Surrogate modeling approximation using a mixture of experts based on EM joint estimation

An automatic method to combine several local surrogate models is presented. This method is intended to build accurate and smooth approximation of discontinuous functions that are to be used in structural optimization problems. It strongly relies on the Expectation−Maximization (EM) algorithm for Gaussian mixture models (GMM). To the end of regression, the inputs are clustered together with their output values by means of parameter estimation of the joint distribution. A local expert is then built (linear, quadratic, artificial neural network, moving least squares) on each cluster. Lastly, the local experts are combined using the Gaussian mixture model parameters found by the EM algorithm to obtain a global model. This method is tested over both mathematical test cases and an engineering optimization problem from aeronautics and is found to improve the accuracy of the approximation.     

Approximate policy iteration: a survey and some new methods

We consider the classical policy iteration method of dynamic programming(DP),where approximations and simulation are used to deal with the curse of dimensionality.We survey a number of issues:convergence and rate of convergence of approximate policy evaluation methods,singularity and susceptibility to simulation noise of policy evaluation,exploration issues,constrained and enhanced policy iteration,policy oscillation and chattering,and optimistic and distributed policy iteration.Our discussion of policy evaluation is couched in general terms and aims to unify the available methods in the light of recent research developments and to compare the two main policy evaluation approaches:projected equations and temporal differences(TD),and aggregation.In the context of these approaches,we survey two different types of simulation-based algorithms:matrix inversion methods,such as least-squares temporal difference(LSTD),and iterative methods,such as least-squares policy evaluation(LSPE) and TD(λ),and their scaled variants.We discuss a recent method,based on regression and regularization,which recti?es the unreliability of LSTD for nearly singular projected Bellman equations.An iterative version of this method belongs to the LSPE class of methods and provides the connecting link between LSTD and LSPE.Our discussion of policy improvement focuses on the role of policy oscillation and its effect on performance guarantees.We illustrate that policy evaluation when done by the projected equation/TD approach may lead to policy oscillation,but when done by aggregation it does not.This implies better error bounds and more regular performance for aggregation,at the expense of some loss of generality in cost function representation capability.Hard aggregation provides the connecting link between projected equation/TD-based and aggregation-based policy evaluation,and is characterized by favorable error bounds.     

Efficient evaluation of generalized tree-pattern queries on XML streams

The streaming evaluation is a popular way of evaluating queries on XML documents. Besides its many advantages, it is also the only option for a number of important XML applications. Unfortunately, existing algorithms focus almost exclusively on tree-pattern queries (TPQs). Requirements for flexible querying of XML data have motivated recently the introduction of query languages that are more general and flexible than TPQs. These languages are not supported by existing algorithms. In this paper, we consider a partial tree-pattern query (PTPQ) language which generalizes and strictly contains TPQs. PTPQs can express a fragment of XPath which comprises reverse axes and the node identity equality (is) operator, in addition to forward axes, wildcards and predicates. They constitute an important subclass of XPath, which is very useful in practice. Unfortunately, previous streaming algorithms for TPQs cannot be applied to PTPQs. PTPQs can be represented as dags enhanced with constraints. We explore this representation to design an original polynomial time streaming algorithm for PTPQs. Our algorithm aggressively filters incoming data that is irrelevant to the query and wisely avoids processing redundant query matches (i.e., matches of the query dag that do not contribute to new solutions). Our algorithm is the first one to support the streaming evaluation of such a broad fragment of XPath. We provide an analysis of it, and conduct an extensive experimental evaluation of its performance and scalability. Compared to the only known streaming algorithm that supports TPQs extended with reverse axes, our algorithm performs better by orders of magnitude while consuming a much smaller fraction of memory space. Current streaming applications have stringent requirements on query response time and memory consumption because of the large (possibly unbounded) size of data they handle. In order to keep memory usage and CPU consumption low for the PTPQ streaming evaluation, we design another streaming algorithm called Eager PSX for PTPQs. Its key feature is that it applies an eager evaluation strategy to quickly determine when node matches should be returned as solutions to the user and also to proactively detect redundant matches. We theoretically analyze Eager PSX, and experimentally test its time and space performance and scalability. We compare it with PSX. Our results show that Eager PSX not only achieves better space performance without compromising time performance, but it also greatly improves query response time for both simple and complex queries, in many cases, by orders of magnitude.     

