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Title: Graph polynomials and approximation of partition functions with Loopy Belief Propagation
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Abstract: The Bethe approximation, or loopy belief propagation algorithm is a successful method for approximating partition functions of probabilistic models associated with a graph. Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an expansion of the partition function. The main term of the series is the Bethe approximation while other terms are labeled by subgraphs called generalized loops. In our recent paper, we derive the loop series expansion in form of a polynomial with coefficients positive integers, and extend the result to the expansion of marginals. In this paper, we give more clear derivation for the results and discuss the properties of the polynomial which is introduced in the paper.
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Title: Computer- and robot-assisted Medical Intervention
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Abstract: Medical robotics includes assistive devices used by the physician in order to make his/her diagnostic or therapeutic practices easier and more efficient. This chapter focuses on such systems. It introduces the general field of Computer-Assisted Medical Interventions, its aims, its different components and describes the place of robots in that context. The evolutions in terms of general design and control paradigms in the development of medical robots are presented and issues specific to that application domain are discussed. A view of existing systems, on-going developments and future trends is given. A case-study is detailed. Other types of robotic help in the medical environment (such as for assisting a handicapped person, for rehabilitation of a patient or for replacement of some damaged/suppressed limbs or organs) are out of the scope of this chapter.
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Title: On the Goodness-of-Fit Testing for Ergodic Diffusion Processes
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Abstract: We consider the goodness of fit testing problem for ergodic diffusion processes. The basic hypothesis is supposed to be simple. The diffusion coefficient is known and the alternatives are described by the different trend coefficients. We study the asymptotic distribution of the Cramer-von Mises type tests based on the empirical distribution function and local time estimator of the invariant density. At particularly, we propose a transformation which makes these tests asymptotically distribution free. We discuss the modifications of this test in the case of composite basic hypothesis.
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Title: Goodness-of-Fit Tests for Perturbed Dynamical Systems
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Abstract: We consider the goodness of fit testing problem for stochastic differential equation with small diffiusion coefficient. The basic hypothesis is always simple and it is described by the known trend coefficient. We propose several tests of the type of Cramer-von Mises, Kolmogorov-Smirnov and Chi-Square. The power functions of these tests we study for a special classes of close alternatives. We discuss the construction of the goodness of fit test based on the local time and the possibility of the construction of asymptotically distribution free tests in the case of composite basic hypothesis.
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Title: Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models
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Abstract: This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient parametric models, such as GARCH, whose coefficients may arbitrarily vary with time. Global parametric, smooth transition, and change-point models are special cases. The method is based on an adaptive pointwise selection of the largest interval of homogeneity with a given right-end point by a local change-point analysis. We construct locally adaptive estimates that can perform this task and investigate them both from the theoretical point of view and by Monte Carlo simulations. In the particular case of GARCH estimation, the proposed method is applied to stock-index series and is shown to outperform the standard parametric GARCH model.
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Title: Multidimensional Online Robot Motion
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Abstract: We consider three related problems of robot movement in arbitrary dimensions: coverage, search, and navigation. For each problem, a spherical robot is asked to accomplish a motion-related task in an unknown environment whose geometry is learned by the robot during navigation. The robot is assumed to have tactile and global positioning sensors. We view these problems from the perspective of (non-linear) competitiveness as defined by Gabriely and Rimon. We first show that in 3 dimensions and higher, there is no upper bound on competitiveness: every online algorithm can do arbitrarily badly compared to the optimal. We then modify the problems by assuming a fixed clearance parameter. We are able to give optimally competitive algorithms under this assumption.
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Title: An Exponential Lower Bound on the Complexity of Regularization Paths
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Abstract: For a variety of regularized optimization problems in machine learning, algorithms computing the entire solution path have been developed recently. Most of these methods are quadratic programs that are parameterized by a single parameter, as for example the Support Vector Machine (SVM). Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but the entire path of solutions, making the selection of an optimal parameter much easier. It has been assumed that these piecewise linear solution paths have only linear complexity, i.e. linearly many bends. We prove that for the support vector machine this complexity can be exponential in the number of training points in the worst case. More strongly, we construct a single instance of n input points in d dimensions for an SVM such that at least \Theta(2^n/2) = \Theta(2^d) many distinct subsets of support vectors occur as the regularization parameter changes.
