Second-order Conditioning Research Articles

Conditioned hedonic responses elicited by contextual cues paired with nausea or with internal pain.

Pairing a taste with either internal pain or nausea, despite equivalent effects on voluntary consumption, has dissociable effects on hedonic responses: Only pairing with nausea results in the production of disgust reactions, while pairing with internal pain results in conditioned fear as indicated by immobility. Here, we use orofacial reactions to examine the hedonic responses elicited by contextual, nonflavor, cues paired with nausea produced by injection of lithium chloride (LiCl) or internal pain caused by injection of hypertonic saline. In Experiment 1, aversive orofacial responses were the specific context-elicited behaviors in the rats injected with LiCl, whereas immobility was seen in the animals injected with hypertonic saline. In Experiment 2, rats first received discriminative training with two contexts, where one context was paired with LiCl or hypertonic saline, and the other context with isotonic saline. After this, rats were intraorally infused with a flavor (conditioned stimulus (CS) +) in the paired context, and with a different flavor (CS-) in the unpaired context. Second-order conditioning was then examined in a test conducted in the unpaired context. The infusion of the CS + flavor produced aversive orofacial responses in the rats injected with LiCl but immobility in the subjects injected with hypertonic saline. The results suggest that nonflavor cues support conditioned hedonic responses in the same way as flavor cues, which implies that the quality of aversion learning (conditioned nausea vs. fear) is primarily determined by the nature of the aversive event and not the type of conditioned cue. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Configural learning: a higher form of learning in Lymnaea.

Events typically occur in a specific context and the ability to assign importance to this occurrence plays a significant role in memory formation and recall. When the scent of a crayfish predator (CE) is encountered in Lymnaea stagnalis strains known to be predator experienced (e.g. the W-strain), enhancement of memory formation and depression of feeding occur, which are part of a suite of anti-predator behaviours. We hypothesized that Lymnaea possess a form of higher-order conditioning, namely configural learning. We tested this by simultaneously exposing W-strain Lymnaea to a carrot food odour (CO) and predator scent (CE). Two hours later, we operantly conditioned these snails with a single 0.5 h training session in CO to determine whether training in CO results in long-term memory (LTM) formation. A series of control experiments followed and demonstrated that only the CO+CE snails trained in CO had acquired enhanced memory-forming ability. Additionally, following CE+CO pairing, CO no longer elicited an increased feeding response. Hence, snails have the ability to undergo configural learning. Following configural learning, CO becomes a risk signal and evokes behavioural responses phenotypically similar to those elicited by exposure to CE.

Replacement and reasoning: a reliabilist account of epistemic defeat

In this paper, I present a solution to the problem that the need to accommodate the phenomenon of epistemic defeat poses for reliabilism. Defeaters are supposed to remove justification for previously justified beliefs. According to standard process reliabilism, the justification of a belief depends on the reliability of a process that is already completed when a defeater for that belief is obtained. It is hard to see, then, how a defeater can affect reliabilist justification, if that justification, from the perspective of the defeater, lies wholly in the past. What is more, undercutting defeaters plausibly defeat by generating incompatibilities with higher-order propositions (Sturgeon in Philos Stud 169(1):105–118, 2014; Melis in Philos Stud 170(3):433–442, 2014). This is hard to integrate with reliabilism which explicitly denies higher-order conditions for justification. I argue that both of these phenomena can be accommodated by it via what I call the “Replacement Principle”: when a defeater is obtained, it generates either a logical incompatibility (in cases of rebutting defeat) or a doxastic incompatibility (in cases of undercutting defeat). The resulting tension is registered and initiates a reasoning process that compares the epistemic support for the defeater with that for the defeated belief. This process may replace the original reliable formation process as a doxastic base for the defeated belief. If the defeater is not given its due weight in the reasoning process, that process was unreliable and if the defeated belief is retained as a result, it will be unjustified. This is intuitively the right result. Since reasoning is reliable, only if it is rational, the account manages to capture the intuition that disregarding a defeater would be irrational without having to make rationality a condition for justification. Replacement is not only plausible on causal pictures of doxastic basing, but also required in order to allow for the possibility of belief reevaluation in general and is therefore not an ad hoc addition to reliabilism, but rather part of its inherent explanatory resources.

