Introducing pre-impact air-cushioning effects into the Wagner model of impact theory

In this analysis, we consider the effects of non-quiescent initial conditions driven by pre-impact air–water interactions on the classical Wagner model of impact theory. We consider the problem of a rigid, solid impactor moving vertically towards a liquid pool. Prior to impact, viscous forces in the air act to deform the liquid free surface, inducing a flow in the pool. These interactions are then incorporated as initial conditions in the post-impact analysis. We derive expressions for the size of the effective contact set, the leading-order pressure and force on the impactor, and the speed and thickness of the jet at its base. In all cases, we show that the effect of the pre-impact behaviour is to cushion the impactor, reducing the size of the effective contact set and, hence, the force on the impactor. Small- and large-time asymptotic solutions are derived for general power-law impactors, and we show that the effects of the air die away as the impact progresses, so that we approach the classical Wagner solution.

Representing uncertainty in the Rescorla-Wagner model: Blocking, the redundancy effect, and outcome base rate

It is generally assumed that the Rescorla and Wagner (1972) model adequately accommodates the full results of simple cue competition experiments in humans (e.g. Dickinson et al., 1984), while the Bush and Mosteller (1951) model cannot. We present simulations that demonstrate this assumption is wrong in at least some circumstances. The Rescorla-Wagner model, as usually applied, fits the full results of a simple forward cue-competition experiment no better than the Bush-Mosteller model. Additionally, we present a novel finding, where letting the associative strength of all cues start at an intermediate value (rather than zero), allows this modified model to provide a better account of the experimental data than the (equivalently modified) Bush-Mosteller model. This modification also allows the Rescorla-Wagner model to account for a redundancy effect experiment (Uengoer et al., 2013); something that the unmodified model is not able to do. Furthermore, the modified Rescorla-Wagner model can accommodate the effect of varying the proportion of trials on which the outcome occurs (i.e. the base rate) on the redundancy effect (Jones et al., 2019). Interestingly, the initial associative strength of cues varies in line with the outcome base rate. We propose that this modification provides a simple way of mathematically representing uncertainty about the causal status of novel cues within the confines of the Rescorla-Wagner model. The theoretical implications of this modification are discussed. We also briefly introduce free and open resources to support formal modelling in associative learning. Keywords: associative learning, prediction error, uncertainty, modelling, blocking, redundancy effect, open science.

Representing uncertainty in the Rescorla-Wagner model: blocking, the redundancy effect, and outcome base rate

It is generally assumed that the Rescorla and Wagner (1972) model adequately accommodates the full results of simple cue competition experiments in humans (e.g. Dickinson et al., 1984), while the Bush and Mosteller (1951) model cannot. We present simulations that demonstrate this assumption is wrong in at least some circumstances. The Rescorla-Wagner model, as usually applied, fits the full results of a simple forward cue-competition experiment no better than the Bush-Mosteller model. Additionally, we present a novel finding, where letting the associative strength of all cues start at an intermediate value (rather than zero), allows this modified model to provide a better account of the experimental data than the (equivalently modified) Bush-Mosteller model. This modification also allows the Rescorla-Wagner model to account for a redundancy effect experiment (Uengoer et al., 2013); something that the unmodified model is not able to do. Furthermore, the modified Rescorla-Wagner model can accommodate the effect of varying the proportion of trials on which the outcome occurs (i.e. the base rate) on the redundancy effect (Jones et al., 2019). Interestingly, the initial associative strength of cues varies in line with the outcome base rate. We propose that this modification provides a simple way of mathematically representing uncertainty about the causal status of novel cues within the confines of the Rescorla-Wagner model. The theoretical implications of this modification are discussed. We also briefly introduce free and open resources to support formal modelling in associative learning.

Simultaneous Modeling of Reaction Times and Brain Dynamics in a Spatial Cuing Task

Understanding how brain activity translates into behavior is a grand challenge in neuroscientific research. Simultaneous computational modeling of both measures offers to address this question. The extension of the dynamic causal modeling (DCM) framework for BOLD responses to behavior (bDCM) constitutes such a modeling approach. However, only very few studies have employed and evaluated bDCM, and its application has been restricted to binary behavioral responses, limiting more general statements about its validity.This study used bDCM to model reaction times in a spatial attention task, which involved two separate runs with either horizontal or vertical stimulus configurations. We recorded fMRI data and reaction times (n=29) and compared bDCM to classical DCM and a behavioral Rescorla-Wagner model using goodness of fit-statistics and machine learning methods.Data showed that bDCM performed equally well as classical DCM when modeling BOLD responses and better than the Rescorla Wagner model when modeling reaction times. Notably, only using bDCM’s parameters enabled classification of the horizontal and vertical runs suggesting that bDCM seems to be more sensitive than the other models. Although our data also revealed practical limitations of the current bDCM approach that warrant further investigation, we conclude that bDCM constitutes a promising method for investigating the link between brain activity and behavior.