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Title: A Combinatorial Algorithm to Compute Regularization Paths
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Abstract: For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but the entire path of solutions, making the selection of an optimal parameter much easier. Most of the currently used algorithms are not robust in the sense that they cannot deal with general or degenerate input. Here we present a new robust, generic method for parametric quadratic programming. Our algorithm directly applies to nearly all machine learning applications, where so far every application required its own different algorithm. We illustrate the usefulness of our method by applying it to a very low rank problem which could not be solved by existing path tracking methods, namely to compute part-worth values in choice based conjoint analysis, a popular technique from market research to estimate consumers preferences on a class of parameterized options.
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Title: Learning Multiple Belief Propagation Fixed Points for Real Time Inference
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Abstract: In the context of inference with expectation constraints, we propose an approach based on the "loopy belief propagation" algorithm LBP, as a surrogate to an exact Markov Random Field MRF modelling. A prior information composed of correlations among a large set of N variables, is encoded into a graphical model; this encoding is optimized with respect to an approximate decoding procedure LBP, which is used to infer hidden variables from an observed subset. We focus on the situation where the underlying data have many different statistical components, representing a variety of independent patterns. Considering a single parameter family of models we show how LBP may be used to encode and decode efficiently such information, without solving the NP hard inverse problem yielding the optimal MRF. Contrary to usual practice, we work in the non-convex Bethe free energy minimization framework, and manage to associate a belief propagation fixed point to each component of the underlying probabilistic mixture. The mean field limit is considered and yields an exact connection with the Hopfield model at finite temperature and steady state, when the number of mixture components is proportional to the number of variables. In addition, we provide an enhanced learning procedure, based on a straightforward multi-parameter extension of the model in conjunction with an effective continuous optimization procedure. This is performed using the stochastic search heuristic CMAES and yields a significant improvement with respect to the single parameter basic model.
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Title: Time manipulation technique for speeding up reinforcement learning in simulations
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Abstract: A technique for speeding up reinforcement learning algorithms by using time manipulation is proposed. It is applicable to failure-avoidance control problems running in a computer simulation. Turning the time of the simulation backwards on failure events is shown to speed up the learning by 260% and improve the state space exploration by 12% on the cart-pole balancing task, compared to the conventional Q-learning and Actor-Critic algorithms.
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Title: Digital Restoration of Ancient Papyri
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Abstract: Image processing can be used for digital restoration of ancient papyri, that is, for a restoration performed on their digital images. The digital manipulation allows reducing the background signals and enhancing the readability of texts. In the case of very old and damaged documents, this is fundamental for identification of the patterns of letters. Some examples of restoration, obtained with an image processing which uses edges detection and Fourier filtering, are shown. One of them concerns 7Q5 fragment of the Dead Sea Scrolls.
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Title: Flow of Activity in the Ouroboros Model
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Abstract: The Ouroboros Model is a new conceptual proposal for an algorithmic structure for efficient data processing in living beings as well as for artificial agents. Its central feature is a general repetitive loop where one iteration cycle sets the stage for the next. Sensory input activates data structures (schemata) with similar constituents encountered before, thus expectations are kindled. This corresponds to the highlighting of empty slots in the selected schema, and these expectations are compared with the actually encountered input. Depending on the outcome of this consumption analysis different next steps like search for further data or a reset, i.e. a new attempt employing another schema, are triggered. Monitoring of the whole process, and in particular of the flow of activation directed by the consumption analysis, yields valuable feedback for the optimum allocation of attention and resources including the selective establishment of useful new memory entries.
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Title: Modified-CS: Modifying Compressive Sensing for Problems with Partially Known Support
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Abstract: We study the problem of reconstructing a sparse signal from a limited number of its linear projections when a part of its support is known, although the known part may contain some errors. The ``known" part of the support, denoted T, may be available from prior knowledge. Alternatively, in a problem of recursively reconstructing time sequences of sparse spatial signals, one may use the support estimate from the previous time instant as the ``known" part. The idea of our proposed solution (modified-CS) is to solve a convex relaxation of the following problem: find the signal that satisfies the data constraint and is sparsest outside of T. We obtain sufficient conditions for exact reconstruction using modified-CS. These are much weaker than those needed for compressive sensing (CS) when the sizes of the unknown part of the support and of errors in the known part are small compared to the support size. An important extension called Regularized Modified-CS (RegModCS) is developed which also uses prior signal estimate knowledge. Simulation comparisons for both sparse and compressible signals are shown.
