Moment instabilities in multidimensional systems with noise

We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a simple, dominant eigenvalue and stationary, white noise. When the noise is small, we obtain general expressions for the approximate asymptotic distribution and moment Lyapunov exponents. In the case of larger noise, the second moment is calculated using a different approach, which gives an exact result for some types of noise. We analyze the dependence of the moments on the system's dimension, relevant system properties, the form of the noise, and the magnitude of the noise. We determine a critical value for noise strength, as a function of the unperturbed system's convergence rate, above which the second moment diverges and large fluctuations are likely. Analytical results are validated by numerical simulations. We show that our results cannot be extended to the continuous time limit except in certain special cases.Comment: 21 pages, 15 figure

Electronic excitations in Bi2_2Sr2_2CaCu2_2O8_8 : Fermi surface, dispersion, and absence of bilayer splitting

From a detailed study, including polarization dependence, of the normal state angle-resolved photoemission spectra for Bi$_2$Sr$_2$CaCu$_2$O$_8$, we find only one CuO$_2$ band related feature. All other spectral features can be ascribed either to umklapps from the superlattice or to ``shadow bands''. Even though the dispersion of the peaks looks like band theory, the lineshape is anomalously broad and no evidence is found for bilayer splitting. We argue that the ``dip feature'' in the spectrum below $T_c$ arises not from bilayer splitting, but rather from many body effects.Comment: 4 pages, revtex, 3 uuencoded postscript figure

