Bell correlations outside physics.

Correlations are ubiquitous in nature and their principled study is of paramount importance in scientific development. The seminal contributions from John Bell offer a framework for analyzing the correlations between the components of quantum mechanical systems and have instigated an experimental tradition which has recently culminated with the Nobel Prize in Physics (2022). In physics, Bell's framework allows the demonstration of the non-classical nature of quantum systems just from the analysis of the observed correlation patterns. Bell's ideas need not be restricted to physics. Our contribution is to show an example of a Bell approach, based on the insight that correlations can be broken down into a part due to common, ostensibly significant causes, and a part due to noise. We employ data from finance (price changes of securities) as an example to demonstrate our approach, highlighting several general applications: first, we demonstrate a new measure of association, informed by the assumed causal relationship between variables. Second, our framework can lead to streamlined Bell-type tests of widely employed models of association, which are in principle applicable to any discipline. In the area of finance, such models of association are Factor Models and the bivariate Gaussian model. Overall, we show that Bell's approach and the models we consider are applicable as general statistical techniques, without any domain specificity. We hope that our work will pave the way for extending our general understanding for how the structure of associations can be analyzed.

The Disjunction Effect in two-stage simulated gambles. An experimental study and comparison of a heuristic logistic, Markov and quantum-like model.

Savage's rational axiom of decision making under uncertainty, called the 'Sure Thing' principle, was purportedly falsified in a two-stage gamble paradigm by Tversky and Shafir (1992). This work revealed that participants would take a second-stage gamble for both possible outcomes of the initial-stage gamble, but would significantly depress this choice when no information was available on the outcome of the initial-stage gamble. Subsequent research has reported difficulty to replicate this Disjunction Effect in the two-stage gamble paradigm. We repeated this simulated two-stage gamble paradigm in an online study (N = 1119) but adapted the range of payoff amounts, and controlled the order of the blocks of two-stage gambles with, respectively without, information on the outcome of the first-stage gamble. The main empirical contributions of this study are that more risk averse participants produced (i) a reliable order effect in relation to the Disjunction Effect and the violation of the Law of Total Probability, and (ii) a novel inflation effect on gambling in the Unknown outcome condition analogous but opposite to the Disjunction Effect when Unknown outcome conditioned two-stage gambles precede the Known outcome conditioned ones. By contrast, we found that less risk averse participants produced neither of these effects. We discuss the underlying choice processes and compare the effectiveness of a logistic model, a Markov model and a quantum-like model. Our main theoretical findings are (i) a standard utility model and a Markov model using heuristic linear utility, contextual influence and carry-over effect cannot accommodate the present empirical results, and (ii) a model based on quantum dynamics, matched in form to the Markov model, can successfully describe all major aspects of our data.

Measuring inhibitory processes for alcohol-related attentional biases: introducing a novel attentional bias measure.

INTRODUCTION: Attentional biases for alcohol related information (AB) have often been reported for heavy drinkers. These attentional biases have been found to have predictive value regarding relapse in abstaining alcoholics. Similarly impaired inhibitory processes have also been found to be associated with heavy drinkers. This paper describes a new experimental paradigm that can be utilised to investigate attentional bias towards alcohol-related visual stimuli, specifically the ability to inhibit the orientation of initial and sustained attention, towards peripherally appearing stimuli. In this way we hope to study a novel aspect of attentional biases and how they relate to substance abuse. METHODS: We used a novel eye-tracking task which aims to measure inhibitory processes for AB. The experiment utilised a gaze contingency paradigm to measure the compulsion to process or attend to alcohol stimuli. 86 undergraduate participants were recruited (31 males; 55 females), aged 18-49 years (m = 20.88; sd = 4.52). A 'break frequency' variable was computed for each participant. This was the number of times that participants tried to look at peripheral stimuli. We argue that this variable is a direct measure of how distracting peripheral stimuli were. RESULTS: It was found that reported alcohol use was associated with the eye-tracking break frequency measure of inhibitory control. Thus, heavy drinking may be associated with decreased inhibitory control and increased attentional bias. CONCLUSIONS: Results suggest that attentional bias is not just a process of stimuli becoming prioritised, but also stimuli becoming compulsory to attend and process.

The role of similarity in artificial grammar learning.

The authors examine the role of similarity in artificial grammar learning (AGL; A. S. Reber, 1989). A standard finite-state language was used to create stimuli that were arrangements of embedded geometric shapes (Experiment 1), connected lines (Experiment 2), and sequences of shapes (Experiment 3). Main effects for well-known predictors from the literature (grammaticality, associative global and anchor chunk strength, novel global and anchor chunk strength, length of items, and edit distance) were observed, thus replicating previous work. However, the authors extend previous research by using a widely known similarity-based exemplar model of categorization (the generalized context model; R. M. Nosofsky, 1989) to fit grammaticality judgments, by nested regression analyses. The results suggest that any explanation of AGL that is based on the existing theories is incomplete without a similarity process as well. Also, the results provide a foundation for further interpreting AGL in the wider context of categorization research.

So concepts aren't definitions, but do they have necessary or sufficient features?

Rips (1989) is one of the most widely cited demonstrations of the relevance of critical features in conceptual structure. A critical feature will impose constraints on how an object is classified, regardless of other factors, such as overall similarity. We review and clarify critical features proposals in terms of whether an assumption is being made about necessary features, sufficient features, or both (i.e. a definition). On the basis of this, we scrutinize Rips' investigation and present our own empirical re-evaluation of this work. The results reported here do not support any strong view of necessary or sufficient features.

Symmetry, repetition, and figural goodness: an investigation of the weight of evidence theory.

Considerable evidence has accumulated on the superiority of symmetry over repetition in the study of figural goodness. The Weight of Evidence theory of figural goodness (WoE) provides a mathematically rigorous, elegant, and testable account of how factors like symmetry and repetition affect figural goodness. In this study we investigate implications of the WoE approach. More specifically, we examine (1) embedded patterns versus simple elements, (2) the number of elements in a pattern, and (3) long-range dependencies within a pattern. Data from two experiments illustrate cases in which figures made of simple repetitions have higher figural goodness than some kinds of symmetrical patterns; thus, the generality of the symmetry over repetition phenomenon is questioned. We discuss our results with respect to WoE and suggest ways to further develop the theory.