Perron–Frobenius theorem for hypermatrices in the max algebra

Recently, there have been many intriguing new developments in the study of hypermatrices and their associated eigenvalue problems. In particular, results coming from the matrix setting when studying the max algebra have shown especially attractive combinatorial features. We now extend this max algebra setting into the realm of hypermatrices. Considering that the max algebra has shown particular significance in optimization problems for the matrix setting, we look to examine and extend these results in the higher order conditions. Furthermore, we establish some algebraic properties for hypermatrices and then proceed to extend the Perron–Frobenius Theorem for this setting and prove the existence of a unique eigenvalue. We continue by stating a result from Nussbaum, that the Min–Max theorem holds, and provide a proof for completeness. For strongly increasing hypermatrices, an iterative algorithm which converges to our unique eigenvalue is given. Finally, we conclude with an analysis of our results in the hypergraph setting.

Absence of second-order conditioning in Japanese fire-bellied newts

Absence of second-order conditioning in Japanese fire-bellied newts

Transcranial direct current stimulation enhances retention of a second (but not first) order conditional visuo-motor sequence

This study examined the role of the left inferior frontal gyrus in the implicit learning and retention of a ‘simple’ first order conditional (FOC) sequence and a relatively ‘complex’ second order conditional (SOC) sequence, using anodal transcranial direct current stimulation (a-tDCS). Groups of healthy adults received either a-tDCS (n = 18) over the left inferior frontal gyrus or sham/placebo (n = 18) stimulation. On separate days, participants completed a serial reaction time (SRT) task whilst receiving stimulation. On one of the days, participants were presented with a FOC sequence and in another, a SOC sequence. Both the learning and short-term retention of the sequences were measured. Results showed a-tDCS enhanced the short-term retention of the SOC sequence but not the FOC sequence. There was no effect of a-tDCS on the learning of either FOC or SOC sequences. The results provide evidence of prefrontal involvement in the retention of a motor sequence. However, its role appears to be influenced by the complexity of the sequence’s structure. Additionally, the results show a-tDCS can enhance retention of an implicitly learnt motor sequence.

Excitatory second-order conditioning using a backward first-order conditioned stimulus: A challenge for prediction error reduction.

Prével and colleagues reported excitatory learning with a backward conditioned stimulus (CS) in a conditioned reinforcement preparation. Their results add to existing evidence of backward CSs sometimes being excitatory and were viewed as challenging the view that learning is driven by prediction error reduction, which assumes that only predictive (i.e., forward) relationships are learned. The results instead were consistent with the assumptions of both Miller's Temporal Coding Hypothesis and Wagner's Sometimes Opponent Processes (SOP) model. The present experiment extended the conditioned reinforcement preparation developed by Prével et al. to a backward second-order conditioning preparation, with the aim of discriminating between these two accounts. We tested whether a second-order CS can serve as an effective conditioned reinforcer, even when the first-order CS with which it was paired is a backward CS that elicits no responding. Evidence of conditioned reinforcement was found, despite no conditioned response (CR) being elicited by the first-order backward CS. The evidence of second-order conditioning in the absence of excitatory conditioning to the first-order CS is interpreted as a challenge to SOP. In contrast, the present results are consistent with the Temporal Coding Hypothesis and constitute a conceptual replication in humans of previous reports of excitatory second-order conditioning in rodents with a backward CS. The proposal is made that learning is driven by "discrepancy" with prior experience as opposed to " prediction error."

On the role of higher-order conditions in distortion gradient plasticity

We focus on Gurtin’s gradient plasticity (GP) theory adopting Nye’s tensor as primal higher-order (HO) kinematic variable, contributing to the free energy. In the absence of other HO kinematic variables, this framework is characterised by kinematic HO boundary conditions (BCs) which admit discontinuity in some components of the plastic distortion. This implies that the finite element (FE) implementation of this theory requires a “non-standard” approach. To address this issue, here, we develop a specific H(curl) FE. A “standard” FE implementation, in which the nodal degrees of freedom are all the displacement and plastic distortion components, is successful if the above theory is extended by including a dissipative HO stress, proportional to a material length L, conjugated to the gradient of the plastic distortion rate, such that the HO BCs must be imposed on each plastic distortion component. The foregoing switch in the kinematic HO BCs makes it difficult to obtain reliable FE solutions for the first theory by particularising the “standard” FE code for the enriched theory with the choice of a suitably small L. Beside showing this, in this work, we aim at shedding light on the distortion GP based on Nye’s tensor only, in which also the use of an appropriately small rate-sensitivity parameter to obtain rate-independent solutions within a viscoplastic framework reveals interesting aspects. To this purpose, we consider three plane strain benchmarks, with focus on limit load capacity: the bending of thin foils, relevant to validate our novel implementation by comparison with literature results; the simple shear of a strip constrained between bodies impenetrable to dislocations, that we discuss on the basis of a new analytical solution for the rate-independent case; a composite problem approximating a polycrystal, whose main feature consists of internal grain boundaries in which we impose homogeneous kinematic HO conditions. This last benchmark shows that the computational model involving HO dissipation cannot predict a collapse mechanism predicted by the novel H(curl) FE model.