New prioritized value iteration for Markov decision processes

The problem of solving large Markov decision processes accurately and quickly is challenging. Since the computational effort incurred is considerable, current research focuses on finding superior acceleration techniques. For instance, the convergence properties of current solution methods depend, to a great extent, on the order of backup operations. On one hand, algorithms such as topological sorting are able to find good orderings but their overhead is usually high. On the other hand, shortest path methods, such as Dijkstra's algorithm which is based on priority queues, have been applied successfully to the solution of deterministic shortest-path Markov decision processes. Here, we propose an improved value iteration algorithm based on Dijkstra's algorithm for solving shortest path Markov decision processes. The experimental results on a stochastic shortest-path problem show the feasibility of our approach. © Springer Science+Business Media B.V. 2011.García Hernández, MDG.; Ruiz Pinales, J.; Onaindia De La Rivaherrera, E.; Aviña Cervantes, JG.; Ledesma Orozco, S.; Alvarado Mendez, E.; Reyes Ballesteros, A. (2012). New prioritized value iteration for Markov decision processes. Artificial Intelligence Review. 37(2):157-167. doi:10.1007/s10462-011-9224-zS157167372Agrawal S, Roth D (2002) Learning a sparse representation for object detection. In: Proceedings of the 7th European conference on computer vision. Copenhagen, Denmark, pp 1–15Bellman RE (1954) The theory of dynamic programming. Bull Amer Math Soc 60: 503–516Bellman RE (1957) Dynamic programming. Princeton University Press, New JerseyBertsekas DP (1995) Dynamic programming and optimal control. Athena Scientific, MassachusettsBhuma K, Goldsmith J (2003) Bidirectional LAO* algorithm. In: Proceedings of indian international conferences on artificial intelligence. p 980–992Blackwell D (1965) Discounted dynamic programming. Ann Math Stat 36: 226–235Bonet B, Geffner H (2003a) Faster heuristic search algorithms for planning with uncertainty and full feedback. In: Proceedings of the 18th international joint conference on artificial intelligence. Morgan Kaufmann, Acapulco, México, pp 1233–1238Bonet B, Geffner H (2003b) Labeled RTDP: improving the convergence of real-time dynamic programming. In: Proceedings of the international conference on automated planning and scheduling. Trento, Italy, pp 12–21Bonet B, Geffner H (2006) Learning depth-first search: a unified approach to heuristic search in deterministic and non-deterministic settings and its application to MDP. In: Proceedings of the 16th international conference on automated planning and scheduling. Cumbria, UKBoutilier C, Dean T, Hanks S (1999) Decision-theoretic planning: structural assumptions and computational leverage. J Artif Intell Res 11: 1–94Chang I, Soo H (2007) Simulation-based algorithms for Markov decision processes Communications and control engineering. Springer, LondonDai P, Goldsmith J (2007a) Faster dynamic programming for Markov decision processes. Technical report. Doctoral consortium, department of computer science and engineering. University of WashingtonDai P, Goldsmith J (2007b) Topological value iteration algorithm for Markov decision processes. In: Proceedings of the 20th international joint conference on artificial intelligence. Hyderabad, India, pp 1860–1865Dai P, Hansen EA (2007c) Prioritizing bellman backups without a priority queue. In: Proceedings of the 17th international conference on automated planning and scheduling, association for the advancement of artificial intelligence. Rhode Island, USA, pp 113–119Dibangoye JS, Chaib-draa B, Mouaddib A (2008) A Novel prioritization technique for solving Markov decision processes. In: Proceedings of the 21st international FLAIRS (The Florida Artificial Intelligence Research Society) conference, association for the advancement of artificial intelligence. Florida, USAFerguson D, Stentz A (2004) Focused propagation of MDPs for path planning. In: Proceedings of the 16th IEEE international conference on tools with artificial intelligence. pp 310–317Hansen EA, Zilberstein S (2001) LAO: a heuristic search algorithm that finds solutions with loops. Artif Intell 129: 35–62Hinderer K, Waldmann KH (2003) The critical discount factor for finite Markovian decision processes with an absorbing set. Math Methods Oper Res 57: 1–19Li L (2009) A unifying framework for computational reinforcement learning theory. PhD Thesis. The state university of New Jersey, New Brunswick. NJLittman ML, Dean TL, Kaelbling LP (1995) On the complexity of solving Markov decision problems.In: Proceedings of the 11th international conference on uncertainty in artificial intelligence. Montreal, Quebec pp 394–402McMahan HB, Gordon G (2005a) Fast exact planning in Markov decision processes. In: Proceedings of the 15th international conference on automated planning and scheduling. Monterey, CA, USAMcMahan HB, Gordon G (2005b) Generalizing Dijkstra’s algorithm and gaussian elimination for solving MDPs. Technical report, Carnegie Mellon University, PittsburghMeuleau N, Brafman R, Benazera E (2006) Stochastic over-subscription planning using hierarchies of MDPs. In: Proceedings of the 16th international conference on automated planning and scheduling. Cumbria, UK, pp 121–130Moore A, Atkeson C (1993) Prioritized sweeping: reinforcement learning with less data and less real time. Mach Learn 13: 103–130Puterman ML (1994) Markov decision processes. Wiley Editors, New YorkPuterman ML (2005) Markov decision processes. Wiley Inter Science Editors, New YorkRussell S (2005) Artificial intelligence: a modern approach. Making complex decisions (Ch-17), 2nd edn. Pearson Prentice Hill Ed., USAShani G, Brafman R, Shimony S (2008) Prioritizing point-based POMDP solvers. IEEE Trans Syst Man Cybern 38(6): 1592–1605Sniedovich M (2006) Dijkstra’s algorithm revisited: the dynamic programming connexion. Control Cybern 35: 599–620Sniedovich M (2010) Dynamic programming: foundations and principles, 2nd edn. Pure and Applied Mathematics Series, UKTijms HC (2003) A first course in stochastic models. Discrete-time Markov decision processes (Ch-6). Wiley Editors, UKVanderbei RJ (1996) Optimal sailing strategies. Statistics and operations research program, University of Princeton, USA ( http://www.orfe.princeton.edu/~rvdb/sail/sail.html )Vanderbei RJ (2008) Linear programming: foundations and extensions, 3rd edn. Springer, New YorkWingate D, Seppi KD (2005) Prioritization methods for accelerating MDP solvers. J Mach Learn Res 6: 851–88

SimSearch: A new variant of dynamic programming based on distance series for optimal and near-optimal similarity discovery in biological sequences

http://www.informatik.uni-trier.de/%7Eley/db/conf/iwpacbb/iwpacbb2008.htmlIn this paper, we propose SimSearch, an algorithm implementing a new variant of dynamic programming based on distance series for optimal and near-optimal similarity discovery in biological sequences. The initial phase of SimSearch is devoted to fulfil the binary similarity matrices by signalling the distances between occurrences of the same symbol. The scoring scheme is further applied, when analysed the maximal extension of the pattern. Employing bit parallelism to analyse the global similarity matrix’s upper triangle, the new methodology searches the sequence(s) for all the exact and approximate patterns in regular or reverse order. The algorithm accepts parameterization to work with greater seeds for near-optimal results. Performance tests show significant efficiency improvement over traditional optimal methods based on dynamic programming. Comparing the new algorithm’s efficiency against heuristic based methods, equalizing the required sensitivity, the proposed algorithm remains acceptable.This work has been partially supported by PRODEP