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Title: Mathematical Model for Transformation of Sentences from Active Voice to Passive Voice
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Abstract: Formal work in linguistics has both produced and used important mathematical tools. Motivated by a survey of models for context and word meaning, syntactic categories, phrase structure rules and trees, an attempt is being made in the present paper to present a mathematical model for structuring of sentences from active voice to passive voice, which is is the form of a transitive verb whose grammatical subject serves as the patient, receiving the action of the verb. For this purpose we have parsed all sentences of a corpus and have generated Boolean groups for each of them. It has been observed that when we take constituents of the sentences as subgroups, the sequences of phrases form permutation roups. Application of isomorphism property yields permutation mapping between the important subgroups. It has resulted in a model for transformation of sentences from active voice to passive voice. A computer program has been written to enable the software developers to evolve grammar software for sentence transformations.
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Title: Quantum decision theory as quantum theory of measurement
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Abstract: We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the quantum theory of measurement, endowed with an action ring, a prospect lattice and a probability operator measure. The algebra of probability operators plays the role of the algebra of local observables. Because of the composite nature of prospects and of the entangling properties of the probability operators, quantum interference terms appear, which make actions noncommutative and the prospect probabilities non-additive. The theory provides the basis for explaining a variety of paradoxes typical of the application of classical utility theory to real human decision making. The principal advantage of our approach is that it is formulated as a self-consistent mathematical theory, which allows us to explain not just one effect but actually all known paradoxes in human decision making. Being general, the approach can serve as a tool for characterizing quantum information processing by means of atomic, molecular, and condensed-matter systems.
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Title: Sure independence screening in generalized linear models with NP-dimensionality
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Abstract: Ultrahigh-dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research. Among others, Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] propose an independent screening framework by ranking the marginal correlations. They showed that the correlation ranking procedure possesses a sure independence screening property within the context of the linear model with Gaussian covariates and responses. In this paper, we propose a more general version of the independent learning with ranking the maximum marginal likelihood estimates or the maximum marginal likelihood itself in generalized linear models. We show that the proposed methods, with Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] as a very special case, also possess the sure screening property with vanishing false selection rate. The conditions under which the independence learning possesses a sure screening is surprisingly simple. This justifies the applicability of such a simple method in a wide spectrum. We quantify explicitly the extent to which the dimensionality can be reduced by independence screening, which depends on the interactions of the covariance matrix of covariates and true parameters. Simulation studies are used to illustrate the utility of the proposed approaches. In addition, we establish an exponential inequality for the quasi-maximum likelihood estimator which is useful for high-dimensional statistical learning.
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Title: Equitable Partitioning Policies for Mobile Robotic Networks
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Abstract: The most widely applied strategy for workload sharing is to equalize the workload assigned to each resource. In mobile multi-agent systems, this principle directly leads to equitable partitioning policies in which (i) the workspace is divided into subregions of equal measure, (ii) there is a bijective correspondence between agents and subregions, and (iii) each agent is responsible for service requests originating within its own subregion. In this paper, we design provably correct, spatially-distributed and adaptive policies that allow a team of agents to achieve a convex and equitable partition of a convex workspace, where each subregion has the same measure. We also consider the issue of achieving convex and equitable partitions where subregions have shapes similar to those of regular polygons. Our approach is related to the classic Lloyd algorithm, and exploits the unique features of power diagrams. We discuss possible applications to routing of vehicles in stochastic and dynamic environments. Simulation results are presented and discussed.
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Title: Heterogeneous knowledge representation using a finite automaton and first order logic: a case study in electromyography
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Abstract: In a certain number of situations, human cognitive functioning is difficult to represent with classical artificial intelligence structures. Such a difficulty arises in the polyneuropathy diagnosis which is based on the spatial distribution, along the nerve fibres, of lesions, together with the synthesis of several partial diagnoses. Faced with this problem while building up an expert system (NEUROP), we developed a heterogeneous knowledge representation associating a finite automaton with first order logic. A number of knowledge representation problems raised by the electromyography test features are examined in this study and the expert system architecture allowing such a knowledge modeling are laid out.