Informal Caregiving, Employment Status and Work Hours of the 50+ Population in Europe

Using panel data on the age group 50–70 in 15 European countries, we analyze the effects of providing informal care to parents, parents-in-law, stepparents, and grandparents on employment status and work hours. We account for fixed individual effects and test for endogeneity of caregiving using moments exploiting standard instruments (e.g., parental death) as well as higher-order moment conditions (Lewbel instruments). Specification tests suggest that informal care provision and daily caregiving can be treated as exogenous variables. We find a significant and negative effect of daily caregiving on employment status and work hours. This effect is particularly strong for women. On the other hand, providing care at a weekly (or less than weekly) frequency does not significantly affect paid work. We do not find evidence of heterogeneous effects of caregiving on paid work across European regions.

Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone

Abstract Using the definitions of μ-th order lower and upper directional derivatives of vector-valued functions, introduced in Rahmo and Studniarski (J. Math. Anal. Appl. 393 (2012), 212–221), we provide some necessary and sufficient conditions for strict local Pareto minimizers of order μ for optimization problems where the partial order is introduced by a pointed polyhedral cone with non-empty interior.

Protein synthesis in the basolateral amygdala complex is required for consolidation of a first-order fear memory, but not for consolidation of a higher-order fear memory

The present series of experiments pursued our recent findings that consolidation of a second-order fear memory requires neuronal activity, but not de novo protein synthesis, in the basolateral amygdala complex (BLA). It used a modified second-order conditioning protocol in which rats were exposed to S1-shock pairings in stage 1 and pairings of the serial S2-S1 compound and shock in stage 2. Experiment 1 showed that responding (freezing) to S2 in this protocol is conditional on its compounding with S1 in stage 2 (Experiment 1), and therefore, the result of associative formation. The remaining experiments then showed that the protein synthesis requirement for consolidation of new learning about S2 varied with the training afforded S1. When S1 was trained in stage 1 and present in stage 2, consolidation of the new S2 fear memory was unaffected by pre- or post-stage 2 infusions of the protein synthesis inhibitor, cycloheximide, into the BLA (Experiments 2 and 5). This result was observed independently of the number of S1-shock pairings in stage 1 (even a single pairing produced the result), and alongside demonstrations that cycloheximide infusions disrupt consolidation of a first-order fear memory (Experiments 2 and 5). However, when S1 was not conditioned in stage 1 (Experiment 3) or was omitted from conditioning in stage 2 (Experiment 4), consolidation of the new S2 fear memory was disrupted by post-stage 2 cycloheximide infusions into the BLA. These results were taken to imply that the consolidation of a higher-order fear memory exploits molecular events associated with consolidation of a reactivated first-order fear memory; hence it occurs independently of de novo protein synthesis in the BLA. Alternatively, the nature of the association formed in higher-order conditioning may be such as to not require de novo protein synthesis for its consolidation.

Prescription opioid misusing chronic pain patients exhibit dysregulated context-dependent associations: Investigating associative learning in addiction with the cue-primed reactivity task

BackgroundAssociative learning undergirds the development of addiction, such that drug-related cues serve as conditioned stimuli to elicit drug-seeking responses. Plausibly, among opioid misusing chronic pain patients, pain-related information may serve as a conditioned stimulus to magnify opioid cue-elicited autonomic and craving responses through a process of second-order conditioning. MethodsWe utilized a novel psychophysiological probe of pain-opioid conditioned associations, the Cue-Primed Reactivity (CPR) task. In this task, participants were presented with images as primes (200 ms) and cues (6000 ms) in pairs organized in four task blocks: “control-opioid,” “pain-opioid,” “control-pain,” and “opioid-pain.” Opioid-treated chronic pain patients (N = 30) recruited from an Army base in the Western United States were classified as opioid misusers (n = 17) or non-misusers (n = 13) via a validated cutpoint on the Prescription Drug Use Questionnaire (PDUQ; Compton et al., 2008). Opioid misuse status was examined as a predictor of HRV, craving, and mood responses on the CPR task. ResultsHRV increased to a greater extent during the pain-opioid block compared to the control-opioid block for non-misusers compared to misusers (p = .003, η2partial = 0.27). In contrast, craving increased to a greater extent from baseline to the pain-opioid block for misusers than for non-misusers (p = .03, η2partial = .16). ConclusionsFindings suggest that opioid-treated chronic pain patients exhibit Pavlovian conditioned responses to opioid cues strengthened by an associative learning process of second-order conditioning when primed by pain-related images. This pain-opioid contingency appears to become disrupted among individuals who engage in opioid misuse, such that opioid-related stimuli elicit motivational responses irrespective of pain-related contextual stimuli.