Pavlovian conditioning under partial reinforcement: The effects of non-reinforced trials versus cumulative CS duration

A core feature of associative models, such as those proposed by Allan Wagner (Rescorla & Wagner, 1972; Wagner, 1981), is that conditioning proceeds in a trial-by-trial fashion, with increments and decrements in associative strength occurring on each occasion that the conditioned stimulus (CS) is present either with or without the unconditioned stimulus (US). A very different approach has been taken by theories that assume animals continuously accumulate information about the total length of time spent waiting for the US both during the CS and in the absence of the CS (e.g., Gallistel & Gibbon, 2000). Here we describe three experiments using within-subject designs that tested between trial-based and time-accumulation accounts of the acquisition of conditioned responding using magazine approach conditioning in rats. We found that responding was affected by the total (cumulative) duration of exposure to the CS without the US rather than the number of trials on which the CS occurred without the US. We also found that exposure to the CS without the US had the same effect on conditioning whether that exposure occurred shortly (60 s) before each CS-US pairing or whether it occurred long (240 s) before each pairing. These findings are more consistent with time-accumulation models of conditioning than trial-based models like the Rescorla-Wagner model and Wagner’s (1981) Sometimes Opponent Process model. We discuss these findings in relation to other evidence that favours trial-based models rather than time-accumulation models.

Understanding Human Learning: Estimating Parameters of Temporal Difference Learning

Previous work in psychology has demonstrated how to use the Rescorla-Wagner model to estimate learning parameters from experimental design data (e.g., Iowa gambling test). Yet, the effect of actions on states often occur with a temporal delay in naturalistic settings, which the Rescorla-Wagner model does not model. To explain how humans learn about the time-delayed consequence of their actions requires a temporal difference (TD) learning model, like the state-action-reward-state-action model (SARSA), to incorporate the process of how humans learn about the temporal relations between state and action. This paper proposes a SARSA-based algorithm to estimate the learning rate and discount factor in such temporal difference learning processes, in order to quantify human learning process from behavior sequence data in naturalistic settings (e.g., experience sampling). Specifically, this paper uses a grid search over possible parameter space of learning rate and discount factor to find the best fitting values. To evaluate this estimation algorithm, simulations are conducted to provide evidence that the estimation algorithm can accurately recover the TD learning parameters. Then this estimation method is applied on an empirical dataset of exercise and stress. This new estimation method of TD learning parameters can open opportunities for important health-related empirical applications, including explaining individual-level TD learning, specifically, how human change their behaviors to achieve health-related goals. Additionally, the estimated learning parameters can also be used to design just-in-time adaptive personalized intervention (control) to induce behavior change.

The redundancy effect is related to a lack of conditioned inhibition: Evidence from a task in which excitation and inhibition are symmetrical

Rescorla and Wagner’s model of learning describes excitation and inhibition as symmetrical opposites. However, tasks used in human causal learning experiments, such as the allergist task, generally involve learning about cues leading to the presence or absence of the outcome, which may not reflect this assumption. This is important when considering learning effects which provide a challenge to this model, such as the redundancy effect. The redundancy effect describes higher causal ratings for the blocked cue X than for the uncorrelated cue Y in the design A+/AX+/BY+/CY–, the opposite pattern to that predicted by the Rescorla–Wagner model, which predicts higher associative strength for Y than for X. Crucially, this prediction depends on cue C gaining some inhibitory associative strength. In this article, we used a task in which cues could have independent inhibitory effects on the outcome, to investigate whether a lack of inhibition was related to the redundancy effect. In Experiment 1, inhibition for C was not detected in the allergist task, supporting this possibility. Three further experiments using the alternative task showed that a lack of inhibition was related to the redundancy effect: the redundancy effect was smaller when C was rated as inhibitory. Individual variation in the strength of inhibition for C also determined the size of the redundancy effect. Given that weak inhibition was detected in the alternative scenario but not in the allergist task, we recommend carefully choosing the type of task used to investigate associative learning phenomena, as it may influence results.

The ability of an extinguished CS and a CS given conditioned inhibition training to pass tests for inhibition

Conditioned inhibition (CI) is a classical conditioning procedure that results in a conditioned stimulus (CS) that predicts the absence of an unconditioned stimulus (US). A procedure known as Pavlovian conditioned inhibition training is the most common procedure for producing CI. In this procedure, a nontarget CS (CS A) is paired with the US and then CS A is presented with the target CS (CS X) without the US. Therefore, AUS trials and AX-noUS trials are given. CS X acquires inhibitory properties during these AX trials. Research has shown that extinction also produces CI. Extinction occurs when a CS (CS X) is paired with the US during conditioning and then this CS is presented alone without the US. The Rescorla-Wagner model predicts that the two CSs during AX-noUS trials will compete for learning and this should lead to slow and limited learning about those cues (a loss of excitation for CS A and inhibition acquired for CS X) due to this competition. During extinction trials, CS X does not compete for learning, so the subject should learn rapidly about the CS. The following experiments found that extinction produced less inhibition than Pavlovian conditioned inhibition training.

Магнитоэлектрический эффект в парамагнитной области в Gd-=SUB=-0.15-=/SUB=-Mn-=SUB=-0.85-=/SUB=-Sе

In the region of the percolation concentration in the GdxMn1-xSe solid solution, the electric polarization without a field and in 12 kOe magnetic field in the temperature range of 80–380 K was measured . For the composition with x = 0.15, the polarization hysteresis and the dependence of the residual polarization on the magnetic field and temperature were found. The hysteresis is explained in the model of migration polarization and the magnetoelectric effect in the Maxwell-Wagner model.