Evaluation Techniques for Generalized Path Pattern Queries on XML Data

Finding the occurrences of structural patterns in XML data is a key operation in XML query processing. Existing algorithms for this operation focus almost exclusively on path patterns or tree patterns. Current applications of XML require querying of data whose structure is complex or is not fully known to the user, or integrating XML data sources with different structures. These applications have motivated recently the introduction of query languages that allow a partial specification of path patterns in a query. In this paper, we consider partial path queries, a generalization of path pattern queries, and we focus on their efficient evaluation under the indexed streaming evaluation model. Our approach explicitly deals with repeated labels (that is, multiple occurrences of the same label in a query). We show that partial path queries can be represented as rooted dags for which a topological ordering of the nodes exists. We present three algorithms for the efficient evaluation of these queries. The first one exploits a structural summary of data to generate a set of path patterns that together are equivalent to a partial path query. To evaluate these path patterns, we extend a previous algorithm for path-pattern queries so that it can work on path patterns with repeated labels. The second one extracts a spanning tree from the query dag, uses a stack-based algorithm to find the matches of the root-to-leaf paths in the tree, and merge-joins the matches to compute the answer. Finally, the third one exploits multiple pointers of stack entries and a topological ordering of the query dag to apply a stack-based holistic technique. We analyze our algorithms and perform extensive experimental evaluations. Our experimental results show that the holistic algorithm outperforms the other ones. Our approaches are the first ones to efficiently evaluate this class of queries in the indexed streaming model.     

Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

This paper examines two engineering methods of evaluating the stress intensity factors for cracked beams and bars subjected to a combined loading and proposes innovative formulations, as far as the circular cross section is concerned. Based on the definition of the stress intensity factors, the compliance matrix is determined as the inverse of the stiffness matrix, modelling the cracked section of a beam through a line‐spring approximation with interactive forces computed within fracture mechanics. A comparative evaluation of numerical predictions based on the proposed methods is also performed with methods available from the literature. Results for free vibration analyses of beams with transverse non‐propagating open cracks are presented and compared in order to estimate the accuracy and efficiency of the proposed methods, where a good agreement is generally found. More specifically, two different coupling effects are herein analysed for circular beams subjected to a combined bending, axial and shear loading, first, and a combined bending, shear and torsion loading, subsequently.     

Improved TDM switching assignments for variable and fixed burst length

In this paper we present two algorithms for improved satellite‐switched TDM slot assignments of N × N traffic matrices under K transponders/carriers (simultaneous connections), 1?K?N. The first algorithm applies to data switching with variable burst length and achieves optimum transmission time with a significantly lower number of switching configurations than a previously proposed algorithm, while still having the same time complexity (O(N⁴)). Experimental results demonstrate the advantage. The second algorithm applies to the case of fixed burst length and offers a faster complexity of O(L·N²), where L is the minimum transmission time, at the cost of occasionally missing the minimum. Extensive simulations indicate that the difference from the minimum is rare and is at most one. They also show that the presented algorithm even improves a previous one which was proposed for the fixed burst length case and has the same time complexity but uses K=N. Copyright © 2006 John Wiley & Sons, Ltd.     

Response of Poplar and Associated Fungal Endophytic Communities to a PAH Contamination Gradient

Microbial populations associated to poplar are well described in non-contaminated and metal-contaminated environments but more poorly in the context of polycyclic aromatic hydrocarbon (PAH) contamination. This study aimed to understand how a gradient of phenanthrene (PHE) contamination affects poplar growth and the fungal microbiome in both soil and plant endosphere (roots, stems and leaves). Plant growth and fitness parameters indicated that the growth of Populus canadensis was impaired when PHE concentration increased above 400 mg kg⁻¹. Values of alpha-diversity indicators of fungal diversity and richness were not affected by the PHE gradient. The PHE contamination had a stronger impact on the fungal community composition in the soil and root compartments compared to that of the aboveground organs. Most of the indicator species whose relative abundance was correlated with PHE contamination decreased along the gradient indicating a toxic effect of PHE on these fungal OTUs (Operational Taxonomic Units). However, the relative abundance of some OTUs such as Cadophora, Alternaria and Aspergillus, potentially linked to PHE degradation or being plant-beneficial taxa, increased along the gradient. Finally, this study allowed a deeper understanding of the dual response of plant and fungal communities in the case of a soil PAH contamination gradient leading to new perspectives on fungal assisted phytoremediation.     