Temporal map formation in appetitive second-order conditioning in rats

Three experiments examined whether second-order conditioning resulted in the formation of a fully-featured temporal map, as proposed by the temporal coding hypothesis. Experiments 1 and 2 examined second-order conditioning with different first- and second-order relationships. Measures of the strength of second-order conditioning were mostly consistent with the temporal coding hypothesis; second-order conditioning was best with arrangements in which CS2 occurred prior to the time that the US normally occurred during CS1-US presentations. However, there was no evidence of anticipatory timing during CS2 during second-order conditioning. A third experiment directly examined whether a fully-featured temporal map was formed during second-order conditioning by examining the acquisition of anticipatory timing in subsequent reinforced second-order trials. The results of Experiment 3 suggested that the effects obtained in Experiments 1 and 2 were due to learning of the temporal order and coincidence of events that resulted in the formation of an ordinal temporal map, but that precise durations were not encoded.

Associative structure of second-order conditioning in humans.

Second-order conditioning (SOC; i.e., conditioned responding to S2 as a result of S1-US pairings followed by S2-S1 pairings) is generally explained by either a direct S2→US association or by an associative chain (i.e., S2→S1→US). Previous research found that differences in responses to S2 after S1 was extinguished often depended on the nature of the S2-S1 pairings (i.e., sequential or simultaneous). In two experiments with human participants, we examined the possibility that such differences result from S1 evoking S2 during extinction of S1 following simultaneous but not sequential S2-S1 pairings. This evocation of S2 by S1 following simultaneous pairings may have paired the evoked representation of S2 with absence of the outcome, thereby facilitating mediated extinction of S2. Using sequential S2-S1 pairings, both Experiments 1 and 2 failed to support this account of how extinction of S1 reduced responding to S2. Experiment 1 found that extinguishing S1 reduced responding to S2, while extinguishing S2 had little effect on responses to S1, although forward evocation of S1 during extinction of S2 paired the evoked representation of S1 with absence of the outcome. In Experiment 2, evocation of S2 during S1 nonreinforced trials was prevented because S2-S1 pairings followed (rather than proceeded) S1-alone exposures. Nevertheless, responding to S2 at test mimicked S1 responding. Responding to S2 was high in the context in which S1 had been reinforced and low in the context in which S1 had been nonreinforced. Collectively, these experiments provide additional support for the associative-chain account of SOC.

Dexamethasone impairs encoding and expression of aversive conditioning promoted by pentylenetetrazole.

Behavioral and neuroendocrine responses following threatening situations promote the release of corticosterone, which is known to modulate trauma-related learning and memory process. However, it remains unknown whether the aversive learning generated by interoceptive fear conditioning is affected by glucocorticoid modulation. Therefore, the present study aimed to investigate the role of dexamethasone suppression in encoding and expression of pentylenetetrazole-induced olfactory fear conditioning (OFC) and in contextual second-order conditioning promoted by the conditioned odor. Adult male Long-Evans rats were treated with dexamethasone 60 min before the encoding or the expression in both OFC and contextual second-order conditioning. Dexamethasone treatment impaired encoding and expression of the OFC, but failed to impair encoding and expression of the contextual second-order conditioning. Altogether, our results show that although OFC and thereafter contextual second-order conditioning may allow the study of traumatic memories, each order of conditioning seems to present specific features related to their pharmacological modulation. These findings highlight the importance of addressing the role of neuromodulatory systems in first-order and second-order conditioning to gain a better understanding of these phenomena and support future therapies related to traumatic memories.

Transfer of discriminative control during stimulus fading conducted without reinforcement.

