Perceptions of randomness in binary sequences: Normative, heuristic, or both?

When people consider a series of random binary events, such as tossing an unbiased coin and recording the sequence of heads (H) and tails (T), they tend to erroneously rate sequences with less internal structure or order (such as HTTHT) as more probable than sequences containing more structure or order (such as HHHHH). This is traditionally explained as a local representativeness effect: Participants assume that the properties of long sequences of random outcomes—such as an equal proportion of heads and tails, and little internal structure—should also apply to short sequences. However, recent theoretical work has noted that the probability of a particular sequence of say, heads and tails of length n, occurring within a larger (>n) sequence of coin flips actually differs by sequence, so P(HHHHH) < P(HTTHT). In this alternative account, people apply rational norms based on limited experience. We test these accounts. Participants in Experiment 1 rated the likelihood of occurrence for all possible strings of 4, 5, and 6 observations in a sequence of coin flips. Judgments were better explained by representativeness in alternation rate, relative proportion of heads and tails, and sequence complexity, than by objective probabilities. Experiments 2 and 3 gave similar results using incentivized binary choice procedures. Overall the evidence suggests that participants are not sensitive to variation in objective probabilities of a sub-sequence occurring; they appear to use heuristics based on several distinct forms of representativeness

How to Change the Weight of Rare Events in Decisions from Experience

When making risky choices, two kinds of information are crucial: outcome values and outcome probabilities. Here, we demonstrate that the juncture at which value and probability information is provided has a fundamental effect on choice. Across four experiments involving 489 participants, we compare two decision making scenarios: one where value information is revealed during sampling (Standard), and one where value information is revealed after sampling (Value-Ignorance). On average, participants made riskier choices when value information was provided after sampling. Moreover, parameter estimates from a hierarchical Bayesian implementation of cumulative prospect theory suggested that participants overweighted rare events when value information was absent during sampling, but showed no overweighting in the Standard condition. This suggests that the impact of rare events on choice relies crucially on the timing of probability and value integration. We provide paths towards mechanistic explanations of our results based on frameworks which assume different underlying cognitive architectures

Steinberg modules and Donkin pairs

We prove that in positive characteristic a module with good filtration for a group of type E6 restricts to a module with good filtration for a subgroup of type F4. (Recall that a filtration of a module for a semisimple algebraic group is called good if its layers are dual Weyl modules.) Our result confirms a conjecture of Brundan for one more case. The method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, in characteristic not 2, with a computer-aided variation on the old method of Donkin.Comment: 16 pages; proof of Brundan's conjecture adde

Relative judgement is relatively difficult: evidence against the role of relative judgement in absolute identification

A variety of processes have been put forward to explain absolute identification performance. One difference between current models of absolute identification is the extent to which the task involves accessing stored representations in long-term memory (e.g. exemplars in memory, Kent & Lamberts, Journal of Experimental Psychology: Learning Memory and Cognition, 31, 289–305, 2005) or relative judgement (comparison of the current stimulus to the stimulus on the previous trial, Stewart, Brown & Chater, Psychological Review, 112, 881–911, 2005). In two experiments we explored this by tapping into these processes. In Experiment 1 participants completed an absolute identification task using eight line lengths whereby a single stimulus was presented on each trial for identification. They also completed a matching task aimed at mirroring exemplar comparison in which eight line lengths were presented in a circular array and the task was to report which of these matched a target presented centrally. Experiment 2 was a relative judgement task and was similar to Experiment 1 except that the task was to report the difference (jump-size) between the current stimulus and that on the previous trial. The absolute identification and matching data showed clear similarities (faster and more accurate responding for stimuli near the edges of the range and similar stimulus-response confusions). In contrast, relative judgment performance was poor suggesting relative judgement is not straightforward. Moreover, performance as a function of jump-size differed considerably between the relative judgement and absolute identification tasks. Similarly, in the relative judgement task, predicting correct stimulus identification based on successful relative judgement yielded the reverse pattern of performance observed in the absolute identification task. Overall, the data suggest that relative judgement does not underlie absolute identification and that the task is more likely reliant on an exemplar comparison process

Assessment of acquired immune response to Rhipicephalus appendiculatus tick infestation in different goat breeds

Changes in serum gamma globulin levels, numbers of replete female ticks and engorged tick mass were used as parameters to monitor the acquired immune response (antibody mediated immune response) elicited by Rhipicephalus appendiculatus adult tick infestations. Three consecutive Rhipicephalus appendiculatus adult tick infestations were applied to South African Indigenous goats (Nguni), Saanen goats and cross-bred goats (Saanen goats crossed with South African Indigenous goats [Nguni]) under laboratory conditions. During the three consecutive Rhipicephalus appendiculatus adult tick infestations the serum gamma globulin levels increased in all three breeds, whilst the mean replete female tick numbers and engorged tick mass decreased. Even though all three goat breeds exhibited an acquired immune response, the South African Indigenous goats (Nguni) response was significantly higher than that of the Saanen and cross-bred goats. However, the acquired immune response elicited by Saanen goats was significantly lower when compared with cross-bred goats.The Medunsa campus of the University of Limpopohttp://www.ojvr.orgam201

Homomorphisms and Higher Extensions for Schur algebras and symmetric groups

This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext groups in the two categories, and discuss those cases where explicit results have been determined

MEM-EX: An exemplar memory model of decisions from experience

Many real-world decisions must be made on basis of experienced outcomes. However, there is little consensus about the mechanisms by which people make these decisions from experience (DfE). Across five experiments, we identified several factors influencing DfE. We also introduce a novel computational modeling framework, the memory for exemplars model (MEM-EX), which posits that decision makers rely on memory for previously experienced outcomes to make choices. Using MEM-EX, we demonstrate how several cognitive mechanisms provide intuitive and parsimonious explanations for the effects of value-ignorance, salience, outcome order, and sample size. We also conduct a cross-validation analysis of several models within the MEM-EX framework, as well as a baseline model built on principles of reinforcement-learning. We find that MEM-EX consistently outperforms this baseline, demonstrating its value as a tool for making quantitative predictions without overfitting. We discuss the implications of these findings on our understanding of the interplay between attention, memory, and experience-based choice

Diffusion versus linear ballistic accumulation: different models but the same conclusions about psychological processes?

Quantitative models for response time and accuracy are increasingly used as tools to draw conclusions about psychological processes. Here we investigate the extent to which these substantive conclusions depend on whether researchers use the Ratcliff diffusion model or the Linear Ballistic Accumulator model. Simulations show that the models agree on the effects of changes in the rate of information accumulation and changes in non-decision time, but that they disagree on the effects of changes in response caution. In fits to empirical data, however, the models tend to agree closely on the effects of an experimental manipulation of response caution. We discuss the implications of these conflicting results, concluding that real manipulations of caution map closely, but not perfectly to response caution in either model. Importantly, we conclude that inferences about psychological processes made from real data are unlikely to depend on the model that is used

The climate crisis - can a community-led approach work?

Climate change is the biggest threat to human health.1 Over 300 Local authorities across the United Kingdom have declared climate emergencies,2 and there have been over 1500 declared by equivalent local authorities across the globe.3 Local authorities recognise the scale of the challenge and have set targets to reach ‘net zero’. Net zero, that is, not releasing more carbon dioxide than is captured, necessitates significantly reducing the amount of carbon dioxide emitted.4 Local authorities and the communities they serve are well placed to address this challenge both in terms of carbon emissions, as they “have powers or influence over roughly a third of emissions in their local areas” (p.3).5 and also through their connection and knowledge of their communities. This article asks the question: how can communities come together to make sustained change and accelerate progress towards net-zero