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The article discusses distribution risk and equity returns to aggregate capital in relation to income shares of capital and labor. It mentions that distribution risk is considered to originate in shifts in balance of power between workers and capitalists. It describes the two technical aspects used in the business cycle model, limited asset market participation and distributional shocks.

Scripts structure the collaborative learning process by constraining interactions, defining a sequence of activities and specifying individual roles. Scripts aim at increasing the probability that collaboration triggers knowledge generative interactions such as conflict resolution, explanation or mutual regulation. Integrative scripts are not bound to collaboration in small groups but include individual activities and class-wide activities. These pre- and post-structuring activities form the didactic envelope of the script. In many cases, the core part of the script is based on one among a few schemata: Jigsaw, conflict, reciprocal. We propose a model for designing this core component. This model postulates that learning results from the interactions that students engage in to build a shared understanding of a task despite the fact that it is distributed. Hence, the way the task is distributed among group members determines the interactions they will engage in. Interactions are viewed as the mechanisms for overcoming task splits. A large variety of scripts can be built from a small number of schemata, embedded within activities that occur across multiple social planes, activities which are integrated with each other by few generic operators. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of the selection of a transversal on the speed of convergence of interval methods based on the nonlinear Gauss-Seidel scheme to solve nonlinear systems of equations. It is shown that, in a marked contrast with the linear case, such a selection does not speed up the computation in the general case; directions for researches on more flexible methods to select projections are then discussed. [ABSTRACT FROM AUTHOR]

Model-based fault detection is based on generating a difference, known as a residual, between the predicted output value from the system model and the real output value measured by the sensors. If this residual is bigger than a threshold, then it is determined that there is a fault in the system. Otherwise, it is considered that the system is working properly. However, it is very important to analyse how the effect of model uncertainty is taken into account when determining the optimal threshold to be used in residual evaluation. In case that uncertainty is located in parameters (interval model), an interval observer has been shown to be a suitable strategy to generate such threshold. However, interval observers can present several problems that in order to be solved, existing approaches require computational demanding algorithms.The aim of this paper is to study the viability of using region based approaches coming from the interval analysis community to solve the interval observation problem. Region based approaches are appealing because of its low computational complexity but they suffer from the wrapping effect. On the other hand, trajectory based approaches are immune to this problem but their computational complexity is higher. In this paper, these two interval observation philosophies will be presented, analysed and compared using in two examples. [ABSTRACT FROM AUTHOR]

The problem of robust model based fault detection of dynamic systems using interval observers has been mainly addressed checking if the measured output is inside the interval of possible estimated outputs obtained considering uncertainty on model parameters. This task can be computationally expensive because the interval observers can be affected by the wrapping effect. In this paper, a mixed approach consisting in determining a computationally cheaper inner approximation of the estimated output interval, based only on simulating vertices of parameter uncertainty region (forward test), is combined with a backward consistency check when the real measured output falls outside this inner solution (backward check). The backward check is implemented using interval constraint satisfaction algorithms which can perform efficiently in deciding if the measured output is consistent with the interval model. The classical alternative to this backward check will force to solve a global optimisation problem, or equivalently, a global consistency problem. Finally, this approach will be tested on a gas turbine nozzle servosystem. [ABSTRACT FROM AUTHOR]

Keywords: interval analysis, state estimation, nonlinear model predictive control. [ABSTRACT FROM AUTHOR]

This paper deals with an original simultaneous localisation and map building paradigm (SLAM) based on the one hand on the use of an omnidirectional stereoscopic vision system and on the other hand on an interval analysis formalism for the state estimation. The first part of our study is linked to the problem of building the sensorial model. The second part is devoted to exploiting this sensorial model to localise the robot in the sense of interval analysis. The third part introduces the problem of map updating and deals with the matching problem of the stereo sensorial model with an environment map, (integrating all the previous primitive observations). The SLAM algorithm was tested on several large and structured environments and some experimental results will be presented. [ABSTRACT FROM AUTHOR]

This work presents a Simulation Based Design environment based on a Global Optimization (GO) algorithm for the solution of optimum design problems. The procedure, illustrated in the framework of a multiobjective ship design optimization problem, make use of high-fidelity, CPU time expensive computational models, including a free surface capturing RANSE solver. The use of GO prevents the optimizer to be trapped into local minima. The optimization is composed by global and local phases. In the global stage of the search, a few computationally expensive simulations are needed for creating surrogate models (metamodels) of the objective functions. Tentative design, created to explore the design variable space are evaluated with these inexpensive analytical approximations. The more promising designs are clustered, then locally minimized and eventually verified with high-fidelity simulations. New exact values are used to improve the metamodels and repeated cycles of the algorithm are performed. A Decision Maker strategy is finally adopted to select the more promising design. [ABSTRACT FROM AUTHOR]

