A Continuation Multilevel Monte Carlo algorithm

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. The actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding weak and strong errors. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients

A Continuation Method for Nash Equilibria in Structured Games

Structured game representations have recently attracted interest as models for multi-agent artificial intelligence scenarios, with rational behavior most commonly characterized by Nash equilibria. This paper presents efficient, exact algorithms for computing Nash equilibria in structured game representations, including both graphical games and multi-agent influence diagrams (MAIDs). The algorithms are derived from a continuation method for normal-form and extensive-form games due to Govindan and Wilson; they follow a trajectory through a space of perturbed games and their equilibria, exploiting game structure through fast computation of the Jacobian of the payoff function. They are theoretically guaranteed to find at least one equilibrium of the game, and may find more. Our approach provides the first efficient algorithm for computing exact equilibria in graphical games with arbitrary topology, and the first algorithm to exploit fine-grained structural properties of MAIDs. Experimental results are presented demonstrating the effectiveness of the algorithms and comparing them to predecessors. The running time of the graphical game algorithm is similar to, and often better than, the running time of previous approximate algorithms. The algorithm for MAIDs can effectively solve games that are much larger than those solvable by previous methods

A continuation semantics of interrogatives that accounts for Baker's ambiguity

Wh-phrases in English can appear both raised and in-situ. However, only in-situ wh-phrases can take semantic scope beyond the immediately enclosing clause. I present a denotational semantics of interrogatives that naturally accounts for these two properties. It neither invokes movement or economy, nor posits lexical ambiguity between raised and in-situ occurrences of the same wh-phrase. My analysis is based on the concept of continuations. It uses a novel type system for higher-order continuations to handle wide-scope wh-phrases while remaining strictly compositional. This treatment sheds light on the combinatorics of interrogatives as well as other kinds of so-called A'-movement.Comment: 20 pages; typo fixe

Fake news. A continuation or rejection of the traditional news paradigm?

In the article, I analysed the problem of fake news in the context of the traditional paradigm of a news story. The traditional paradigm posits that, most of all, a piece of information is true. However in contemporary media, there exist pieces of information which are fabricated and untrue. It is not a new phenomenon, yet it has intensified in recent years. News stories are fabricated for entertainment, political, or commercial purposes. They are carriers of propaganda and profit. The essence of fake news is the intentional misleading of the receiver for achieving the above gains. It is difficult to verify their veracity, and identify fake news items due to their similarity to real pieces of news. That is why they are becoming a part of the media landscape in which we will probably have to exist

Letter from Julia to Marie August 17, 1943

This is a continuation or very long postscript to the letter from August 1

A continuation principle for a class of periodically perturbed autonomous systems

In this paper we evaluate the topological index of periodic solutions otained via the Malkin-Loud bifurcation result. Incidentally, we do not assume that the perturbation is differentiale.Comment: Accepted to Math. Nachr., Vol. 281, (2008), No.

Spirituality, Economics, and Education A Dialogic Critique of Spiritual Capital

This paper consists of a conversation between a philosopher specialising in ethics and religion and an educational researcher with an interest in cultural studies and contemporary social theory. Dialogic in form, this paper employs an interdisciplinary response to an interdisciplinary project and offers the following components: a dialogic theorizing of the implications for education of a research project on spiritual capital; a continuation of the project of analyzing moral thinking in various cultural and societal settings; a continuation of the project of analyzing political rhetoric (towards an understanding of the polemics of political rhetoric); a reaffirmation of the value of recognizing difference and ambiguity in the global moment