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Title: A Mixture-Based Approach to Regional Adaptation for MCMC
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Abstract: Recent advances in adaptive Markov chain Monte Carlo (AMCMC) include the need for regional adaptation in situations when the optimal transition kernel is different across different regions of the sample space. Motivated by these findings, we propose a mixture-based approach to determine the partition needed for regional AMCMC. The mixture model is fitted using an online EM algorithm (see Andrieu and Moulines, 2006) which allows us to bypass simultaneously the heavy computational load and to implement the regional adaptive algorithm with online recursion (RAPTOR). The method is tried on simulated as well as real data examples.
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Title: A Stochastic View of Optimal Regret through Minimax Duality
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Abstract: We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary.
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Title: Exact Non-Parametric Bayesian Inference on Infinite Trees
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Abstract: Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A Bayesian would assign a data-independent prior probability to "subdivide", which leads to a prior over infinite(ly many) trees. We derive an exact, fast, and simple inference algorithm for such a prior, for the data evidence, the predictive distribution, the effective model dimension, moments, and other quantities. We prove asymptotic convergence and consistency results, and illustrate the behavior of our model on some prototypical functions.
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Title: Missing values: sparse inverse covariance estimation and an extension to sparse regression
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Abstract: We propose an l1-regularized likelihood method for estimating the inverse covariance matrix in the high-dimensional multivariate normal model in presence of missing data. Our method is based on the assumption that the data are missing at random (MAR) which entails also the completely missing at random case. The implementation of the method is non-trivial as the observed negative log-likelihood generally is a complicated and non-convex function. We propose an efficient EM algorithm for optimization with provable numerical convergence properties. Furthermore, we extend the methodology to handle missing values in a sparse regression context. We demonstrate both methods on simulated and real data.
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Title: On Solving Boolean Multilevel Optimization Problems
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Abstract: Many combinatorial optimization problems entail a number of hierarchically dependent optimization problems. An often used solution is to associate a suitably large cost with each individual optimization problem, such that the solution of the resulting aggregated optimization problem solves the original set of hierarchically dependent optimization problems. This paper starts by studying the package upgradeability problem in software distributions. Straightforward solutions based on Maximum Satisfiability (MaxSAT) and pseudo-Boolean (PB) optimization are shown to be ineffective, and unlikely to scale for large problem instances. Afterwards, the package upgradeability problem is related to multilevel optimization. The paper then develops new algorithms for Boolean Multilevel Optimization (BMO) and highlights a large number of potential applications. The experimental results indicate that the proposed algorithms for BMO allow solving optimization problems that existing MaxSAT and PB solvers would otherwise be unable to solve.
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Title: Faith in the Algorithm, Part 2: Computational Eudaemonics
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Abstract: Eudaemonics is the study of the nature, causes, and conditions of human well-being. According to the ethical theory of eudaemonia, reaping satisfaction and fulfillment from life is not only a desirable end, but a moral responsibility. However, in modern society, many individuals struggle to meet this responsibility. Computational mechanisms could better enable individuals to achieve eudaemonia by yielding practical real-world systems that embody algorithms that promote human flourishing. This article presents eudaemonic systems as the evolutionary goal of the present day recommender system.
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Title: Learning for Dynamic subsumption
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Abstract: In this paper a new dynamic subsumption technique for Boolean CNF formulae is proposed. It exploits simple and sufficient conditions to detect during conflict analysis, clauses from the original formula that can be reduced by subsumption. During the learnt clause derivation, and at each step of the resolution process, we simply check for backward subsumption between the current resolvent and clauses from the original formula and encoded in the implication graph. Our approach give rise to a strong and dynamic simplification technique that exploits learning to eliminate literals from the original clauses. Experimental results show that the integration of our dynamic subsumption approach within the state-of-the-art SAT solvers Minisat and Rsat achieves interesting improvements particularly on crafted instances.
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Title: Stiffness Analysis of Overconstrained Parallel Manipulators
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Abstract: The paper presents a new stiffness modeling method for overconstrained parallel manipulators with flexible links and compliant actuating joints. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-dof virtual springs that describe both translational/rotational compliance and the coupling between them. In contrast to other works, the method involves a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations for the unloaded manipulator configuration, which allows computing the stiffness matrix for the overconstrained architectures, including singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators of 3-PUU and 3-PRPaR architectures. Accuracy of the proposed approach was evaluated for a case study, which focuses on stiffness analysis of Orthoglide parallel manipulator.