Using trial-and-error training, eight pigeons did not learn to discriminate between 45° and 135° lines, but did learn to discriminate between red and green colors. Control by line tilt was induced by stimulus fading that did not include reinforcement while fading out the colors. After establishing the red-green discrimination, low-intensity lines were superimposed on colors and were gradually faded in. All of this was done using reinforcement. At the end of the line fade-in, the lines had not acquired control of responding. Finally, color intensity was gradually faded out in the absence of reinforcement, and the lines acquired discriminative control by six of the eight pigeons. Thus, reinforcement during the color fade-out was not necessary for the acquisition of discriminative control by the lines during fading. Acquisition of control by lines was attributed to overshadowing, the reduction of stimulus blocking by generalization, and the evocation of correct responding by the colors while the participants were attending to the lines. This last process was also responsible for the induction of discriminative control during sensory preconditioning, higher order conditioning, and response transfer in equivalence classes. Errors, however, were not correlated with discrimination learning during stimulus fading. Finally, transfer of control occurred very quickly with or without errors.

A Conditional Moment Closure Study of Chemical Reaction Source Terms in SCCI Combustion

The objective of this study is to evaluate conditional moment closure (CMC) approaches to model chemical reaction rates in compositionally stratified, autoigniting mixtures, in thermochemical conditions relevant to stratified charge compression ignition (SCCI) engines. First-order closure, second-order closure and double conditioning are evaluated and contrasted as options in comparison to a series of direct numerical simulations (DNSs). The two-dimensional (2D) DNS cases simulate ignitions in SCCI-like thermochemical conditions with compositionally stratified n-heptane/air mixtures in a constant volume. The cases feature two different levels of stratification with three mean temperatures in the negative-temperature coefficient (NTC) regime of ignition delay times. The first-order closure approach for reaction rates is first assessed using hybrid DNS-CMC a posteriori tests when implemented in an open source computational fluid dynamics (CFD) package known as OpenFOAM $^{{\circledR }}$ . The hybrid DNS-CMC a posteriori tests are not a full CMC but a DNS-CMC hybrid in that they compute the scalar and velocity fields at the DNS resolution, thus isolating the first-order reaction rate closure model as the main source of modelling error (as opposed to turbulence model, scalar probability density function model, and scalar dissipation rate model). The hybrid DNS-CMC a posteriori test reveals an excellent agreement between the model and DNS for the cases with low levels of stratification, whereas deviations from the DNS are observed in cases which exhibit high level of stratifications. The a priori analysis reveals that the reason for disagreement is failure of the first-order closure hypothesis in the model due to the high level of conditional fluctuations. Second-order and double conditioning approaches are then evaluated in a priori tests to determine the most promising path forwards in addressing higher levels of stratification. The a priori tests use the DNS data to compute the model terms, thus directly evaluating the model assumptions. It is shown that in the cases with a high level of stratification, even the second-order estimation of the reaction rate source term cannot provide a reasonably accurate closure. Double conditioning using mixture-fraction and sensible enthalpy, however, provides an accurate first-order closure to the reaction rate source term.

Pigeons and the Ambiguous-Cue Problem: A Riddle that Remains Unsolved.

The ambiguous-cue task is composed of two-choice simultaneous discriminations involving three stimuli: positive (P), ambiguous (A), and negative (N). Two different trial types are presented: PA and NA. The ambiguous cue (A) served as an S- in PA trials, but as an S+ in NA trials. When using this procedure, it is typical to observe a less accurate performance in PA trials than in NA trials. This is called the ambiguous-cue effect. Recently, it was reported in starlings that the ambiguous-cue effect decreases when the stimuli are presented on an angled (120°) panel. The hypothesis is that the angled panel facilitates that the two cues from each discrimination are perceived as a compound, precluding value transfer via a second-order conditioning mechanism. In this experiment, we used pigeons and a flat panel. Nevertheless, our data were quite similar to the previous data in starlings. We conclude that the form of the panel cannot explain the ambiguous-cue effect. Several alternatives to be explored in future experiments are suggested. The riddle of the ambiguous-cue problem still remains unsolved.

Optimality conditions in set optimization employing higher-order radial derivatives

There are two approaches of defining the solutions of a set-valued optimization problem: vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated (weak) minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.

Abnormal Optimal Trajectory Planning of Multi-Body Systems in the Presence of Holonomic and Nonholonomic Constraints

In optimal control problems, the Hamiltonian function is given by the weighted sum of the integrand of the cost function and the dynamic equation. The coefficient multiplying the integrand of the cost function is either zero or one; and if this coefficient is zero, then the optimal control problem is known as abnormal; otherwise it is normal. This paper provides a characterization of the abnormal optimal control problem for multi-body mechanical systems, subject to external forces and moments, and holonomic and nonholonomic constraints. This study does not only account for first-order necessary conditions, such as Pontryagin’s principle, but also for higher-order conditions, which allow the analysis of singular optimal controls.