Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct a number of families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the noncrucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice.

Implicit synthesis

In this reply to Neal and Hesketh and to the commentators, we argue that implicit knowledge is partly abstract and can be usefully defined by the criteria of both metaknowledge and intentional control. We suggest that the pattern of dissociations supports a claim of separate implicit and explicit learning modes. According to our characterization, implicit learning leads to knowledge that is not automatically represented as knowledge by the learning process; instead, the presence of knowledge has to be inferred by the subject (partial explicitation) if metaknowledge is gained at all. During explicit learning, knowledge is automatically labeled as knowledge by the learning process, so that metaknowledge comes immediately and to the fullest extent. Finally, we suggest that implicit knowledge may to some degree apply regardless of intention.

Effects of divided attention and speeded responding on implicit and explicit retrieval of artificial grammar knowledge

The artificial grammar (AG) learning literature (see, e.g., Mathews et al., 1989; Reber, 1967) has relied heavily on a single measure of implicitly acquired knowledge. Recent work comparing this measure (string classification) with a more indirect measure in which participants make liking ratings of novel stimuli (e.g., Manza & Bornstein, 1995; Newell & Bright, 2001) has shown that string classification (which we argue can be thought of as an explicit, rather than an implicit, measure of memory) gives rise to more explicit knowledge of the grammatical structure in learning strings and is more resilient to changes in surface features and processing between encoding and retrieval. We report data from two experiments that extend these findings. In Experiment 1, we showed that a divided attention manipulation (at retrieval) interfered with explicit retrieval of AG knowledge but did not interfere with implicit retrieval. In Experiment 2, we showed that forcing participants to respond within a very tight deadline resulted in the same asymmetric interference pattern between the tasks. In both experiments, we also showed that the type of information being retrieved influenced whether interference was observed. The results are discussed in terms of the relatively automatic nature of implicit retrieval and also with respect to the differences between analytic and nonanalytic processing (Whittlesea Price, 2001).

Reducing implicit prejudice by blurring intergroup boundaries

In two experiments we examined whether and when blurring intergroup boundaries reduces implicit prejudice. In Experiment 1 we observed that when participants first completed a task in which they generated characteristics that overlapped between an ingroup and an outgroup they showed less implicit bias as measured by an Implicit Association Test. In Experiment 2 we found that the effectiveness of blurring intergroup boundaries for reducing implicit bias was moderated by pretask levels of ingroup identification. We discuss these findings in the context of extending differentiation-based interventions for reducing explicit bias to the domain of implicit attitudes.

Implicit memory and consumer choice: the mediating role of brand familiarity

Two experiments investigated the influence of implicit memory on consumer choice for brands with varying levels of familiarity. Priming was measured using a consideration-choice task, developed by Coates, Butler and Berry (2004). Experiment 1 employed a coupon-rating task at encoding that required participants to meaningfully process individual brand names, to assess whether priming could affect participants' final (preferred) choices for familiar brands. Experiment 2 used this same method to assess the impact of implicit memory on consideration and choice for unknown and leader brands, presented in conjunction with familiar competitors. Significant priming was obtained in both experiments, and was shown to directly influence final choice in the case of familiar and highly familiar leader brands. Moreover, it was shown that a single prior exposure could lead participants to consider buying an unknown, and indeed fictitious, brand. Copyright (c) 2006 John Wiley & Sons, Ltd.

Implicit memory: a prime example for brand consideration and choice

Three experiments investigated the influence of implicit memory for familiar brand names on consumer choice. Priming was measured using modified preference judgment tasks that comprised both brand consideration and choice components. Experiment 1 used a 'complex choice task' where consideration and choice stages were characterized as acting in sequence. Experiment 2 explored a different formulation whereby consideration and choice were assumed to act in parallel, Both experiments demonstrated that priming had an influence on brand consideration but not on final or preferred choice. Finally, Experiment 3 replicated and extended these findings under more realistic conditions where participants actually received some of the products that they selected. Overall, the experiments suggested that for many decisions involving the consideration of familiar brands prior to choice, previous exposure to brand names can increase the likelihood that they will enter the consumers' consideration set. However, the advantage does not appear to extend to choice itself. Copyright (C) 2004 John Wiley Sons, Ltd.