Assessing Interaction Networks with Applications to Catastrophe Dynamics and Disaster Management

In this paper we present a versatile method for the investigation of interaction networks and show how to use it to assess effects of indirect interactions and feedback loops. The method allows to evaluate the impact of optimization measures or failures on the system. Here, we will apply it to the investigation of catastrophes, in particular to the temporal development of disasters (catastrophe dynamics). The mathematical methods are related to the master equation, which allows the application of well-known solution methods. We will also indicate connections of disaster management with excitable media and supply networks. This facilitates to study the effects of measures taken by the emergency management or the local operation units. With a fictious, but more or less realistic example of a spreading epidemic disease or a wave of influenza, we illustrate how this method can, in principle, provide decision support to the emergency management during such a disaster. Similar considerations may help to assess measures to fight the SARS epidemics, although immunization is presently not possible

A statistical learning strategy for closed-loop control of fluid flows

This work discusses a closed-loop control strategy for complex systems utilizing scarce and streaming data. A discrete embedding space is first built using hash functions applied to the sensor measurements from which a Markov process model is derived, approximating the complex system’s dynamics. A control strategy is then learned using reinforcement learning once rewards relevant with respect to the control objective are identified. This method is designed for experimental configurations, requiring no computations nor prior knowledge of the system, and enjoys intrinsic robustness. It is illustrated on two systems: the control of the transitions of a Lorenz’63 dynamical system, and the control of the drag of a cylinder flow. The method is shown to perform well

A knowledge-free path planning approach for smart ships based on reinforcement learning

With the development of artificial intelligence, intelligent and unmanned driving has received extensive attention. Compared with the rapid technological advance of unmanned vehicles, the research on unmanned ship technology is relatively rare. The autonomous navigation of cargo ships needs to meet their huge inertia and obey existing complex rules. Therefore, the requirements for smart ships are much higher than those for unmanned vehicles. A smart ship has to realise autonomous driving instead of manual operation, which consists of path planning and controlling. Toward to this goal, this research proposes a path planning and manipulating approach based on Qlearning, which can drive a cargo ship by itself without requiring any input from human experiences or guidance rules. At the very beginning, a ship is modelled in a simulation waterway. Then, a number of simple rules of navigation are introduced and regularized as rewards or punishments, which are used to judge the performance, or manipulation decisions of the ship. Subsequently, Q-learning is introduced to learn the action–reward model and the learning outcome is used to manipulate the ship’s movement. By chasing higher reward values, the ship can find an appropriate path or navigation strategies by itself. After a sufficient number of rounds of training, a convincing path and manipulating strategies will likely be produced. By comparing the proposed approach with the existing Rapid-exploring Random Tree (RRT) and the Artificial Potential Field A* methods, it is shown that this approach is more effective in self-learning and continuous optimisation, and therefore closer to human manoeuvring

An advanced Bayesian model for the visual tracking of multiple interacting objects

Visual tracking of multiple objects is a key component of many visual-based systems. While there are reliable algorithms for tracking a single object in constrained scenarios, the object tracking is still a challenge in uncontrolled situations involving multiple interacting objects that have a complex dynamics. In this article, a novel Bayesian model for tracking multiple interacting objects in unrestricted situations is proposed. This is accomplished by means of an advanced object dynamic model that predicts possible interactive behaviors, which in turn depend on the inference of potential events of object occlusion. The proposed tracking model can also handle false and missing detections that are typical from visual object detectors operating in uncontrolled scenarios. On the other hand, a Rao-Blackwellization technique has been used to improve the accuracy of the estimated object trajectories, which is a fundamental aspect in the tracking of multiple objects due to its high dimensionality. Excellent results have been obtained using a publicly available database, proving the efficiency of the proposed approach

Automatic Design of Synthetic Gene Circuits through Mixed Integer Non-linear Programming

Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits