Three experiments investigated the impact of delay on human causal learning. We present a new paradigm based on the presentation of continuous event streams, and use it to test two hypotheses drawn from associative learning theories of causal inference. Unlike free-operant procedures traditionally used to study temporal aspects of causal learning (Shanks, Pearson, & Dickinson, 1989; Shanks & Di...

The baby-step giant-step algorithm, due to Shanks, may be used to solve the discrete logarithm problem in arbitrary groups. The paper explores a generalisation of this algorithm, where extra baby steps may be computed after carrying out giant steps (thus increasing the giant step size). The paper explores the problem of deciding how many, and when, extra baby steps should be computed so that th...

We describe preliminary work on applying the Penn Discourse Treebank framework (PDTB, Prasad et al., 2008) and the Cognitive approach to Coherence Relations (CCR, Sanders, Spooren & Noordman, 1992) to spoken language. Due to register differences, we do not only expect to see a distribution of discourse relations that deviates from the one in written text, but also expect to come across new rela...

In this article we discuss a weaker version of Liouville’s theorem on the integrability of Hamiltonian systems. We show that in the case of Tonelli Hamiltonians the involution hypothesis on the integrals of motion can be completely dropped and still interesting information on the dynamics of the system can be deduced. Moreover, we prove that on the n-dimensional torus this weaker condition impl...

In this paper, we propose a multistep extension of the Shanks’ sequence transformation [2, 3]. It is defined as a ratio of determinants. Then, we show that this transformation can be recursively implemented by a multistep extension of the ε–algorithm of Wynn [4]. Some of their properties are specified. These results are obtained by using the Hirota’s bilinear method [1], a procedure quite usefu...

This paper presents a general framework for Shanks transformations of sequences of elements in a vector space. It is shown that the Minimal Polynomial Extrapolation (MPE), the Modified Minimal Polynomial Extrapolation (MMPE), the Reduced Rank Extrapolation (RRE), the Vector Epsilon Algorithm (VEA), the Topological Epsilon Algorithm (TEA), and Anderson Acceleration (AA), which are standard gener...