A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

Differential Equations in Abstract Cones

We extend the method of quasilinearization to differential equations in abstract normal cones. Under some assumptions, corresponding monotone iterations converge to the unique solution of our problem and this convergence is superlinear or semi–superlinear

Multiple iterations : mapping the trace

This paper explores the concept that individual dancers leave traces in a choreographer’s body of work and similarly, that dancers carry forward residue of embodied choreographies into other working processes. This presentation will be grounded in a study of the multiple iterations of a programme of solo works commissioned in 2008 from choreographers John Jasperse, Jodi Melnick, Liz Roche and Rosemary Butcher and danced by the author. This includes an exploration of the development by John Jasperse of themes from his solo into the pieces PURE (2008) and Truth, Revised Histories, Wishful Thinking and Flat Out Lies (2009); an adaptation of the solo Business of the Bloom by Jodi Melnick in 2008 and a further adaptation of Business of the Bloom by this author in 2012. It will map some of the developments that occurred through a number of further performances over five years of the solo Shared Material on Dying by Liz Roche and the working process of the (uncompleted) solo Episodes of Flight by Rosemary Butcher. The purpose is to reflect back on authorship in dance, an art form in which lineages of influence can often be clearly observed. Normally, once a choreographic work is created and performed, it is archived through video recording, notation and/or reviews. The dancer is no longer called upon to represent the dance piece within the archive and thus her/his lived presence and experiential perspective disappears. The author will draw on the different traces still inhabiting her body as pathways towards understanding how choreographic movement circulates beyond this moment of performance. This will include the interrogation of ownership of choreographic movement, as once it becomes integrated in the body of the dancer, who owns the dance? Furthermore, certain dancers, through their individual physical characteristics and moving identities, can deeply influence the formation of choreographic signatures, a proposition that challenges the sole authorship role of the choreographer in dance production. This paper will be delivered in a presentation format that will bleed into movement demonstrations alongside video footage of the works and auto-ethnographic accounts of dancing experience. A further source of knowledge will be drawn from extracts of interviews with other dancers including Sara Rudner, Rebecca Hilton and Catherine Bennett.

Risk-sensitive optimal control for Markov decision processes with monotone cost

The existence of an optimal feedback law is established for the risk-sensitive optimal control problem with denumerable state space. The main assumptions imposed are irreducibility and a near monotonicity condition on the one-step cost function. A solution can be found constructively using either value iteration or policy iteration under suitable conditions on initial feedback law.

Iterated stochastic filters with additive updates for dynamic system identification: Annealing-type iterations and the filter bank

A nonlinear stochastic filtering scheme based on a Gaussian sum representation of the filtering density and an annealing-type iterative update, which is additive and uses an artificial diffusion parameter, is proposed. The additive nature of the update relieves the problem of weight collapse often encountered with filters employing weighted particle based empirical approximation to the filtering density. The proposed Monte Carlo filter bank conforms in structure to the parent nonlinear filtering (Kushner-Stratonovich) equation and possesses excellent mixing properties enabling adequate exploration of the phase space of the state vector. The performance of the filter bank, presently assessed against a few carefully chosen numerical examples, provide ample evidence of its remarkable performance in terms of filter convergence and estimation accuracy vis-a-vis most other competing filters especially in higher dimensional dynamic system identification problems including cases that may demand estimating relatively minor variations in the parameter values from their reference states. (C) 2014 Elsevier Ltd. All rights reserved.

Generic differentiability of convex functions and monotone operators

The aim of this paper is to investigate to what extent the known theory of subdifferentiability and generic differentiability of convex functions defined on open sets can be carried out in the context of convex functions defined on not necessarily open sets. Among the main results obtained I would like to mention a Kenderov type theorem (the subdifferential at a generic point is contained in a sphere), a generic Gâteaux differentiability result in Banach spaces of class S and a generic Fréchet differentiability result in Asplund spaces. At least two methods can be used to prove these results: first, a direct one, and second, a more general one, based on the theory of monotone operators. Since this last theory was previously developed essentially for monotone operators defined on open sets, it was necessary to extend it to the context of monotone operators defined on a larger class of sets, our "quasi open" sets. This is done in Chapter III. As a matter of fact, most of these results have an even more general nature and have roots in the theory of minimal usco maps, as shown in Chapter II.

Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces

In this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.

Contraction of monotone phase-coupled oscillators

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state. © 2012 Elsevier B.V. All rights reserved.

Cubically convergent iterations for invariant subspace computation

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.

[Book review] Iterations: The New Image

Tony Mann provides a review of the book: Timothy Druckrey (ed.) Iterations: The New Image. MIT Press, (1994), 199pp. ISBN: 0-2620-4143-X. £35.95

Monotone scheme and boundary conditions for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number

A monotone scheme for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number is presented. The numerical stability is analysed with respect to the electromagnetic force. Standard central finite differences applied to finite volumes can only be numerically stable if the vector products involved in this force are computed with a scheme using a fully staggered grid. The electromagnetic quantities (electric currents and electric potential) must be shifted by half the grid size from the mechanical ones (velocity and pressure). An integral treatment of the boundary layers is used in conjunction with boundary conditions for electrically conducting walls. The simulations are performed with inhomogeneous electrical conductivities of the walls and reach high Hartmann numbers in three-dimensional simulations, even though a non-adaptive grid is used.