases, learning abilities. General studies in this direction began in the 1960s (Fu & Li, 1969; Tsetlin, 1973) and resulted in practical methods of on-line decision-making and navigation of mobile robots (Unsal, 1998; Kagan & Ben-Gal, 2008). Along with the indicated studies, in recent years, the methods of mobile robot’s navigation and control are considered in the framework of quantum computation (Nielsen & Chuang, 2000), which gave rise to the concept of quantum mobile robot (Benioff, 1998; Dong, et al., 2006). Such approach allowed including both an environmental influence on the robot’s actions and the changes of the environment by the robot by the use of the same model, and the ability to apply the methods of quantum communication and decision-making (Levitin, 1969; Helstrom, 1976; Davies, 1978; Holevo, 2001) to the mobile robot’s control. Following Benioff, quantum robots are “mobile systems that have a quantum computer and any other needed ancillary systems on board... Quantum robots move in and interact (locally) with environments of quantum systems” (Benioff, 1998). If, in contrast, the quantum robots interact with a non-quantum environment, then they are considered as quantum-controlled mobile robots. According to Perkowski, these robots are such that “their controls are quantum but sensors and effectors are classical” (Raghuvanshi, et al., 2007). In the other words, in the quantum-controlled mobile robot, the input data obtained by classical (non-quantum) sensors are processed by the use of quantum-mechanical methods, and the results are output to classical (non-quantum) effectors. In this chapter, we present a brief practical introduction into quantum computation and information theory and consider the methods of path planning and navigation of quantumcontrolled mobile robots based on quantum decision-making.

Probabilistic mobile robot with quantum decision-making

This work addresses informational-based methods for decision-making in Hilbert space, widely known as quantum decision-making, and their application to the control of mobile robot. We consider a mobile robot, whose objective is to find objects in a changing environment. We compare the robot performance under both a classical and a quantum decision making (control) approaches. Both approaches are driven by similar information-theory decision criteria. The robot behavior is physically studied by using an NXT Lego Robot at the CIM lab in Tel Aviv University.

A group testing algorithm with online informational learning

An online group testing method to search for a hidden object in a discrete search space is proposed. A relevant example is a search after a nonconforming unit in a batch, while many other applications can be related. A probability mass function is defined over the search space to represent the probability of an object (e.g., a nonconforming unit) to be located at some point or subspace. The suggested method follows a stochastic local search procedure and can be viewed as a generalization of the Learning Real-Time A* (LRTA*) search algorithm, while using informational distance measures over the searched space. It is proved that the proposed Informational LRTA* (ILRTA*) algorithm converges and always terminates. Moreover, it is shown that under relevant assumptions, the proposed algorithm generalizes known optimal information-theoretic search procedures, such as the offline Huffman search or the generalized optimum testing algorithm. However, the ILRTA* can be applied to new situations, such as a search with side information or an online search where the probability distribution changes. The obtained results can help to bridge the gap between different search procedures that are related to quality control, artificial intelligence, and information theory.

The Dynamics of Concepts in a Homogeneous Community

The paper addresses informational interactions in a community and considers the dynamics of concepts that represent distribution of knowledge among the individuals. The evolution of a set of concepts maintained by a community is derived by the use of the concepts’ significance in the communication between “cognoscenti” and “dilettanti” and of birth-death processes. The dynamics of concepts depend on the allocation of communication resources and can be governed by an informational principle that requires minimum self-information of the set of concepts over a time horizon. With respect to that principle, the introduction of a new concept into a community’s disposal is shown to lead to a steady-state self-information, which is smaller than that before the introduction of the new concept.