A global optimization approach for convex multiplicative problems based on the generalized Benders decomposition is proposed. A suitable representation of the multiplicative problem in the outcome space reduces its global solution to the solution of a sequence of quasiconcave minimizations over polytopes. Some similarities between convex multiplicative and convex multiobjective programming become evident through the methodology proposed. The algorithm is easily implemented; its performance is illustrated by a test problem. Keywords: Global optimization, convex multiplicative programming, multiobjective programming, duality theory, numerical methods. [ABSTRACT FROM AUTHOR]

This paper considers the use of cooperative solvers for solving global optimization problems. We present the cooperative solver Sibcalc and show how it can be used in solution of different optimization problems. Several examples of applying the Sibcalc solver for solving optimization problems are given. Keywords: cooperative solvers, interval mathematics, interval constraint programming, global optimizations, distributive computations. [ABSTRACT FROM AUTHOR]

In this paper the problem of finding an affine lower bound function for a multivariate polynomial is considered. For this task, a number of methods are presented, all based on the expansion of the given polynomial into Bernstein polynomials. Error bounds and numerical results for a series of randomly-generated polynomials are given. Keywords: Bernstein polynomials, control points, convex hull, bound functions, complexity, global optimization. [ABSTRACT FROM AUTHOR]

In previous work, we have presented a novel global feasibility solver for the large system of quadratic constraints that arise as subproblems in the solving of hard hybrid problems, such as the scheduling of refineries. In this paper we present the Gradient Optimal Constraint Equation Subdivision (GOCES) algorithm, which incorporates a standard NLP solver and the global feasibility solver to find and establish global optimums for systems of quadratic equations, and present benchmarks. [ABSTRACT FROM AUTHOR]

We describe four approaches to solving nonconvex global optimization problems by convex nonlinear programming methods. It is assumed that the problem becomes convex when selected variables are fixed. The selected variables must be discrete, or else discretized if they are continuous. We first survey some existing methods: disjunctive programming with convex relaxations, logic-based outer approximation, and logic-based Benders decomposition. We then introduce a branch-and-bound method with convex quasi-relaxations (BBCQ) that can be effective when the discrete variables take a large number of real values. The BBCQ method generalizes work of Bollapragada, Ghattas and Hooker on structural design problems. It applies when the constraint functions are concave in the discrete variables and have a weak homogeneity property in the continuous variables. [ABSTRACT FROM AUTHOR]

In this paper the problem of parameter estimation for exponential sums is considered, i.e., of finding the set of parameters (amplitudes as well as decay constants) such that the exponential sum attains values in specified intervals at prescribed time data points. These intervals represent uncertainties in the measurements. An interval variant of Prony's method is given by which a box can be found containing all the consistent values of the parameters. Subsequently this box is tightened by the use of consistency techniques, which are accelerated by the introduction of redundant constraints. The use of interval arithmetic results in enclosures for the consistent values of the parameters which can be guaranteed also in the presence of rounding errors. Keywords: Parameter estimation, exponential sum, Prony's method, interval arithmetic, constraint propagation, redundant constraint. [ABSTRACT FROM AUTHOR]

This paper details a technique, called inter-block backtracking (IBB), which improves interval solving of decomposed systems with non-linear equations over the reals. This technique, introduced in 1998 by Bliek et al., handles a system of equations previously decomposed into a set of (small) k × k sub-systems, called blocks. All solutions are obtained by combining the solutions computed in the different blocks. The approach seems particularly suitable for improving interval solving techniques. In this paper, we analyze into detail the different variants of IBB which differ in their backtracking and filtering strategies. We also introduce IBB-GBJ, a new variant based on Dechter's graph-based backjumping. An extensive comparison on a sample of eight CSPs allows us to better understand the behavior of IBB. It shows that the variants IBB-BT+ and IBB-GBJ are good compromises between simplicity and performance. Moreover, it clearly shows that limiting the scope of the filtering to the blocks is very useful. For all the tested instances, IBB gains several orders of magnitude as compared to a global solving. Keywords: intervals, decomposition, backtracking, solving sparse systems. [ABSTRACT FROM AUTHOR]

This paper extends the Quad-filtering algorithm for handling general nonlinear systems. This extended algorithm is based on the RLT (Reformulation-Linearization Technique) schema. In the reformulation phase, tight convex and concave approximations of nonlinear terms are generated, that's to say for bilinear terms, product of variables, power and univariate terms. New variables are introduced to linearize the initial constraint system. A linear programming solver is called to prune the domains. A combination of this filtering technique with Box-consistency filtering algorithm has been investigated. Experimental results on difficult problems show that a solver based on this combination outperforms classical CSP solvers. [ABSTRACT FROM AUTHOR]