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Title: Kinematics of A 3-PRP planar parallel robot
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Abstract: Recursive modelling for the kinematics of a 3-PRP planar parallel robot is presented in this paper. Three planar chains connecting to the moving platform of the manipulator are located in a vertical plane. Knowing the motion of the platform, we develop the inverse kinematics and determine the positions, velocities and accelerations of the robot. Several matrix equations offer iterative expressions and graphs for the displacements, velocities and accelerations of three prismatic actuators.
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Title: Kinematic and Dynamic Analysis of the 2-DOF Spherical Wrist of Orthoglide 5-axis
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Abstract: This paper deals with the kinematics and dynamics of a two degree of freedom spherical manipulator, the wrist of Orthoglide 5-axis. The latter is a parallel kinematics machine composed of two manipulators: i) the Orthoglide 3-axis; a three-dof translational parallel manipulator that belongs to the family of Delta robots, and ii) the Agile eye; a two-dof parallel spherical wrist. The geometric and inertial parameters used in the model are determined by means of a CAD software. The performance of the spherical wrist is emphasized by means of several test trajectories. The effects of machining and/or cutting forces and the length of the cutting tool on the dynamic performance of the wrist are also analyzed. Finally, a preliminary selection of the motors is proposed from the velocities and torques required by the actuators to carry out the test trajectories.
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Title: Safe Reasoning Over Ontologies
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Abstract: As ontologies proliferate and automatic reasoners become more powerful, the problem of protecting sensitive information becomes more serious. In particular, as facts can be inferred from other facts, it becomes increasingly likely that information included in an ontology, while not itself deemed sensitive, may be able to be used to infer other sensitive information. We first consider the problem of testing an ontology for safeness defined as its not being able to be used to derive any sensitive facts using a given collection of inference rules. We then consider the problem of optimizing an ontology based on the criterion of making as much useful information as possible available without revealing any sensitive facts.
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Title: Design, development and implementation of a tool for construction of declarative functional descriptions of semantic web services based on WSMO methodology
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Abstract: Semantic web services (SWS) are self-contained, self-describing, semantically marked-up software resources that can be published, discovered, composed and executed across the Web in a semi-automatic way. They are a key component of the future Semantic Web, in which networked computer programs become providers and users of information at the same time. This work focuses on developing a full-life-cycle software toolset for creating and maintaining Semantic Web Services (SWSs) based on the Web Service Modelling Ontology (WSMO) framework. A main part of WSMO-based SWS is service capability - a declarative description of Web service functionality. A formal syntax and semantics for such a description is provided by Web Service Modeling Language (WSML), which is based on different logical formalisms, namely, Description Logics, First-Order Logic and Logic Programming. A WSML description of a Web service capability is represented as a set of complex logical expressions (axioms). We develop a specialized user-friendly tool for constructing and editing WSMO-based SWS capabilities. Since the users of this tool are not specialists in first-order logic, a graphical way for constricting and editing axioms is proposed. The designed process for constructing logical expressions is ontology-driven, which abstracts away as much as possible from any concrete syntax of logical language. We propose several mechanisms to guarantees the semantic consistency of the produced logical expressions. The tool is implemented in Java using Eclipse for IDE and GEF (Graphical Editing Framework) for visualization.
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Title: Time Hopping technique for faster reinforcement learning in simulations
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Abstract: This preprint has been withdrawn by the author for revision
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Title: Eligibility Propagation to Speed up Time Hopping for Reinforcement Learning
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Abstract: A mechanism called Eligibility Propagation is proposed to speed up the Time Hopping technique used for faster Reinforcement Learning in simulations. Eligibility Propagation provides for Time Hopping similar abilities to what eligibility traces provide for conventional Reinforcement Learning. It propagates values from one state to all of its temporal predecessors using a state transitions graph. Experiments on a simulated biped crawling robot confirm that Eligibility Propagation accelerates the learning process more than 3 times.
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Title: The Derivational Complexity Induced by the Dependency Pair Method
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Abstract: We study the derivational complexity induced by the dependency pair method, enhanced with standard refinements. We obtain upper bounds on the derivational complexity induced by the dependency pair method in terms of the derivational complexity of the base techniques employed. In particular we show that the derivational complexity induced by the dependency pair method based on some direct technique, possibly refined by argument filtering, the usable rules criterion, or dependency graphs, is primitive recursive in the derivational complexity induced by the direct method. This implies that the derivational complexity induced by a standard application of the dependency pair method based on traditional termination orders like KBO, LPO, and MPO is exactly the same as if those orders were applied as the only termination technique.
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