Peeling dynamics of fluid membranes bridged by molecular bonds: moving or breaking

Biological adhesion is a critical mechanical function of complex organisms. At the scale of cell–cell contacts, adhesion is remarkably tunable to enable both cohesion and malleability during development, homeostasis and disease. It is physically supported by transient and laterally mobile molecular bonds embedded in fluid membranes. Thus, unlike specific adhesion at solid–solid or solid–fluid interfaces, peeling at fluid–fluid interfaces can proceed by breaking bonds, by moving bonds or by a combination of both. How the additional degree of freedom provided by bond mobility changes the mechanics of peeling is not understood. To address this, we develop a theoretical model coupling diffusion, reactions and mechanics. Mobility and reaction rates determine distinct peeling regimes. In a diffusion-dominated Stefan-like regime, bond motion establishes self-stabilizing dynamics that increase the effective fracture energy. In a reaction-dominated regime, peeling proceeds by travelling fronts where marginal diffusion and unbinding control peeling speed. In a mixed reaction–diffusion regime, strengthening by bond motion competes with weakening by bond breaking in a force-dependent manner, defining the strength of the adhesion patch. In turn, patch strength depends on molecular properties such as bond stiffness, force sensitivity or crowding. We thus establish the physical rules enabling tunable cohesion in cellular tissues and in engineered biomimetic systems.     

Multiagent Reinforcement Learning:Rollout and Policy Iteration

We discuss the solution of complex multistage decision problems using methods that are based on the idea of policy iteration(PI),i.e.,start from some base policy and generate an improved policy.Rollout is the simplest method of this type,where just one improved policy is generated.We can view PI as repeated application of rollout,where the rollout policy at each iteration serves as the base policy for the next iteration.In contrast with PI,rollout has a robustness property:it can be applied on-line and is suitable for on-line replanning.Moreover,rollout can use as base policy one of the policies produced by PI,thereby improving on that policy.This is the type of scheme underlying the prominently successful Alpha Zero chess program.In this paper we focus on rollout and PI-like methods for problems where the control consists of multiple components each selected(conceptually)by a separate agent.This is the class of multiagent problems where the agents have a shared objective function,and a shared and perfect state information.Based on a problem reformulation that trades off control space complexity with state space complexity,we develop an approach,whereby at every stage,the agents sequentially(one-at-a-time)execute a local rollout algorithm that uses a base policy,together with some coordinating information from the other agents.The amount of total computation required at every stage grows linearly with the number of agents.By contrast,in the standard rollout algorithm,the amount of total computation grows exponentially with the number of agents.Despite the dramatic reduction in required computation,we show that our multiagent rollout algorithm has the fundamental cost improvement property of standard rollout:it guarantees an improved performance relative to the base policy.We also discuss autonomous multiagent rollout schemes that allow the agents to make decisions autonomously through the use of precomputed signaling information,which is sufficient to maintain the cost improvement property,without any on-line coordination of control selection between the agents.For discounted and other infinite horizon problems,we also consider exact and approximate PI algorithms involving a new type of one-agent-at-a-time policy improvement operation.For one of our PI algorithms,we prove convergence to an agentby-agent optimal policy,thus establishing a connection with the theory of teams.For another PI algorithm,which is executed over a more complex state space,we prove convergence to an optimal policy.Approximate forms of these algorithms are also given,based on the use of policy and value neural networks.These PI algorithms,in both their exact and their approximate form are strictly off-line methods,but they can be used to provide a base policy for use in an on-line multiagent rollout scheme.     

Fault tolerant network design inspired by Physarum polycephalum

Physarum polycephalum, a true slime mould, is a primitive, unicellular organism that creates networks to transport nutrients while foraging. The design of these natural networks proved to be advanced, e.g. the slime mould was able to find the shortest path through a maze. The underlying principles of this design have been mathematically modelled in literature. As in real life the slime mould can design fault tolerant networks, its principles can be applied to the design of man-made networks. In this paper, an existing model and algorithm are adapted and extended with stimulation and migration mechanisms which encourage formation of alternative paths, optimize edge positioning and allow for automated design. The extended model can then be used to better design fault tolerant networks. The extended algorithm is applied to several national and international network configurations. Results show that the extensions allow the model to capture the fault tolerance requirements more accurately. The resulting extended algorithm overcomes weaknesses in geometric graph design and can be used to design fault tolerant networks such as telecommunication networks with varying fault tolerance requirements.